WyNDA: A method to discover mathematical models of dynamical systems from data

This paper introduces a novel method called Wide-Array of Nonlinear Dynamics Approximation (WyNDA) for extracting mathematical models of dynamical systems from data. A key advantage of this method over existing approaches lies in its suitability for online implementation. Moreover, WyNDA stands out by not relying on optimization or machine learning, ensuring computational efficiency. The fundamental concept revolves around approximating the unknown function of a dynamical system through a diverse set of basis functions that encapsulate the available data. An adaptive observer is then employed to iteratively refine this approximation and estimate the associated parameters. The efficacy of the proposed method is demonstrated through numerical simulations encompassing linear systems, nonlinear systems, and control systems. The results underscore the method's ability to successfully unveil the governing equations of dynamical systems, highlighting its potential for extracting intricate system dynamics from observational data.•WyNDA represents a novel approach for uncovering mathematical models of dynamical systems from data.•Utilizing a series of basis functions, WyNDA effectively approximates the unknown structure inherent in dynamical systems.•The validation of WyNDA involves benchmark equations of dynamical systems, confirming its efficacy in diverse scenarios.

Time-dependent ligand-receptor binding kinetics and functionality in a heterodimeric receptor model

GPCRs heteromerize both in CNS and non-CNS regions. The cell uses receptor heteromerization to modulate receptor functionality and to provide fine tuning of receptor signaling. In order for pharmacologists to explore these mechanisms for therapeutic purposes, quantitative receptor models are needed. We have developed a time-dependent model of the binding kinetics and functionality of a preformed heterodimeric receptor involving two drugs. Two cases were considered: both or only one of the drugs are in excess with respect to the total concentration of the receptor. The latter case can be applied to those situations in which a drug causes unwanted side effects that need to be reduced by decreasing its concentration. The required efficacy can be maintained by the allosteric effects mutually exerted by the two drugs in the two-drug combination system. We discuss this concept assuming that the drug causing unwanted side effects is an opioid and that analgesia is the therapeutic effect. As additional points, allosteric modulation by endogenous compounds and synthetic bivalent ligands was included in the study. Receptor heteromerization offers a mechanistic understanding and quantification of the pharmacological effects elicited by combinations of two drugs at different doses and with different efficacies and cooperativity effects, thus providing a conceptual framework for drug combination therapy.

Generation of genetic codes with 2-adic codon algebra and adaptive dynamics

This is a brief review on modeling genetic codes with the aid of 2-adic dynamical systems. In this model amino acids are encoded by the attractors of such dynamical systems. Each genetic code is coupled to the special class of 2-adic dynamics. We consider the discrete dynamical systems, These are the iterations of a function F:Z2→Z2, where Z2 is the ring of 2-adic numbers (2-adic tree). A genetic code is characterized by the set of attractors of a function belonging to the code generating functional class. The main mathematical problem is to reduce degeneration of dynamic representation and select the optimal generating function. Here optimality can be treated in many ways. One possibility is to consider the Lipschitz functions playing the crucial role in general theory of iterations. Then we minimize the Lip-constant. The main issue is to find the proper biological interpretation of code-functions. One can speculate that the evolution of the genetic codes can be described in information space of the nucleotide-strings endowed with ultrametric (treelike) geometry. A code-function is a fitness function; the solutions of the genetic code optimization problem are attractors of the code-function. We illustrate this approach by generation of the standard nuclear and (vertebrate) mitochondrial genetics codes.

A geometrical model of cell fate specification in the mouse blastocyst

The lineage decision that generates the epiblast and primitive endoderm from the inner cell mass (ICM) is a paradigm for cell fate specification. Recent mathematics has formalized Waddington's landscape metaphor and proven that lineage decisions in detailed gene network models must conform to a small list of low-dimensional stereotypic changes called bifurcations. The most plausible bifurcation for the ICM is the so-called heteroclinic flip that we define and elaborate here. Our re-analysis of recent data suggests that there is sufficient cell movement in the ICM so the FGF signal, which drives the lineage decision, can be treated as spatially uniform. We thus extend the bifurcation model for a single cell to the entire ICM by means of a self-consistently defined time-dependent FGF signal. This model is consistent with available data and we propose additional dynamic experiments to test it further. This demonstrates that simplified, quantitative and intuitively transparent descriptions are possible when attention is shifted from specific genes to lineages. The flip bifurcation is a very plausible model for any situation where the embryo needs control over the relative proportions of two fates by a morphogen feedback.

A dynamical systems analysis of change in PTSD symptoms, depression symptoms, and suicidal ideation among military personnel during treatment for PTSD

OBJECTIVE

The connections among posttraumatic stress disorder (PTSD), depression, and suicidal ideation are elusive because of an overreliance on cross-sectional studies. In this secondary analysis of pooled data from three clinical trials of 742 military personnel, we examined the dynamic relationships among PTSD, depression, and suicidal ideation severity assessed repeatedly during and after outpatient treatment for PTSD.

METHODS

We conducted dynamical systems analyses to explore the potential for coordinated change over time in psychotherapy for PTSD.

RESULTS

Over the course of psychotherapy, PTSD, depression, and suicidal ideation severity changed in coordinated ways, consistent with an interdependent network. Results of eigenvalue decomposition analysis indicated the dominant change dynamic involved high stability and resistance to change but indicators of cycling were also observed, indicating participants "switched" between states that resisted change and states that promoted change. Depression (B = 0.48, SE = 0.11) and suicidal desire (B = 0.15, SE = 0.01) at a given assessment were associated with greater change in PTSD symptom severity at the next assessment. Suicidal desire (B = 0.001, SE < 0.001) at a given assessment was associated with greater change in depression symptom severity at the next assessment. Neither PTSD (B = -0.004, SE = 0.007) nor depression symptom severity (B = 0.000, SE = 0.001) was associated with subsequent change in suicidal ideation severity.

CONCLUSIONS

In a sample of treatment-seeking military personnel with PTSD, change in suicidal ideation and depression may precede change in PTSD symptoms but change in suicidal ideation was not preceded by change in PTSD or depression symptoms.

Similarity in evoked responses does not imply similarity in macroscopic network states

It is commonplace in neuroscience to assume that if two tasks activate the same brain areas in the same way, then they are recruiting the same underlying networks. Yet computational theory has shown that the same pattern of activity can emerge from many different underlying network representations. Here we evaluated whether similarity in activation necessarily implies similarity in network architecture by comparing region-wise activation patterns and functional correlation profiles from a large sample of healthy subjects (N = 242). Participants performed two executive control tasks known to recruit nearly identical brain areas, the color-word Stroop task and the Multi-Source Interference Task (MSIT). Using a measure of instantaneous functional correlations, based on edge time series, we estimated the task-related networks that differed between incongruent and congruent conditions. We found that the two tasks were much more different in their network profiles than in their evoked activity patterns at different analytical levels, as well as for a wide range of methodological pipelines. Our results reject the notion that having the same activation patterns means two tasks engage the same underlying representations, suggesting that task representations should be independently evaluated at both node and edge (connectivity) levels.

