Understanding how multi-scale network structure influences circadian rhythms in the suprachiasmatic nucleus (SCN) is essential for uncovering the principles of rhythmic robustness and synchronization. Previous studies using synthetic SCN networks suggested a size-dependent phenomenon, in which rhythmic activity initially strengthens with network size and then saturates, but it remains unclear whether this occurs in real SCN networks. Here, we apply geometric branch growth (GBG) and geometric renormalization (GR) to generate self-similar scaled-up and scaled-down replicas from a single-scale functional mouse SCN network. Unlike synthetic models, these SCN replicas do not exhibit size-dependent rhythms: average period, amplitude, and synchronization remain stable across scales. By increasing the average degree with network size, we reproduce size-dependent rhythms and show that they arise from network connectivity, whereas low-degree networks fragment and fail to sustain oscillations. Disrupting clustering self-similarity slightly reduces synchronization, but circadian rhythms remain robust, indicating that average degree, rather than clustering, is the dominant structural driver. Th
Circadian rhythms are endogenous oscillations that regulate various physiological processes and their disruption has been linked to many diseases, making it important to determine how gene-expression rhythms are altered across genotypes, treatments, or environmental exposures. Existing approaches for circadian transcriptomic analysis are often limited to pairwise comparisons or to a single aspect of rhythmic behavior, making them inadequate for comprehensive inference in multi-condition experimental designs. We propose CARhy (Comprehensive Analysis of Rhythmicity), a unified statistical framework for transcriptomic data collected under more than two conditions. Based on first-harmonic Fourier regression, CARhy provides formal tests for the presence of rhythmicity and for differences across conditions in rhythmicity, amplitude, phase, and baseline level. By allowing condition-specific variances and accommodating unbalanced designs, the framework remains reliable under heteroscedastic noise and realistic sampling constraints. Simulations show that CARhy controls type I error and false discovery rates well while achieving higher power than existing approaches in challenging settings.
Gene expression levels, hormone secretion, and internal body temperature each oscillate over an approximately 24-hour cycle, or display circadian rhythms. Many circadian biology studies have investigated how these rhythms vary across cohorts, uncovering associations between atypical rhythms and diseases such as cancer, metabolic syndrome, and sleep disorders. A challenge in analyzing circadian biology data is that the oscillation peak and trough times for a phenomenon differ across individuals. If these individual-level differences are not accounted for in trigonometric regression, which is prevalent in circadian biology studies, then estimates of the population-level amplitude parameters can suffer from attenuation bias. This attenuation bias could lead to inaccurate study conclusions. To address attenuation bias, we propose a refined two-stage (RTS) method for trigonometric regression given longitudinal data obtained from each individual participating in a study. In the first stage, the parameters of individual-level models are estimated. In the second stage, transformations of these individual-level estimates are aggregated to produce population-level parameter estimates for inf
In this study, we consider users' online communication rhythms (online social rhythms) as coupled oscillators in a complex social network. Users' rhythms may be entrained onto those of their friends, and macro-scale pattern of such rhythms can emerge. We investigated the entrainment in online social rhythms and long-range correlations of the rhythms using an avatar communication dataset. We indicated entrainment in online social rhythms to emerge if the strength of a new connection reaches a threshold. This entrainment spread via densely-connected clusters. Consequently, long-range correlations of online social rhythms extended to about 36% of the network, although offline social life naturally restricts online social rhythms. This research supports an understanding of human social dynamics in terms of systems of coupled oscillators.
