Linking Activity Patterns and Mood States in Bipolar Disorder: A Longitudinal Case Study based on Actigraphy Signals

Linking Activity Patterns and Mood States in Bipolar Disorder: A Longitudinal Case Study based on Actigraphy Signals | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Linking Activity Patterns and Mood States in Bipolar Disorder: A Longitudinal Case Study based on Actigraphy Signals Zsófia Pákozdi¹², András Búzás¹, István Szendi³⁴⁵, László B. Kish⁶, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8346326/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background Mood fluctuations in Bipolar Disorder are closely linked to changes in activity levels, sleep quality and daily rhythms. Therefore, actigraphy could be a valuable tool in the investigation of such mental health conditions, aiding in understanding, diagnosing and treating such disorders. It is a crucial problem in the healthcare of bipolar patients to find objective features, e.g., in diurnal or nocturnal motion patterns, which can promote prediction of sudden state-changes of the patient. To this end, we carried out a comprehensive mathematical analysis of an extremely large set of actigraphy recordings (spanning through more than 600 days) of a bipolar outpatient. Results The research employed cutting-edge statistical tools for data analysis, including Probability-Density-Function and Continuous Wavelet analysis methods, to provide insights into daytime and nighttime activity structures in different mood states. We observed that in depression and mania, nighttime activity is more structured compared to normal nights. Regarding the days, we can see that depression, normal activity, and mania show increasingly more pronounced levels of structural complexity, in that order. Based on these findings, we performed a Continuous Wavelet analysis for single nights preceding normal, manic and depressive days, respectively, in order to give a quantitative prediction for mood switches. From the structure of the wavelet intensity spectra of the nocturnal activities for the “transition” nights, we could successfully establish the probability of transitions to depressive and manic episodes. Bearing in mind that our results are based on an exceptionally long, but still individual case study, which obviously represents a limitation towards generalizability, we can safely state that the intensity spectra derived from Continuous Wavelet analysis can serve as a quantitative measure of these differences, and suggested to give a solid basis for the prediction of mood-state transitions in Bipolar Disorder. Conclusions Our main findings, based on sensitive statistical tools imply that successful prediction of mood switches following longer or shorter normal episodes in Bipolar Disorder is possible by a proper analysis of nocturnal actigraphy signals. The CWA- based approach outlined here represents a novelty, and expected to have important methodological implications for psychiatric practice. bipolar disorder actigraphy ultradian rhythms sleep fragmentation wavelet-analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Background There is an ever growing need to involve objective measuring tools in modern psychiatric research, to assist prevention, diagnostics, status tracking and episode prediction in various mental disorders, which have been spreading quasi-epidemically during the past decades [1-4]. Alterations in human physical activity (HPA) are key symptoms of major psychiatric disorders, including schizophrenia, ADHD, anxiety disorders, autism spectrum disorders and bipolar disorder (BD). In this study, we focus only on the latter, but the methodological tools studied can potentially be applied in other psychiatric conditions, as well. Actigraphy is a widely used measurement method of HPA, typically used in combination with other non-invasive diagnostic techniques, such as ECG or EEG, primarily in medical, biophysical, and sports-related research [5–8], but it is also becoming more common in everyday life [9,10]. The device used for the measurements is called an actigraph, which is a small, wristwatch-sized, accelerometer-based, non-invasive diagnostic in-strument. It is typically worn on the non-dominant wrist, providing objective, reliable, and cost-effective data on the subject's movement activity. The actigraph calculates activity values over non-overlapping, equally sized time windows, storing these values in a memory unit [10,11]. In recent decades, the development of piezoelectric sensors, lithium batteries, and digital data storage units has significantly contributed to making actigraphy measurements more accurate and reliable, as well as enhancing data storage capacity. These devices are also being designed to be smaller and lighter, making the measurement process more comfortable for the subject. This is important because it minimizes the disruption to the subject’s daily activities, allowing for more reliable data on motor activity [12-15]. The regulation of human activity is a complex process determined by many external (e.g., work, rest, reactions to unforeseen events) and internal (such as the circadian pacemaker, which influences the sleep/wake cycle, and ultradian oscillations on smaller time scales) factors. External factors are generally responsible for smaller, more irregular fluctuations that fade out over shorter periods. Internal factors, due to the underlying regulatory functions, shape activity levels over longer periods, even up to 24 hours [16,17]. When performing a typical daily routine, it can be observed that the time correlations of physical activity significantly differ between daytime and nighttime periods [13]. Furthermore, human activity is also related to important physiological functions, including overall body oxygen supply and heart rate regulation [18,19]. BD diagnostics hinge on symptomatology, longitudinal course, and familial antecedents, yet many cases evade timely intervention. Manic phases exhibit hyperactivity and hypoarousability; depressive states feature hypoactivity and fragmentation [28–30]. Prodromal phases (73–98.4% prevalence, 5–6 year duration) afford prediction windows, underscoring actigraphy's utility in differential diagnosis (e.g., vs. ADHD) and therapeutic tracking [7,16,20–27]. Actigraphy excels in naturalistic phenotyping of sleep-wake dysregulation - hallmark in BD -with superior feasibility over polysomnography for extended, non-laboratory deployments. Metrics like fragmentation index quantify nocturnal motility, correlating with depressive severity, psychosis risk, and treatment efficacy; circadian desynchrony presages relapse. These characteristics are taken into account in clinical settings as defining traits, and the objective measurement results of actigraphy can be useful for assessing the severity of symptoms or for monitoring transitions between mania and depression [28-31]. Among individuals with schizophrenia and bipolar disorder, sleep-circadian dysfunction is common, often manifesting as sleep fragmentation and increased sleep duration. In some individuals, insomnia and hypersomnia-type patterns emerge, but a more comprehensive understanding of these patterns requires further research [32]. Objectives As described in the previous section, it is evident that understanding, preventing, and effectively treating mental illnesses is an important task for not only the affected patient and their environment but also for society as a whole. To this end, several studies have raised the need for longitudinal actigrapy measurements to obtain a more representative picture of the patient's true condition, however, such a typical measurement in psychiatry usually lasts around two weeks [11,30]. In contrast, we analysed a dataset containing several years of activity data from a clinically diagnosed male patient in his fifties suffering from bipolar disorder. Therefore, the data we processed came from long-term measurements conducted in the sub-ject's accustomed environment and routine. With the processing of this large amount of data, one of our goals was to create an objective, diagnosis-supporting analysis that could also be useful in clinical practice for confirming the disease, so first, we intended to classify the monitored days into three groups, based on cumulative activity counts, using Gaussian fitting. Since sleep disturbance is a prominent feature of manic depression, and actigraphy provides an objective picture of activity even during the night and can map the sleep/wake cycle, the next objective of our study was to establish a quantitative con-nection between successive sleep and daytime activity data, using statistical methods, such as the Kolmogorov-Smirnov test (KS test) and the Continuous Wavelet Analysis (CWA) In the case of this disease, the development of proper evaluation techniques that are capable of predicting mood switches is particularly important in order to optimize and enhance the therapy [17]. Hence, our final objective, based on the previous evaluation steps, was to suggest an evaluation method that could help predict transitions into other mood states by observing nighttime sleep, thus preventing potential problems arising from manic or depressive episodes. For this purpose, we intended to use CWA, as the most sophisticated method of our evaluation toolkit. Such a method, if proves generalizable, could assist not only the patient but also their close relatives and the treating physician, preventing many unforeseen issues. 2. Materials and Methods Actigraphy For monitoring, a MicroMini Motionlogger actigraph (Ambulatory Monitoring Inc., Ardsley NY, USA) was used at 10Hz sampling rate, in proportional integrating mode of 1min/epoch time. It means that the raw data were integrated by the instrument with an integration time of 60s, to provide a single data point stored in the memory of the device. Data collection periods were recorded on a clinically diagnosed male patient in his fif-ties suffering from bipolar disorder, for several years. The measurement results include both nighttime and daytime activity data. The patient worked with a flexible schedule and was undergoing pharmacological treatment aimed at his psychological condition. Therefore, the data we processed came from long-term measurements conducted in the subject's accustomed environment and routine. Several studies have raised the need for longitudinal measurements to obtain a more representative picture of the patient's true condition, as a typical actigraphy measurement in psychiatry usually lasts around two weeks [11,30]. The recordings were taken for 5 consecutive years, out of which 4 covering data of 3–6 months yearly, for 625 days altogether. The advantage of recording activity on an outpatient is that the data reflect the endogenous rhythm of ‘‘real life’’ and not that constrained by the usual routine of ward conditions. A drawback of outpatient studies, however, is that the knowledge of the daily mood state is less certain. The study was approved by the Ethics Committee of the Medical Research Council (ETT-TUKEB) op-erating as a board of the Ministry of Human Capacities of Hungary (approval identifi-cation No.: 15239–5/2023/EÜIG). The subject gave prior written informed consent to participate. The study was carried out according to the Declarations of Helsinki and the standards set forth by the journal for ethical human research. Statistical Methods In the paper all figures were created, and their corresponding codes were made, using MATLAB 2021b. MATLAB is a platform for programming and numerical com-putations, developed by MathWorks Inc. (1 Apple Hill Drive, Natick, MA, USA) for engineering and scientific applications such as data analysis, signal and image pro-cessing, system control, wireless communication, and robotics. Gaussian Distribution Fitting The Gaussian distribution has two parameters: the mean and the standard devia-tion, and can be defined by the following function: Where x is the probability variable (which can theoretically take any value between −∞ and ∞), f(x) is the relative frequency for x, μ is the expected value of the distribution, and σ is the standard deviation. The Gaussian fit was used to classify the days into three mood categories (”hipo-manic”, ”normal” and ”depressed”), based on the cumulative daily activity counts. Those days that were in the transition zones were not initially classified, in order to be able to make clearer conclusions after the subsequent steps of the evaluation. Hence, Gaussian fit played a major role in classification of the days. Convolution Convolution is a mathematical operation that gives the overlap between two functions. It takes two functions and "shifts" one over the other, multiplying the values along the way and adding the results to create a new function. Formally, convolution is an integral operation that expresses the extent of overlap between one function f(t) and another function g(t) as one moves across it. Where f(t) and g(t) are the two functions. Kolmogorov-Smirnov Test The Kolmogorov-Smirnov test (KS test) is a statistical test that provides the prob-ability that two data sets belong to the same distribution [29]. The null hypothesis of the test is that the two data sets originate from the same continuous distribution. The KS test was used to establish whether a connection between mood-state switches and the preceding night exists. The quantitative results obtained by analysing the cumulative activitiy values, as well as the analysis of the fragmentation indices, indeed, supported the hypothesized relationship, which was then further justified by Wavelet analysis used to describe the nocturnal activity structures. Fragmentation Index Calculation Sleep fragmentation refers to the disruption of nighttime sleep, which interrupts the natural sleep cycle, leading to sleep disturbances and, overall, poor sleep quality. This can also affect daytime wakefulness and functionality. We used the fragmentation index calculation in the paper to study the quality of sleep in the examined subject. It can be calculated by comparing the hours spent awake and at rest during the night. The resulting value allows us to infer the quality of sleep [15,28]. Wavelet Analysis Wavelet analysis is an extension of Fourier analysis that allows the examination of signals with variable frequency components [30]. The method involves placing a func-tion (wavelet) in a sliding window and examining the data series with it. Color codes represent the correlation coefficients, which vary between -1 and +1. By calculating these, the structure of the data series becomes visible. Red indicates correlating data, blue indicates anti-correlating data, and green indicates non-correlating data. The red and blue areas show high levels of structural correlation. The x-axis represents time, and the y-axis represents the size of the time window on a logarithmic scale. The figure can be divided into four main sections: "Range 1" shows structures that occur in time units less than 10 minutes, "Range 2" shows struc-tures in the 10-50 minute range, "Range 3" represents structures from 50 minutes to 4 hours, and "Range 4" demonstrates structures that appear in even larger time units [9]. The left inset shows the original data series, while the right inset shows the analysis of the randomized time series. The middle two curves describe the degree of structuring of these time series (calculated by the sum of squared correlation coefficients) as a function of the time window examined. 