Linking fast and slow: The case for generative models

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space

We extend a previously published model for the dynamics of a single strain of an influenza-like infection. The model incorporates a waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of coupled integral equations within a season and a discrete map between seasons. The long term behaviour of the model is demonstrated by examples where immunity to infection depends on the time since a host was last infected, and where immunity depends on the number of times that a host has been infected. The first scenario leads to complicated dynamics in some regions of parameter space, and to regions of parameter space with more than one attractor. The second scenario leads to a stable fixed point, corresponding to an identical epidemic each season. We also examine the model with both paradigms in combination, almost always but not exclusively observing a stable fixed point or periodic solution. Adding stochastic perturbations to the between season map fails to destroy the model's qualitative dynamics. Our results suggest that if the level of host immunity depends on the elapsed time since the last infection then the epidemiological dynamics may be unpredictable.

Structural instability and linear allocation control in generalized models of substance use disorder

Substance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, including opioid use disorder developed through prescription use and alcoholism developed primarily due to genetic factors or stress, depression, and other psychological factors. In this paper we will demonstrate that even a simple infectious disease model is structurally unstable with respect to a linear perturbation in the infection term - precisely the sort of term necessary to model SUD development in isolation. This implies that models of SUD which exclusively treat problematic substance use as an infectious disease will have misleading dynamics whenever a non-trivial rate of isolated SUD development exists in actuality. As we will show, linearly perturbed SUD models do not have a use disorder-free equilibrium. To investigate management strategies, we implement optimal control techniques with the goal of minimizing the number of SUD cases over time.

Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters

A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations. At low diffusion, the origin is a repulsor, causing the orbits to flow nearly parallel to the axes, risking stochastic extinctions. Higher diffusion turns the repeller into a saddle point. Orbits then quickly converge to the saddle's unstable manifold, reducing extinction chances. This change in the vector field enhances metapopulation robustness. On the other hand, the well-known fact that asymmetric conditions on the patches is beneficial for the total population is further investigated. This phenomenon has been studied in previous works for large enough or small enough values of the dispersal. In this work, we complete the theory for all values of the dispersal. In particular, we derive analytically a formula for the optimal value of the dispersal that maximizes the total population.

Coevolutionary stability of host-symbiont systems with mixed-mode transmission

The coevolution of hosts and symbionts based on virulence and mode of transmission is a complex and diverse biological phenomenon. We introduced a conceptual model to study the stable coexistence and coevolution of an obligate symbiont (mutualist or parasite) with mixed-mode transmission and its host. Using an age-structured Leslie model for the host, we demonstrated how the obligate symbiont could modify the host's life history traits (survival and fecundity) and the long-term growth rate of the infected lineage. When the symbiont is vertically transmitted, we found that the host and its symbiont could maximize the infected lineage's evolutionary success (multi-level selection). Our model showed that symbionts' effect on host longevity and reproduction might differ, even be opposing, and their net effect might often be counterintuitive. The evolutionary stability of the ecologically stable coexistence was analyzed in the framework of coevolutionary dynamics. Moreover, we found conditions for the ecological and evolutionary stability of the resident host-symbiont pair, which does not allow invasion by rare mutants (each mutant dies out by ecological selection). We concluded that, within the context of our simplified model conditions, a host-symbiont system with mixed-mode transmission is evolutionarily stable unconditionally only if the host can maximize the Malthusian parameters of the infected and non-infected lineages using the same strategy. Finally, we performed a game-theoretical analysis of our selection situation and compared two stability definitions.

Metastasis Models: Thermodynamics and Complexity

The thermodynamic formalism of nonequilibrium systems together with the theory of complex systems and systems biology offer an appropriate theoretical framework to explain the complexity observed at the macroscopic level in physiological phenomena. In turn, they allow the establishment of an appropriate conceptual and operational framework to address the study of phenomena such as the emergence and evolution of cancer.This chapter is organized as follows: In Subheading 1, an integrated vision of these disciplines is offered for the characterization of the emergence and evolution of cancer, seen as a nonlinear dynamic system, temporally and spatially self-organized out of thermodynamic equilibrium. The development of the various mathematical models and different techniques and approaches used in the characterization of cancer metastasis is presented in Subheading 2. Subheading 3 is devoted to the time course of cancer metastasis, with particular emphasis on the epithelial-mesenchymal transition (EMT henceforth) as well as chronotherapeutic treatments. In Subheading 4, models of the spatial evolution of cancer metastasis are presented. Finally, in Subheading 5, some conclusions and remarks are presented.

A yeast cell cycle pulse generator model shows consistency with multiple oscillatory and checkpoint mutant datasets

Modeling biological systems holds great promise for speeding up the rate of discovery in systems biology by predicting experimental outcomes and suggesting targeted interventions. However, this process is dogged by an identifiability issue, in which network models and their parameters are not sufficiently constrained by coarse and noisy data to ensure unique solutions. In this work, we evaluated the capability of a simplified yeast cell-cycle network model to reproduce multiple observed transcriptomic behaviors under genomic mutations. We matched time-series data from both cycling and checkpoint arrested cells to model predictions using an asynchronous multi-level Boolean approach. We showed that this single network model, despite its simplicity, is capable of exhibiting dynamical behavior similar to the datasets in most cases, and we demonstrated the drop in severity of the identifiability issue that results from matching multiple datasets.

A Dynamical Systems Investigation of the Co-regulation between Perceived Daily Parental Warmth and Adolescent Attention-deficit/hyperactivity Disorder Symptoms

Longitudinal research demonstrates that child ADHD symptoms and behaviors exhibit reciprocal associations with parenting behaviors over time. However, minimal research has investigated these associations and their dynamic links at the daily level. Intensive longitudinal data can disentangle stable between-person differences from within-person fluctuations and reveal nuanced short-term family dynamics on a micro timescale. Using 30-day daily diary data from a community sample of 86 adolescents (Mage = 14.5, 55% female, 56% White, 22% Asian) and latent differential equation modeling, this study examined the links between perceived daily parental warmth and ADHD symptoms as coupled dynamical systems. The results show that the magnitude of fluctuations in perceived daily parental warmth generally remains stable, while elevated ADHD symptoms return to their normal level over time. Perceived parental warmth is sensitive to change in ADHD symptoms such that adolescents feel that their parents will fine-tune their warmth with gradual changes when adolescents demonstrate heightened symptoms. There are substantial between-family differences in these regulating system dynamics. Among families with more baseline parental non-harsh discipline, both perceived parental warmth and ADHD symptoms tend to be more stable and fluctuate less often. Intensive longitudinal data and dynamical systems approaches offer a new lens to uncover short-term family dynamics and adolescent adjustment at a refined micro level. Future research should explore antecedents and consequences of between-family differences in these short-term family dynamics on multiple timescales.

