Chaos: An Interdisciplinary Journal of Nonlinear Science

Despite extensive study of cellular mechanisms underlying long-term potentiation, no single specific protein or gene has been identified which encodes an individual unit of information, or memory bit. Indeed, the brain engram remains a knowledge gap. The theory of exclusion led us to cancel one-by-one several unrealistic biological options, suggesting that the explanation resides somewhere else. Superposition of up to concentric 300 myelin layers, spiraled, and highly compacted wrapping a single axon and each wrap could host hundreds to thousands of niches, as memory cells, collectively consisting of a massive array of cells. The disjointed 3D spatial superposition allows storage of charges, nodes not facing from a layer to next. The thickness of a single myelin layer ranges from 7.0 to 20 nm. The dimension scale is approximately the exact dimensions of the charge trap, the tunnel and dielectric also equipping current AI microchips. Stored charges are positive ions, with similar effect whether charges are negative or positive charges creating an electromagnetic field. To write data, following an action potential, this voltage applies to the control gates of the myelin layers producing an ionic charge injection. This causes charges to gain energy and tunnel through the myelin layer across Ranvier nodes, via quantum tunneling, and deep into the concentric myelin multilayers. This is creating an insulated trapping of K+ ions isolated from the system. In a long white matter tract bundle, the near-perfect isolation of millions of axons within compressed myelin wrap-ion channel K+/Na+ systems provides quantum coherence and precision of asynchronous firing property. The injected ionic charges (K+) become physically stuck in traps within the myelin layers. The K+ ions may not move freely, completely trapped after AP ceases. Mirroring a single-bit, single-level-cell, a trapped ionic charge (ions K+) may represent a 1, while an empty cell (absence of K+) represents a 0. The trial-and-error process, with a Bayesian inference which may have also been the core evolution of the learning human brain. Based on selected mathematical equations, we analyzed the general scheme on how deep learning may be embedded in the brain

Thymosin {beta}4 (T{beta}4) is a conserved acidic polypeptide with 43-amino acids participating in multiple pathophysiological processes. In this study in vivo effects of T{beta}4 on liver regeneration are investigated in carbon-tetrachloride (CCL4) induced rodent animal liver jury models. Results illustrate that exogenous T{beta}4 treatment significantly reduced CCL4-rendered liver necrosis around central vein. At 48 hours after CCL4 insults hepatocytes proliferation occur mainly around the periportal area, while hepatocytes proliferation around the necrosis area is prominently increased by exogenous T{beta}4 treatment. The holistic proliferation level of liver tissues are also enhanced by exogenous T{beta}4. Hepatocyte proliferation activities negatively correlate with the necrosis extent of the liver tissue. These results suggested firstly exogenous T{beta}4 treatment could enhance liver regeneration and exhibit prosperous potential for application in clinical conditions such as liver transplantation.

We develop a theoretical proposal linking vacuum stability and brain dynamics through superconductivity-inspired coherence, symmetry reduction, and the thermodynamic stabilization of low-entropy regimes. We take an unbroken SU(3) structure as a candidate stable residue of the low-temperature vacuum. At the neural level, we formulate a coarse-grained analog in which a two-fluid model with dissipative and coherence-supporting components describes brain dynamics. Specifically, the coherence-supporting component is proposed as a possible basis for the efficient binding and integration required to sustain a stable, unified conscious state. The proposal offers a common geometric language for relating physics and neuroscience with falsifiable signatures in coherence and state-dependent transitions. The main technical contribution is a computational algebraic model of conscious-state dynamics, where neural data are mapped to reconstructed state trajectories. Effective generators are inferred from those trajectories, and the two-fluid split is tested as a Cartan-root decomposition of su(3), with a rank-two commuting sector for coherence-preserving balance and six root directions for state transitions. This structure can be tested on neural data and contrasted with alternative dynamical models.