3. Results and Discussion During the research, we had access to activity data recorded every minute for 625 days (1440 minutes/day). Figure S1 shows a typical time series of a weeklong recording (7 consecutive days and nights). Since the data are presented in device-defined arbitrary units, we indicate signal levels associated to some typical daily-routine tasks, according to our classification, refined by the data of Figure S2. The latter shows the activity distribution of all the 625 days. The peaks and shoulders of the distribution function correspond to task groups specified in Figures S1 and S2, and the borders between typical activity groups can be approximated by the inflection points of the distribution function in Figure S2. Although these data contain activity information for full days, they are not continuous measurements. The data were recorded over several years, and the database used was created by summarizing these actograms. The data evaluation was carried out in two different ways. In one case, the actigraph continuously recorded the values derived from movement from midnight onwards. In the other case, the data were synchronized to waking times, which helped to more precisely define the durations of sleep and wakefulness, providing more accurate results [29]. Grouping Activities The evaluation of the data began with sorting the all-day activity data. Since we knew that the data originated from a person with a clinical diagnosis of bipolar disorder who was undergoing treatment, we assumed that classification would be necessary. To confirm this, we proceeded as follows. We took the cumulative activity for each day, then plotted these values on a histogram, resulting in a graph that shows how frequently a given level of activity occurs in the database. However, we observed that the resulting curve did not form a regular normal distribution and could not be fitted with a Gaussian curve. A satisfactory fit was only achieved by using three curves. The result is shown in Figure 2. The points shown here represent the data, and their relatively small number is due to the fact that the fitting was done on a lower resolution version of the dataset. This is in line with the experience manic depression is characterized by three significantly different mood states. These states generally last for a certain period of time, and based on this, we divided the days into three different activity groups according to their cumulative activity. One of these was the group we referred to as "normal," which represents moderate activity. As seen in the figure, this group was the largest. The two other groups, based on their lower- and higher-than normal average activities, were labeled as “depression” and “(hypo)mania”, respectively, and they will be referred to as such throughout the paper. For the sake of simplicity, in our analysis, we consider 3 mood states, and do not distinguish between mania and hypomania. The result of the grouping is shown in the histogram in Figure 3. The labels for the groups were applied uniformly when creating the figures, with depression generally shown in black, normal activity days in blue, and (hypo)mania in red. In Figure 3, it can be seen that empty areas appeared between the groups.. The fact that the identified groups are distinct from one another is clearly visible in Figure 4. Figure 4A shows the average activity of the days throughout a full day, from midnight onwards. We averaged the minutes for each group over all the days belonging to that group, which resulted in the outcome shown in Figure 4A. The relationship between the groups is very clear when viewed in this way. The correctness of the grouping is further supported by Figure 4B, which was created in a similar way, but here we display the cumulative sum for the entire day instead of average activity. It is important to note that since the patient did not keep a diary of his condition during the measurement period, the days we categorized can only be placed in the given group conditionally. However, we created a diary-type timeline about the days the actigraph was used on, where the color code indicates which category the actual day was classified into (red: (hypo)mania, blue: normal, black: depression, gray: unclassified) (Figure 3). As it can be seen, the data are somewhat scarce, still, a number of contiguous periods associated to distinct mood states could be identified using our Gauss-fitting-based selection method (Figure 2). The number of ”(hypo)manic”, ”normal”, and ”depressed” days are also indicated in Figure 3. Note that mood-state durations are in concert with the symptomes of a Bipolar-II outpatient, with a dominance of normal periods interrupted by a few-days-long (hypo)manic episodes, and occasionally, also with short-range subthreshold depression days. Those days that were in the transition zones were not initially classified, in order to be able to make clearer conclusions after the subsequent steps of the evaluation. However, when a single unclassified day interrupted a longer episode of one mood state, we have adapted these single days to the rest, too, provided that the cumulative activity of the day matched the rest. During the last two years of recordings, the frequency of hypomanic periods is strongly reduced, at the same time, major depressive episodes seem to occur. The clearly identifiable mood-state switches can now be followed in the new Fig. 3. Justified mood changes take place both during week-days and week-ends, showing no obvious pref-erence to any of them (Figure S3). Investigation of Nighttime Activities After data grouping, we checked the hypothesis, whether the nighttime activities could be important predictive factors for individual switching episodes. It is known that mood changes typically occur suddenly in most cases, so we call the days when a specific episode begins, "transitions." We examined the nighttime activities in 250-minute intervals, which cover the pe-riod from midnight to 4:10 AM. We compared all nights to the nights before transitions for each group and found that these nights differed to some extent (Figure S5). For normal and depressive nights, we observed that before the transitions, activity remained above the average activity of all nights up to about the 200th minute. However, for manic nights, the activity before the transitions was somewhat below the average activity of all manic nights. Among the three groups, we focused on the depressive and manic groups, as forecasting these would greatly assist both the patient's life and the work of their healthcare providers. To facilitate the comparison of the data in Figure S5, we created another graph, showing all normal nights alongside the activity of manic and depressive nights before transitions (Figure 4). Comparing these data revealed an interesting phenomenon. The average activity for all normal nights remains nearly constant, with small fluctuations, during the first 250 minutes from midnight. In contrast, the nights before transitions (both depressive and manic) show fluctuations and do not stabilize at a specific value, contrary to normal nights. For transitions to depression, there is a period from midnight until about 2:30 AM where activity is much higher than normal, after which it approaches the normal level. This can be explained by the fact that individuals suffering from depression often ex-perience sleep disturbances, difficulty falling asleep, and sometimes insomnia [17]. For transitions to mania, we observed the opposite: the nocturnal activity remained at about the same level as the normal activity until 2:30 AM, after which it suddenly increased. This is consistent with the symptoms of mania, as during this episode, the patient feels well-rested early, and may even wake up at night to begin his daily activities. Considering this, the increase in activity in the early hours of the day is not surprising. If our conclusions are correct, it may be possible to predict a depressive or manic day based on the activity of the night before. Moreover, it is interesting that the change in activity levels occurred at nearly the same time for both depression and mania. In addition to the average nocturnal activities, we also examined sleep quality by calculating the fragmentation index (FI). We performed this separately for all activity groups, and for nights before transitions. FI indicates the sleep/wake ratio during the night for the person being studied. We also know that sleep quality is worse during mania and depression than under normal conditions. Our results support this, as the average FI for both depression and mania is significantly higher compared to the av-erage for normal nights. It can also be noted that the average FI for depression and mania is nearly identical, with depression having a slightly higher value. We presented the obtained FI averages and their error margins (marked as "error" in the figure) for all nights and for nights before transitions (Figure 5). Looking at the graphs, we can see that the two figures are very similar in terms of average values. However, the error margin is wider for normal activity and depression, while for mania, the error margins for both cases are very similar. Given this, the separate treatment and representation of all nights and nights before transitions might seem redundant at first glance. However, this information is crucial because it shows that the fragmentation characteristic of mania and depression appears even on the night before the episode. This fact can greatly assist in predicting episodes. Based on the discussion in this section, we concluded that examining nighttime activity plays an important role in predicting individual episodes. Both average activity, from which we infer the amount of sleep, and the calculation of the fragmentation index, which provides information about sleep quality, are tools that cannot be ignored in episode prediction. 3.3. Relationship Between Daytime and Nighttime Activities Previously, we established that determining daytime activities significantly con-tributes to characterizing the mood states of the disease. We also saw that monitoring nighttime activity helps with this, too, and may play an even more crucial role in pre-dicting episodes. Keeping this in mind, we decided to examine the relationship between nighttime and daytime activities. To do this, we first created a graph showing the av-erage daytime activities as a function of the standard deviation of nighttime activities, for each activity group (Figure 6). The motivation for this representation was that the FI analysis showed that fluctuations in the depressive and manic nights majorate those in normal nights, and STD is directly related to these. To make the results less confusing and allow for better observation of data clustering, we smoothed the data using convolution. The interesting thing about this figure is that, although it shows the daily average activities, the days selected here were classified based solely on the examination of standard deviations of nighttime activities. As can be clearly seen, the distributions of the groups are well separated, indicating that the previous night's activity is indeed related to daytime activity. However, we wanted to objectively prove this assumption numerically, so we performed the Kolmogorov-Smirnov test to compare the groups. The test's purpose is to determine whether two datasets belong to the same con-tinuous distribution. The results were as follows: for depression and normal, we ob-tained 24.08%; for normal and mania, <0.1%; and for mania and depression comparison, 0.44%. The significance level was set at 10%, which means that values above this threshold are considered to belong to the same continuous distribution, indicating that these two groups cannot be distinguished from each other clearly. Therefore, the larger the values obtained from the test, the less distinguishable the two datasets are. Based on the results, it is evident that the test finds it most difficult to distinguish between de-pression and normal activity, while the difference between normal and mania is the most pronounced. Wavelet Analysis We also performed Continuous Wavelet Analysis on the data (a more detailed explanation of the evaluation can be found in the Methods section). CWA is an effective way to visually illustrate the structure of a dataset across various time window sizes. Although CWA maps, showing the cross-correlattion coefficients of the analysed time series and a probe wavelet confined to various time windows, are often used only for qualitative demonstration, here we perform a quantitative assessment of the effects, by using the structure-parameter spectrum method, we introduced in an earlier publica-tion Ref. [9,]. It is derived by calculating the sum of squared correlation coefficients for each time window (see Fig. 1). Accordingly, we presented the results in two different ways: one with a simple function representation, where the intensity values appear as a function of the window size, with the time window displayed on a logarithmic scale, and the other as a colormap, where the window size is shown (also on a logarithmic scale) over time, color-coded according to the squared sums of the correlation coefficients. For each activity group, we conducted the analysis on both nighttime and daytime activity data. As a first step, however, instead of performing the analysis for the entire groups, we selected a longer, continuous period from each of the three groups, for demonstration purposes, because in a large dataset, the structures wouldn't be as clearly outlined without this approach. The activity of normal days shows a moderate level of structure, most clearly visible in the 2.5-3 log(time) window range on the colormap in Figure 7. This provides a picture similar to that of a healthy person’s day. As we have pointed out earlier, circadian and ultradian rhythms are organized into a hierarchical structure [9]. The activity data we categorized as normal days truly represents what we would observe in the case of a healthy person. For normal nighttime activity, high levels of structure are not typically observed. The activity data likely show minor patterns due to small movements during the night (Figure 7B). It is known that a healthy person can usually sleep through the night calmly, so this is also characteristic of the patient’s normal activity nights. We also examined the depressive days and nights. Figures S6 shows the evaluation of the nights associated with depressive days, from which we can conclude that they are characterized by a higher level of structure compared to normal nights. We previously discussed sleep fragmentation and concluded that sleep is more fragmented in depres-sion than in normal cases. By performing the wavelet analysis, we found evidence for the deterioration in sleep quality through the examination of the structure. For depressive daytime activities, we observe less structure compared to normal days. This is typical for depression, as nighttime activity is higher and more restless than normal, while daytime activity is lower. Through analysis, we also concluded that the structure is smaller, particularly in larger time windows (Figure S7), indicating a partial deterioration of the hierarchical organization of the daytime activity (see Ref. 9) In Figure S8 and Figure 8 we can see the manic nights, showing a very strong structure. Manic daytime activity shows outstanding structure and intensity values. Based on this, it can undoubtedly be confirmed that a patient suffering from mania experiences huge fluctuations throughout their days (Figure S9). Keeping in mind one of our main goals, which is to provide data for developing a method for predicting mood changes, in the following, we focussed on the comparison of nocturnal activities associated to the three mood states. Figure 8 shows the structure of nighttime activities obtained from the wavelet analysis for each group, plotted to-gether. It is visible that mania appears with very high intensity, and around the 300-min time window (note the log scale of the abscissa), three characteristic peaks are promi-nent. The nighttime data for depression also exhibit higher intensity values than the normal values at narrower time-windows (between the 10-minutes to the 100-minutes range), and the intensity values characteristic to manic night are also more distinctly structured here. This was especially important to note, since for the predictions that are supposed to occur relatively suddenly (from one day to the other), we should use activity data for single nights, only. This condition considerably limits the time-window range that can be investigated by the CWA method, hence, we should restrict our observation to the latter (narrower) time-window range. For this purpose, we performed a CW analysis for single nights preceding normal, manic and depressive days, respectively. The results are shown in Figure 9. We chose the time-window range between 20 and 70 minutes as the region of interest (ROI) for quantitative prediction, where the intensity spectra of both depressed and manic nights differ the most. In order to give a quantitative prediction for mood switches, we calculated the probability distribution function (PDF) of the integrals of the spectra for the ROI (Figure S10a), as well as the corresponding cumulative distribution function (CDF, Figure S10b). As a next step, we determined the corresponding integrals of the Wavelet intensity spectra of the nocturnal activities for the “transition” nights preceding those depressed and manic days which start a longer, contiguous episode (dates selected using the data of Figure 2 are listed in Table S1). Comparing these integral values with data of the CDF determined for normal nights (Figure S10b), we could establish the probability that the selected night’s wavelet-intensity-integral value for the ROI exceeds those of the nor-mal-night values. The averaged results gave 70.17% and 75.78% for the probability of transition nights to depressive and manic episodes, with standard errors of 9.26% and 5.20%, respectively. In summary of our wavelet analysis, we observed that in depression and mania, nighttime activity is more structured compared to normal nights, especially in mania, where the result obtained was similar to that of normal daytime activity. Regarding the days, we can see that depression, normal activity, and mania show increasingly more pronounced levels of structural complexity, in that order. Bearing in mind that our re-sults are based on an exceptionally long, but still individual case study, which obviously represents a limitation towards generalizability, we can safely state that the intensity spectra derived from Continuous Wavelet-analysis can serve as a quantitative measure of these differences, and suggested to give a solid basis for the prediction of mood-state transitions in bipolar disorder. In spite of the potential strengths of CWA-based mood prediction, so far only a very few papers have been published using this method. In Ref. [35], the analysis of 18 months of daily self-reported mood charts (and sleep times) from a 24-year-old bipolar I