Mathematical Modeling of Photo- and Thermomorphogenesis in Plants

Increased day lengths and warm conditions inversely affect plant growth by directly modulating nuclear phyB, ELF3, and COP1 levels. Quantitative measures of the hypocotyl length have been key to gaining a deeper understanding of this complex regulatory network, while similar quantitative data are the foundation for many studies in plant biology. Here, we explore the application of mathematical modeling, specifically ordinary differential equations (ODEs), to understand plant responses to these environmental cues. We provide a comprehensive guide to constructing, simulating, and fitting these models to data, using the law of mass action to study the evolution of molecular species. The fundamental principles of these models are introduced, highlighting their utility in deciphering complex plant physiological interactions and testing hypotheses. This brief introduction will not allow experimentalists without a mathematical background to run their own simulations overnight, but it will help them grasp modeling principles and communicate with more theory-inclined colleagues.

Physics-Constrained Data-Driven Variational Method for Discrepancy Modeling

This paper presents a data-driven discrepancy modeling method that variationally embeds measured data in the modeling and analysis framework. The proposed method exploits the residual between the first-principles theory and sensor-based measurements from the dynamical system, and it augments the physics-based model with a variationally derived loss function that is comprised of this residual. The method was first developed in the context of linear elasticity (Masud and Goraya, J. Appl. Mech. 89 (11), 111001 (2022)) wherein the relation between the discrepancy model and loss terms was derived to show that the data embedding terms behave like residual-based least-squares regression functions. An interpretation of the stabilization tensor as a kernel function was formally established and its role in assimilating a-priori knowledge of the problem in the modeling method was highlighted. The present paper employs linear elastodynamics as a model problem where the Data-Driven Variational (DDV) method incorporates high-fidelity data into the forward simulations, thereby driving the problem with not only the boundary and initial conditions, but also by measurement data that is taken at only a small subset of the total domain. The effect of the loss function on the time-dependent response of the system is investigated under a variety of loading conditions and model discrepancies. The energy and Morlet wavelet analyses reveal that the problem with embedded data recovers the energy and the fundamental frequency band of the target system. Time histories of strain energy and kinetic energy of a cantilever beam undergoing damped oscillations are recovered by including known data in an undamped model to highlight the data-driven discrepancy modeling feature of the method under the combined effect of parameter and model discrepancy.

What Dynamic Approaches Have Taught Us About Cognition and What They Have Not: On Values in Motion and the Importance of Replicable Forms

Over the past several decades, research in the cognitive sciences has foregrounded the importance of active bodies and their continuous dependence on the changing environment, strengthening the relevance of dynamical models. These models have been steadily developed within the ecological psychology approach to cognition, which arguably contributes to the "ecological turn" we are witnessing today. The embodied and situated nature of cognition, regarded by some as a passing trend, is presently becoming a largely accepted assumption. In this paper, I claim that in light of these developments, ecological psychology, in alliance with related approaches, such as enactivism and interactivism, has the potential to deeply transform our perspectives on cognition and action, restoring their pertinence to humans as persons. However, an important challenge to the realization of this potential has to be noted: neither the mainstream information-processing approach nor the dynamics-oriented perspective on cognition provides an account of how the capacity of humans to use language and think "symbolically" can be derived from the continuous flow of agent-environment interaction. I will attempt to show that posing the "dynamical" and "computational" hypotheses about the nature of cognition as mutually exclusive approaches to cognition results in undesirable reductionism, which makes it difficult to meet this challenge. There are good reasons, advanced over half a century ago by, for example, Michael Polanyi or Howard Pattee, to think that we need complementary descriptions to understand cognizing systems, in order to grasp the fact that they are governed both by physical laws and by emergent historical constraints. Details of such a complementarity-based approach still await elucidation, but some proposed solutions have the potential to ease the tension between the information-processing and dynamical approaches to cognition and to lead to a better understanding of their interrelation.

The Dynamicist Landscape

The dynamical hypothesis states that cognitive systems are dynamical systems. While dynamical systems play an important role in many cognitive phenomena, the dynamical hypothesis as stated applies to every system and so fails both to specify what makes cognitive systems distinct and to distinguish between proposals regarding the nature of cognitive systems. To avoid this problem, I distinguish several different types of dynamical systems, outlining four dimensions along which dynamical systems can vary: total-state versus partial-state, internal versus external, macroscopic versus microscopic, and systemic versus componential, and illustrate these with examples. I conclude with two illustrations of partial-state, internal, microscopic, componential dynamicism.

Recurrence Quantification Analysis of Crowd Sound Dynamics

When multiple individuals interact in a conversation or as part of a large crowd, emergent structures and dynamics arise that are behavioral properties of the interacting group rather than of any individual member of that group. Recent work using traditional signal processing techniques and machine learning has demonstrated that global acoustic data recorded from a crowd at a basketball game can be used to classify emergent crowd behavior in terms of the crowd's purported emotional state. We propose that the description of crowd behavior from such global acoustic data could benefit from nonlinear analysis methods derived from dynamical systems theory. Such methods have been used in recent research applying nonlinear methods to audio data extracted from music and group musical interactions. In this work, we used nonlinear analyses to extract features that are relevant to the behavioral interactions that underlie acoustic signals produced by a crowd attending a sporting event. We propose that recurrence dynamics measured from these audio signals via recurrence quantification analysis (RQA) reflect information about the behavioral dynamics of the crowd itself. We analyze these dynamics from acoustic signals recorded from crowds attending basketball games, and that were manually labeled according to the crowds' emotional state across six categories: angry noise, applause, cheer, distraction noise, positive chant, and negative chant. We show that RQA measures are useful to differentiate the emergent acoustic behavioral dynamics between these categories, and can provide insight into the recurrence patterns that underlie crowd interactions.

Abduction and Deduction in Dynamical Cognitive Science

This paper reviews the recent history of a subset of research in dynamical cognitive science, in particular that subset that allies itself with the sciences of complexity and casts cognitive systems as interaction dominant, noncomputational, and nonmodular. I look at this history in the light of C.S. Peirce's understanding of scientific reasoning as progressing from abduction to deduction to induction. In particular, I examine the development of a controversy concerning the use of the interaction dominance of human cognitive systems as an explanation of the ubiquitous 1/f noise, multifractality, and complexity matching in human behavior.