Abnormal states such as erroneous behaviors are generally difficult to represent from neural data. However, such states are also known to have specific spatiotemporal features, indicating a feasibility of developing a method to focus on them. If a method can highlight these spatiotemporal features, it may effectively represent such abnormal states, helping evaluate abnormal brain functions. In the present study, we proposed the hierarchy of supported modules (HSM) to highlight spatiotemporal features that can represent abnormal states. HSM spatiotemporally transforms multidimensional neural time-series based on their spatiotemporal context. We evaluated HSM through decoding and similarity analyses using multiple publicly available datasets. In the HSM results, decoding accuracies were higher for erroneous behaviors than for normal behaviors, and similarities were lower between erroneous behaviors and normal behaviors than between normal behaviors, demonstrating the ability of HSM to capture the spatiotemporal features of erroneous behaviors. Surprisingly, many parts of these results were also present even before HSM learning, showing the virtue of HSM as a simple-to-use method. The proposed HSM method may help elucidate the mechanisms underlying erroneous behaviors.

The aim of this paper is to model homeless accommodation settings to investigate how vaccination mitigates the outbreaks, highlighting the importance of vaccination in vulnerable settings. We estimate the daily per capita contact rate with wider community, the internal transmission rate, and the achieved vaccine coverage. We present stochastic simulation of the final size of disease outbreaks given choices of internal and external transmission. We conclude that vaccine that has effect in reducing transmission will mitigate the outbreak in homeless hostels but it will have better results when the household population has large vaccination coverage, which may lead to more cost from the health economic perspective.

AO_SCPLOWBSTRACTC_SCPLOWCell fate decisions are driven by gene regulatory networks (GRNs). While the mutually inhibitory toggle switch effectively models binary fate decisions, fully connected inhibitory networks with more than two nodes fail to capture multi-fate decisions due to the low prevalence of "single high states", where only a single master regulator is highly expressed. The goal of this study is to find network structures that support all single high states. We find that the only network that attains the highest possible prevalence of all single high states within the set of monotone Boolean (MB) models is completely disconnected. Since biological networks typically require connectivity, we investigate network structures that support equipotency, where all single high states have equal prevalence within MB models. Finally, we characterize the networks that support multistability between all single high states, finding that it is possible only in networks in which each node either has self-activations or is inhibited by every other network node. Our findings provide a theoretical framework for understanding the network design principles that can support simultaneous differentiation into multiple distinct cell types.

We develop a mathematical model of Rift Valley Fever integrating mosquito vectors, ruminants, and humans, based on an SEIR-type structure with vertical transmission in vectors. Local data from the Sudanian and especially the Sahelian zones are used to capture the impact of climatic variations on mosquito population dynamics. The mathematical analysis establishes the models positivity, determines the basic reproduction number R0, and demonstrates the local and global stability of the disease-free equilibrium. Sensitivity analysis (PRCC) highlights the most influential parameters, while the stochastic approach using a continuous-time Markov chain confirms the major role of seasonal rainfall. Numerical simulations reveal a peak in animal and human infections around the 9th month, correlating with periods of heavy rainfall. This model provides a relevant tool for surveillance and prevention within a "One Health" approach in Chad.

Malaria and diabetes represent two globally significant metabolic disorders whose co-occurrence leads to complex, poorly understood pathophysiological interactions. Plasmodium infection disrupts glucose homeostasis through parasite-driven glucose consumption, inflammatory cytokine production, and pancreatic /{beta}-cell dysfunction, while diabetes impairs host immunity and increases malaria susceptibility. To date, no mathematical framework has captured the bidirectional coupling between these systems. Here we extend the insulin-glucose-glucagon (IGG) model of Dalton et al.\ (2026) by introducing a fourth state variable representing parasite load, incorporating malaria-induced insulin suppression, parasite-driven glucose consumption, inflammatory gluconeogenesis, bidirectional glucagon dysregulation, and insulin-dependent immune enhancement of parasite clearance. We establish positivity, boundedness, existence and uniqueness of steady states, local stability via Routh-Hurwitz criteria, global stability via Lyapunov functions, and sensitivity analysis of parameters driving hypoglycemia risk. Numerical simulations characterise the model across healthy, diabetic, and co-infected states. They show that parasite-driven glucose consumption and inflammatory gluconeogenesis act antagonistically on circulating glucose, that insulin-enhanced immunity lowers peak parasitemia through a saturating clearance term, and that increasing the half-life of exogenous insulin raises hypoglycemia risk in all host states. These mechanisms provide testable hypotheses for the clinical management of malaria-diabetes patients and identify potential therapeutic targets (TNF- blockade, glucagon analogues) for mitigating co-infection morbidity.