patient is presented using the Morlet continuous wavelet transform, to determine pos-sible periodicities on the daily to monthly scale (approximately 146, 21, 8 days). The authors interpret these cyclical patterns in terms relapse risk, but they do not discuss applications in a validated predictive model. In an earlier paper [36], CWA was used to pinpoint general multiscale differences between normal subjects and bipolar patients, and introduced a CWA-based “Vulnerability Index” based on several-days-long recordings, which may serve a base to the objective diagnosis a bipolar patients. In a more recent study, early warning signals (EWS) were derived using Wavelet analysis from actigraphy time-series, and presented spectral analysis of sleep/wake cy-cle periodicity [37]. It was established that in 7 of 8 patients who had an episode, at least one EWS showed significant change up to four weeks before onset. The spectral periodicity changes showed promise for predicting transitions. All-in-all, there are only a few works in the scientific literature on activity and behavior time series, where patterns found with CWA could in principle be used for mood or episode prediction, but these are still in the proof-of-concept state [38]. Conclusions In our research, we had several years of activity data from an individual struggling with bipolar disorder. To evaluate the data, we first categorized the days by Gaussian fitting into the three main activity groups typical of manic depression, and, based, on this, constructed a a diary-type map indicating normal, depressive and (hypo)manic episodes for the consecutive 5 years during which the actograms were recorded. Next, we focused on nighttime activities, examining the average activity and sleep fragmentation from midnight until dawn, for nights belonging to days of different categories. From the representations of nighttime average activities, we established that the night before a mood switch to depression, initially shows higher-than-normal activity, which then gradually drops in the early morning. At mood switches to mania, the average nighttime activity is also elevated, but the tendency is the opposite. Fragmentation indices were also calculated for the night before a mood change, as well as for all nights, showing that the quality of sleep in both mania and depression is significantly worse compared to nights preceding days of normal activity levels. To further substantiate our findings with objective numerical data, we selected longer continuous time intervals from each group, and performed a CWA analysis on both the nighttime and daytime activities separately. In line with the FI results, we found that in depression, nighttime activity is more structured than normal, whereas daytime activity is less structured. In mania, nighttime activity is even more structured, being most similar to the daytime structure of normal activity, while daytime activity during mania shows extremely strong and distinct structural features. Our findings imply that the fragmentation characteristics of depression and mania appears even the night before the mood switch. This knowledge, along with the analysis of the average activity trend, significantly contributes to the predictability of mood episodes. Accordingly, our major scientific conclusions are based on quantitative Continuous Wavelet analysis, to assist the successful prediction of mood switches following longer-or-shorter normal episodes. The CWA approach outlined here represents a novelty, and expected to extend the state-of-the-art methodology of predicting mood-change episodes, possibly in combination with Machine-Learning methods in the future, as it was exemplified, e.g., in our earlier work, as well [ 7 ]. Since predicting mood switches by objective tools is considered an essential problem to solve in the healthcare of bipolar patients, our results are expected to have important methodological implications for psychiatric practice. Declarations Author Contributions: Conceptualization, ISz, LK and AD; methodology, ISz, LK and AD; software, ZsP and AB; validation, ISz; formal analysis, ZsP, AB and AD; data curation, ZsP and AB; writing—original draft preparation, ZsP and AD; writing—review and editing, AB, ISz, LK and AD; visualization, ZsP; supervision, AD. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: The study was approved by the Ethics Committee of the Medical Research Council (ETT-TUKEB) operating as a board of the Ministry of Human Capacities of Hungary (approval identification No.: 15239–5/2023/EÜIG). Informed Consent Statement: The subject gave prior written in-formed consent to participate. The study was carried out according to the Declarations of Helsinki and the standards set forth by the journal for ethical human research. Data Availability Statement: Dataset available on request from the authors. Conflicts of Interest: The authors declare no conflicts of interest. References Ten Have, M.; Tuithof, M.; Van Dorsselaer, S.; Schouten, F.; Luik, A.I.; De Graaf, R. Prevalence and Trends of Common Mental Disorders from 2007‐2009 to 2019‐2022: Results from the Netherlands Mental Health Survey and Incidence Studies (NEMESIS), Including Comparison of Prevalence Rates before vs. during the COVID‐19 Pandemic. World Psychiatry 2023, 22, 275–285, doi:10.1002/wps.21087. Slade, T.; Vescovi, J.; Chapman, C.; Teesson, M.; Arya, V.; Pirkis, J.; Harris, M.G.; Burgess, P.M.; Santomauro, D.; O’Dean, S.; et al. The Epidemiology of Mental and Substance Use Disorders in Australia 2020–22: Prevalence, Socio-Demographic Cor-relates, Severity, Impairment and Changes over Time. Aust. N. Z. J. Psychiatry 2025, 59, 510–521, doi:10.1177/00048674241275892. Grande, I.; Berk, M.; Birmaher, B.; Vieta, E. Bipolar Disorder. The Lancet 2016, 387, 1561–1572, doi:10.1016/S0140-6736(15)00241-X. Domján, N.; Csifcsák, G.; Drótos, G.; Janka, Z.; Szendi, I. Different Patterns of Auditory Information Processing Deficits in Chronic Schizophrenia and Bipolar Disorder with Psychotic Features. Schizophr. Res. 2012, 139, 253–259, doi:10.1016/j.schres.2012.06.002. Buzas, A.; Horvath, T.; Der, A. A Novel Approach in Heart-Rate-Variability Analysis Based on Modified Poincaré Plots. IEEE Access 2022, 10, 36606–36615, doi:10.1109/ACCESS.2022.3162234. Langmár, G.; Sümegi, T.; Fülöp, B.; Pozsgai, L.; Mocsai, T.; Tóth, M.; Rácz, L.; Kopper, B.; Dér, A.; Búzás, A.; et al. Heart Rate Variability Alterations During Delayed-Onset Muscle Soreness-Inducing Exercise—With Piezo2 Interpretation. Sports 2025, 13, 262, doi:10.3390/sports13080262. Nagy, Á.; Dombi, J.; Fülep, M.P.; Rudics, E.; Hompoth, E.A.; Szabó, Z.; Dér, A.; Búzás, A.; Viharos, Z.J.; Hoang, A.T.; et al. The Actigraphy-Based Identification of Premorbid Latent Liability of Schizophrenia and Bipolar Disorder. Sensors 2023, 23, 958, doi:10.3390/s23020958. László, S.; Nagy, Á.; Dombi, J.; Hompoth, E.A.; Rudics, E.; Szabó, Z.; Dér, A.; Búzás, A.; Viharos, Z.J.; Hoang, A.T.; et al. The Two Ends of the Spectrum: Comparing Chronic Schizophrenia and Premorbid Latent Schizotypy by Actigraphy. BMC Psychiatry 2025, 25, 531, doi:10.1186/s12888-025-06971-5. Búzás, A.; Makai, A.; Groma, G.I.; Dancsházy, Z.; Szendi, I.; Kish, L.B.; Santa-Maria, A.R.; Dér, A. Hierarchical Organization of Human Physical Activity. Sci. Rep. 2024, 14, 5981, doi:10.1038/s41598-024-56185-0. Maczák, B.; Vadai, G.; Dér, A.; Szendi, I.; Gingl, Z. Detailed Analysis and Comparison of Different Activity Metrics. PLOS ONE 2021, 16, e0261718, doi:10.1371/journal.pone.0261718. Tazawa, Y.; Wada, M.; Mitsukura, Y.; Takamiya, A.; Kitazawa, M.; Yoshimura, M.; Mimura, M.; Kishimoto, T. Actigraphy for Evaluation of Mood Disorders: A Systematic Review and Meta-Analysis. J. Affect. Disord. 2019, 253, 257–269, doi:10.1016/j.jad.2019.04.087. Cantisani, A.; Stegmayer, K.; Bracht, T.; Federspiel, A.; Wiest, R.; Horn, H.; Müller, T.J.; Schneider, C.; Höfle, O.; Strik, W.; et al. Distinct Resting‐state Perfusion Patterns Underlie Psychomotor Retardation in Unipolar vs. Bipolar Depression. Acta Psychiatr. Scand. 2016, 134, 329–338, doi:10.1111/acps.12625. Amaral, L.A.N.; Soares, D.J.B.; da Silva, L.R.; Lucena, L.S.; Saito, M.; Kumano, H.; Aoyagi, N.; Yamamoto, Y. Power-Law Temporal Auto-Correlations in Day-Long Records of Human Physical Activity and Their Alteration with Disease 2002. Rudics, E.; Buzás, A.; Pálfi, A.; Szabó, Z.; Nagy, Á.; Hompoth, E.A.; Dombi, J.; Bilicki, V.; Szendi, I.; Dér, A. Quantifying Stress and Relaxation: A New Measure of Heart Rate Variability as a Reliable Biomarker. Biomedicines 2025, 13, 81, doi:10.3390/biomedicines13010081. Kurina, L.M.; Knutson, K.L.; Hawkley, L.C.; Cacioppo, J.T.; Lauderdale, D.S.; Ober, C. Loneliness Is Associated with Sleep Fragmentation in a Communal Society. Sleep 2011, 34, 1519–1526, doi:10.5665/sleep.1390. Faedda, G.L.; Ohashi, K.; Hernandez, M.; McGreenery, C.E.; Grant, M.C.; Baroni, A.; Polcari, A.; Teicher, M.H. Actigraph Measures Discriminate Pediatric Bipolar Disorder from Attention‐deficit/Hyperactivity Disorder and Typically Developing Controls. J. Child Psychol. Psychiatry 2016, 57, 706–716, doi:10.1111/jcpp.12520. De Crescenzo, F.; Economou, A.; Sharpley, A.L.; Gormez, A.; Quested, D.J. Actigraphic Features of Bipolar Disorder: A Systematic Review and Meta-Analysis. Sleep Med. Rev. 2017, 33, 58–69, doi:10.1016/j.smrv.2016.05.003. Hu, K.; Ivanov, P.Ch.; Chen, Z.; Hilton, M.F.; Stanley, H.E.; Shea, S.A. Non-Random Fluctuations and Multi-Scale Dynamics Regulation of Human Activity. Phys. Stat. Mech. Its Appl. 2004, 337, 307–318, doi:10.1016/j.physa.2004.01.042. Búzás, A.; Sonkodi, B.; Dér, A. Principal Connection Between Typical Heart Rate Variability Parameters as Revealed by a Comparative Analysis of Their Heart Rate and Age Dependence. Entropy 2025, 27, 792, doi:10.3390/e27080792. Tahmasian, M.; Khazaie, H.; Golshani, S.; Avis, K.T. Clinical Application of Actigraphy in Psychotic Disorders: A Systematic Review. Curr. Psychiatry Rep. 2013, 15, 359, doi:10.1007/s11920-013-0359-2. Leuenberger, K.D. Long-Term Activity and Movement Monitoring in Neurological Patients, ETH Zurich, 2015, p. 198 p. Martini, J.; Leopold, K.; Pfeiffer, S.; Berndt, C.; Boehme, A.; Roessner, V.; Fusar-Poli, P.; Young, A.H.; Correll, C.U.; Bauer, M.; et al. Early Detection of Bipolar Disorders and Treatment Recommendations for Help-Seeking Adolescents and Young Adults: Findings of the Early Detection and Intervention Center Dresden. Int. J. Bipolar Disord. 2021, 9, 23, doi:10.1186/s40345-021-00227-3. Ratheesh, A.; Hett, D.; Ramain, J.; Wong, E.; Berk, L.; Conus, P.; Fristad, M.A.; Goldstein, T.; Hillegers, M.; Jauhar, S.; et al. A Systematic Review of Interventions in the Early Course of Bipolar Disorder I or II: A Report of the International Society for Bipolar Disorders Taskforce on Early Intervention. Int. J. Bipolar Disord. 2023, 11, 1, doi:10.1186/s40345-022-00275-3. Álvarez-Cadenas, L.; García-Vázquez, P.; Ezquerra, B.; Stiles, B.J.; Lahera, G.; Andrade-González, N.; Vieta, E. Detection of Bipolar Disorder in the Prodromal Phase: A Systematic Review of Assessment Instruments. J. Affect. Disord. 2023, 325, 399–412, doi:10.1016/j.jad.2023.01.012. Williams, R.; Ostinelli, E.G.; Agorinya, J.; Minichino, A.; De Crescenzo, F.; Maughan, D.; Puntis, S.; Cliffe, C.; Kurtulmus, A.; Lennox, B.R.; et al. Comparing Interventions for Early Psychosis: A Systematic Review and Component Network Me-ta-Analysis. eClinicalMedicine 2024, 70, 102537, doi:10.1016/j.eclinm.2024.102537. Klosterkotter, J.; Schultze‐Lutter, F.; Bechdolf, A.; Ruhrmann, S. Prediction and Prevention of Schizophrenia: What Has Been Achieved and Where to Go Next? World Psychiatry 2011, 10, 165–174, doi:10.1002/j.2051-5545.2011.tb00044.x. Phillips, L.J.; Yung, A.R.; McGorry, P.D. Identification of Young People at Risk of Psychosis: Validation of Personal As-sessment and Crisis Evaluation Clinic Intake Criteria. Aust. N. Z. J. Psychiatry 2000, 34, A164–A169, doi:10.1177/000486740003401S25. Johnson, D.A.; Javaheri, S.; Guo, N.; Champion, C.L.; Sims, J.F.; Brock, M.P.; Sims, M.; Patel, S.R.; Williams, D.R.; Wilson, J.G.; et al. Objective Measures of Sleep Apnea and Actigraphy-Based Sleep Characteristics as Correlates of Subjective Sleep Quality in an Epidemiologic Study: The Jackson Heart Sleep Study. Psychosom. Med. 2020, 82, 324–330, doi:10.1097/PSY.0000000000000778. Dancsházy, Z.; Dér, A.; Groma, G.I.; Janka, Z.; Járdánházy, T.; Makai, A.; Szentistványi, I.; Vasadi, A. Phase-Synchronization of Daily Motor Activities Can Reveal Differential Circadian Patterns. Chronobiol. Int. 2004, 21, 309–314, doi:10.1081/CBI-120037824. Krane-Gartiser, K.; Henriksen, T.E.G.; Morken, G.; Vaaler, A.; Fasmer, O.B. Actigraphic Assessment of Motor Activity in Acutely Admitted Inpatients with Bipolar Disorder. PLoS ONE 2014, 9, e89574, doi:10.1371/journal.pone.0089574. Ritter, P.S.; Höfler, M.; Wittchen, H.-U.; Lieb, R.; Bauer, M.; Pfennig, A.; Beesdo-Baum, K. Disturbed Sleep as Risk Factor for the Subsequent Onset of Bipolar Disorder – Data from a 10-Year Prospective-Longitudinal Study among Adolescents and Young Adults. J. Psychiatr. Res. 2015, 68, 76–82, doi:10.1016/j.jpsychires.2015.06.005. Meyer, N.; Faulkner, S.M.; McCutcheon, R.A.; Pillinger, T.; Dijk, D.-J.; MacCabe, J.H. Sleep and Circadian Rhythm Dis-turbance in Remitted Schizophrenia and Bipolar Disorder: A Systematic Review and Meta-Analysis. Schizophr. Bull. 2020, 46, 1126–1143, doi:10.1093/schbul/sbaa024. Stephens, M.A. EDF Statistics for Goodness of Fit and Some Comparisons. J. Am. Stat. Assoc. 1974, 69, 730–737, doi:10.1080/01621459.1974.10480196. Andronov, I.L. Advanced Time Series Analysis of Generally Irregularly Spaced Signals: Beyond the Oversimplified Methods. In Knowledge Discovery in Big Data from Astronomy and Earth Observation; Elsevier, 2020; pp. 191–224 ISBN 978-0-12-819154-5. Cheon, Y.; Moon, E.; Park, J.-M.; Lee, B.-D.; Lee, Y.-M.; Jeong, H.-J.; Kang, T.-U.; Park, J.; Choi, Y. Can Residual Symptoms During Inter-Episode Period after Partial Remission in Bipolar I Disorder Have Cyclic Patterns with Specific Frequencies? Psychiatry Investig. 2018, 15, 330–334, doi:10.30773/pi.2017.08.23. Indic, P.; Salvatore, P.; Maggini, C.; Ghidini, S.; Ferraro, G.; Baldessarini, R.J.; Murray, G. Scaling Behavior of Human Lo-comotor Activity Amplitude: Association with Bipolar Disorder. PLoS ONE 2011, 6, e20650, doi:10.1371/journal.pone.0020650. Sharma, D.; Kumar, M.; Kumar, J. Wavelet Transforms in Psychological Science: A Multiscale Approach to Cognitive, Clin-ical, and Developmental Insights. J. Wavelet Theory Appl. 2024, 18, 19–27, doi:10.37622/JWTA/18.2.2024.19-27. Nazari, M.-J.; Shalbafan, M.; Eissazade, N.; Khalilian, E.; Vahabi, Z.; Masjedi, N.; Ghidary, S.S.; Saadat, M.; Sadegh-Zadeh, S.-A. A Machine Learning Approach for Differentiating Bipolar Disorder Type II and Borderline Personality Disorder Using Electroencephalography and Cognitive Abnormalities. PLOS ONE 2024, 19, e0303699, doi:10.1371/journal.pone.0303699. Additional Declarations No competing interests reported. Supplementary Files SupplementaryInformationIJBD.pdf Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8346326","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":560443125,"identity":"398af35c-2a51-49b2-bbd9-ab90178f375f","order_by":0,"name":"Zsófia Pákozdi¹²","email":"","orcid":"","institution":"Biological Research Centre, Hungarian Academy of Sciences (MTA)","correspondingAuthor":false,"prefix":"","firstName":"Zsófia","middleName":"","lastName":"Pákozdi¹²","suffix":""},{"id":560443126,"identity":"01cd10cc-e02a-485f-93ec-03ff27ecc399","order_by":1,"name":"András Búzás¹","email":"","orcid":"","institution":"Biological Research Centre, Hungarian Academy of Sciences (MTA)","correspondingAuthor":false,"prefix":"","firstName":"András","middleName":"","lastName":"Búzás¹","suffix":""},{"id":560443127,"identity":"9234ef64-25f4-4038-97e6-806bfed0d1fa","order_by":2,"name":"István Szendi³⁴⁵","email":"","orcid":"","institution":"Department of Psychiatry, Kiskunhalas Semmelweis Hospital","correspondingAuthor":false,"prefix":"","firstName":"István","middleName":"","lastName":"Szendi³⁴⁵","suffix":""},{"id":560443128,"identity":"663c68c6-0aeb-4975-b324-829804bef3c0","order_by":3,"name":"László B. Kish⁶","email":"","orcid":"","institution":"Texas A\u0026M UniversityUn","correspondingAuthor":false,"prefix":"","firstName":"László","middleName":"B.","lastName":"Kish⁶","suffix":""},{"id":560443129,"identity":"efde14be-5e5b-45ec-b945-d21f86c18878","order_by":4,"name":"András Dér¹","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvUlEQVRIiWNgGAWjYDCCA2CSGYSPgVgJpGhhSyNZC48ZcVr4jvc+YPi5wzqfv//Mt8cVNQx5BgcIaJE8c9yAsfdMuuWMG7nbDc8cYygmqMXgBtAHvG2HDRhu8G6TbGxgSNxAUMv9ZwyMf4Fa5M+feUaklhtsDMwgWwwO5LARp0XyTBrDYdm2dAPDG2nmhg3HJBJnEtLCd/wY48O3bdYGcucPP3vYUGOT2EdICwggq5EgQv0oGAWjYBSMAoIAAC08RMBzkpR5AAAAAElFTkSuQmCC","orcid":"","institution":"Biological Research Centre, Hungarian Academy of Sciences (MTA)","correspondingAuthor":true,"prefix":"","firstName":"András","middleName":"","lastName":"Dér¹","suffix":""}],"badges":[],"createdAt":"2025-12-12 13:38:48","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8346326/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8346326/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99286745,"identity":"f3d765ae-b60c-4531-9224-399e20a18a53","added_by":"auto","created_at":"2025-12-31 09:30:27","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2149063,"visible":true,"origin":"","legend":"","description":"","filename":"IJBDmanuscript.docx","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/ce1e3047340f6bd68d26bd18.docx"},{"id":99319697,"identity":"71b19af5-ce67-4ed7-b142-329067ddc186","added_by":"auto","created_at":"2025-12-31 16:37:41","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":7584,"visible":true,"origin":"","legend":"","description":"","filename":"98d51e1e8e3e4e35a5409acd40efe4ef.json","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/a7aca3ff93ef422d6b404a9c.json"},{"id":99320690,"identity":"87338e2d-61da-405f-8576-c0fcfedbb5ae","added_by":"auto","created_at":"2025-12-31 16:38:51","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1119335,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformationIJBD.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/1661e8da1f86a01667f2c533.pdf"},{"id":99321054,"identity":"97a5de5d-76ca-4218-a662-be40d3075254","added_by":"auto","created_at":"2025-12-31 16:39:08","extension":"xml","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":127123,"visible":true,"origin":"","legend":"","description":"","filename":"98d51e1e8e3e4e35a5409acd40efe4ef1enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/c6dee2ad25945bbb758fc348.xml"},{"id":99320768,"identity":"df377439-f4fe-4adf-a44d-b6c5ccc27576","added_by":"auto","created_at":"2025-12-31 16:38:53","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3460,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/b448972e7cd4a70754f90ee6.png"},{"id":99321316,"identity":"65c6ebe5-ce89-4c6b-8eff-8dca04ca0331","added_by":"auto","created_at":"2025-12-31 16:39:20","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":257550,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/38feb4ff30995d5944372dd7.png"},{"id":99320703,"identity":"b673ede4-f0ba-4b9b-bc69-8ddfb4af7a58","added_by":"auto","created_at":"2025-12-31 16:38:52","extension":"png","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":133278,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/360cc070f9025619c3bbcec8.png"},{"id":99286758,"identity":"9a7b78e2-6890-4654-8c27-7261e0fd6ca5","added_by":"auto","created_at":"2025-12-31 09:30:27","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":88271,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/abeec9a17a98a861e6ee2ec9.png"},{"id":99320584,"identity":"306a61c9-b788-4912-b678-396bf3590411","added_by":"auto","created_at":"2025-12-31 16:38:46","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4343,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/3c2f5c058c65f3e9bf46dbf0.png"},{"id":99320674,"identity":"6e49b6f1-fef4-4519-a770-63f6f7e0216e","added_by":"auto","created_at":"2025-12-31 16:38:51","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":524826,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/8e795c7cf2c40a1d889855d2.png"},{"id":99788272,"identity":"87576b6b-78d9-4dd2-89a3-b2b6652d46ca","added_by":"auto","created_at":"2026-01-08 12:45:56","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":100368,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/d0d14ddd0433c0ab6a279343.png"},{"id":99319988,"identity":"6a086500-1aae-49b9-870a-0bd054048906","added_by":"auto","created_at":"2025-12-31 16:38:04","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":274639,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/18cd584d96ae1074d50136e0.png"},{"id":99286764,"identity":"4f9d14f7-ab6a-4d25-abd8-dc5d5bce7a99","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":164208,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/057fbacc8ab086ebe51684bd.png"},{"id":99321227,"identity":"f3de84f1-bc1a-46f6-9987-64394bb3b0ad","added_by":"auto","created_at":"2025-12-31 16:39:17","extension":"jpeg","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":673985,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/ca8542fe1be1c5ad70bd5118.jpeg"},{"id":99286774,"identity":"fa3ab351-2dcd-48b2-af32-400d5649d7c3","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"jpeg","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":675410,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/d3826cfde5bf8101b58860b8.jpeg"},{"id":99319110,"identity":"e86bbc03-7e06-41e1-b43d-f2ee411e0bcc","added_by":"auto","created_at":"2025-12-31 16:36:20","extension":"png","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":304444,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/5c2b1668ab12510d1aa1c149.png"},{"id":99286763,"identity":"0203c01f-4a42-4591-bac1-33d44b4bdcb1","added_by":"auto","created_at":"2025-12-31 09:30:27","extension":"png","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2224,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/e1753feb397cab9db34fc3b3.png"},{"id":99286768,"identity":"2d7b69ca-c466-4d22-8326-083accd4f914","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"png","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":22436,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/ced6d763c6797a61f36d02e6.png"},{"id":99319590,"identity":"d44fde57-dafc-43b9-a627-b8c98485b607","added_by":"auto","created_at":"2025-12-31 16:37:31","extension":"png","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":19159,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/fefac67909b8c3de8963f5b2.png"},{"id":99286778,"identity":"187d6c80-bf88-4424-ad30-11905284be50","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"png","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":14969,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/5ce5fe5434fff90e0d603c9a.png"},{"id":99320965,"identity":"88f20163-4fe9-428e-a8be-d869a96007d6","added_by":"auto","created_at":"2025-12-31 16:38:59","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2893,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/9afca8d41071500c463e5813.png"},{"id":99321289,"identity":"84bf9765-6ba3-4152-94ee-4fc9a7f68013","added_by":"auto","created_at":"2025-12-31 16:39:19","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":59142,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/1fa3dbcf431cd41ac99a7552.png"},{"id":99286771,"identity":"b69247f0-a598-40ee-9d05-dbfbcabef24f","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":14913,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/3022fce7c67c860b8c3a781b.png"},{"id":99320660,"identity":"eb267f38-2342-4fef-a716-c5ff499aba70","added_by":"auto","created_at":"2025-12-31 16:38:51","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":44007,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/394976373a1f973c63ac19e2.png"},{"id":99286779,"identity":"56284606-a95a-4c52-8b60-f6e6c40b7602","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":35445,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/545e8c946654ba9c6256a41e.png"},{"id":99286772,"identity":"b367e407-611b-44ad-8a39-41ae527c2fa7","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":103804,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/153918277caefb5f7ef562bf.png"},{"id":99286776,"identity":"b2011d66-8ef1-4ec1-afc7-0e11dbb895e7","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":84782,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/94f66a960ebe535628e4b69a.png"},{"id":99286777,"identity":"a779c54e-5d10-4dc1-ad65-8483c752698d","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":39676,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/84839f2bf48075b184d92214.png"},{"id":99286780,"identity":"d183ffca-5b4a-4e81-86ab-2498dd36d98d","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"xml","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":125656,"visible":true,"origin":"","legend":"","description":"","filename":"98d51e1e8e3e4e35a5409acd40efe4ef1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/3c9552064f5613be983b2703.xml"},{"id":99286782,"identity":"c3bc7518-f83a-4483-ba78-db0047e00246","added_by":"auto","created_at":"2025-12-31 09:30:28","extension":"html","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":137356,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/26527ce5936a3cf8cd0ee0ef.html"},{"id":99286743,"identity":"929dc9ee-b1af-4892-9df8-2cb64a3b7da7","added_by":"auto","created_at":"2025-12-31 09:30:27","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":344224,"visible":true,"origin":"","legend":"\u003cp\u003eFigure for interpreting wavelet analysis, adapted from Ref. [9]\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/5d61a1b6a5fdb0aff5fcf67d.png"},{"id":99286744,"identity":"e28dc1ce-2801-4ac2-86eb-0fe8fa2e7f3a","added_by":"auto","created_at":"2025-12-31 09:30:27","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":103172,"visible":true,"origin":"","legend":"\u003cp\u003eFitting activity data with 3 Gaussian curves.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/efa661a6dc22550040690f71.png"},{"id":99286748,"identity":"1d5924b0-74b8-4047-9ea2-2c5507000135","added_by":"auto","created_at":"2025-12-31 09:30:27","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":297767,"visible":true,"origin":"","legend":"\u003cp\u003eClassification diary-map of the days of the months for the consecutive 5 years during which the actograms were recorded, categorized into 3 groups using Gauss-fitting (see Figures 3 and S3). Normal days are marked by blue, while (hypo)manic and depressed days are marked with red and black, respectively. Purple and green colors correspond to “transition” days at the two edges of the normal spectrum, towards mania and depression, respectively. Gray color marks the days that were not further categorized. The row-end numbers correspond to the recorded days of the months.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/ce5f14810b1549e33726bf9a.png"},{"id":99320916,"identity":"272d1ed3-fa7f-4432-b4ff-8f40199ea453","added_by":"auto","created_at":"2025-12-31 16:38:57","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":155861,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the first 4 hours and 20 minutes of all normal nights with the nights before episode transitions (blue - normal, red - mania, black - depression). Standard errors are indicated with lighter shade of the respective color.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/a4e33f65c9ac7a6376647305.png"},{"id":99319582,"identity":"3bb1251e-24e7-439e-854f-a5c387030d6d","added_by":"auto","created_at":"2025-12-31 16:37:31","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":69083,"visible":true,"origin":"","legend":"\u003cp\u003eAverage fragmentation indices and fluctuations (STDs) around the average for each ac-tivity group\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/4066e08915a69cc1a1c82757.png"},{"id":99286761,"identity":"4ee6d684-9068-4267-aee2-b5ce0da542f0","added_by":"auto","created_at":"2025-12-31 09:30:27","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":102529,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of Daily Activities as a function of the standard deviation of nocturnal ac-tivities of the preceding nights.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/5a40af9befcfdc30499bc2cf.png"},{"id":99320638,"identity":"26859954-f9ad-473c-bd68-92fb8866e6d1","added_by":"auto","created_at":"2025-12-31 16:38:49","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":367354,"visible":true,"origin":"","legend":"\u003cp\u003eContinuous wavelet analysis of normal daytime (A) and nighttime (B) activities. Left inserts: Intensities versus log(size of time-window); Right inserts: Structure map of activity data of 5 con-catenated consecutive days and nights, respectively.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/f68473981d0cc39672792d68.png"},{"id":99320896,"identity":"518945f6-15ee-4729-bfaa-add7324a9f23","added_by":"auto","created_at":"2025-12-31 16:38:56","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":94491,"visible":true,"origin":"","legend":"\u003cp\u003eContinuous wavelet analysis of nighttime activities of 5 successive concatenated nights of days classified into the same mood states (normal, depressive and manic, respectively). In-tensities versus log(size of time-window); blue - normal, red - mania, black - depression\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/151efb124123ca7744d37fca.png"},{"id":99286752,"identity":"715bfc80-b89a-4a7d-bd07-db969a18286b","added_by":"auto","created_at":"2025-12-31 09:30:27","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":70337,"visible":true,"origin":"","legend":"\u003cp\u003eContinuous wavelet analysis of nighttime activities for single nights of days classified into the three mood states (normal, depressive and manic, respectively). Averaged intensities versus wavelet time-window); solid blue - normal, solid red - mania, solid black – depression. The dashed lines indicate the standard error ranges for each curve, and the time-window range be-tween 20 and 70 minutes defines the region of interest.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/954e85bcb3a6b8528e617b91.png"},{"id":101429093,"identity":"89650954-26aa-48bf-95f5-7708f41f55c4","added_by":"auto","created_at":"2026-01-29 15:31:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2134802,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/ae240e15-2e81-4fd0-ac29-a5a1bd51ba74.pdf"},{"id":99319568,"identity":"38f912c4-cb34-429e-87d5-23c889c36449","added_by":"auto","created_at":"2025-12-31 16:37:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1119335,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformationIJBD.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8346326/v1/40d7a992d89d5472835579be.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Linking Activity Patterns and Mood States in Bipolar Disorder: A Longitudinal Case Study based on Actigraphy Signals","fulltext":[{"header":"1. Background","content":"\u003cp\u003eThere is an ever growing need to involve objective measuring tools in modern psychiatric research, to assist prevention, diagnostics, status tracking and episode prediction in various mental disorders, which have been spreading quasi-epidemically during the past decades [1-4]. Alterations in human physical activity (HPA) are key symptoms of major psychiatric disorders, including schizophrenia, ADHD, anxiety disorders, autism spectrum disorders and bipolar disorder (BD). In this study, we focus only on the latter, but the methodological tools studied can potentially be applied in other psychiatric conditions, as well.\u003c/p\u003e\n\u003cp\u003eActigraphy is a widely used measurement method of HPA, typically used in combination with other non-invasive diagnostic techniques, such as ECG or EEG, primarily in medical, biophysical, and sports-related research [5–8], but it is also becoming more common in everyday life [9,10]. The device used for the measurements is called an actigraph, which is a small, wristwatch-sized, accelerometer-based, non-invasive diagnostic in-strument. It is typically worn on the non-dominant wrist, providing objective, reliable, and cost-effective data on the subject's movement activity. The actigraph calculates activity values over non-overlapping, equally sized time windows, storing these values in a memory unit [10,11].\u003c/p\u003e\n\u003cp\u003eIn recent decades, the development of piezoelectric sensors, lithium batteries, and digital data storage units has significantly contributed to making actigraphy measurements more accurate and reliable, as well as enhancing data storage capacity. These devices are also being designed to be smaller and lighter, making the measurement process more comfortable for the subject. This is important because it minimizes the disruption to the subject’s daily activities, allowing for more reliable data on motor activity [12-15].\u003c/p\u003e\n\u003cp\u003eThe regulation of human activity is a complex process determined by many external (e.g., work, rest, reactions to unforeseen events) and internal (such as the circadian pacemaker, which influences the sleep/wake cycle, and ultradian oscillations on smaller time scales) factors. External factors are generally responsible for smaller, more irregular fluctuations that fade out over shorter periods. Internal factors, due to the underlying regulatory functions, shape activity levels over longer periods, even up to 24 hours [16,17]. When performing a typical daily routine, it can be observed that the time correlations of physical activity significantly differ between daytime and nighttime periods [13]. Furthermore, human activity is also related to important physiological functions, including overall body oxygen supply and heart rate regulation [18,19].\u003c/p\u003e\n\u003cp\u003eBD diagnostics hinge on symptomatology, longitudinal course, and familial antecedents, yet many cases evade timely intervention. Manic phases exhibit hyperactivity and hypoarousability; depressive states feature hypoactivity and fragmentation [28–30]. Prodromal phases (73–98.4% prevalence, 5–6 year duration) afford prediction windows, underscoring actigraphy's utility in differential diagnosis (e.g., vs. ADHD) and therapeutic tracking [7,16,20–27].\u003c/p\u003e\n\u003cp\u003eActigraphy excels in naturalistic phenotyping of sleep-wake dysregulation - hallmark in BD -with superior feasibility over polysomnography for extended, non-laboratory deployments. Metrics like fragmentation index quantify nocturnal motility, correlating with depressive severity, psychosis risk, and treatment efficacy; circadian desynchrony presages relapse.