Understanding the timing and sequencing of activity participation in tourist mobility is central to travel behavior research, yet GPS trajectories are noisy, irregularly sampled, and only weakly linked to activity locations, which limits interpretation and scenario analysis. We address this by mapping each stay event to candidate points of interest (POIs) probabilistically, using explicit prior-likelihood weighting that yields a normalized compatibility distribution rather than hard matching. Using one month of high-density tourist trajectories in Hakone, Japan (November 2021), we construct semantic stay-event sequences based on observed place-category labels (MID10) and describe mobility rhythms through hour-by-category profiles, category transitions, and expected dwell patterns. Building on these rhythm signatures, we develop a rhythm-consistent semi-Markov simulator that generates synthetic stay-event sequences with time-conditioned transitions and category-dependent dwell behavior. In the observed data, hour-by-category summaries are computed by probability-weighted aggregation over soft labels; in simulation, each event is generated with a discrete category and a sampled dwell
Ultradian rhythms - quasi-rhythmic fluctuations in behavior and physiology with periods shorter than 24 hours - are observed across various organisms, including humans. Despite their role in key biological processes such as sleep architecture and hormone regulation, their underlying mechanisms remain poorly understood. Here, we leveraged wearable sensor technology for continuous monitoring of physiological signals in 16 healthy participants over two weeks. By systematically removing circadian and longer-scale rhythms, we isolated ultradian dynamics and modeled them using the Hankel Alternative View of Koopman (HAVOK) framework,a data-driven approach based on Takens' embedding theorem and Koopman operator theory. This allowed us to characterize ultradian rhythms as an intermittently forced linear system and distinguish between regular oscillatory behavior and more complex dynamics. Across participants, ultradian fluctuations were well-described by the HAVOK model, with intermittent forcing consistently observed. The model demonstrated strong forecasting accuracy, with root mean squared error (RMSE) of $0.0315 \pm 0.02$, $0.0306 \pm 0.02$, and $0.0218 \pm 0.02$ in the leading time-de
Brain rhythms seem central to understanding the neurophysiological basis of human cognition. Yet, despite significant advances, key questions remain unresolved. In this comprehensive position paper, we review the current state of the art on oscillatory mechanisms and their cognitive relevance. The paper critically examines physiological underpinnings, from phase-related dynamics like cyclic excitability, to amplitude-based phenomena, such as gating by inhibition, and their interactions, such as phase-amplitude coupling, as well as frequency dynamics, like sampling mechanisms. We also critically evaluate future research directions, including travelling waves and brain-body interactions. We then provide an in-depth analysis of the role of brain rhythms across cognitive domains, including perception, attention, memory, and communication, emphasising ongoing debates and open questions in each area. By summarising current theories and highlighting gaps, this position paper offers a roadmap for future research, aimed at facilitating a unified framework of rhythmic brain function underlying cognition.
Intermittent transitions, associated with critical dynamics and characterized by power-law distributions, are commonly observed during sleep. These critical behaviors are evident at the microscopic level through neuronal avalanches and at the macroscopic level through transitions between sleep stages. To clarify these empirical observations, models grounded in statistical physics have been proposed. At the mesoscopic level of cortical activity, critical behavior is indicated by the intermittent transitions between various cortical rhythms. For instance, empirical investigations utilizing EEG data from rats have identified intermittent transitions between $δ$ and $θ$ rhythms, with the duration of $θ$ rhythm exhibiting a power-law distribution. However, a dynamic model to account for this phenomenon is currently absent. In this study, we introduce a network of sparsely coupled excitatory and inhibitory populations of quadratic integrate-and-fire (QIF) neurons to demonstrate that intermittent transitions can emerge from the intrinsic fluctuations of a finite-sized system, particularly when the system is positioned near a Hopf bifurcation point, which is a critical point. The resulting
Chronobiological rhythms, such as the circadian rhythm, have long been linked to neurological disorders, but it is currently unknown how pathological processes affect the expression of biological rhythms in the brain. Here, we use the unique opportunity of long-term, continuous intracranially recorded EEG from 38 patients (totalling 6338 hours) to delineate circadian (daily) and ultradian (minute to hourly) rhythms in different brain regions. We show that functional circadian and ultradian rhythms are diminished in pathological tissue, independent of regional variations. We further demonstrate that these diminished rhythms are persistent in time, regardless of load or occurrence of pathological events. These findings provide evidence that brain pathology is functionally associated with persistently diminished chronobiological rhythms in vivo in humans, independent of regional variations or pathological events. Future work interacting with, and restoring, these modulatory chronobiological rhythms may allow for novel therapies.