Objectives; The role of nuclear receptor subfamily 4, group A, member 3 (NR4A3) in hepatic steatosis, inflammation, and insulin resistance (IR) within the context of metabolic dysfunction-associated steatotic liver disease (MASLD) remains largely underexplored. Consequently, this study aimed to examine NR4A3's impact on MASLD and the potential underlying mechanisms. Methods; We aimed to elucidate the functional role of NR4A3 in MASLD through its knockdown in cell culture and animal models. To establish the cell culture model of MASLD, LO2 cells were treated with free fatty acids (FFAs), while male C57BL/6 mice were fed a high-fat diet (HFD) to create the animal model. NR4A3 knockdown was achieved using specific short hairpin RNA (NR4A3-shRNA) in the mice model and three small interfering RNAs (NR4A3-siRNAs) in the cell culture model. The lipids content, fatty acid synthesis, inflammatory factors, and IR were then assessed with and without NR4A3 knockdown. Furthermore, the underlying mechanism through which NR4A3 exerts its influence was explored by analyzing the interaction between NR4A3 and activating transcription factor 3 (ATF3). Results: In the cell culture experiments, the knockdown of NR4A3 significantly decreased the lipids content, fatty acid synthesis, and inflammatory factors in the LO2 cells treated with FFAs in the NR4A3-shRNA group compared with those in the NC-shRNA control group. In the animal model experiments, NR4A3 knockdown in the HFD male C57BL/6 mice significantly ameliorated HFD-induced hepatic steatosis, inflammation, and IR. Mechanistically, the knockdown of NR4A3 downregulated the expression and transcriptional activity of ATF3, resulting in an impaired ATF3 function. ATF3 overexpression significantly reversed lipid accumulation decline and reduced inflammation after NR4A3 knockdown. Conclusion: The downregulation of NR4A3 alleviates MASLD by modulating ATF3, suggesting this may be a promising therapeutic target.

Every brain must adapt to an unpredictable world, yet individuals differ in how readily they learn. Theoretical work suggests that learning is fastest when a system, whether biological or synthetic, is initialized in a state close to instability - i.e., near criticality - because critical dynamics are imbued with a diverse repertoire of patterns and multi-scale correlations. Here, we empirically estimate distance to criticality in the brain and show that it predicts the rate of adaptability underlying learning, neuronal tuning, and general intelligence. In mouse motor cortex, proximity to criticality forecasts learning rate of two future complex tasks: prey capture hunt and ladder crossing. In contrast, distance to criticality predicted neither an animal's naive ability nor its asymptotic skill - isolating the rate of learning itself. In visual cortex of young ferrets, proximity to criticality predicts how strongly experience reshapes neural tuning. In human frontal cortex, it correlates with general cognitive ability. A minimal recurrent network model reproduced these results and offers a mechanism: proximity to criticality defines the timescale over which a system can learn from its past experiences, directly setting the rate of learning. A single dynamical property can account for the capacity to learn, from artificial networks to the mammalian brain.

In this paper, we propose a new model to estimate the impact of an intervention on human hosts of a vector-borne infection, such as dengue, which occurs in yearly outbreaks of different magnitudes. The model applies to these outbreaks and, in fact, is independent of their intensity, that is, it does not require the steady-state assumption. The model takes as input the officially reported age-dependent number of cases of a vector-borne infection. It is deterministic and does not account for stochasticity. Our objective is to estimate the impact of the intervention (the efficacy), and we rely on the observed fact that the age distribution of the proportion of cases of the infections transmitted by the same vector is independent of both the intensity of transmission and the geographic area studied, at least for Brazilian regions. This finding is highlighted in the main text and forms the basis of our calculations. A hypothetical intervention is simulated using a dengue vaccine, which allows the determination of the optimal strategy for a vaccination campaign.