Interplay of p53 and XIAP protein dynamics orchestrates cell fate in response to chemotherapy

Chemotherapeutic drugs are used to treat almost all types of cancer, but the intended response, i.e., elimination, is often incomplete, with a subset of cancer cells resisting treatment. Two critical factors play a role in chemoresistance: the p53 tumour suppressor gene and the X-linked inhibitor of apoptosis (XIAP). These proteins have been shown to act synergistically to elicit cellular responses upon DNA damage induced by chemotherapy, yet, the mechanism is poorly understood. This study introduces a mathematical model characterising the apoptosis pathway activation by p53 before and after mitochondrial outer membrane permeabilisation upon treatment with the chemotherapy Doxorubicin (Dox). "In-silico" simulations show that the p53 dynamics change dose-dependently. Under medium to high doses of Dox, p53 concentration ultimately stabilises to a high level regardless of XIAP concentrations. However, caspase-3 activation may be triggered or not depending on the XIAP induction rate, ultimately determining whether the cell will perish or resist. Consequently, the model predicts that failure to activate apoptosis in some cancer cells expressing wild-type p53 might be due to heterogeneity between cells in upregulating the XIAP protein, rather than due to the p53 protein concentration. Our model suggests that the interplay of the p53 dynamics and the XIAP induction rate is critical to determine the cancer cells' therapeutic response.

Stage 2: Visual information and communication context as modulators of interpersonal coordination in face-to-face and videoconference-based interactions

Interpersonal coordination of body movement-or similarity in patterning and timing of body movement between interaction partners-is well documented in face-to-face (FTF) conversation. Here, we investigated the degree to which interpersonal coordination is impacted by the amount of visual information available and the type of interaction conversation partners are having. To do so within a naturalistic context, we took advantage of the increased familiarity with videoconferencing (VC) platforms and with limited visual information in FTF conversation due to the COVID-19 pandemic. Pairs of participants communicated in one of three ways: FTF in a laboratory setting while socially distanced and wearing face masks; VC in a laboratory setting with a view of one another's full movements; or VC in a remote setting with a view of one another's face and shoulders. Each pair held three conversations: affiliative, argumentative, and cooperative task-based. We quantified interpersonal coordination as the relationship between the two participants' overall body movement using nonlinear time series analyses. Coordination changed as a function of the contextual constraints, and these constraints interacted with coordination patterns to affect subjective conversation outcomes. Importantly, we found patterns of results that were distinct from previous research; we hypothesize that these differences may be due to changes in the broader social context from COVID-19. Taken together, our results are consistent with a dynamical systems view of social phenomena, with interpersonal coordination emerging from the interaction between components, constraints, and history of the system.

Beyond Nature Versus Nurture: the Emergence of Emotion

Affective science is stuck in a version of the nature-versus-nurture debate, with theorists arguing whether emotions are evolved adaptations or psychological constructions. We do not see these as mutually exclusive options. Many adaptive behaviors that humans have evolved to be good at, such as walking, emerge during development - not according to a genetically dictated program, but through interactions between the affordances of the body, brain, and environment. We suggest emotions are the same. As developing humans acquire increasingly complex goals and learn optimal strategies for pursuing those goals, they are inevitably pulled to particular brain-body-behavior states that maximize outcomes and self-reinforce via positive feedback loops. We call these recurring, self-organized states emotions. Emotions display many of the hallmark features of self-organized attractor states, such as hysteresis (prior events influence the current state), degeneracy (many configurations of the underlying variables can produce the same global state), and stability. Because most bodily, neural, and environmental affordances are shared by all humans - we all have cardiovascular systems, cerebral cortices, and caregivers who raised us - similar emotion states emerge in all of us. This perspective helps reconcile ideas that, at first glance, seem contradictory, such as emotion universality and neural degeneracy.

Transcranial stimulation of alpha oscillations modulates brain state dynamics in sustained attention

The brain operates an advanced complex system to support mental activities. Cognition is thought to emerge from dynamic states of the complex brain system, which are organized spatially through large-scale neural networks and temporally via neural synchrony. However, specific mechanisms underlying these processes remain obscure. Applying high-definition alpha-frequency transcranial alternating-current stimulation (HD α-tACS) in a continuous performance task (CPT) during functional resonance imaging (fMRI), we causally elucidate these major organizational architectures in a key cognitive operation-sustained attention. We demonstrated that α-tACS enhanced both electroencephalogram (EEG) alpha power and sustained attention, in a correlated fashion. Akin to temporal fluctuations inherent in sustained attention, our hidden Markov modeling (HMM) of fMRI timeseries uncovered several recurrent, dynamic brain states, which were organized through a few major neural networks and regulated by the alpha oscillation. Specifically, during sustain attention, α-tACS regulated the temporal dynamics of the brain states by suppressing a Task-Negative state (characterized by activation of the default mode network/DMN) and Distraction state (with activation of the ventral attention and visual networks). These findings thus linked dynamic states of major neural networks and alpha oscillations, providing important insights into systems-level mechanisms of attention. They also highlight the efficacy of non-invasive oscillatory neuromodulation in probing the functioning of the complex brain system and encourage future clinical applications to improve neural systems health and cognitive performance.

A Methodological Framework to Study Change in Team Cognition Under the Dynamical Hypothesis

The dynamical hypothesis claims that cognitive systems, such as teams, are dynamical systems (i.e., an interdependent collection of individuals and their technology that change together over time). Following this hypothesis, team researchers have adopted dynamical approaches to better understand the team cognitive processes and states that form team cognition, as well as how they emerge over time. One approach focuses on team coordination dynamics, which examines the coupling of signals between interacting individuals in various modalities, and has been shown to reflect aspects of team functioning including team cognition. However, how changes in team coordination relate to high-level team cognitive processes and states, as well as important events, are not yet fully understood. To this end, we advance a methodological framework for researching team cognition under the dynamical hypothesis. Subsequently, we provided an empirical case-study application of this framework. Thereby, this work contributes methodologically and empirically to a deeper understanding of team cognition, the dynamical hypothesis, and the synergy between them.

Stable invariant models via Koopman spectra

Weight-tied models have attracted attention in the modern development of neural networks. The deep equilibrium model (DEQ) represents infinitely deep neural networks with weight-tying, and recent studies have shown the potential of this type of approach. DEQs are needed to iteratively solve root-finding problems in training and are built on the assumption that the underlying dynamics determined by the models converge to a fixed point. In this paper, we present the stable invariant model (SIM), a new class of deep models that in principle approximates DEQs under stability and extends the dynamics to more general ones converging to an invariant set (not restricted in a fixed point). The key ingredient in deriving SIMs is a representation of the dynamics with the spectra of the Koopman and Perron-Frobenius operators. This perspective approximately reveals stable dynamics with DEQs and then derives two variants of SIMs. We also propose an implementation of SIMs that can be learned in the same way as feedforward models. We illustrate the empirical performance of SIMs with experiments and demonstrate that SIMs achieve comparative or superior performance against DEQs in several learning tasks.

