CyberSec Research

We investigate the transition to synchronization in adaptive multilayer networks with higher-order interactions both analytically and numerically in the presence of phase frustration ($\beta$). The higher order topology consists of pairwise and triadic couplings. The analytical framework for the investigation is based on the Ott-Antonsen ansatz which leads to a convenient low-dimensional model. Extensive bifurcation analysis of the low-dimensional model and the numerical simulation of the full networks are performed to explore the paths to synchronization. The combined analysis shows a complex dependence of the transition to synchronization on adaptation exponents, coupling strengths, phase lag parameter, and multilayer configuration. Various types of transitions to synchronization, namely continuous, tiered, and explosive, are exhibited by the system in different regions of the parameter space. In all the cases, a satisfactory match between the low-dimensional model and the numerical simulation results is observed. The origin of different transitions to synchronization is clearly understood using the low-dimensional model. Exploration of a wide region of the parameter space suggests that the phase frustration parameter inhibits tired as well as explosive synchronization transitions for fixed triadic coupling strength ($K_2$). On the other hand, discontinuous transition is promoted by the phase frustration parameter for fixed pairwise coupling strength ($K_1$). Moreover, the exponent of the adaptation function with the pairwise coupling decreases the width of the hysteresis, despite the dominance of the higher-order coupling for fixed $\beta$ and $K_2$. While, the exponent of the function adapted with higher-order coupling shows the opposite effect, it promotes bistability in spite of dominance of pairwise coupling strength for fixed $\beta$, and $K_1$.

Traditional machine learning approaches in physics rely on global optimization, limiting interpretability and enforcing physical constraints externally. We introduce the Hebbian Physics Network (HPN), a self-organizing computational framework in which learning emerges from local Hebbian updates driven by violations of conservation laws. Grounded in non-equilibrium thermodynamics and inspired by Prigogine/'s theory of dissipative structures, HPNs eliminate the need for global loss functions by encoding physical laws directly into the system/'s local dynamics. Residuals - quantified imbalances in continuity, momentum, or energy - serve as thermodynamic signals that drive weight adaptation through generalized Hebbian plasticity. We demonstrate this approach on incompressible fluid flow and continuum diffusion, where physically consistent structures emerge from random initial conditions without supervision. HPNs reframe computation as a residual-driven thermodynamic process, offering an interpretable, scalable, and physically grounded alternative for modeling complex dynamical systems.

Negative extensibility refers to the category of mechanical metamaterials having an unusual phenomenon where the system contracts upon expansion. The dynamic analysis of such systems is crucial for exploring the vibration isolation characteristics, forming the prime focus of the present study. Inspired by the Braess paradox, the mechanical model incorporates coupled tunable nonlinear spring stiffness properties (strain hardening and softening), which alternate when a certain displacement threshold is exceeded. This stiffness switching mechanism facilitates low frequency passive vibration isolation using the phenomenon of countersnapping instability. The vibration isolation characteristics resulting from the stiffness switching mechanism are investigated using time and frequency domain plots. Furthermore, the relationship between the stiffness switching mechanism and various system parameters is visualized using a three dimensional parametric space. The efficacy of the proposed system is evaluated by comparing it with the existing bistable systems, revealing superior performance in isolating high-amplitude vibrations. The proposed mechanism enhances the understanding of dynamic behaviors in critical structural elements for multistable mechanical metamaterials, providing insights and opportunities for innovative adaptive designs.

Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties, and allow for sampling from distinct ensembles. Here we introduce a new random graph model, inspired by assembly theory, and characterize the graphs it generates. We show that graphs generated using our method represent a diverse ensemble, characterized by a broad range of summary statistics, unexpected even in graphs with identical degree sequences. Finally we demonstrate that the distinct properties of these graphs are enabled by historical contingencies during the generative process. These results lay the foundation for further development of novel sampling methods based on assembly theory with applications to drug discovery and materials science.

Chemical Reaction Networks (CRNs) provide a powerful framework for modeling complex systems due to their compositionality, which makes them well-suited for analyzing interactions of subsystems within larger aggregate systems. This work presents a thermodynamic formalism for ranking CRN pathways under fixed throughput currents (fixed velocities of species flowing in and out of the system), where pathways represent subnetworks capable of performing the stipulated chemical conversion. We define a thermodynamic cost function for pathways derived from the large-deviation theory of stochastic CRNs, which decomposes into two components: an ongoing maintenance cost to sustain a non-equilibrium steady state (NESS), and a restriction cost, quantifying the ongoing improbability of neutralizing reactions outside the specified pathway. Applying this formalism to detailed-balanced CRNs in the linear response regime, we prove that the resistance of a CRN decreases as reactions are added that support the throughput current, and that the maintenance cost, the restriction cost, and the thermodynamic cost of nested pathways are bounded below by those of their hosting network. Extending the analysis far from equilibrium, we find that while cost is non-decreasing for progressively more restricted nested pathways near equilibrium, multimolecular CRN examples can be found that assign lower costs to more restricted pathways at far-from-equilibrium NESSs. The possibility to reduce the resistance of a network at fixed throughput, while also simplifying the network, may have implications for enzyme family evolution, in which novel reaction mechanisms may first lead to a proliferation of pathways through non-specific catalysis, but later selection for specificity may benefit both from species retention, and more efficient use of autocatalysts to improve throughput.