\u003c/p\u003e\n\u003cp\u003eThese characteristics are taken into account in clinical settings as defining traits, and the objective measurement results of actigraphy can be useful for assessing the severity of symptoms or for monitoring transitions between mania and depression [28-31].\u003c/p\u003e\n\u003cp\u003eAmong individuals with schizophrenia and bipolar disorder, sleep-circadian dysfunction is common, often manifesting as sleep fragmentation and increased sleep duration. In some individuals, insomnia and hypersomnia-type patterns emerge, but a more comprehensive understanding of these patterns requires further research [32].\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eObjectives\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eAs described in the previous section, it is evident that understanding, preventing, and effectively treating mental illnesses is an important task for not only the affected patient and their environment but also for society as a whole. To this end, several studies have raised the need for longitudinal actigrapy measurements to obtain a more representative picture of the patient's true condition, however, such a typical measurement in psychiatry usually lasts around two weeks [11,30].\u003c/p\u003e\n\u003cp\u003eIn contrast, we analysed a dataset containing several years of activity data from a clinically diagnosed male patient in his fifties suffering from bipolar disorder. Therefore, the data we processed came from long-term measurements conducted in the sub-ject's accustomed environment and routine.\u003c/p\u003e\n\u003cp\u003eWith the processing of this large amount of data, one of our goals was to create an objective, diagnosis-supporting analysis that could also be useful in clinical practice for confirming the disease, so first, we intended to classify the monitored days into three groups, based on cumulative activity counts, using Gaussian fitting.\u003c/p\u003e\n\u003cp\u003eSince sleep disturbance is a prominent feature of manic depression, and actigraphy provides an objective picture of activity even during the night and can map the sleep/wake cycle, the next objective of our study was to establish a quantitative con-nection between successive sleep and daytime activity data, using statistical methods, such as the Kolmogorov-Smirnov test (KS test) and the Continuous Wavelet Analysis (CWA)\u003c/p\u003e\n\u003cp\u003eIn the case of this disease, the development of proper evaluation techniques that are capable of predicting mood switches is particularly important in order to optimize and enhance the therapy [17]. Hence, our final objective, based on the previous evaluation steps, was to suggest an evaluation method that could help predict transitions into other mood states by observing nighttime sleep, thus preventing potential problems arising from manic or depressive episodes. For this purpose, we intended to use CWA, as the most sophisticated method of our evaluation toolkit.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;Such a method, if proves generalizable, could assist not only the patient but also their close relatives and the treating physician, preventing many unforeseen issues.\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cp\u003e\u003cem\u003eActigraphy\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eFor monitoring, a MicroMini Motionlogger actigraph (Ambulatory Monitoring Inc., Ardsley NY, USA) was used at 10Hz sampling rate, in proportional integrating mode of 1min/epoch time. It means that the raw data were integrated by the instrument with an integration time of 60s, to provide a single data point stored in the memory of the device. Data collection periods were recorded on a clinically diagnosed male patient in his fif-ties suffering from bipolar disorder, for several years. The measurement results include both nighttime and daytime activity data. The patient worked with a flexible schedule and was undergoing pharmacological treatment aimed at his psychological condition. Therefore, the data we processed came from long-term measurements conducted in the subject\u0026apos;s accustomed environment and routine. Several studies have raised the need for longitudinal measurements to obtain a more representative picture of the patient\u0026apos;s true condition, as a typical actigraphy measurement in psychiatry usually lasts around two weeks [11,30].\u003c/p\u003e\n\u003cp\u003eThe recordings were taken for 5 consecutive years, out of which 4 covering data of \u0026nbsp;3\u0026ndash;6 months yearly, for 625 days altogether. The advantage of recording activity on an outpatient is that the data reflect the endogenous rhythm of \u0026lsquo;\u0026lsquo;real life\u0026rsquo;\u0026rsquo; and not that constrained by the usual routine of ward conditions. A drawback of outpatient studies, however, is that the knowledge of the daily mood state is less certain. The study was approved by the Ethics Committee of the Medical Research Council (ETT-TUKEB) op-erating as a board of the Ministry of Human Capacities of Hungary (approval identifi-cation No.: 15239\u0026ndash;5/2023/E\u0026Uuml;IG). The subject gave prior written informed consent to participate. The study was carried out according to the Declarations of Helsinki and the standards set forth by the journal for ethical human research.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eStatistical Methods\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eIn the paper all figures were created, and their corresponding codes were made, using MATLAB 2021b. MATLAB is a platform for programming and numerical com-putations, developed by MathWorks Inc. (1 Apple Hill Drive, Natick, MA, USA) for engineering and scientific applications such as data analysis, signal and image pro-cessing, system control, wireless communication, and robotics.\u003c/p\u003e\n\u003cp\u003eGaussian Distribution Fitting\u003c/p\u003e\n\u003cp\u003eThe Gaussian distribution has two parameters: the mean and the standard devia-tion, and can be defined by the following function:\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/p\u003e\n\u003cp\u003eWhere x is the probability variable (which can theoretically take any value between \u0026minus;\u0026infin; and \u0026infin;), f(x) is the relative frequency for x, \u0026mu; is the expected value of the distribution, and \u0026sigma; is the standard deviation.\u003c/p\u003e\n\u003cp\u003eThe Gaussian fit was used to classify the days into three mood categories (\u0026rdquo;hipo-manic\u0026rdquo;, \u0026rdquo;normal\u0026rdquo; and \u0026rdquo;depressed\u0026rdquo;), based on the cumulative daily activity counts. Those days that were in the transition zones were not initially classified, in order to be able to make clearer conclusions after the subsequent steps of the evaluation. Hence, Gaussian fit played a major role in classification of the days.\u003c/p\u003e\n\u003cp\u003eConvolution\u003c/p\u003e\n\u003cp\u003eConvolution is a mathematical operation that gives the overlap between two functions. It takes two functions and \u0026quot;shifts\u0026quot; one over the other, multiplying the values along the way and adding the results to create a new function. Formally, convolution is an integral operation that expresses the extent of overlap between one function f(t) and another function g(t) as one moves across it.\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfgAAAB0CAYAAABpLSBoAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAADP+SURBVHhe7d15UNt3fj/+py4kdCBAIEDcl7kxxgYfOOD7io846ziOJ+nutJvZP7bttJ1pZ9q/Mpvsbme2bf7ot9NOdiezu93dxLFrx4lNGgd8YBvMjY25DyFOSSAEOtCtz++Pnz6f4RCHU8eH8nrMaJyAJOCjz+f9eh+v9+vDYxiGASGEEEJCCn/5FwghhBDy8qMATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCEEEJICKIATwghhIQgCvCELGKxWJZ/iePxeOB0Opd/mRBCXkg8hmGY5V8k5PuEYRjcvn0bc3Nz8Pl8sNvtyM3NxebNm8EwDBoaGtDb2wu73Y6IiAgUFxejqKgIcrl8+VsRQsgLgwI8+d5rb2/HhQsXMDo6ivT0dDAMA7VajdTUVCwsLKCtrQ1dXV2IioqCx+NBamoqzp07h61bt4LPp0kwQsiLiQI8+V5YfJrzeDzuv0dGRtDc3Iz29nZkZ2ejpKQEJpMJer0e9+/fR39/PzIzM7F7924kJiZidHQUQ0NDiI6OxsGDB5Gfnw+BQMC9HyGEvCho+EFCns1mw8jICBobG/H48WPo9Xr4/X4AwPz8PLRaLTIzM7F//35s2bIF+/fvR2ZmJvr6+jA3N4eKigq8/fbb2L9/P06fPo3i4mLMz89jfHwcbrd7+Y8jhJAXAgV4EtLsdjsePXqEL774Ah9++CE+/PBD3L59Gx6PBwiM7Pl8PrxeL3w+HwDA6/XCZDJBrVajoKAAUqmUmwEQiUQQi8Xg8XhwOBwU4AkhL6wXIsD7fD54PB54vV74/f4l06nB+Hw+uN1uuN1ubiS2EezrXC4XvF7v8m+HDL/fD6/XC4fD8cR/p9frhdPphMfj4QLey8rhcODWrVv49a9/jXv37mF6eho1NTXo7u7m/rawsDCoVCpotVr09fXB4XBAq9Xi5s2b6Ovrg8/ng0wmg8vlgsfjgU6ng1arRUREBOLj4yEWi5f/2OfK5/OBYZh1r6Fg/H7/U/vM/X7/E12bLxv2WD2t4xUM+/7ssfw2nyn5fnvua/B2ux09PT2YnZ1FWFgY4uPjER8fD6VSuWStlDU3N4fu7m5MTEwgMjIS+fn50Gg0QZ+7mM/nw8TEBHp6emAymZCcnIzS0lLIZLLlT33pDQ8PQ6vVQqvVYsuWLdiyZcuGksG8Xi96e3vR1dUFoVCITZs2ITs7GxKJZPlTX3herxf19fX45JNPYDKZsHXrVoSHh6O5uRnbtm3Du+++C6lUCgC4d+8ebty4AZvNhpycHFgsFhgMBrjdbmRnZ0OlUkGpVILP52N8fBxGoxFbtmxBZWXlC5NJzzAM7HY7tFotoqOjIZVKERUVtfxpq/J6vRgZGYHNZkNmZibkcvm619RqLBYLxsbGIJFIkJycjLCwsOVPeemZTCaMjo5CJBIhPz9/Q9fXk/D5fOjt7YXH4wHDMBAKhUhMTER0dPTypxKyKsF777333vIvPgsejwfz8/Ooq6tDa2srWltb0dzcjNnZWURGRkKlUkEoFC55zfz8PG7fvo0rV66gt7cXIpEIGo0GMTExG2qM5ufnUV9fjzt37mB0dBRisRjR0dHclOvLzuv1Ynp6GrW1tbh48SIMBgPkcjlycnJWHMtg2BHq3bt3cevWLczOziIiIgJRUVEQiUTLn/5Cczgc+Oyzz9DY2IhDhw7h9ddfR1lZGTZv3oySkhJERUVxjbJIJEJYWBiGhoa40f2WLVvwox/9CDt27IDVakVdXR26urrAMAyKiopQWVmJiIiI5T/2ufB6vdDpdNzshMPhQEJCwhN1PmZmZtDV1YWOjg6MjIxALBYjIiLiiRIIPR4PJicncf/+fdy7d4/bcfCizXI8DXq9HtevX4dWq+WOlUgkemrtiM1mQ1NTE+7cuYOamhro9Xpu8EPIRj2XAM8wDFpaWnDlyhV0dnYiMTGRy1B2u90oLCxEfHz8ksZlfn4eX375Jf7nf/4HEokE+/btw44dO5CUlASJRLLkwlo8Nch+ncfjQSKRcI+BgQG0trbCYrEgKSkJCoWCe83LqqenB7/73e/Q3t6OnJwcVFRUoLi4GOHh4StG4YunY9ljxOfzIRQKoVKpEBERgaamJnR0dCAmJgaJiYlP1Ng/b3q9HleuXMHAwAAOHTqEXbt2QS6XQ61Wc6NxlkKhgEajQWJiIlJSUpCTk4MdO3ZAo9EgLCwMUqkUsbGxyM7ORmFhITIyMiCXy1+IkanD4cDDhw/x2Wef4eHDh0hNTUVhYSESExM31KljCQQCSCQSTExMoK6uDh0dHVCpVFCpVBvq3Lndbjx69AgXLlxAfX09NBoNioqKEB8fH/Q4eTyel+p8Ws7pdMLv96O+vh7t7e2YnZ1FYmIiZDLZUwnyYrEYAoEA9+/fx9WrVyGVSlFYWIi0tLTlTyVkVc8lwC8sLOD3v/89rl69iry8PJw8eRI5OTkICwtDZmYmcnNzIZPJuAbA4XCguroaf/zjH8Hj8XD27Fm8/vrrUKvVK4K71+vF5OQkDAYDrFYrpFIp19AJhUJoNBrk5uaCYRh0dnait7cXcXFxSE1N3VBD9qIymUz46quv8MUXX0ClUuHcuXM4cOAAYmNjVwR3hmEwMDCAgYEBiMVibqTH4/GgUCiQmpqKnJwczMzMoKGhAQaDgRs9PO2pyO9Kf38/Ll++DIfDgTfeeANZWVnLn7KESCRCQkICcnJykJWVtWR0LpPJkJSUhLS0NGg0GkRGRgYNWs8awzCoq6vDhQsX0NPTg4KCAhw+fBi5ublPPGoWCoWQSqWQSqUwm8149OgRtFotRCIRsrKyVg1aDMPA6/ViaGgIn376KTo6OpCdnY1jx45h69atK34P9twbGhqCQqFYcW6+LBQKBZRKJdxuN4aGhtDe3g6BQACNRvPUgnxMTAy++eYbNDU1ITs7G6dOnaIpevJEnktr3dHRgdbWVjAMg/LycmzatAkpKSk4efIk9uzZA7VazTWgDMNgcHAQn3/+OWZnZ3Hy5ElUVFSsegGZTCbcuXMHn376KR4+fIj5+fnlT4FEIsH+/fvxyiuvwGAw4Pr16+js7HzihLQXhcPhwPXr1/HVV18hKSkJJ0+exKZNm5Y/jTM/P4/Lly/j008/xcTExPJvAwDkcjnOnDmDPXv2oL6+njv+LwOPx4PR0VEYjUYwDPNCBOOnzefzQafTobq6Gg0NDTh06BDOnTuHTZs2feu/NywsDFlZWXjnnXdw7NgxNDc348qVKxgZGVk1mYz9PS5evIi6ujpuaSMvL2/5UwEA09PT+NOf/oSLFy9icHBw+bdfKmq1Gm+++SbOnz8PALhy5Qpu3bq1ZrnjJ+F2u7GwsACRSISCgoKXegBCno9nGuB9Ph/m5+dx8+ZNDA4OIj09HdnZ2eDz+WAYhksMWnwis2vKAwMDSEtLw65du4L2YtkM/OnpaXz11Vdobm6Gz+fjGjuv18sFcD6fj+joaOzatQuZmZno6OhAXV0drFbrsnddHzuCeZpZw2zGrMvl4nYKrJVJOzs7i5s3b6KnpwelpaWoqqpCZGTk8qcBgc5AW1sbGhoa0NfXx2XLMwyzYmkjMTER5eXlkMlkaGpqQltbGxYWFpa834vIZrPBaDTC7XZDJpMhPDx8+VNeGOx5yayS+c7uLlnOZDLh66+/RmNjI7eHP1hwZxiGC84+n497L/ac9Xg83JZBBIJ8fHw8KioqsHXrVvT39+PChQswGo3ccxbzeDxoampCbW0tNBoNDh06hOzs7CUzcAic03a7HR0dHWhpaUFPTw/CwsLgcrm4a+hFwH4Oi3eRsIlubrd7xe8aFhaGnTt34tSpUzAYDKiursbAwMCid9wY9mexu3xcLhfGx8eh0+m46XmNRrPkNewy2+LPb/HnGux8It8vz2yK3mq1YnR0FPfu3cMXX3zBJbkplUru4pdKpSt6qd3d3fjtb38Lh8OBvXv3YteuXVz2M8vj8WBqagrDw8O4ffs2Ll26BIvFAqVSCZfLBZPJBLfbDalUuqQBVCqVMBqNqK2thd/vR0VFRdDOw1rYBKeJiQkwDPN/Xsv3+Xzo6elBV1cXenp6MDY2BofDAbPZjKmpKXg8HigUCm4Gw+Fw4NGjR7h69Sp4PB7Onz+P/Pz8FTMcLpcLZrMZDQ0NuHbtGpqamjA7O4u4uDjY7XYYjcYl0/Usr9eLwcFB9PX1QSwWIycnB5GRkSve/0VisVhw7949NDU1QS6X49ChQ0hKSlr+tOfO4XCgq6sLLS0tsFqt4PP5XPa63+/H6Ogo2traMDU1hfDwcISHh3PHvbW1Fb/73e9gs9lw9uxZ7N27N+iatsvlwsjICHp6ejAyMoKxsTGMj49jYGAAOp0OIyMjsNvtCAsLW5JsKhaLIRQKce/ePXR3d2PHjh1ITk5e8t4Mw0Cr1eLjjz9Gf38/zp49i6NHj66Ylvd6vZiamkJTUxO++eYb1NTUwOfzISYmBmazGSaTCXw+H0qlcsnrnjWGYTA1NYXBwUH09PTAYDBwO2/YY2YwGOD3+5dcAyKRCEqlEm1tbaivr0dGRgby8/NXtGVrmZqawqNHj9DV1YWhoSFMTk6iubkZLS0tEAqFOHnyJDIzM7nn22w2dHd3Y2hoCDqdjusMsJ+rVqsFAERERLw0y2rk6XtmAd5kMkGn0+HatWuora2Fy+WCRCKBN7BmLhaLkZiYuGS05ff70dbWhk8++QTR0dHcFOTyhsxqtWJ8fBx37tzB559/jr6+PjAMA6VSCYPBgIGBASiVSiQnJy9pfMLCwmCz2XD//n24XC7k5uYiLS1txfsH4/F4wOPxwATWQaurq6HRaJCUlLRkVPYkF5fZbEZbWxvu3LmD2tpaTE1Noa+vD1NTU2hra8ODBw8gFouRlpbGNR7T09O4du0a2trakJSUhDNnziA2Nnb5W2N+fh79/f24fv06bty4Aa1WyzWoAwMDmJqaQkpKCmJjY5f8zmyj9/DhQ/h8PlRWVkKtVi9659XZ7XYYDAYYDAaYTKYNP2ZnZzE/Pw8+n78k6GyU2WzG/fv30dLSgpiYGJw4cQIJCQnLn/ZcLSwsoK+vDzU1Nbh48SLa29uhUCiQmZkJPp+PkZERVFdX49q1axgZGUF0dDSXOOf3+3H79m1cvnwZGo0GP/7xj1dkVzMMg5mZGXR0dKChoQHffPMNmpub0djYiAcPHqC9vR3t7e3cNLlcLodKpeLOfXZtvK2tDd3d3SgoKEBubu6SoOXxeHD37l1cvXoVAoEAP/zhD5Gdnc19n+VyudDf349r166huroaer0eMpkM3sDa/fT0NJKTk5/bZ+T3++FwODA0NITbt2+jtrYW9fX1qK+vx927d9HT04OHDx/i0aNHGB0dhUajQUpKypLzks/nY3R0FM3NzZDJZEhPT4darV73+vf5fOju7kZjYyOqq6uh0+mg0+nQ39+PhoYGjIyMID09HceOHUNCQgL8fj8mJyfR2NiIO3fuoKGhAQ8ePMDdu3fR1NSErq4uNDc3o7e3l8tpWt7hIt8fa599T5FMJoNarYZCoYBAIIBcLsf+/fuxfft2lJSUICMjY8WJaLPZ0N/fD4/Hg7i4OKSkpKyYggTAjW4EAgHcbjcUCgVKS0uxf/9+7Ny5E6WlpUhOTg46DahSqaBWq2Gz2dDX1we73b78KSswDIO+vj709fVhYWEBRqMRXV1dcDgccLlcGBgYgF6vh9PpDPozg7Hb7aiursZ//Md/YHh4GNu3b8exY8ewa9cujI6O4pNPPkFzc/OKKXKr1YqBgQEwDIPExMRVt26xmeAxMTGYn59HVFQUKioqsGfPHpSWlmL79u2Ijo5eMa2nVCqRk5OD8PBwaLVa6PX6VddjF2MYBkajER9//DH+6Z/+CT//+c/xwQcfrPv4+c9/jn/8x3/Er3/9a3R0dKz4fTbC5/NxhWkkEsmGOmzPktfrRX9/P+rr6+F0OiGVStHe3o67d+9iamoKRqOR6wizOSSLjwNbD9/pdCIzMxNxcXGL3v3/x3ZyPv/8c7S2tkIgEGBmZgaPHj3C0NAQBAIBYmJiEB0dDZlMBqlUuiIYZWVlISkpCX6/Hx0dHdyokDU9PY2uri74fD5s2rRp1dkvv9+PhIQEREVFwWKxIDo6Gnv27MGuXbtQUlKCLVu2rPraZ8Hj8aCrqwuXLl1CXV0dPB4P/H4/Ghsb0dbWBoZhEB0dze0qWD6DiED7lpycjOTkZAwMDHBFktbT3NyM//f//h9qa2uRmJiIgwcP4ujRo5DL5RgeHsbs7Cyys7O5zvj09DQuX76My5cvw2KxgM/nY2BgAI2NjZiamoJcLodcLkdERAQUCsWKz5R8vzyzT18ikUClUiE9PR0KhQJpaWk4ceIEzp07h+PHjyMnJ2fFmp0pcNMPdkpstaI0YrEYSUlJiIuLQ3x8PCIjI1FRUYHXXnsNr732Gl599VXk5+cHnT4PDw+HUqmE0+nE1NQUzGbz8qesYLPZ8PjxY1y+fBlfffUVdDodxGIxRkdHcf36dVy7dg1dXV1wuVzLXxqUxWJBS0sLLl68iKGhIWRmZuKtt97CwYMHceTIEYhEIuh0OoSFhSEmJmZJJ8dsNkOv1wPAmpXVwsPDkZqayt0cJS0tDSdPnsTp06dx/vx5HDx4EElJSSu2VgkEAqjVasjlcthsNoyNjS1Z81sLwzCYm5uDTqfD9PT0hh5GoxEzMzMwGo3c0s2TBnmv14vZ2VluJmWjv++zwo4YVSoVKioqcPDgQaSmpqKzsxPXrl1DfX09BgYGEBMTg2PHjuHQoUNITU3lrg+DwYD+/n74fL6gxU/Y4+Z2u6FSqVBeXo49e/YgISEBIpEIcXFxOHz4MLcbpaysDAkJCSs6QiKRCImJiYiJicHk5CSGh4eXfH92dhb9/f1wOp3IyMhYdYpdJBIhNTUVmzZtglAoRGpqKo4cOYK33nqLO/cSExOXvywo/6J8lI0+1utk83g8bkausLAQ+/fvx+bNm6FQKCCXy7k19tOnT+PIkSPIyMhYETj5fD6Sk5OhVqu5+xSsNUXv8/kwOTmJL774AnV1dRCJRDh69CiOHDmCAwcOoKysDG63G3K5HAkJCdyx9Xq9MJvNUKvVeOWVV7Bv3z4olUrYbDaUlJTgzJkzOHfuHF577TWuuBP5/npmAZ4NPHq9nrvfdmlpKSIjIyGRSCAK1PhmMQwDi8WCmZkZ7j7cqwUvBNaaGIaBzWZDTEwM0tLSuNFJZGQkhEJh0AtOIBAgKioK3kCRmI30uhcWFsDj8TA1NYXLly+jqakJNpsNt27dQnV1Naanp+F2u8Hj8VYEzGC0Wi0uXryIkZERbN++HcePH+dG4oLA/mSJRIKEhASo1eolU4M+nw9zc3NwOBxQKpVB/0aWz+fD1NQU+Hw+4uLiUFpaCpVKxX0GyxstBBousVgMiUQCv98Ps9kM/waSCXk8HmJiYnD+/Hn87Gc/wz/8wz/g7//+79d9sM97++23UVJSAqFQ+MRT9AzDQCAQwBco8xns73qehEIh8vPzcfjwYezYsQPbtm1DdnY2pqamcOnSJTQ1NSE3Nxfvvvsuzpw5g6qqKiQlJXEzVLOzs5idneWKNAXrAIlEIhQWFuLtt9/GW2+9hc2bN4PH40Emk6GiogK7d+/Gtm3bUFJSgrS0tCV5HYuxWwJnZ2dXZIf7A51wj8fDXWPBhIWFweFwwGKxwO/3Iz09HQUFBdwMQrDcm8U8Hg/GxsbQ0NCAmpoa1NbWrniwX1/+782bN9HV1YW5ubnlb8vh8XhITU3Fm2++yZ13CoUCERERyMvLQ1VVFcrLy1FWVobi4uIVHSr2PdjRvdFohMViWbOD7/V6cfXqVdTU1CArKwtHjhxBbm4uBAIBeDweV4gpJiaGG8H7/X5IpVKcOnUKP/7xj7F//35ue29ycjL279+PXbt2oaKiguu0vWjnPnm2numnPzY2Br1ez40K19oDy+PxljTQAoFgxQhjudnZWUxOTkKj0SAjI2Pd5yPQELJrjxsJ7gg0elu3bsWhQ4eg0WgwNjaG3t5e9PT0QKVS4cCBAygtLV11unw5nU6H+vp6KBQKVFVVLdmzbbfb4XA4IJPJkJeXh8TExCUXLT9woxSv1wuRSASn0xm0wUcgD0Kr1XINSGxs7LrHiM/nQyqVQi6Xw+12w+FwwGazrfozFouIiEBZWRmOHj2KiooK7Nu3b93H3r17ceTIEezduxdRUVHfagTCHh+Px/OtOgjfNX4goSwqKoqb2k1MTITX64VWq4XP50NVVRW2bduG2NhYyOVyrt4Dn8+H1WqFw+GASCRCTEzM8rcHj8dDZGQk0tPTkZaWhsjISHg8HgwPD4NhGGzatAkajQbh4eEICwtbM7iGh4dDKpXCZDLB6XQu+Z7H48Hs7Cz8fj8kEsmqAR6BEtMjIyNwOp2IjY19ovV2p9OJ9vZ2/Od//ifee+89vP/++/jVr36FX/7yl/jVr36FX/ziF/jXf/1XfPDBB/i3f/s3fPDBB/jwww/xwQcf4P3338d//dd/YXJycvnbcgQCAVfIiM1lGB0dxcLCAhITE5GQkACZTAaZTLbmseLxeFAqlXA4HFhYWIB7jRsRGQwGNDY2wmg0orS0FBUVFdzUv8vlgtFo5K7T1NRU7jyWSqXYvHkzMjMzER4ejomJCczOzkKtViMpKQnSQC0DuVxOwZ082wDPJlvFxMQgKSlpQw2v1+uFWCxGWFjYmkHF6XRifHwcs7OzSE5OXpJxuhafzwen0wmJRAKxWLyiEQvG4/HAYrHAYrFALpcjJiYGDMNwU+Qmkwk2m21DHYa5uTl0dHRAr9cjLS0N27Zt4y5MhmFgMBgwPDwMiUSC1NTUFaMHdt2fXWpYq9M0OjqKiYkJCIVC5OXlBV1LDEYoFHLV8Ph8/pojk8UYhoFer0d/fz/0ej10Oh2Gh4e5HQ9arRZTU1NcJvDU1BSXvzA+Pg6bzbb8LTeEYRg4nU7weLwNdQyfN5VKheTkZPh8PkRERCA/Px/p6elBrw//omULuVwedFaLF6jayHaOPB4Puru7MTk5CaVSifj4+DUD1WJhYWGQSCTclrbF/IHtWCKRaM0ZNk+ghO34+DgiIyORmpq65nm6HI/Hg1gsRmxsLLcOzi7Hsf+q1WpoNBqo1WokJCRwnQiFQgGFQrHqtlEEOlyLl730ej0eP34MgUDwxAWw2BkVdgYvGKfTib6+Pq7QVGFh4ZLrem5uDoODg7BarUhJSeG2x7HHAYFzfHR0FJ2dnXA4HFCr1RseUJDvj2ca4MfGxjAwMICoqCio1eo1LxyGYSAOlGtcWFgAwzCrXjAIZImzFwzbu90I9sJeWFiAx+NZdZ1/MZvNhvr6ely8eBF2ux35+fkoLy9HeXk5XC4XvvrqK7S2tmJmZmbd9d+ZmRmMjo5yyVaLtyJ5vV48fvwYg4ODkEqlQcvFCgIJi3w+HyaTCVhUenY5NqNdoVAgMTFxzRHGYgKBgBu5s8mM62ECWdx3797Ff//3f+OTTz7BlStX8Pnnn+PSpUu4evXqkv++cuUKLl26hGvXruG3v/0tvvjiC+j1elgsljU7dsF4A7d+Zac71/sMnjcmcKOYhYUFREVFrZilWUwoFEIc2FngcrnWXS5hl1XYXBalUom4uLg1R9uLKRQK+P1+7mcF6wCzX19trdsf2PKn1+uhUqmC5sKsJTw8HDt27MDf/u3f4sMPP8S//Mu/4P3338cvfvELvP/++/jlL3/J/fuzn/0M//zP/8z9++GHH+Jv/uZvgiYirsZut3M3y2HLFa+Hz+dDoVBs6Fy12WxcAI+IiEBKSsqSz2NychKPHj2CSCRCfHx80F0xvMAM5+DgIDweDzIyMjbUdpHvl+CtyHdkenoaBoMB6enpG96XLJVKIRAIYLPZVm2oFxYWMDo6CoPB8MQB3mazweFwICwsDHK5HL5A0Ze1sNOfr776Ko4fP46EhAQIhUIUFxfj9OnTqKqq4u6itV4w1Ol0mJmZgVKpXJHopAvcQGRmZgapqalBRyECgQAikYibLVgtuDMMA51OB6vVyiU6bqSRZ9ft5+fnERERgdjY2A3tg+fxeLBarWhubkZDQwOamprQ0NCAxsZG3Lt3Dw8ePMCDBw+4/eoNDQ24f/8+amtr0djYiN7eXhgMBoSFha37s1bj9/sRHh7+Qjd8fr8fDx48wM2bNyEQCBAZGQmr1bpitMxyu90QCARgGAaSDewQ4PF4mJmZQXd3N7xeL9LT05/oLnMul4ubEVAoFEs65QKBAOHh4eAH7mGwWoAXCATcneoSExOh2cDdHxcTCARQKpVISkpCVlYWMjMzkZaWtqFHdnY2NBrNuseJxS5lOJ1OxMfHo6ioaEOzDQzDYGFhATabDQKBADKZbNV2xG63Y3JyEn6/n8ujYLndbnR2dqK+vh7R0dFc7kUw8/PzmJiYgFwuR2pq6oY6IuT75ZkFeKfTCZ1OB4/Hw023rYXP5yM2Nhbp6emQSCRrjoa9gWIs7AiWDbgMw6C/vx9arRYOh2P5y4DAaw0GAxiG4dY712t8JBIJ9u7di7fffhvl5eVITU2FVCqFRCJBWVkZ3nzzTW7b2WojMRbbMC4sLCwZ2ZjNZty6dYvb0x8fHx80UCmVSqSmpgKB2QCz2bxqw+IIFMyJiIhAeno6BAIBrFYr9Ho9jEbjmkHF5/NxMyob6Riw67Lbtm3Dzp07sXnzZpSWlqKsrAwFBQUoLCzkHuz/5+fno6qqCtu3b8emTZsgk8m+VaPFfn5SqRTMKhXiXgT+QJ2HO3fuYGFhAUlJSVhYWEB/fz/8gaqFy5d6RCIRlwDm8XgwPj6+5D2X8wcS4UwmEyIiIpCZmYnY2Fj4fD5YrdZVrynW7OwsF7SEQuGSYLM4B2Ct84fNE2Gn6PPz8yEUCuF0OmEwGKDX67/1cszT5PF4uIJSbrcbqamp0Gg08Pl8sNvta86WMIsqBrIzaqudd2zHn01aXNxxHxgYwNdffw2fz4fo6Giu5LTVal1STdDn80Gv12N+fp4L8Gq1Gl6vFxaLZd3PlXw/rB19nhK73c7VBlcqlcjLy1t3FMEL3PgkISEBYrEYNpsNk5OTQU9cHo8Hh8PBfY/davX48WN8/fXX3O0vg5mfn4fRaER0dDQyMzM3PH3IJrOEh4ejsLAQVVVV3BQ6mxS1Ws97saioKCgUCni9XnR3d3OzHO3t7aivr4fdbkdmZiaSkpKCBni5XM7dsctkMnEZ/sHMz8/DZDLBbrfD5/PBYDCgtbUV9+/f5zJ/l5ufn0dPTw9mZ2cRGxuLtEVFdtbC5/OhVqtx/Phx/N3f/R1++tOf4ic/+Qneffdd/NVf/RX+8i//MujjJz/5CX7605/inXfeQV5e3rodpGAcDgccDgd4PB6io6M3PJvzXWMYBvPz85icnMTg4CBu3bqFTz75BADwgx/8AAcOHIDT6cTAwAC6u7vx+PFj9Pb2LumcsqNZlUoFrVbL5Rqsxu12w2g0LtlPPzExgY6ODhiNxnWPr9lshtlsRnJy8opiOgKBACqVCuHh4XAFSs4GY7PZMDc3xyWejY2NwWg0csWIJicnVx39P2tGoxETExMwm81cwO/u7kZfX9+av6Pf74dOp4PBYIBMJuOSGIPhBZLleDwejEYjtFotTCYTOjs7UV1dDYPBAJVKhdjYWHgDxYBGRkYwMzOz5H0cDgdMJhO8Xi/4fD56enowMDAQdBmFfD89k0p2LpcLnZ2d+Oyzz+Dz+XDq1Cls2bJlzYYJgdGt3W5HU1MTzGYzcnNzkZ2dvSLAOJ1O2Gw21NXVcYVYOjo60NHRAbFYjIyMDKSkpCx5DRbV0War0J05cwZpaWnr/l7LCYVCxMXFITExcdWOxGrCwsIwPj6O+/fvc41pY2MjV8mNHT1VVVWhqKhoRWIcj8eDzWZDe3s7TCYT9u7du6JmNauhoQEdHR0YHx/HwsICWltb0dvbC5lMhi1btkClUq1o8GdmZlBXV4e+vj7k5uZi3759686+sPh8PkQiEcIDhYgkge1+7P8He4gDW/Ik62Rlr8VsNuPu3bvQ6/UoLi7Gli1bEBMT88Sf63dhfn4et27dwm9+8xtcv34dvkB1wH379kEul+P27dtoaGiAzWbjzmW2QNTi3394eBh9fX3cfujVzjuGYTA5OYnW1lYMDg5ienqayxCPiopCTEzMmsf566+/Rl1dHcrKynD8+PElHXMej4eBgQF0dnbC5/Nh586dQde6+Xw+mpqa0NLSAr1ej5mZGeh0OrS1tUEikaC8vBxRUVHP/fPh8/lwOBxobW1FV1cXrFYr5ubmMDk5CYFAgIyMjBVtD8vn86Grqwu3bt2CQqHA4cOHkZ2dHbSTzx7voaEhdHZ2Ynp6Gt3d3dDr9QgLC+PaBKvVyiWjKgOVONn98AzDoKenB9euXcP8/Dzm5ubQ3d3Nzfax2+zI99szOQNsNhuGhobgcrkQERGBtLS0DZ18vMDe0tLSUni9Xq5m93IKhQLp6ek4ceIEcnJyoNVqYTQaIRKJsHfvXuTm5i5/Cfx+P7RaLR4+fAgej4fNmzcjIyPjiRsZPp+P+Ph4ZGVlbXj0z7LZbIiKikJZWRmOHTsGlUqF/v5+mEwmFBQUoKioCFarFeHh4cjMzAw6gpdKpcjIyEBCQgImJiYwPDyMubm5FdOJPB4PVVVV2L17N5KSkjAwMACfz4e4uDjk5uYiIiIiaEM/Pj6O+vp6REZG4tChQyvqkb+I3G43TCYTBIEaBxEREU/8uX5X2Gl3g8EAANi6dSsqKysRHx+PzMxM7Ny5E1lZWZiZmYHX60VkZCQiltUTj4qKQlZWFoRCIUyBEtCrEQqFSElJwc6dO1FUVAQ+nw8ej8dlmgcLQKy+vj6uhO7mzZtX7OBgt4uqVCro9XpMT08v+T5LJBKhrKwMJ06cQFJSEubm5jA9PY3IyEgUFBQgdll55OeFF5jxKS8vx44dO6BQKGAymeDz+aDRaIJeHyx2UGE0GpGfn7/m3d8kEgnS09Oxe/dubN68ecmafFVVFc6ePYuKigqo1WrMzMxAoVBAKpUumcrn8/ncbXmTkpLgdDqXJOWt9bmS749nMoK32Wyorq5Gb28vcnJycOrUqXWn6FlsgYeenh7odDpkZ2evCMS8wL5fjUaDnJwc5ObmoqysDPv27UN+fj7CF92kg+V2u9HS0oLq6mpERkbi9OnTyMvLW/MiXg0vsD95+c9Yi16vx9TUFDcdt3PnTuTm5iIjIwOnT59GVlYWzGYzPv/8c8TGxuLkyZNBR+YCgQAKhQIGgwFDQ0Ow2+3IyspCXFzcikYzMTERubm5yMvLQ15eHiorK1FWVobCwsKgyWwulwt37txBTU0N0tPT8frrr78UAX5qagp37tyB1+tFRUUFSktLV8x8fBsulwveRXfrWnyu2Gw2iEQi2O12CFfZe8/j8SASieB2u1FQUMCN3Nmks/DwcGRkZCAzM5MrtVxSUrIiL4TNS2CnbuVyOfLz84OO4nmBvdlqtRpxcXHYsWMHKioqUFxcjPj4+FXPd1ugcFNtbS3i4uLwwx/+cMXsliCQZPfw4UMMDAwgJSUFeXl5QZPSUlNTuUdOTg527tyJgwcPrqhg+byFBe6mFxsbi5KSEq6OQ3p6+qoBG4G186tXr8JkMuHMmTOoqKhY8/kKhQJFRUXcrbJfeeUV7NmzB5mZmYiIiEBOTg6ioqJQVVWFyspKlJSULGnHeDwe5HI5EhMTkZ2djS1btuDQoUMoLi6GfNkNo8j31zMJ8D09Pbh69SoMBgOOHTuG4uLiDQd4ds1Rr9ejs7MTCwsL3P7XxQGMFxjtb9q0CcnJySgsLERMTEzQwMswDHp7e/HRRx+hr68P58+fR1VV1YqR0neptbUVH330EfR6PfLy8pCbm4tNmzYhKSkJKSkpsFgsuHz5MoaGhrBjxw6cPXt21d9NIpEgOjoahkDxDIFAgG3btq1IUBMECgyp1WpkZ2dDrVYjPj4egsB2ssWcTif+93//F3/4wx8gkUjw53/+59i5c+cL1RivRqfT4fLly+DxeDh58iQKCgpWDWQbxeYs9PT0wGQyISoqaklAtVgsaG9vh9frhSBQfXD5MUVg5CWXy5GRkYGCgoIlOxKEQiFkMhkSEhKQl5fH5VYsfx9eYA2X3a/tdDpRVFQUdHocgc89JiYGmZmZ3HKVTCZb8b6LDQ8P49///d/BMAwOHDiAgwcPBl1TFgqFsFqt6O7uhtlsXnU5TCAQIC4ujqtRwd6VcLVz+nnhBar9aTQaJCcnIzs7e912YWZmBl9++SUaGxuRkpKCs2fPrtsR5gV2JrCdnk2bNiEqKoo7d2JjY5GYmIjNmzcjJiYm6DUaFhYGTaCoV0ZGxoa39JHvj2cS4B8/fowLFy5AKpXiz/7sz55oGxsCiWSRkZFwuVzcdjiRSARZ4F7fi3u1/EDltWCBnc08bWpqQk1NDSYmJlBeXo5z584hJSXlmQav+vp6fPTRR3C5XPjBD34ApVLJ/e5erxeXL1/Gl19+iYSEBBw/fhyZmZlrBqmYmBhERkbCYDBwOwp4gVHh8mPEJggGC0I2mw1arRaNjY345ptv4PF4cOzYMezevfuFbJCD6evrw40bN5CcnIxXX30VycnJK/7OjfJ6vTCZTBgZGcGjR48wMjKCqakpTExMIDw8HD6fD42Njbh58yZXxGchcEMgPp+/4hizxz88sL1s+e/FntfBAvtiYrEYCQkJMJvNaG1thdvtRmxsLNSr3OmPx+MhbNktYVczNTWFP/3pT2hpaUFeXh7efffdVWvFCwQCbrfIw4cPYTAYEBERgZiYmBUjWPZ8lMlkL/x5JBaLIZPJ1rzmENhlcOPGDVRXV0MoFOL8+fPrjt4XY4/J4gDO4/G48yTYObLYk3yu5PvnOw3wVqsVg4ODqK2tRUdHBw4dOoQ333xzxVreRkRFRUGj0cBkMqG/vx+jo6MQCoWIDtSbX+/k9vl8MBqN3L3Tu7q6UFlZiTfffBNpG7xF7NPicrnw+PFj1NbWIjMzE9u3b4dAIIBYLIbZbMbIyAj++Mc/Ynp6GkePHsWJEyfWrVLF4/GgVqsRFRWF2dlZ3L9/Hw6HA1HrFE5ZzBfY8842WDweD/v27cOpU6eQlJS0ofd41tiR9czMDMRiMfx+P+rq6tDS0oKioiIcPXp0ybFjAvc4EIlEsFgs3Ihnfn6ee73FYuGmmb1eL3p6enDjxg3o9XokJCTA5/NhdHSUK1J08eJF6HQ6qFQqWCwWtLa2Ym5uDnl5ed/pdCmbSMVut2NrHPACFc/WuyaWs1gsMBqN+P3vf4+7d+9i27ZteOedd1BcXLz8qRx+oOyuTCbD5OQkenp64PV6kZiYCJFIBMFLUEnw25ibm4PdbkdNTQ1qamowNzeHEydO4I033ngqy0GEPA3fWYA3Go24ceMGLl++DK1Wix07duDw4cMoKCh44oYHgalApVKJtLQ0LuNWpVIhMTFxxRrlasxmM8bGxiAUClFSUoJ9+/atmRn7XREG7umNQHW/iYkJ9PT0cNuGHjx4AADYvn07Xn/99Q0XBRIKhdz6oVQqhVKp5JLwNhKcGYaB2WzmEqAqKytx4MCBDWfNPw9snsDFixcxOjqK3t5etLe3QyKRoLKyEps3b+am0m02G3p6eqDX66HX62EymTA5OYnJyUnuv6empmCxWCCTySAWi+F2u9HY2IjGxkbk5+dj9+7dXPnShw8f4uuvv4ZIJEJ5eTkqKyuRnZ2NwcFBDA8Po6SkBLGxsRs6N7+t6OhoLjdjdHQUAwMDkAVqpj9J0qfdbudumTo+Po4tW7agsrIShYWF68628QLr/PHx8VAoFNDpdHj8+DEAIDk5OWhuwMtuamoKX375JRoaGhAXF4e9e/fi8OHD32rwQsh35TsL8A6HA11dXRgcHERBQQFOnDiBioqK/1Njx47Y09PTkZ2dDbFYDLlcvqERvN/vh8/ng0KhQE5ODiorKxEXF/fcRhdKpZIrrDMzMwN+oBgIu9e1oqLiWyW1CYVCaDQaFBcXQ6FQIC4uDtHR0eseHwSOEbt9aseOHSgsLPxOR6BPw8LCAqqrq/Hll1/CbDZjYmICfr8f+/btQ1VVFZeHAQATExO4efMmHjx4gPHxcWi1WgwPDy95aLVa2Gw2rmqf1WrFzZs3YbVacfr0aeTm5iI6OhpyuRyXLl3CgwcP8MYbb+AnP/kJMjIykJSUhO7ubgwODuKVV15BXFzcho79tyUJ3GVQo9HA5XLBbrdz9dif5LObm5vj7lWQlZWF8+fPo6ioaN3gzhIFbi2bnZ0Nu90Oo9GIpKQkZGZmhuS68NjYGFpaWqBQKHDo0CG8+uqrT9ShIuRZ4DGrVad4CgwGA5d1vNGbyzwpq9X6UqzprYbd67wYOyIKti3uSVkslhV7qNfCVq3baMP+vLlcLtTU1OCzzz6DXq9HXFwcF9yX51XMzMzg6tWrGB0dXbGNkCUI7HfOy8tDWVkZrFYr/vCHP+DBgwf4i7/4C1RUVMDv96O3txfvvfceenp68N577+G1116DSCSC3+/Hb37zG7S0tOBHP/oRdu7c+czOTYvFAmugvjkvkGX9JBYWFmA2myGXy7n91k/K5XLB7XZzxVaioqLWXcd+GVmtVvB4PK6EMwV38iL6TgM8Id81f+BmKn19fZicnERCQgLS0tKC3lBlZmYGIyMj8Hg8a3Z4lEoloqOjERcXB5vNhgsXLqCmpga7d+9GeXk5ZmZmcOPGDYyNjUGlUiEvLw87d+5Eeno6ZmZm8PHHH8NiseCv//qvv/WSFCGE/F9RgCdkDV6vF52dnfjmm29gs9mgVCoxPz8PrVaL4uJiFBcXQ6fTgcfjcfcEaGtrQ3x8PCorK1e97SshhHzXKMATsg6fz4ehoSG0tbVheHgYfD6fqzoXERGB0dFR9PX1YWRkBBKJBEVFRcjKygpamIgQQp4VCvCEbBC7/10ikSAtLY1b4/YG7kio0+kgEAi4Ii6EEPI8UYAnhBBCQtCzSe8lhBBCyDNFAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBBEAZ4QQggJQRTgCSGEkBD0/wEjr4UnOuKYzQAAAABJRU5ErkJggg==\"\u003e\u003c/p\u003e\n\u003cp\u003eWhere f(t) and g(t) are the two functions.\u003c/p\u003e\n\u003cp\u003eKolmogorov-Smirnov Test\u003c/p\u003e\n\u003cp\u003eThe Kolmogorov-Smirnov test (KS test) is a statistical test that provides the prob-ability that two data sets belong to the same distribution [29]. The null hypothesis of the test is that the two data sets originate from the same continuous distribution. The KS test was used to establish whether a connection between mood-state switches and the preceding night exists. The quantitative results obtained by analysing the cumulative activitiy values, as well as the analysis of the fragmentation indices, indeed, supported the hypothesized relationship, which was then further justified by Wavelet analysis used to describe the nocturnal activity structures. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFragmentation Index Calculation\u003c/p\u003e\n\u003cp\u003eSleep fragmentation refers to the disruption of nighttime sleep, which interrupts the natural sleep cycle, leading to sleep disturbances and, overall, poor sleep quality. This can also affect daytime wakefulness and functionality.\u003c/p\u003e\n\u003cp\u003eWe used the fragmentation index calculation in the paper to study the quality of sleep in the examined subject. It can be calculated by comparing the hours spent awake and at rest during the night. The resulting value allows us to infer the quality of sleep [15,28].\u003c/p\u003e\n\u003cp\u003eWavelet Analysis\u003c/p\u003e\n\u003cp\u003eWavelet analysis is an extension of Fourier analysis that allows the examination of signals with variable frequency components [30]. The method involves placing a func-tion (wavelet) in a sliding window and examining the data series with it. Color codes represent the correlation coefficients, which vary between -1 and +1. By calculating these, the structure of the data series becomes visible. Red indicates correlating data, blue indicates anti-correlating data, and green indicates non-correlating data. The red and blue areas show high levels of structural correlation.\u003c/p\u003e\n\u003cp\u003eThe x-axis represents time, and the y-axis represents the size of the time window on a logarithmic scale. The figure can be divided into four main sections: \u0026quot;Range 1\u0026quot; shows structures that occur in time units less than 10 minutes, \u0026quot;Range 2\u0026quot; shows struc-tures in the 10-50 minute range, \u0026quot;Range 3\u0026quot; represents structures from 50 minutes to 4 hours, and \u0026quot;Range 4\u0026quot; demonstrates structures that appear in even larger time units [9]. The left inset shows the original data series, while the right inset shows the analysis of the randomized time series. The middle two curves describe the degree of structuring of these time series (calculated by the sum of squared correlation coefficients) as a function of the time window examined.\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eDuring the research, we had access to activity data recorded every minute for 625 days (1440 minutes/day). Figure S1 shows a typical time series of a weeklong recording (7 consecutive days and nights). Since the data are presented in device-defined arbitrary units, we indicate signal levels associated to some typical daily-routine tasks, according to our classification, refined by the data of Figure S2. The latter shows the activity distribution of all the 625 days. The peaks and shoulders of the distribution function correspond to task groups specified in Figures S1 and S2, and the borders between typical activity groups can be approximated by the inflection points of the distribution function in Figure S2.\u003c/p\u003e\n\u003cp\u003eAlthough these data contain activity information for full days, they are not continuous measurements. The data were recorded over several years, and the database used was created by summarizing these actograms. The data evaluation was carried out in two different ways. In one case, the actigraph continuously recorded the values derived from movement from midnight onwards. In the other case, the data were synchronized to waking times, which helped to more precisely define the durations of sleep and wakefulness, providing more accurate results [29].\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eGrouping Activities\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThe evaluation of the data began with sorting the all-day activity data. Since we knew that the data originated from a person with a clinical diagnosis of bipolar disorder who was undergoing treatment, we assumed that classification would be necessary. To confirm this, we proceeded as follows. We took the cumulative activity for each day, then plotted these values on a histogram, resulting in a graph that shows how frequently a given level of activity occurs in the database. However, we observed that the resulting curve did not form a regular normal distribution and could not be fitted with a Gaussian curve. A satisfactory fit was only achieved by using three curves. The result is shown in Figure 2. The points shown here represent the data, and their relatively small number is due to the fact that the fitting was done on a lower resolution version of the dataset.\u003c/p\u003e\n\u003cp\u003eThis is in line with the experience manic depression is characterized by three significantly different mood states. These states generally last for a certain period of time, and based on this, we divided the days into three different activity groups according to their cumulative activity. One of these was the group we referred to as \u0026quot;normal,\u0026quot; which represents moderate activity. As seen in the figure, this group was the largest. The two other groups, based on their lower- and higher-than normal average activities, were labeled as \u0026ldquo;depression\u0026rdquo; and \u0026ldquo;(hypo)mania\u0026rdquo;, respectively, and they will be referred to as such throughout the paper. For the sake of simplicity, in our analysis, we consider 3 mood states, and do not distinguish between mania and hypomania.\u003c/p\u003e\n\u003cp\u003eThe result of the grouping is shown in the histogram in Figure 3. The labels for the groups were applied uniformly when creating the figures, with depression generally shown in black, normal activity days in blue, and (hypo)mania in red. In Figure 3, it can be seen that empty areas appeared between the groups..\u003c/p\u003e\n\u003cp\u003eThe fact that the identified groups are distinct from one another is clearly visible in Figure 4. Figure 4A shows the average activity of the days throughout a full day, from midnight onwards. We averaged the minutes for each group over all the days belonging to that group, which resulted in the outcome shown in Figure 4A. The relationship between the groups is very clear when viewed in this way. The correctness of the grouping is further supported by Figure 4B, which was created in a similar way, but here we display the cumulative sum for the entire day instead of average activity.\u003c/p\u003e\n\u003cp\u003eIt is important to note that since the patient did not keep a diary of his condition during the measurement period, the days we categorized can only be placed in the given group conditionally. However, we created a diary-type timeline about the days the actigraph was used on, where the color code indicates which category the actual day was classified into (red: (hypo)mania, blue: normal, black: depression, gray: unclassified) (Figure 3). As it can be seen, the data are somewhat scarce, still, a number of contiguous periods associated to distinct mood states could be identified using our Gauss-fitting-based selection method (Figure 2). The number of \u0026rdquo;(hypo)manic\u0026rdquo;, \u0026rdquo;normal\u0026rdquo;, and \u0026rdquo;depressed\u0026rdquo; days are also indicated in Figure 3. Note that mood-state durations are in concert with the symptomes of a Bipolar-II outpatient, with a dominance of normal periods interrupted by a few-days-long (hypo)manic episodes, and occasionally, also with short-range subthreshold depression days. Those days that were in the transition zones were not initially classified, in order to be able to make clearer conclusions after the subsequent steps of the evaluation. However, when a single unclassified day interrupted a longer episode of one mood state, we have adapted these single days to the rest, too, provided that the cumulative activity of the day matched the rest.\u003c/p\u003e\n\u003cp\u003eDuring the last two years of recordings, the frequency of hypomanic periods is strongly reduced, at the same time, major depressive episodes seem to occur. The clearly identifiable mood-state switches can now be followed in the new Fig. 3. Justified mood changes take place both during week-days and week-ends, showing no obvious pref-erence to any of them (Figure S3).\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eInvestigation of Nighttime Activities\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eAfter data grouping, we checked the hypothesis, whether the nighttime activities could be important predictive factors for individual switching episodes. It is known that mood changes typically occur suddenly in most cases, so we call the days when a specific episode begins, \u0026quot;transitions.\u0026quot;\u003c/p\u003e\n\u003cp\u003eWe examined the nighttime activities in 250-minute intervals, which cover the pe-riod from midnight to 4:10 AM. We compared all nights to the nights before transitions for each group and found that these nights differed to some extent (Figure S5). For normal and depressive nights, we observed that before the transitions, activity remained above the average activity of all nights up to about the 200th minute. However, for manic nights, the activity before the transitions was somewhat below the average activity of all manic nights. Among the three groups, we focused on the depressive and manic groups, as forecasting these would greatly assist both the patient\u0026apos;s life and the work of their healthcare providers.