Principles of collective motion are now well established, though research has largely focused on homogeneous groups. Heterogeneity is widespread in animal groups, e.g. arising from sex, size or even species, raising a central question: can collective behaviour emerge when individuals have distinct behaviours? Here, we combine experiments and modelling to investigate mixed-species collective motion using two closely related fish species, rosy barbs and tiger barbs. In conspecific groups, both species exhibit collective motion, but they differ strikingly in their intrinsic movement: tiger barbs exhibit slowand fast-swimming, whereas rosy barbs display fast swimming only. Despite this difference, these species readily form mixed-species schools where the slow swimming speed of tiger barbs disappears, and the collective motion is dominated by a single fast-swimming mode. We develop an individual-based model incorporating local interactions involving speed matching. Our model demonstrates that bimodal speed in conspecific schools of tiger barbs is an emergent property that is lost in mixed-species groups. Additionally, despite high cohesion, we observe spatial sorting of the two species within the mixed-species groups, which our model explains through differences in inter- and intra-specific interactions. Our results provide experimental evidence that canonical principles of collective motion extend to heterogeneous mixed-species groups.

Flexible brain network dynamics unfold on several timescales, despite being constrained by a relatively static structural connectome. Recent cross-species evidence has described infra-slow network modulation, <0.1 Hz, through two distinct but fundamentally aligned frameworks: transitions between states of integration and segregation identified by high and low global coherence respectively, and periodic transitions between internally and externally oriented attention indexed by the dynamic modulation of alpha power. Here we propose that these infra-slow, structured fluctuations in network engagement stem from a common underlying dynamical motif. Using a network of coupled oscillators embedded in human and macaque empirical connectomes, we show that topological features of brain organization such as modularity, hierarchy and intrinsic dynamical asymmetries naturally give rise to low-frequency collective modes that could nest high frequency states of neuronal communication. These 'breathing' dynamics, analogous to beat phenomena in acoustic systems, produce infra-slow fluctuations in global synchrony. Disrupting the connectome topology abolishes such slow coherence oscillations, indicating their dependence on network topology. Furthermore, analytical results from reduced oscillator models reveal how small frequency differences between weakly coupled modules generate slow coherence oscillations, highlighting the importance of dynamical asymmetry. Finally, how neuromodulatory inputs can tune these emergent timescales is discussed, providing a mechanistic link between structural architecture and the dynamic regulation of large-scale brain function.

Biomolecular condensates are widespread cellular self-assembled structures with essential functions. There are suggestions of condensates formed by different proteins being near criticality. However, systematic investigation of the criticality of condensates is absent, and critical exponents defining their universality class have not been found. Here, using long-time simulations, we show that condensates exhibit typical critical phenomena, including scale-free spatiotemporal correlations, critical slowing down, divergence of correlation length and dynamic scaling. From these scaling behaviors, a set of critical exponents is determined. Based on dynamic critical exponent, diverse condensates can be divided into two distinct universality classes, arising from differences in their molecular components and interaction types.

Understanding how network connectivity shapes neural representations is central to systems neuroscience. While dimensionality reduction methods uncover low-dimensional manifold structure in population recordings, a rigorous framework connecting manifold geometry to network mechanisms and information encoding remains lacking. We develop a differential geometric approach for analyzing neural manifolds in rate-based recurrent networks receiving tuned feedforward inputs. We derive expressions for the pullback metric of neural manifolds, showing how input tuning curves, feedforward and recurrent synaptic connectivity shape manifold geometry. Critically, we establish that the Fisher information matrix at steady states also has the structure of a pullback metric, directly linking intrinsic manifold geometry to stimulus discriminability and information encoding. For noise with slow temporal correlations propagated through the network, we show that recurrent effects on information geometry cancel: Fisher information depends only on the feedforward connectivity. Thus, feedforward connectivity critically determines representational geometry. As an example, we demonstrate that the representation of space by a module of hexagonal grid cells is approximately isometric for random distribution of grid phases. Moreover, a linear feedforward transformation can map spatially random input tuning curves into a population of hexagonal grid cells, forming a toroidal manifold. Thus, feedforward connectivity alone can generate structured spatial representations without requiring carefully tuned recurrent connectivity or continuous attractor dynamics. Recurrent connectivity, however, is shown to improve stimulus encoding under fast noise, thereby implementing a selective noise reduction.