Event-related variability is modulated by task and development

In carefully designed experimental paradigms, cognitive scientists interpret the mean event-related potentials (ERP) in terms of cognitive operations. However, the huge signal variability from one trial to the next, questions the representability of such mean events. We explored here whether this variability is an unwanted noise, or an informative part of the neural response. We took advantage of the rapid changes in the visual system during human infancy and analyzed the variability of visual responses to central and lateralized faces in 2-to 6-month-old infants compared to adults using high-density electroencephalography (EEG). We observed that neural trajectories of individual trials always remain very far from ERP components, only moderately bending their direction with a substantial temporal jitter across trials. However, single trial trajectories displayed characteristic patterns of acceleration and deceleration when approaching ERP components, as if they were under the active influence of steering forces causing transient attraction and stabilization. These dynamic events could only partly be accounted for by induced microstate transitions or phase reset phenomena. Importantly, these structured modulations of response variability, both between and within trials, had a rich sequential organization, which in infants, was modulated by the task difficulty and age. Our approaches to characterize Event Related Variability (ERV) expand on classic ERP analyses and provide the first evidence for the functional role of ongoing neural variability in human infants.

Optimal protein production by a synthetic microbial consortium: coexistence, distribution of labor, and syntrophy

The bacterium E. coli is widely used to produce recombinant proteins such as growth hormone and insulin. One inconvenience with E. coli cultures is the secretion of acetate through overflow metabolism. Acetate inhibits cell growth and represents a carbon diversion, which results in several negative effects on protein production. One way to overcome this problem is the use of a synthetic consortium of two different E. coli strains, one producing recombinant proteins and one reducing the acetate concentration. In this paper, we study a mathematical model of such a synthetic community in a chemostat where both strains are allowed to produce recombinant proteins. We give necessary and sufficient conditions for the existence of a coexistence equilibrium and show that it is unique. Based on this equilibrium, we define a multi-objective optimization problem for the maximization of two important bioprocess performance metrics, process yield and productivity. Solving numerically this problem, we find the best available trade-offs between the metrics. Under optimal operation of the mixed community, both strains must produce the protein of interest, and not only one (distribution instead of division of labor). Moreover, in this regime acetate secretion by one strain is necessary for the survival of the other (syntrophy). The results thus illustrate how complex multi-level dynamics shape the optimal production of recombinant proteins by synthetic microbial consortia.

Temporal Mapper: Transition networks in simulated and real neural dynamics

Characterizing large-scale dynamic organization of the brain relies on both data-driven and mechanistic modeling, which demands a low versus high level of prior knowledge and assumptions about how constituents of the brain interact. However, the conceptual translation between the two is not straightforward. The present work aims to provide a bridge between data-driven and mechanistic modeling. We conceptualize brain dynamics as a complex landscape that is continuously modulated by internal and external changes. The modulation can induce transitions between one stable brain state (attractor) to another. Here, we provide a novel method-Temporal Mapper-built upon established tools from the field of topological data analysis to retrieve the network of attractor transitions from time series data alone. For theoretical validation, we use a biophysical network model to induce transitions in a controlled manner, which provides simulated time series equipped with a ground-truth attractor transition network. Our approach reconstructs the ground-truth transition network from simulated time series data better than existing time-varying approaches. For empirical relevance, we apply our approach to fMRI data gathered during a continuous multitask experiment. We found that occupancy of the high-degree nodes and cycles of the transition network was significantly associated with subjects' behavioral performance. Taken together, we provide an important first step toward integrating data-driven and mechanistic modeling of brain dynamics.

Interpersonal coordination of opposing player dyads during attacks performed in official football matches

The purpose of this study was to characterise the interpersonal coordination between opponent players during offensive sequences in official matches and to verify if offensive sequences ended in shots to goal present different coordination patterns when compared than those that ended in defensive tackles. A total of 580 offensive sequences occurred during matches resulting in shots to goal (n = 172) or defensive tackles (n = 408) were analysed. The bidimensional coordinates and technical actions of male professional football players (n = 1160) were obtained using a video-based tracking system. Dyads were defined using a network analysis and composed of the nearest opponent. Interpersonal coordination of the dyads was analysed using the vector coding and the frequency for each coordination pattern was computed. In-phase was predominant for all displacement directions and offensive sequences outcomes, and antiphase was the least frequent. For lateral displacements, offensive sequences ending in shot to goal presented lower frequency for in-phase and higher frequency for offensive player phase than ended in defensive tackle. This information about the relationship of opponent players dyads during decisive moments of the matches provides fundamentals for future research and assists coaches to understand the different behaviours in successful and unsuccessful attacks.

More frequent, persistent, and deadly heat waves in the 21st century over the Eastern Mediterranean

Heat waves are extreme events characterized by sweltering weather over an extended period. Skillful projections of heat waves and their impacts on human mortality can help develop appropriate adaptation strategies. Here, we provide nuanced projections of heat wave characteristics and their effect on human mortality over the Eastern Mediterranean based on ERA5 reanalysis and CORDEX ensemble simulations. Heat waves were identified according to the 90th percentile threshold of the Climatic Stress Index (CSI), specifically tailored for the summer conditions in this region. We provide evidence that heat waves in the region are projected to occur seven times more often and last three times longer by the end of the 21st century (RCP8.5). We find that heat waves will become more persistent in a warmer world. Finally, we offer a conservative estimate of excess mortality in Israel based on a simple linear model. The projected changes in heat stress intensity and frequency may result in ~330 excess deaths per summer at the end of the 21st century (RCP8.5) compared to the historical baseline of ~30 heat-related deaths, particularly pronounced in the elderly (65+ years). We conclude that heat waves increasingly threaten society in the vulnerable Eastern Mediterranean. We also emphasize that true interdisciplinary regional collaborations are required to achieve adequate public health adaptation to extreme weather events in a changing climate.