The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms to perform functionally important tasks. To address those questions, it is first useful to understood in a mechanistic way the origin of the rhythms, their interactions, the signals which create the transitions among rhythms, and the ways in which rhythms filter the signals to a network of neurons. This talk discusses how dynamical systems have been used to investigate the origin, properties and interactions of rhythms in the nervous system. It focuses on how the underlying physiology of the cells and synapses of the networks shape the dynamics of the network in different contexts, allowing the variety of dynamical behaviors to be displayed by the same network. The work is presented using a series of related case studies on different rhythms. These case studies are chosen to highlight mathematical issues, and suggest further mathematical work to be done. The topics include: different roles of excitation and inhibition in creating synchronous asse
The COVID-19 pandemic has significantly impacted daily activity rhythms and life routines. Understanding the dynamics of these impacts on different groups of people is essential for creating environments where people's lives and well-being are least disturbed during such circumstances. Starting in June 2021, we conducted a year-long study to collect high-resolution data from fitness trackers as well as answers to monthly questionnaires from 128 working adults. Using questionnaires, we investigate how routines of exercising and working have changed throughout the pandemic for different people. In addition to that, for each person in the study, we build temporal distributions of daily step counts to quantify their daily movement rhythms and use the inverse of the Earth mover's distance between different movement rhythms to quantify the movement consistency over time. Throughout the pandemic, our cohort shows a shift in exercise routines, manifested in a decrease in time spent on non-walking physical exercises as opposed to the unchanged amount of time spent on walking. In terms of daily rhythms of movement, we show that migrants and those who live alone demonstrate a lower level of c
Cells can use periodic enzyme activities to adapt to periodic environments or existing internal rhythms and to establish metabolic cycles that schedule biochemical processes in time. A periodically changing allocation of the protein budget between reactions or pathways may increase the overall metabolic efficiency. To study this hypothesis, I quantify the possible benefits of small-amplitude enzyme rhythms in kinetic models. Starting from an enzyme-optimised steady state, I score the effects of possible enzyme rhythms on a metabolic objective and optimise their amplitudes and phase shifts. Assuming small-amplitude rhythms around an optimal reference state, optimal phases and amplitudes can be computed by solving a quadratic optimality problem. In models without amplitude constraints, general periodic enzyme profiles can be obtained by Fourier synthesis. The theory of optimal enzyme rhythms combines the dynamics and economics of metabolic systems and explains how optimal small-amplitude enzyme profiles are shaped by network structure, kinetics, external rhythms, and the metabolic objective. The formulae show how orchestrated enzyme rhythms can exploit synergy effects to improve meta
We propose a new mean-field model of brain rhythms governed by astrocytes. This theoretical framework describes how astrocytes can regulate neuronal activity and contribute to the generation of brain rhythms. The model describes at the population level the interactions between two large groups of excitatory and inhibitory neurons. The excitatory population is governed by astrocytes via a so-called tripartite synapse. This approach allows us to describe how the interactions between different groups of neurons and astrocytes can give rise to various patterns of synchronized activity and transitions between them. Using methods of nonlinear analysis we show that astrocytic modulation can lead to a change in the period and amplitude of oscillations in the populations of neurons.
Modeling biological rhythms helps understand the complex principles behind the physical and psychological abnormalities of human bodies, to plan life schedules, and avoid persisting fatigue and mood and sleep alterations due to the desynchronization of those rhythms. The first step in modeling biological rhythms is to identify their characteristics, such as cyclic periods, phase, and amplitude. However, human rhythms are susceptible to external events, which cause irregular fluctuations in waveforms and affect the characterization of each rhythm. In this paper, we present our exploratory work towards developing a computational framework for automated discovery and modeling of human rhythms. We first identify cyclic periods in time series data using three different methods and test their performance on both synthetic data and real fine-grained biological data. We observe consistent periods are detected by all three methods. We then model inner cycles within each period through identifying change points to observe fluctuations in biological data that may inform the impact of external events on human rhythms. The results provide initial insights into the design of a computational fram
Mental disorders (MD) are among the top most demanding challenges in world-wide health. According to the World Health Organization, the burden of MDs continues to grow with significant impact on health and major social and human rights. A large number of MDs exhibit pathological rhythms, which serve as the disorders characteristic biomarkers. These rhythms are the targets for neurostimulation techniques. Open-loop neurostimulation employs stimulation protocols, which are rather independent of the patients health and brain state in the moment of treatment. Most alternative closed-loop stimulation protocols consider real-time brain activity observations but appear as adaptive open-loop protocols, where e.g. pre-defined stimulation sets in if observations fulfil pre-defined criteria. The present theoretical work proposes a fully-adaptive closed-loop neurostimulation setup, that tunes the brain activities power spectral density (PSD) according to a user-defined PSD. The utilized brain model is non-parametric and estimated from the observations via magnitude fitting in a pre-stimulus setup phase. Moreover, the algorithm takes into account possible conduction delays in the feedback conne
Mental disorders may exhibit pathological brain rhythms and neurostimulation promises to alleviate of patients' symptoms by modifying these rhythms. Today, most neurostimulation schemes are open-loop, i.e. administer experimental stimulation protocols independent of the patients brain activity which may yield a sub-optimal treatment. We propose a closed-loop feedback control scheme estimating an optimal stimulation based on observed brain activity. The optimal stimulation is chosen according to a user-defined target frequency distribution, which permits frequency tuning of the brain activity in real-time. The mathematical description details the major control elements and applications to biologically realistic simulated brain activity illustrate the scheme's possible power in medical practice. Clinical relevance - The proposed neurostimulation control theme promises to permit the medical personnel to tune a patient's brain activity in real-time.