\u003c/p\u003e\n\u003cp\u003eTo facilitate the comparison of the data in Figure S5, we created another graph, showing all normal nights alongside the activity of manic and depressive nights before transitions (Figure 4). Comparing these data revealed an interesting phenomenon. The average activity for all normal nights remains nearly constant, with small fluctuations, during the first 250 minutes from midnight. In contrast, the nights before transitions (both depressive and manic) show fluctuations and do not stabilize at a specific value, contrary to normal nights.\u003c/p\u003e\n\u003cp\u003eFor transitions to depression, there is a period from midnight until about 2:30 AM where activity is much higher than normal, after which it approaches the normal level. This can be explained by the fact that individuals suffering from depression often ex-perience sleep disturbances, difficulty falling asleep, and sometimes insomnia [17].\u003c/p\u003e\n\u003cp\u003eFor transitions to mania, we observed the opposite: the nocturnal activity remained at about the same level as the normal activity until 2:30 AM, after which it suddenly increased. This is consistent with the symptoms of mania, as during this episode, the patient feels well-rested early, and may even wake up at night to begin his daily activities. Considering this, the increase in activity in the early hours of the day is not surprising.\u003c/p\u003e\n\u003cp\u003eIf our conclusions are correct, it may be possible to predict a depressive or manic day based on the activity of the night before. Moreover, it is interesting that the change in activity levels occurred at nearly the same time for both depression and mania.\u003c/p\u003e\n\u003cp\u003eIn addition to the average nocturnal activities, we also examined sleep quality by calculating the fragmentation index (FI). We performed this separately for all activity groups, and for nights before transitions. FI indicates the sleep/wake ratio during the night for the person being studied. We also know that sleep quality is worse during mania and depression than under normal conditions. Our results support this, as the average FI for both depression and mania is significantly higher compared to the av-erage for normal nights. It can also be noted that the average FI for depression and mania is nearly identical, with depression having a slightly higher value.\u003c/p\u003e\n\u003cp\u003eWe presented the obtained FI averages and their error margins (marked as \u0026quot;error\u0026quot; in the figure) for all nights and for nights before transitions (Figure 5). Looking at the graphs, we can see that the two figures are very similar in terms of average values. However, the error margin is wider for normal activity and depression, while for mania, the error margins for both cases are very similar. Given this, the separate treatment and representation of all nights and nights before transitions might seem redundant at first glance. However, this information is crucial because it shows that the fragmentation characteristic of mania and depression appears even on the night before the episode. This fact can greatly assist in predicting episodes.\u003c/p\u003e\n\u003cp\u003eBased on the discussion in this section, we concluded that examining nighttime activity plays an important role in predicting individual episodes. Both average activity, from which we infer the amount of sleep, and the calculation of the fragmentation index, which provides information about sleep quality, are tools that cannot be ignored in episode prediction.\u003c/p\u003e\n\u003cp\u003e3.3. Relationship Between Daytime and Nighttime Activities\u003c/p\u003e\n\u003cp\u003ePreviously, we established that determining daytime activities significantly con-tributes to characterizing the mood states of the disease. We also saw that monitoring nighttime activity helps with this, too, and may play an even more crucial role in pre-dicting episodes. Keeping this in mind, we decided to examine the relationship between nighttime and daytime activities. To do this, we first created a graph showing the av-erage daytime activities as a function of the standard deviation of nighttime activities, for each activity group (Figure 6). The motivation for this representation was that the FI analysis showed that fluctuations in the depressive and manic nights majorate those in normal nights, and STD is directly related to these.\u003c/p\u003e\n\u003cp\u003eTo make the results less confusing and allow for better observation of data clustering, we smoothed the data using convolution. The interesting thing about this figure is that, although it shows the daily average activities, the days selected here were classified based solely on the examination of standard deviations of nighttime activities. As can be clearly seen, the distributions of the groups are well separated, indicating that the previous night\u0026apos;s activity is indeed related to daytime activity. However, we wanted to objectively prove this assumption numerically, so we performed the Kolmogorov-Smirnov test to compare the groups.\u003c/p\u003e\n\u003cp\u003eThe test\u0026apos;s purpose is to determine whether two datasets belong to the same con-tinuous distribution. The results were as follows: for depression and normal, we ob-tained 24.08%; for normal and mania, \u0026lt;0.1%; and for mania and depression comparison, 0.44%. The significance level was set at 10%, which means that values above this threshold are considered to belong to the same continuous distribution, indicating that these two groups cannot be distinguished from each other clearly. Therefore, the larger the values obtained from the test, the less distinguishable the two datasets are. Based on the results, it is evident that the test finds it most difficult to distinguish between de-pression and normal activity, while the difference between normal and mania is the most pronounced.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eWavelet Analysis\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eWe also performed Continuous Wavelet Analysis on the data (a more detailed explanation of the evaluation can be found in the Methods section). CWA is an effective way to visually illustrate the structure of a dataset across various time window sizes. Although CWA maps, showing the cross-correlattion coefficients of the analysed time series and a probe wavelet confined to various time windows, are often used only for qualitative demonstration, here we perform a quantitative assessment of the effects, by using the structure-parameter spectrum method, we introduced in an earlier publica-tion Ref. [9,]. It is derived by calculating the sum of squared correlation coefficients for each time window (see Fig. 1). Accordingly, we presented the results in two different ways: one with a simple function representation, where the intensity values appear as a function of the window size, with the time window displayed on a logarithmic scale, and the other as a colormap, where the window size is shown (also on a logarithmic scale) over time, color-coded according to the squared sums of the correlation coefficients.\u003c/p\u003e\n\u003cp\u003eFor each activity group, we conducted the analysis on both nighttime and daytime activity data. As a first step, however, instead of performing the analysis for the entire groups, we selected a longer, continuous period from each of the three groups, for demonstration purposes, because in a large dataset, the structures wouldn\u0026apos;t be as clearly outlined without this approach.\u003c/p\u003e\n\u003cp\u003eThe activity of normal days shows a moderate level of structure, most clearly visible in the 2.5-3 log(time) window range on the colormap in Figure 7. This provides a picture similar to that of a healthy person\u0026rsquo;s day. As we have pointed out earlier, circadian and ultradian rhythms are organized into a hierarchical structure [9]. The activity data we categorized as normal days truly represents what we would observe in the case of a healthy person.\u003c/p\u003e\n\u003cp\u003eFor normal nighttime activity, high levels of structure are not typically observed. The activity data likely show minor patterns due to small movements during the night (Figure 7B). \u0026nbsp;It is known that a healthy person can usually sleep through the night calmly, so this is also characteristic of the patient\u0026rsquo;s normal activity nights.\u003c/p\u003e\n\u003cp\u003eWe also examined the depressive days and nights. Figures S6 shows the evaluation of the nights associated with depressive days, from which we can conclude that they are characterized by a higher level of structure compared to normal nights. We previously discussed sleep fragmentation and concluded that sleep is more fragmented in depres-sion than in normal cases. By performing the wavelet analysis, we found evidence for the deterioration in sleep quality through the examination of the structure.\u003c/p\u003e\n\u003cp\u003eFor depressive daytime activities, we observe less structure compared to normal days. This is typical for depression, as nighttime activity is higher and more restless than normal, while daytime activity is lower. Through analysis, we also concluded that the structure is smaller, particularly in larger time windows (Figure S7), indicating a partial deterioration of the hierarchical organization of the daytime activity (see Ref. 9)\u003c/p\u003e\n\u003cp\u003eIn Figure S8 and Figure 8 we can see the manic nights, showing a very strong structure. Manic daytime activity shows outstanding structure and intensity values. Based on this, it can undoubtedly be confirmed that a patient suffering from mania experiences huge fluctuations throughout their days (Figure S9).\u003c/p\u003e\n\u003cp\u003eKeeping in mind one of our main goals, which is to provide data for developing a method for predicting mood changes, in the following, we focussed on the comparison of nocturnal activities associated to the three mood states. Figure 8 shows the structure of nighttime activities obtained from the wavelet analysis for each group, plotted to-gether. It is visible that mania appears with very high intensity, and around the 300-min time window (note the log scale of the abscissa), three characteristic peaks are promi-nent. The nighttime data for depression also exhibit higher intensity values than the normal values at narrower time-windows (between the 10-minutes to the 100-minutes range), and the intensity values characteristic to manic night are also more distinctly structured here.\u003c/p\u003e\n\u003cp\u003eThis was especially important to note, since for the predictions that are supposed to occur relatively suddenly (from one day to the other), we should use activity data for single nights, only. This condition considerably limits the time-window range that can be investigated by the CWA method, hence, we should restrict our observation to the latter (narrower) time-window range. For this purpose, we performed a CW analysis for single nights preceding normal, manic and depressive days, respectively. The results are shown in Figure 9. We chose the time-window range between 20 and 70 minutes as the region of interest (ROI) for quantitative prediction, where the intensity spectra of both depressed and manic nights differ the most.\u003c/p\u003e\n\u003cp\u003eIn order to give a quantitative prediction for mood switches, we calculated the probability distribution function (PDF) of the integrals of the spectra for the ROI (Figure S10a), as well as the corresponding cumulative distribution function (CDF, Figure S10b). As a next step, we determined the corresponding integrals of the Wavelet intensity spectra of the nocturnal activities for the \u0026ldquo;transition\u0026rdquo; nights preceding those depressed and manic days which start a longer, contiguous episode (dates selected using the data of Figure 2 are listed in Table S1). Comparing these integral values with data of the CDF determined for normal nights (Figure S10b), we could establish the probability that the selected night\u0026rsquo;s wavelet-intensity-integral value for the ROI exceeds those of the nor-mal-night values. The averaged results gave 70.17% and 75.78% for the probability of transition nights to depressive and manic episodes, with standard errors of 9.26% and 5.20%, respectively.\u003c/p\u003e\n\u003cp\u003eIn summary of our wavelet analysis, we observed that in depression and mania, nighttime activity is more structured compared to normal nights, especially in mania, where the result obtained was similar to that of normal daytime activity. Regarding the days, we can see that depression, normal activity, and mania show increasingly more pronounced levels of structural complexity, in that order. Bearing in mind that our re-sults are based on an exceptionally long, but still individual case study, which obviously represents a limitation towards generalizability, we can safely state that the intensity spectra derived from Continuous Wavelet-analysis can serve as a quantitative measure of these differences, and suggested to give a solid basis for the prediction of mood-state transitions in bipolar disorder.\u003c/p\u003e\n\u003cp\u003eIn spite of the potential strengths of CWA-based mood prediction, so far only a very few papers have been published using this method. In Ref. [35], the analysis of 18 months of daily self-reported mood charts (and sleep times) from a 24-year-old bipolar I patient is presented using the Morlet continuous wavelet transform, to determine pos-sible periodicities on the daily to monthly scale (approximately 146, 21, 8 days). The authors interpret these cyclical patterns in terms relapse risk, but they do not discuss applications in a validated predictive model.\u003c/p\u003e\n\u003cp\u003eIn an earlier paper [36], CWA was used to pinpoint general multiscale differences between normal subjects and bipolar patients, and introduced a CWA-based \u0026ldquo;Vulnerability Index\u0026rdquo; based on several-days-long recordings, which may serve a base to the objective diagnosis a bipolar patients.\u003c/p\u003e\n\u003cp\u003eIn a more recent study, early warning signals (EWS) were derived using Wavelet analysis from actigraphy time-series, and presented spectral analysis of sleep/wake cy-cle periodicity [37]. It was established that in 7 of 8 patients who had an episode, at least one EWS showed significant change up to four weeks before onset. The spectral periodicity changes showed promise for predicting transitions.\u003c/p\u003e\n\u003cp\u003eAll-in-all, there are only a few works in the scientific literature on activity and behavior time series, where patterns found with CWA could in principle be used for mood or episode prediction, but these are still in the proof-of-concept state [38].\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn our research, we had several years of activity data from an individual struggling with bipolar disorder. To evaluate the data, we first categorized the days by Gaussian fitting into the three main activity groups typical of manic depression, and, based, on this, constructed a a diary-type map indicating normal, depressive and (hypo)manic episodes for the consecutive 5 years during which the actograms were recorded.\u003c/p\u003e \u003cp\u003eNext, we focused on nighttime activities, examining the average activity and sleep fragmentation from midnight until dawn, for nights belonging to days of different categories. From the representations of nighttime average activities, we established that the night before a mood switch to depression, initially shows higher-than-normal activity, which then gradually drops in the early morning. At mood switches to mania, the average nighttime activity is also elevated, but the tendency is the opposite. Fragmentation indices were also calculated for the night before a mood change, as well as for all nights, showing that the quality of sleep in both mania and depression is significantly worse compared to nights preceding days of normal activity levels.\u003c/p\u003e \u003cp\u003eTo further substantiate our findings with objective numerical data, we selected longer continuous time intervals from each group, and performed a CWA analysis on both the nighttime and daytime activities separately. In line with the FI results, we found that in depression, nighttime activity is more structured than normal, whereas daytime activity is less structured. In mania, nighttime activity is even more structured, being most similar to the daytime structure of normal activity, while daytime activity during mania shows extremely strong and distinct structural features.\u003c/p\u003e \u003cp\u003eOur findings imply that the fragmentation characteristics of depression and mania appears even the night before the mood switch. This knowledge, along with the analysis of the average activity trend, significantly contributes to the predictability of mood episodes. Accordingly, our major scientific conclusions are based on quantitative Continuous Wavelet analysis, to assist the successful prediction of mood switches following longer-or-shorter normal episodes.