Dynamical systems model of development of the action differentiation in early infancy: a requisite of physical agency

Young infants are sensitive to whether their body movements cause subsequent events or not during the interaction with the environment. This ability has been revealed by empirical studies on the reinforcement of limb movements when a string is attached between an infant limb and a mobile toy suspended overhead. A previous study reproduced the experimental observation by modeling both the infant's limb and a mobile toy as a system of coupled oscillators. The authors then argued that emergence of agency could be explained by a phase transition in the dynamical system: from a weakly coupled state to a state where the both movements of the limb and the toy are highly coordinated. However, what remains unexplained is the following experimental observation: When the limb is connected to the mobile toy by a string, the infant increases the average velocity of the arm's movement. On the other hand, when the toy is controlled externally, the average arm's velocity is greatly reduced. Since young infants produce exuberant spontaneous movements even with no external stimuli, the inhibition of motor action to suppress the formation of spurious action-perception coupling should be also a crucial sign for the emergence of agency. Thus, we present a dynamical system model for the development of action differentiation, to move or not to move, in the mobile task. In addition to the pair of limb and mobile oscillators for providing positive feedback for reinforcement in the previous model, bifurcation dynamics are incorporated to enhance or inhibit self-movements in response to detecting contingencies between the limb and mobile movements. The results from computer simulations reproduce experimental observations on the developmental emergence of action differentiation between 2 and 3 months of age in the form of a bifurcation diagram. We infer that the emergence of physical agency entails young infants' ability not only to enhance a specific action-perception coupling, but also to decouple it and create a new mode of action-perception coupling based on the internal state dynamics with contingency detection between self-generated actions and environmental events.

Cognitive Science Progresses Toward Interactive Frameworks

Despite its many twists and turns, the arc of cognitive science generally bends toward progress, thanks to its interdisciplinary nature. By glancing at the last few decades of experimental and computational advances, it can be argued that-far from failing to converge on a shared set of conceptual assumptions-the field is indeed making steady consensual progress toward what can broadly be referred to as interactive frameworks. This inclination is apparent in the subfields of psycholinguistics, visual perception, embodied cognition, extended cognition, neural networks, dynamical systems theory, and more. This pictorial essay briefly documents this steady progress both from a bird's eye view and from the trenches. The conclusion is one of optimism that cognitive science is getting there, albeit slowly and arduously, like any good science should.

A novel application of entropy analysis for assessing changes in movement variability during cumulative tackles in young elite rugby league players

The aim of this study was to identify between-position (forwards vs. backs) differences in movement variability in cumulative tackle events training during both attacking and defensive roles. Eleven elite adolescent male rugby league players volunteered to participate in this study (mean ± SD, age; 18.5 ± 0.5 years, height; 179.5 ± 5.0 cm, body mass; 88.3 ± 13.0 kg). Participants performed a drill encompassing four blocks of six tackling (i.e. tackling an opponent) and six tackled (i.e. being tackled by an opponent while carrying a ball) events (i.e. 48 total tackles) while wearing a micro-technological inertial measurement unit (WIMU, Realtrack Systems, Spain). The acceleration data were used to calculate sample entropy (SampEn) to analyse the movement variability during tackles performance. In tackling actions SampEn showed significant between-position differences in block 1 (p = 0.0001) and block 2 (p = 0.0003). Significant between-block differences were observed in backs (block 1 vs 3, p = 0,0021; and block 1 vs 4, p = 0,0001) but not in forwards. When being tackled, SampEn showed significant between-position differences in block 1 (p = 0.0007) and block 3 (p = 0.0118). Significant between-block differences were only observed for backs in block 1 vs 4 (p = 0,0025). Movement variability shows a progressive reduction with cumulative tackle events, especially in backs and when in the defensive role (tackling). Forwards present lower movement variability values in all blocks, particularly in the first block, both in the attacking and defensive role. Entropy measures can be used by practitioners as an alternative tool to analyse the temporal structure of variability of tackle actions and quantify the load of these actions according to playing position.

A partially averaged system to model neuron responses to interferential current stimulation

The interferential current (IFC) therapy is a noninvasive electrical neurostimulation technique intended to activate deep neurons using surface electrodes. In IFC, two independent kilohertz-frequency currents purportedly intersect where an interference field is generated. However, the effects of IFC on neurons within and outside the interference field are not completely understood, and it is unclear whether this technique can reliable activate deep target neurons without side effects. In recent years, realistic computational models of IFC have been introduced to quantify the effects of IFC on brain cells, but they are often complex and computationally costly. Here, we introduce a simplified model of IFC based on the FitzHugh-Nagumo (FHN) model of a neuron. By considering a modified averaging method, we obtain a non-autonomous approximated system, with explicit representation of relevant IFC parameters. For this approximated system we determine conditions under which it reliably approximates the complete FHN system under IFC stimulation, and we mathematically prove its ability to predict nonspiking states. In addition, we perform numerical simulations that show that the interference effect is observed only for a narrow set of IFC parameters and, in particular, for a beat frequency no higher than about 100 [Hz]. Our novel model tailored to the IFC technique contributes to the understanding of neurostimulation modalities using this type of signals, and can have implications in the design of noninvasive electrical stimulation therapies.

Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition

Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system to describe the evolution of the average firing rates of the populations. In the present work, we investigate the impact of the often neglected refractory state and show that taking it into account can introduce new dynamics. Starting from a continuous-time Markov chain, we perform a rigorous derivation of a mean-field model that includes the refractory fractions of populations as dynamical variables. Then, we perform bifurcation analysis to explain the occurrence of periodic solutions in cases where the classical Wilson-Cowan does not predict oscillations. We also show that our mean-field model is able to predict chaotic behavior in the dynamics of networks with as little as two populations.

The effects of Hh morphogen source movement on signaling dynamics

Morphogens of the Hh family trigger gene expression changes in receiving cells in a concentration-dependent manner to regulate their identity, proliferation, death or metabolism, depending on the tissue or organ. This variety of responses relies on a conserved signaling pathway. Its logic includes a negative-feedback loop involving the Hh receptor Ptc. Here, using experiments and computational models we study and compare the different spatial signaling profiles downstream of Hh in several developing Drosophila organs. We show that the spatial distributions of Ptc and the activator transcription factor CiA in wing, antenna and ocellus show similar features, but are markedly different from that in the compound eye. We propose that these two profile types represent two time points along the signaling dynamics, and that the interplay between the spatial displacement of the Hh source in the compound eye and the negative-feedback loop maintains the receiving cells effectively in an earlier stage of signaling. These results show how the interaction between spatial and temporal dynamics of signaling and differentiation processes may contribute to the informational versatility of the conserved Hh signaling pathway.

Reconstructing gene regulatory networks of biological function using differential equations of multilayer perceptrons

BACKGROUND

Building biological networks with a certain function is a challenge in systems biology. For the functionality of small (less than ten nodes) biological networks, most methods are implemented by exhausting all possible network topological spaces. This exhaustive approach is difficult to scale to large-scale biological networks. And regulatory relationships are complex and often nonlinear or non-monotonic, which makes inference using linear models challenging.