Compartmental models of infectious disease transmission make assumptions about human behaviors. Specifically, they parameterize interactions across population groups, assumed to have distinct epidemiologically-relevant behavioral patterns, primarily through contact matrices stratified by demographic variables such as age, gender, or socioeconomic status. Although such demographic characteristics are readily measurable, they may inadequately capture the social and psychological forces that govern protective behaviors. Drawing on 20 waves of a national survey conducted throughout the COVID-19 pandemic in the United States, we show that institutional trust - particularly trust in public health agencies, physicians, and hospitals - is a dominant predictor of protective behavior adoption. For mask wearing during periods of strongest pandemic activity, for example, institutional trust explains more behavioral variance across population groups than age, income, education, and partisan affiliation combined. In unadjusted analyses, the difference in protective behavior adoption between individuals with the highest and lowest trust in the CDC was four- to six-fold larger than the corresponding differences by age, income, or educational attainment, and exceeded the difference between Democratic and Republican respondents. This association was institutionally specific (e.g., the relationship attenuates for trust in banks), and behaviorally specific (e.g., trust in the CDC is associated with protective behaviors but not visiting a doctor). The latter suggests that trust modifies voluntary compliance with public health recommendations rather than access to or use of healthcare. We conclude that compartmental models of disease transmission would be substantially improved by incorporating institutional trust as a stratifying variable. We additionally offer a trust-integrated mathematical modeling framework and recommendations for the data infrastructure needed for its implementation.

Cancer remains a global health challenge requiring sophisticated understanding of tumor-immune dynamics for effective treatment design. Mathematical oncology has emerged as a rapidly evolving interdisciplinary field that uses mathematical models to enhance our understanding of cancer dynamics, including tumor growth, metastasis, and treatment response. This paper presents a comprehensive multiscale framework integrating patient-specific data, machine learning, and optimal control for personalized immunotherapy design. We develop a hybrid model that combines deterministic dynamics with stochastic elements and time delays, capturing the inherent variability and temporal lags in biological processes. The model incorporates biologically realistic Holling Type-II functional responses and is validated against longitudinal clinical data from 100+ cancer patients and patient-derived organoid experiments. Using deep neural networks with Bayesian regularization, we learn patient-specific parameter distributions from clinical biomarkers and predict treatment responses with high accuracy. Our optimal control framework, incorporating clinical constraints and toxicity limits, generates personalized treatment protocols that stabilize otherwise unstable dynamics. The framework establishes a new paradigm for precision immuno-oncology, bridging mathematical theory, computational methods, and clinical practice. Author summaryCancer remains one of the leading causes of death worldwide, and the immune system plays a crucial role in controlling tumor growth. However, the complex interactions between tumor cells and immune cells make it difficult to predict how individual patients will respond to immunotherapy. In this work, we develop a mathematical framework that integrates patient-specific data, machine learning, and optimal control to design personalized immunotherapy strategies. Our model captures the realistic dynamics of tumor-immune interactions by incorporating biologically relevant features such as time delays (representing immune response lags) and stochastic effects (representing biological variability). Using deep learning, we estimate patient-specific parameters from clinical biomarkers, enabling personalized predictions of treatment outcomes. We validate our framework against data from over 100 cancer patients and patient-derived organoid experiments, demonstrating excellent agreement. Our optimal control approach generates personalized treatment protocols that stabilize otherwise unstable tumor dynamics, achieving 78% tumor reduction compared to 52% for standard-of-care protocols. These findings suggest that therapies targeting immunological thresholds may be as important as those directly killing tumor cells, providing a new perspective for immunotherapy design. This framework bridges mathematical theory, computational methods, and clinical practice, offering a pathway toward truly personalized cancer treatment.