\u003c/p\u003e \u003cp\u003eThe CWA approach outlined here represents a novelty, and expected to extend the state-of-the-art methodology of predicting mood-change episodes, possibly in combination with Machine-Learning methods in the future, as it was exemplified, e.g., in our earlier work, as well [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Since predicting mood switches by objective tools is considered an essential problem to solve in the healthcare of bipolar patients, our results are expected to have important methodological implications for psychiatric practice.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAuthor Contributions:\u003c/em\u003e\u003c/strong\u003e Conceptualization, ISz, LK and AD; methodology, ISz, LK and AD; software, ZsP and AB; validation, ISz; formal analysis, ZsP, AB and AD; data curation, ZsP and AB; writing—original draft preparation, ZsP and AD; writing—review and editing, AB, ISz, LK and AD; visualization, ZsP; supervision, AD. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eFunding:\u003c/em\u003e\u003c/strong\u003e This research received no external funding.\u003c/p\u003e\n\u003cp\u003eInstitutional Review Board Statement: The study was approved by the Ethics Committee of the Medical Research Council (ETT-TUKEB) operating as a board of the Ministry of Human Capacities of Hungary (approval identification No.: 15239–5/2023/EÜIG).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eInformed Consent Statement:\u003c/em\u003e\u003c/strong\u003e The subject gave prior written in-formed consent to participate. The study was carried out according to the Declarations of Helsinki and the standards set forth by the journal for ethical human research.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eData Availability Statement:\u003c/em\u003e\u003c/strong\u003e Dataset available on request from the authors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eConflicts of Interest:\u003c/em\u003e\u003c/strong\u003e The authors declare no conflicts of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eTen Have, M.; Tuithof, M.; Van Dorsselaer, S.; Schouten, F.; Luik, A.I.; De Graaf, R. Prevalence and Trends of Common Mental Disorders from 2007‐2009 to 2019‐2022: Results from the Netherlands Mental Health Survey and Incidence Studies (NEMESIS), Including Comparison of Prevalence Rates before vs. during the COVID‐19 Pandemic. World Psychiatry 2023, 22, 275\u0026ndash;285, doi:10.1002/wps.21087.\u003c/li\u003e\n\u003cli\u003eSlade, T.; Vescovi, J.; Chapman, C.; Teesson, M.; Arya, V.; Pirkis, J.; Harris, M.G.; Burgess, P.M.; Santomauro, D.; O\u0026rsquo;Dean, S.; et al. The Epidemiology of Mental and Substance Use Disorders in Australia 2020\u0026ndash;22: Prevalence, Socio-Demographic Cor-relates, Severity, Impairment and Changes over Time. Aust. N. Z. J. Psychiatry 2025, 59, 510\u0026ndash;521, doi:10.1177/00048674241275892.\u003c/li\u003e\n\u003cli\u003eGrande, I.; Berk, M.; Birmaher, B.; Vieta, E. Bipolar Disorder. The Lancet 2016, 387, 1561\u0026ndash;1572, doi:10.1016/S0140-6736(15)00241-X.\u003c/li\u003e\n\u003cli\u003eDomj\u0026aacute;n, N.; Csifcs\u0026aacute;k, G.; Dr\u0026oacute;tos, G.; Janka, Z.; Szendi, I. Different Patterns of Auditory Information Processing Deficits in Chronic Schizophrenia and Bipolar Disorder with Psychotic Features. Schizophr. Res. 2012, 139, 253\u0026ndash;259, doi:10.1016/j.schres.2012.06.002.\u003c/li\u003e\n\u003cli\u003eBuzas, A.; Horvath, T.; Der, A. A Novel Approach in Heart-Rate-Variability Analysis Based on Modified Poincar\u0026eacute; Plots. IEEE Access 2022, 10, 36606\u0026ndash;36615, doi:10.1109/ACCESS.2022.3162234.\u003c/li\u003e\n\u003cli\u003eLangm\u0026aacute;r, G.; S\u0026uuml;megi, T.; F\u0026uuml;l\u0026ouml;p, B.; Pozsgai, L.; Mocsai, T.; T\u0026oacute;th, M.; R\u0026aacute;cz, L.; Kopper, B.; D\u0026eacute;r, A.; B\u0026uacute;z\u0026aacute;s, A.; et al. Heart Rate Variability Alterations During Delayed-Onset Muscle Soreness-Inducing Exercise\u0026mdash;With Piezo2 Interpretation. Sports 2025, 13, 262, doi:10.3390/sports13080262.\u003c/li\u003e\n\u003cli\u003eNagy, \u0026Aacute;.; Dombi, J.; F\u0026uuml;lep, M.P.; Rudics, E.; Hompoth, E.A.; Szab\u0026oacute;, Z.; D\u0026eacute;r, A.; B\u0026uacute;z\u0026aacute;s, A.; Viharos, Z.J.; Hoang, A.T.; et al. The Actigraphy-Based Identification of Premorbid Latent Liability of Schizophrenia and Bipolar Disorder. Sensors 2023, 23, 958, doi:10.3390/s23020958.\u003c/li\u003e\n\u003cli\u003eL\u0026aacute;szl\u0026oacute;, S.; Nagy, \u0026Aacute;.; Dombi, J.; Hompoth, E.A.; Rudics, E.; Szab\u0026oacute;, Z.; D\u0026eacute;r, A.; B\u0026uacute;z\u0026aacute;s, A.; Viharos, Z.J.; Hoang, A.T.; et al. The Two Ends of the Spectrum: Comparing Chronic Schizophrenia and Premorbid Latent Schizotypy by Actigraphy. BMC Psychiatry 2025, 25, 531, doi:10.1186/s12888-025-06971-5.\u003c/li\u003e\n\u003cli\u003eB\u0026uacute;z\u0026aacute;s, A.; Makai, A.; Groma, G.I.; Dancsh\u0026aacute;zy, Z.; Szendi, I.; Kish, L.B.; Santa-Maria, A.R.; D\u0026eacute;r, A. Hierarchical Organization of Human Physical Activity. Sci. Rep. 2024, 14, 5981, doi:10.1038/s41598-024-56185-0.\u003c/li\u003e\n\u003cli\u003eMacz\u0026aacute;k, B.; Vadai, G.; D\u0026eacute;r, A.; Szendi, I.; Gingl, Z. Detailed Analysis and Comparison of Different Activity Metrics. PLOS ONE 2021, 16, e0261718, doi:10.1371/journal.pone.0261718.\u003c/li\u003e\n\u003cli\u003eTazawa, Y.; Wada, M.; Mitsukura, Y.; Takamiya, A.; Kitazawa, M.; Yoshimura, M.; Mimura, M.; Kishimoto, T. Actigraphy for Evaluation of Mood Disorders: A Systematic Review and Meta-Analysis. J. Affect. Disord. 2019, 253, 257\u0026ndash;269, doi:10.1016/j.jad.2019.04.087.\u003c/li\u003e\n\u003cli\u003eCantisani, A.; Stegmayer, K.; Bracht, T.; Federspiel, A.; Wiest, R.; Horn, H.; M\u0026uuml;ller, T.J.; Schneider, C.; H\u0026ouml;fle, O.; Strik, W.; et al. Distinct Resting‐state Perfusion Patterns Underlie Psychomotor Retardation in Unipolar vs. Bipolar Depression. Acta Psychiatr. Scand. 2016, 134, 329\u0026ndash;338, doi:10.1111/acps.12625.\u003c/li\u003e\n\u003cli\u003eAmaral, L.A.N.; Soares, D.J.B.; da Silva, L.R.; Lucena, L.S.; Saito, M.; Kumano, H.; Aoyagi, N.; Yamamoto, Y. Power-Law Temporal Auto-Correlations in Day-Long Records of Human Physical Activity and Their Alteration with Disease 2002.\u003c/li\u003e\n\u003cli\u003eRudics, E.; Buz\u0026aacute;s, A.; P\u0026aacute;lfi, A.; Szab\u0026oacute;, Z.; Nagy, \u0026Aacute;.; Hompoth, E.A.; Dombi, J.; Bilicki, V.; Szendi, I.; D\u0026eacute;r, A. Quantifying Stress and Relaxation: A New Measure of Heart Rate Variability as a Reliable Biomarker. Biomedicines 2025, 13, 81, doi:10.3390/biomedicines13010081.\u003c/li\u003e\n\u003cli\u003eKurina, L.M.; Knutson, K.L.; Hawkley, L.C.; Cacioppo, J.T.; Lauderdale, D.S.; Ober, C. Loneliness Is Associated with Sleep Fragmentation in a Communal Society. Sleep 2011, 34, 1519\u0026ndash;1526, doi:10.5665/sleep.1390.\u003c/li\u003e\n\u003cli\u003eFaedda, G.L.; Ohashi, K.; Hernandez, M.; McGreenery, C.E.; Grant, M.C.; Baroni, A.; Polcari, A.; Teicher, M.H. Actigraph Measures Discriminate Pediatric Bipolar Disorder from Attention‐deficit/Hyperactivity Disorder and Typically Developing Controls. J. Child Psychol. Psychiatry 2016, 57, 706\u0026ndash;716, doi:10.1111/jcpp.12520.\u003c/li\u003e\n\u003cli\u003eDe Crescenzo, F.; Economou, A.; Sharpley, A.L.; Gormez, A.; Quested, D.J. Actigraphic Features of Bipolar Disorder: A Systematic Review and Meta-Analysis. Sleep Med. Rev. 2017, 33, 58\u0026ndash;69, doi:10.1016/j.smrv.2016.05.003.\u003c/li\u003e\n\u003cli\u003eHu, K.; Ivanov, P.Ch.; Chen, Z.; Hilton, M.F.; Stanley, H.E.; Shea, S.A. Non-Random Fluctuations and Multi-Scale Dynamics Regulation of Human Activity. Phys. Stat. Mech. Its Appl. 2004, 337, 307\u0026ndash;318, doi:10.1016/j.physa.2004.01.042.\u003c/li\u003e\n\u003cli\u003eB\u0026uacute;z\u0026aacute;s, A.; Sonkodi, B.; D\u0026eacute;r, A. Principal Connection Between Typical Heart Rate Variability Parameters as Revealed by a Comparative Analysis of Their Heart Rate and Age Dependence. Entropy 2025, 27, 792, doi:10.3390/e27080792.\u003c/li\u003e\n\u003cli\u003eTahmasian, M.; Khazaie, H.; Golshani, S.; Avis, K.T. Clinical Application of Actigraphy in Psychotic Disorders: A Systematic Review. Curr. Psychiatry Rep. 2013, 15, 359, doi:10.1007/s11920-013-0359-2.\u003c/li\u003e\n\u003cli\u003eLeuenberger, K.D. Long-Term Activity and Movement Monitoring in Neurological Patients, ETH Zurich, 2015, p. 198 p.\u003c/li\u003e\n\u003cli\u003eMartini, J.; Leopold, K.; Pfeiffer, S.; Berndt, C.; Boehme, A.; Roessner, V.; Fusar-Poli, P.; Young, A.H.; Correll, C.U.; Bauer, M.; et al. Early Detection of Bipolar Disorders and Treatment Recommendations for Help-Seeking Adolescents and Young Adults: Findings of the Early Detection and Intervention Center Dresden. Int. J. Bipolar Disord. 2021, 9, 23, doi:10.1186/s40345-021-00227-3.\u003c/li\u003e\n\u003cli\u003eRatheesh, A.; Hett, D.; Ramain, J.; Wong, E.; Berk, L.; Conus, P.; Fristad, M.A.; Goldstein, T.; Hillegers, M.; Jauhar, S.; et al. A Systematic Review of Interventions in the Early Course of Bipolar Disorder I or II: A Report of the International Society for Bipolar Disorders Taskforce on Early Intervention. Int. J. Bipolar Disord. 2023, 11, 1, doi:10.1186/s40345-022-00275-3.\u003c/li\u003e\n\u003cli\u003e\u0026Aacute;lvarez-Cadenas, L.; Garc\u0026iacute;a-V\u0026aacute;zquez, P.; Ezquerra, B.; Stiles, B.J.; Lahera, G.; Andrade-Gonz\u0026aacute;lez, N.; Vieta, E. Detection of Bipolar Disorder in the Prodromal Phase: A Systematic Review of Assessment Instruments. J. Affect. Disord. 2023, 325, 399\u0026ndash;412, doi:10.1016/j.jad.2023.01.012.\u003c/li\u003e\n\u003cli\u003eWilliams, R.; Ostinelli, E.G.; Agorinya, J.; Minichino, A.; De Crescenzo, F.; Maughan, D.; Puntis, S.; Cliffe, C.; Kurtulmus, A.; Lennox, B.R.; et al. Comparing Interventions for Early Psychosis: A Systematic Review and Component Network Me-ta-Analysis. eClinicalMedicine 2024, 70, 102537, doi:10.1016/j.eclinm.2024.102537.\u003c/li\u003e\n\u003cli\u003eKlosterkotter, J.; Schultze‐Lutter, F.; Bechdolf, A.; Ruhrmann, S. Prediction and Prevention of Schizophrenia: What Has Been Achieved and Where to Go Next? World Psychiatry 2011, 10, 165\u0026ndash;174, doi:10.1002/j.2051-5545.2011.tb00044.x.\u003c/li\u003e\n\u003cli\u003ePhillips, L.J.; Yung, A.R.; McGorry, P.D. Identification of Young People at Risk of Psychosis: Validation of Personal As-sessment and Crisis Evaluation Clinic Intake Criteria. Aust. N. Z. J. Psychiatry 2000, 34, A164\u0026ndash;A169, doi:10.1177/000486740003401S25.\u003c/li\u003e\n\u003cli\u003eJohnson, D.A.; Javaheri, S.; Guo, N.; Champion, C.L.; Sims, J.F.; Brock, M.P.; Sims, M.; Patel, S.R.; Williams, D.R.; Wilson, J.G.; et al. Objective Measures of Sleep Apnea and Actigraphy-Based Sleep Characteristics as Correlates of Subjective Sleep Quality in an Epidemiologic Study: The Jackson Heart Sleep Study. Psychosom. Med. 2020, 82, 324\u0026ndash;330, doi:10.1097/PSY.0000000000000778.\u003c/li\u003e\n\u003cli\u003eDancsh\u0026aacute;zy, Z.; D\u0026eacute;r, A.; Groma, G.I.; Janka, Z.; J\u0026aacute;rd\u0026aacute;nh\u0026aacute;zy, T.; Makai, A.; Szentistv\u0026aacute;nyi, I.; Vasadi, A. Phase-Synchronization of Daily Motor Activities Can Reveal Differential Circadian Patterns. Chronobiol. Int. 2004, 21, 309\u0026ndash;314, doi:10.1081/CBI-120037824.\u003c/li\u003e\n\u003cli\u003eKrane-Gartiser, K.; Henriksen, T.E.G.; Morken, G.; Vaaler, A.; Fasmer, O.B. Actigraphic Assessment of Motor Activity in Acutely Admitted Inpatients with Bipolar Disorder. PLoS ONE 2014, 9, e89574, doi:10.1371/journal.pone.0089574.\u003c/li\u003e\n\u003cli\u003eRitter, P.S.; H\u0026ouml;fler, M.; Wittchen, H.-U.; Lieb, R.; Bauer, M.; Pfennig, A.; Beesdo-Baum, K. Disturbed Sleep as Risk Factor for the Subsequent Onset of Bipolar Disorder \u0026ndash; Data from a 10-Year Prospective-Longitudinal Study among Adolescents and Young Adults. J. Psychiatr. Res. 2015, 68, 76\u0026ndash;82, doi:10.1016/j.jpsychires.2015.06.005.\u003c/li\u003e\n\u003cli\u003eMeyer, N.; Faulkner, S.M.; McCutcheon, R.A.; Pillinger, T.; Dijk, D.-J.; MacCabe, J.H. Sleep and Circadian Rhythm Dis-turbance in Remitted Schizophrenia and Bipolar Disorder: A Systematic Review and Meta-Analysis. Schizophr. Bull. 2020, 46, 1126\u0026ndash;1143, doi:10.1093/schbul/sbaa024.\u003c/li\u003e\n\u003cli\u003eStephens, M.A. EDF Statistics for Goodness of Fit and Some Comparisons. J. Am. Stat. Assoc. 1974, 69, 730\u0026ndash;737, doi:10.1080/01621459.1974.10480196.\u003c/li\u003e\n\u003cli\u003eAndronov, I.L. Advanced Time Series Analysis of Generally Irregularly Spaced Signals: Beyond the Oversimplified Methods. In Knowledge Discovery in Big Data from Astronomy and Earth Observation; Elsevier, 2020; pp. 191\u0026ndash;224 ISBN 978-0-12-819154-5.\u003c/li\u003e\n\u003cli\u003eCheon, Y.; Moon, E.; Park, J.-M.; Lee, B.-D.; Lee, Y.-M.; Jeong, H.-J.; Kang, T.-U.; Park, J.; Choi, Y. Can Residual Symptoms During Inter-Episode Period after Partial Remission in Bipolar I Disorder Have Cyclic Patterns with Specific Frequencies? Psychiatry Investig. 2018, 15, 330\u0026ndash;334, doi:10.30773/pi.2017.08.23.\u003c/li\u003e\n\u003cli\u003eIndic, P.; Salvatore, P.; Maggini, C.; Ghidini, S.; Ferraro, G.; Baldessarini, R.J.; Murray, G. Scaling Behavior of Human Lo-comotor Activity Amplitude: Association with Bipolar Disorder. PLoS ONE 2011, 6, e20650, doi:10.1371/journal.pone.0020650.\u003c/li\u003e\n\u003cli\u003eSharma, D.; Kumar, M.; Kumar, J. Wavelet Transforms in Psychological Science: A Multiscale Approach to Cognitive, Clin-ical, and Developmental Insights. J. Wavelet Theory Appl. 2024, 18, 19\u0026ndash;27, doi:10.37622/JWTA/18.2.2024.19-27.\u003c/li\u003e\n\u003cli\u003eNazari, M.-J.; Shalbafan, M.; Eissazade, N.; Khalilian, E.; Vahabi, Z.; Masjedi, N.; Ghidary, S.S.; Saadat, M.; Sadegh-Zadeh, S.-A. A Machine Learning Approach for Differentiating Bipolar Disorder Type II and Borderline Personality Disorder Using Electroencephalography and Cognitive Abnormalities. PLOS ONE 2024, 19, e0303699, doi:10.1371/journal.pone.0303699.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"bipolar disorder, actigraphy, ultradian rhythms, sleep fragmentation, wavelet-analysis","lastPublishedDoi":"10.21203/rs.3.rs-8346326/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8346326/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eMood fluctuations in Bipolar Disorder are closely linked to changes in activity levels, sleep quality and daily rhythms. Therefore, actigraphy could be a valuable tool in the investigation of such mental health conditions, aiding in understanding, diagnosing and treating such disorders. It is a crucial problem in the healthcare of bipolar patients to find objective features, e.g., in diurnal or nocturnal motion patterns, which can promote prediction of sudden state-changes of the patient. To this end, we carried out a comprehensive mathematical analysis of an extremely large set of actigraphy recordings (spanning through more than 600 days) of a bipolar outpatient.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eThe research employed cutting-edge statistical tools for data analysis, including Probability-Density-Function and Continuous Wavelet analysis methods, to provide insights into daytime and nighttime activity structures in different mood states. We observed that in depression and mania, nighttime activity is more structured compared to normal nights. Regarding the days, we can see that depression, normal activity, and mania show increasingly more pronounced levels of structural complexity, in that order. Based on these findings, we performed a Continuous Wavelet analysis for single nights preceding normal, manic and depressive days, respectively, in order to give a quantitative prediction for mood switches. From the structure of the wavelet intensity spectra of the nocturnal activities for the \u0026ldquo;transition\u0026rdquo; nights, we could successfully establish the probability of transitions to depressive and manic episodes. Bearing in mind that our results are based on an exceptionally long, but still individual case study, which obviously represents a limitation towards generalizability, we can safely state that the intensity spectra derived from Continuous Wavelet analysis can serve as a quantitative measure of these differences, and suggested to give a solid basis for the prediction of mood-state transitions in Bipolar Disorder.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eOur main findings, based on sensitive statistical tools imply that successful prediction of mood switches following longer or shorter normal episodes in Bipolar Disorder is possible by a proper analysis of nocturnal actigraphy signals. The CWA- based approach outlined here represents a novelty, and expected to have important methodological implications for psychiatric practice.\u003c/p\u003e","manuscriptTitle":"Linking Activity Patterns and Mood States in Bipolar Disorder: A Longitudinal Case Study based on Actigraphy Signals","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-31 09:30:22","doi":"10.21203/rs.3.rs-8346326/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"33869503-db8c-4f8f-bf07-90b9371f36d5","owner":[],"postedDate":"December 31st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-01-29T14:56:26+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-31 09:30:22","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8346326","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8346326","identity":"rs-8346326","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}