RESULTS

In this paper, we propose a multi-layer perceptron-based differential equation method, which operates by training a fully connected neural network (NN) to simulate the transcription rate of genes in traditional differential equations. We verify whether the regulatory network constructed by the NN method can continue to achieve the expected biological function by verifying the degree of overlap between the regulatory network discovered by NN and the regulatory network constructed by the Hill function. And we validate our approach by adapting to noise signals, regulator knockout, and constructing large-scale gene regulatory networks using link-knockout techniques. We apply a real dataset (the mesoderm inducer Xenopus Brachyury expression) to construct the core topology of the gene regulatory network and find that Xbra is only strongly expressed at moderate levels of activin signaling.

CONCLUSION

We have demonstrated from the results that this method has the ability to identify the underlying network topology and functional mechanisms, and can also be applied to larger and more complex gene network topologies.

A dynamic gradient architecture generates brain activity states

The human brain exhibits a diverse yet constrained range of activity states. While these states can be faithfully represented in a low-dimensional latent space, our understanding of the constitutive functional anatomy is still evolving. Here we applied dimensionality reduction to task-free and task fMRI data to address whether latent dimensions reflect intrinsic systems and if so, how these systems may interact to generate different activity states. We find that each dimension represents a dynamic activity gradient, including a primary unipolar sensory-association gradient underlying the global signal. The gradients appear stable across individuals and cognitive states, while recapitulating key functional connectivity properties including anticorrelation, modularity, and regional hubness. We then use dynamical systems modeling to show that gradients causally interact via state-specific coupling parameters to create distinct brain activity patterns. Together, these findings indicate that a set of dynamic, intrinsic spatial gradients interact to determine the repertoire of possible brain activity states.

Multi-omic phenotyping reveals host-microbe responses to bariatric surgery, glycaemic control and obesity

Background

Resolution of type 2 diabetes (T2D) is common following bariatric surgery, particularly Roux-en-Y gastric bypass. However, the underlying mechanisms have not been fully elucidated.

Methods

To address this we compare the integrated serum, urine and faecal metabolic profiles of participants with obesity ± T2D (n = 80, T2D = 42) with participants who underwent Roux-en-Y gastric bypass or sleeve gastrectomy (pre and 3-months post-surgery; n = 27), taking diet into account. We co-model these data with shotgun metagenomic profiles of the gut microbiota to provide a comprehensive atlas of host-gut microbe responses to bariatric surgery, weight-loss and glycaemic control at the systems level.

Results

Here we show that bariatric surgery reverses several disrupted pathways characteristic of T2D. The differential metabolite set representative of bariatric surgery overlaps with both diabetes (19.3% commonality) and body mass index (18.6% commonality). However, the percentage overlap between diabetes and body mass index is minimal (4.0% commonality), consistent with weight-independent mechanisms of T2D resolution. The gut microbiota is more strongly correlated to body mass index than T2D, although we identify some pathways such as amino acid metabolism that correlate with changes to the gut microbiota and which influence glycaemic control.

Conclusion

We identify multi-omic signatures associated with responses to surgery, body mass index, and glycaemic control. Improved understanding of gut microbiota - host co-metabolism may lead to novel therapies for weight-loss or diabetes. However, further experiments are required to provide mechanistic insight into the role of the gut microbiota in host metabolism and establish proof of causality.

Weight-loss surgery is a highly effective treatment of type 2 diabetes in people with obesity. Interestingly, the improvement in diabetes after weight-loss surgery occurs before any significant weight-loss. Through better understanding of this metabolic improvement, weight-loss surgery provides a unique avenue to identify novel ways of treating diabetes and obesity. 

Here we combine measurements of metabolism, gut bacteria and diet in people with obesity, with or without type 2 diabetes and in patients before and after weight-loss surgery. We have used these data to identify changes associated with weight-loss surgery, obesity and diabetes. 

Improved understanding of the mechanisms behind these changes, including how changes to gut bacteria influence metabolism, may lead to new treatments for weight-loss or diabetes.

Penney et al. conduct microbial and metabolic profiling in people with obesity, with or without type 2 diabetes, undergoing two types of bariatric surgery. Integrative analysis identifies multi-omic signatures associated with response to surgery, body mass index, and glycaemic control.

Inter- and intra-limb coordination during initial sprint acceleration

In complex movements, centre of mass translation is achieved through effective joint and segment rotations. Understanding segment organisation and coordination is therefore paramount to understanding technique. This study sought to comprehensively describe inter- and intra-limb coordination and assess step-to-step changes and between-individual variation in coordination during initial sprint acceleration. Twenty-one highly trained to world class male (100 m PB 9.89-11.15 s) and female (100 m PB:11.46-12.14 s) sprinters completed sprint trials of at least 20 m from which sagittal plane kinematics were obtained for the first four steps using inertial measurement units (200 Hz). Thigh-thigh, trunk-shank and shank-foot coordination was assessed using a modified vector coding and segment dominancy approach. Common coordination patterns emerged for all segment couplings across sexes and performance levels, suggesting strong task constraints. Between-individual variation in inter-limb thigh coordination was highest in early flight, while trunk-shank and shank-foot variation was highest in late flight, with a second peak in late stance for the trunk-shank coupling. There were clear step-to-step changes in coordination, with step 1 being distinctly different to subsequent steps. The results demonstrate that inter-limb coordination is primarily anti-phase and trailing leg dominant while ankle motion in flight and late stance appears to be primarily driven by the foot.

The complex interplay between COVID-19 and economic activity

We introduce a dynamical system to model the complex interaction between COVID-19 and economic activity. The model introduces some novelties not accounted by SIR-like models. The equilibrium of the system is an unstable focus, with fluctuations having increasing size and periodicity. Numerical simulations of the model produce waves which reproduce the pandemic dynamics. In observing the stylized facts linking economics and pandemic and stating related reasonable assumptions, we obtain a Lotka-Volterra co-dynamics. This outcome is confirmed by extensive simulations. The outcomes obtained qualitatively replicate some important stylized facts deepening the knowledge about the role of some parameters in their origin and eventually in their shaping.