To investigate whether a deep learning model can detect Covid-19 from disruptions in the human body's physiological (heart rate) and rest-activity rhythms (rhythmic dysregulation) caused by the SARS-CoV-2 virus. We propose CovidRhythm, a novel Gated Recurrent Unit (GRU) Network with Multi-Head Self-Attention (MHSA) that combines sensor and rhythmic features extracted from heart rate and activity (steps) data gathered passively using consumer-grade smart wearable to predict Covid-19. A total of 39 features were extracted (standard deviation, mean, min/max/avg length of sedentary and active bouts) from wearable sensor data. Biobehavioral rhythms were modeled using nine parameters (mesor, amplitude, acrophase, and intra-daily variability). These features were then input to CovidRhythm for predicting Covid-19 in the incubation phase (one day before biological symptoms manifest). A combination of sensor and biobehavioral rhythm features achieved the highest AUC-ROC of 0.79 [Sensitivity = 0.69, Specificity=0.89, F$_{0.1}$ = 0.76], outperforming prior approaches in discriminating Covid-positive patients from healthy controls using 24 hours of historical wearable physiological. Rhythmic fe
Circadian rhythms are known to be important drivers of human activity and the recent availability of electronic records of human behaviour has provided fine-grained data of temporal patterns of activity on a large scale. Further, questionnaire studies have identified important individual differences in circadian rhythms, with people broadly categorised into morning-like or evening-like individuals. However, little is known about the social aspects of these circadian rhythms, or how they vary across individuals. In this study we use a unique 18-month dataset that combines mobile phone calls and questionnaire data to examine individual differences in the daily rhythms of mobile phone activity. We demonstrate clear individual differences in daily patterns of phone calls, and show that these individual differences are persistent despite a high degree of turnover in the individuals' social networks. Further, women's calls were longer than men's calls, especially during the evening and at night, and these calls were typically focused on a small number of emotionally intense relationships. These results demonstrate that individual differences in circadian rhythms are not just related to b
Human activities follow daily, weekly, and seasonal rhythms. The emergence of these rhythms is related to physiology and natural cycles as well as social constructs. The human body and biological functions undergo near 24-hour rhythms (circadian rhythms). The frequency of these rhythms is more or less similar across people, but its phase is different. In the chronobiology literature, based on the propensity to sleep at different hours of the day, people are categorized into morning-type, evening-type, and intermediate-type groups called \textit{chronotypes}. This typology is typically based on carefully designed questionnaires or manually crafted features drawing on data on timings of people's activity. Here we develop a fully data-driven (unsupervised) method to decompose individual temporal activity patterns into components. This has the advantage of not including any predetermined assumptions about sleep and activity hours, but the results are fully context-dependent and determined by the most prominent features of the activity data. Using a year-long dataset from mobile phone screen usage logs of 400 people, we find four emergent temporal components: morning activity, night act
Although recurrent neural networks (RNNs) trained on cognitive tasks have become a widely used framework for studying neural computation, the internal mechanisms by which RNNs switch between rhythms across multiple frequency bands, and how these mechanisms relate to neuronal time constants, have not been systematically analyzed. We trained leaky integrator RNNs with neuron-specific learnable time constants on a four-band (theta, alpha, beta, gamma) rhythm-switching task and analyzed 20 independently trained networks. Whereas low-frequency rhythms were produced by distributed participation of many neurons, high-frequency rhythms were dominated by a small subpopulation of short-time-constant neurons, and the negative correlation between time constant and matched-mode amplitude strengthened monotonically with frequency. Rhythm switching was supported by multiple coexisting mechanisms: turnover of the active subpopulation, network-wide baseline shifts that reposition the operating point near distinct unstable fixed points, and inter-neuronal phase reorganization that selectively cancels or supports band components in the population output. The mechanism deployed for each mode pair vari