Although neural activity often evolves along low-dimensional manifolds, such descriptions do not explain the dynamical mechanisms that generate, constrain, and stabilize computation. Identifying these mechanisms is essential for predicting responses to perturbations, understanding generalization to untrained signals, and explaining how similar computations arise from distinct circuit implementations. Here we use recurrent neural networks trained on an interval timing task as a model system to uncover the dynamical mechanisms of neural computation. We show that, despite converging to highly diverse attractor architectures, trained networks share a conserved transient dynamics. During learning, networks self-organize near dynamical bifurcations, forming structured ghost sets of slow points characterized by graded spectra of near-zero eigenvalues. These slow sets form a dynamical scaffold that constrains trajectory evolution. Inputs transiently reconfigure the vector field and reposition activity within this scaffold, while the underlying slow set governs subsequent dynamics. As a result, temporal computation is implemented through structured transient evolution rather than convergence to fixed points or persistent activity states. The extent of the slow sets predicts generalization to unseen temporal intervals, and networks lacking such organization fail to extrapolate reliably. To test sufficiency, we construct a minimal dynamical system endowed with analogous slow set geometry that reproduces interval timing without learning, providing a benchmark for identifying the essential dynamical ingredients of temporal computation. Together, these results identify structured slow transients as a candidate dynamical mechanism for temporal computation, provide a mechanistic interpretation of slow low-dimensional manifolds as emergent consequences of underlying state-space structure, and suggest that computational capacity in near-critical systems arises from the organization of transient flow rather than attractor states alone.

Many neural recordings have revealed low-dimensional sets of behaviorally relevant variables encoded within large-scale neural activity patterns. However, dimensionality reduction analyses alone cannot yield causal explanations for how networks stably implement computations that are resilient to the substantial variability of single neuron dynamics. Further, existing methods for dimensionality reduction often rely on simplifying assumptions about network structure that limit their applicability and explanatory power. To provide a theoretical framework describing the dynamics of low-dimensional computation in high-dimensional neural networks, here we introduce the concept of latent processing units (LPUs), which are architecture-agnostic computational elements operating within biological neural circuitry. Six theorems governing coding and computation by LPUs collectively provide explanations for a range of common biological findings: low-dimensional sets of coding variables can generate high-dimensional neural dynamics; many neurons have activity patterns that represent behaviorally relevant variables but exert little influence on downstream circuits; linear readouts of neural population activity commonly permit near-optimal decoding; the drift of neural representations is often substantial even while network computations remain intact. Overall, our treatment of LPUs, as enacted in network dynamics, unifies the geometric and dynamical views of neural computation under a joint framework and provides systems neuroscience with a causal account of how the brain executes reliable computations.

Viral infection can coactivate interferon (IFN)--JAK/STAT1 signalling and the p53--Mdm2 stress-response pathway, two modules that jointly shape antiviral defence and cell-fate decisions. Here, we focus on viral infection contexts capable of inducing genotoxic stress associated with DNA double-strand breaks, thereby triggering oscillatory or sustained p53--Mdm2 dynamics. Whether p53 acts merely as a parallel stress pathway, or actively reshapes how an activated JAK/STAT1 response is temporally decoded and functionally routed, remains unclear. We develop a coupled ordinary [ndash]differential-equation model linking an IFN{gamma}centred JAK/STAT1 core, a p53--Mdm2 module, downstream antiviral and apoptotic effectors, and a coarse-grained viral-burden layer, with p53 regulation placed downstream of STAT1 activation. We find that p53 does not simply increase nuclear STAT1 availability; it redistributes the response towards DNA-bound STAT1 persistence, transcriptional memory and STAT1-driven feedback, producing a persistence--recovery trade-off in which prior p53 stress prolongs the transcriptionally active STAT1 state but delays re-inducibility after repeated IFN stimulation. When IFN and p53-associated stress are both driven by viral burden, p53 is not a uniform amplifier of host defence: p53 preactivation strengthens the upstream memory layer, but downstream effectors buffer rather than mirror this priming. The model further separates antiviral-state engagement from realised viral control: strong effector activation does not guarantee suppression of poorly sensitive viral classes, whereas sensitive viral classes can be cleared before apoptosis. The origin of the stimulus also matters: exogenous IFN or p53 stimulation allows us to assess the host's intrinsic response capacity, whereas virus-induced IFN and p53 stress remain coupled to viral persistence. Persistent viral burden thus emerges as the dynamical link between IFN induction, p53 stress-memory, antiviral maintenance, viral control and the choice between JAK/STAT--IRF1-associated, p53-autonomous or dual apoptotic routing.