Cell size homeostasis under the circadian regulation of cell division in cyanobacteria

Bacterial cells maintain their characteristic cell size over many generations. Several rod-shaped bacteria, such as Escherichia coli and the cyanobacteria Synechococcus elongatus, divide after adding a constant length to their length at birth. Through this division control known as the adder mechanism, perturbation in cell length due to physiological fluctuation decays over generations at a rate of 2^-1 per cell division. However, previous experiments have shown that the circadian clock in cyanobacteria reduces cell division frequency at a specific time of day under constant light. This circadian gating should modulate the division control by the adder mechanism, but its significance remains unknown. Here we address how the circadian gating affects cell length, doubling time, and cell length stability in cyanobacteria by using mathematical models. We show that a cell subject to circadian gating grows for a long time, and gives birth to elongated daughter cells. These elongated daughter cells grow faster than the previous generation, as elongation speed is proportional to cell length and divide in a short time before the next gating. Hence, the distributions of doubling time and cell length become bimodal, as observed in experimental data. Interestingly, the average doubling time over the population of cells is independent of gating because the extension of doubling time by gating is compensated by its reduction in the subsequent generation. On the other hand, average cell length is increased by gating, suggesting that the circadian clock controls cell length. We then show that the decay rate of perturbation in cell length depends on the ratio of delay in division by the gating τ_G to the average doubling time τ₀ as [Formula: see text] . We estimated τ_G≈2.5, τ₀≈13.6 hours, and τ_G/τ₀≈0.18 from experimental data, indicating that a long doubling time in cyanobacteria maintains the decay rate similar to that of the adder mechanism. Thus, our analysis suggests that the acquisition of the circadian clock during evolution did not impose a constraint on cell size homeostasis in cyanobacteria.

Reconstructing Kinetic Models for Dynamical Studies of Metabolism using Generative Adversarial Networks

Kinetic models of metabolism relate metabolic fluxes, metabolite concentrations and enzyme levels through mechanistic relations, rendering them essential for understanding, predicting and optimizing the behaviour of living organisms. However, due to the lack of kinetic data, traditional kinetic modelling often yields only a few or no kinetic models with desirable dynamical properties, making the analysis unreliable and computationally inefficient. We present REKINDLE (Reconstruction of Kinetic Models using Deep Learning), a deep-learning-based framework for efficiently generating kinetic models with dynamic properties matching the ones observed in cells. We showcase REKINDLE's capabilities to navigate through the physiological states of metabolism using small numbers of data with significantly lower computational requirements. The results show that data-driven neural networks assimilate implicit kinetic knowledge and structure of metabolic networks and generate kinetic models with tailored properties and statistical diversity. We anticipate that our framework will advance our understanding of metabolism and accelerate future research in biotechnology and health.

Dynamic of a two-strain COVID-19 model with vaccination

COVID-19 is a respiratory illness caused by an ribonucleic acid (RNA) virus prone to mutations. In December 2020, variants with different characteristics that could affect transmissibility emerged around the world. To address this new dynamic of the disease, we formulate and analyze a mathematical model of a two-strain COVID-19 transmission dynamics with strain 1 vaccination. The model is theoretically analyzed and sufficient conditions for the stability of its equilibria are derived. In addition to the disease-free and endemic equilibria, the model also has single-strain 1 and strain 2 endemic equilibria. Using the center manifold theory, it is shown that the model does not exhibit the phenomenon of backward bifurcation, and global stability of the model equilibria are proved using various approaches. Simulations to support the model theoretical results are provided. We calculate the basic reproductive number R 1 and R 2 for both strains independently. Results indicate that - both strains will persist when R 1 > 1 and R 2 > 1 - Stain 2 could establish itself as the dominant strain if R 1 < 1 and R 2 > 1 , or when R 2 > R 1 > 1 . However, because of de novo herd immunity due to strain 1 vaccine efficacy and provided the initial stain 2 transmission threshold parameter R 2 is controlled to remain below unity, strain 2 will not establish itself/persist in the community.

Changes in Affective Network Variability Among Youth Treated for Anxiety Disorders

Cognitive behavioral therapy (CBT) has been shown to be an efficacious treatment for youth anxiety, but we need to know more about the process of change. Affective network variability, or the "spread" of positive and negative emotions activated across a given time period, has been found to be positively associated with anxiety disorder symptomatology, but it is not yet known how this construct changes in response to intervention or its association with anxiety-focused treatment outcomes. The present study used a dynamical systems framework to model ecological momentary assessment (EMA) data collected via a cellular telephone from 114 youth aged 9-14 years (M_age = 10.94, SD = 1.46) who were seeking treatment for a primary anxiety disorder. We examined patterns of affective network variability over time and across (a) CBT and (b) client-centered therapy (CCT) to determine whether affective network changes were specific to CBT or due to nonspecific factors. Associations between treatment outcomes and patterns of affect at pretreatment and over the course of the treatments were also examined. Results revealed significant decreases in affective network variability over the course of treatment for youth who received CBT, but not for youth who received CCT. Changes in affective network variability over the course of treatment did not predict treatment outcomes. Findings provide initial support for the dynamical systems approach to examining changes that occur during treatment. Implications and future research are discussed.

Altered Periodic Dynamics in the Default Mode Network in Autism and Attention-Deficit/Hyperactivity Disorder

BACKGROUND

Altered resting-state functional connectivity in the default mode network (DMN) is characteristic of both autism spectrum disorder (ASD) and attention-deficit/hyperactivity disorder (ADHD). Standard analytical pipelines for resting-state functional connectivity focus on linear correlations in activation time courses between neural networks or regions of interest. These features may be insensitive to temporally lagged or nonlinear relationships.

METHODS

In a twin cohort study comprising 292 children, including 52 with a diagnosis of ASD and 70 with a diagnosis of ADHD, we applied nonlinear analytical methods to characterize periodic dynamics in the DMN. Using recurrence quantification analysis and related methods, we measured the prevalence, duration, and complexity of periodic processes within and between DMN regions of interest. We constructed generalized estimating equations to compare these features between neurotypical children and children with ASD and/or ADHD while controlling for familial relationships, and we leveraged machine learning algorithms to construct models predictive of ASD or ADHD diagnosis.

RESULTS

In within-pair analyses of twins with discordant ASD diagnoses, we found that DMN signal dynamics were significantly different in dizygotic twins but not in monozygotic twins. Considering our full sample, we found that these patterns allowed a robust predictive classification of both ASD (81.0% accuracy; area under the curve = 0.85) and ADHD (82% accuracy; area under the curve = 0.87) cases.

CONCLUSIONS

These findings indicate that synchronized periodicity among regions comprising the DMN relates both to neurotypical function and to ASD and/or ADHD, and they suggest generally that a dynamical analysis of network interconnectivity may be a useful methodology for future neuroimaging studies.

How deterministic is the Earth ionosphere's response to solar activity?

This contribution is aimed at an analysis of the dynamics of free-electron density fluctuations in the ionospheric critical plasma frequency f0F2 by using some tools from the theory of nonlinear dynamical systems. The results suggest the existence of low-dimensional attractors that point to a characterization of the free electron density fluctuations in the f0F2 as a deterministic chaotic system. The study carried out focused on the response of the ionosphere to solar activity as a function of the ascending and descending phases of the solar cycle.