We utilize dynamical modes as features derived from Continuous Glucose Monitoring (CGM) data to detect meal events. By leveraging the inherent properties of underlying dynamics, these modes capture key aspects of glucose variability, enabling the identification of patterns and anomalies associated with meal consumption. This approach not only improves the accuracy of meal detection but also enhances the interpretability of the underlying glucose dynamics. By focusing on dynamical features, our method provides a robust framework for feature extraction, facilitating generalization across diverse datasets and ensuring reliable performance in real-world applications. The proposed technique offers significant advantages over traditional approaches, improving detection accuracy,

We investigate the finite-size effects on the dynamical evolution of the Kuramoto model with inertia coupled through triadic interactions. Our findings reveal that fluctuations resulting from the finite size drive the system toward a synchronized state at finite coupling, which contrasts with the analytical predictions {in thermodynamic limit} made for the same system. Building on the analytical calculations performed at the thermodynamic limit, we identify the origin of the synchronization transition that arises because of the finite size. We discover a power-law relationship between the network size and the critical coupling at which the first-order transition to synchronization occurs. Additionally, as inertia increases, there is a significant shift in the critical coupling toward higher values, indicating that inertia counteracts the effects caused by finite size.

We demonstrate that nonlocal coupling enables control of the collective stochastic dynamics in the regime of coherence resonance. The control scheme based on the nonlocal interaction properties is presented by means of numerical simulation on an example of coupled FitzHugh-Nagumo oscillators. In particular, increasing the coupling radius is shown to enhance or to suppress the effect of coherence resonance which is reflected in the evolution of the dependence of the correlation time and the deviation of interspike intervals on the noise intensity. Nonlocal coupling is considered as an intermediate option between local and global coupling topologies which are also discussed in the context of the coherence resonance control.

We investigate proteins within heterogeneous cell membranes where non-equilibrium phenomena arises from spatial variations in concentration and temperature. We develop simulation methods building on non-equilibrium statistical mechanics to obtain stochastic hybrid continuum-discrete descriptions which track individual protein dynamics, spatially varying concentration fluctuations, and thermal exchanges. We investigate biological mechanisms for protein positioning and patterning within membranes and factors in thermal gradient sensing. We also study the kinetics of Brownian motion of particles with temperature variations within energy landscapes arising from heterogeneous microstructures within membranes. The introduced approaches provide self-consistent models for studying biophysical mechanisms involving the drift-diffusion dynamics of individual proteins and energy exchanges and fluctuations between the thermal and mechanical parts of the system. The methods also can be used for studying related non-equilibrium effects in other biological systems and soft materials.

The Kuramoto model, a paradigmatic framework for studying synchronization, exhibits a transition to collective oscillations only above a critical coupling strength in the thermodynamic limit. However, real-world systems are finite, and their dynamics can deviate significantly from mean-field predictions. Here, we investigate finite-size effects in the Kuramoto model below the critical coupling, where the infinite-size theory predicts complete asynchrony. Using a shot-noise approach, we derive analytically the power spectrum of emergent collective oscillations and demonstrate their dependence on the coupling strength. Numerical simulations confirm our theoretical results, though deviations arise near the critical coupling due to nonlinear effects. Our findings reveal how finite-size fluctuations sustain synchronization in regimes where classical mean-field theories fail, offering insights for applications in neural networks, power grids, and other coupled oscillator systems.

Extreme weather events are projected to intensify global migration, increase resource competition, and amplify socio-spatial phenomena, including intergroup conflicts, socioeconomic inequalities, and unplanned displacements, among others. Addressing these challenges requires consolidating heterogeneous data to identify, estimate, and predict the dynamical process behind climate-induced movements. We propose a novel hybrid approach to reconstruct hazard-induced displacements by analysing the statistical properties of stochastic walks that explore the spatial network constructed from real movements. The likely trajectories produced by the walker inform the typical journey experienced by individuals, helping identify likely hazards encountered when fleeing high-risk areas. As a proof of concept, we apply this method to Somalia's detailed displacement tracking matrix, containing 20,220 movements dating from February 8th to June 18th, 2025. We reconstruct the likely routes that displaced persons could have taken when fleeing areas affected by conflict or climate hazards. We find that individuals using the most likely paths based on current flows would experience mainly droughts and conflicts, while the latter become less prominent at every next step. We also find that the probability of conflict and drought across all trajectories is widely dispersed, meaning that there is no typical exposure. This work provides an understanding of the mechanisms underlying displacement patterns and a framework for estimating future movements from areas expected to face increasing hazards. We also provide avenues to develop tools that can support policymakers implementing proactive responses and early interventions.

People make strategic decisions multiple times a day. We act strategically in negotiations, when we coordinate our actions with others, or when we choose with whom to cooperate. The resulting dynamics can be studied with evolutionary game theory. This framework explores how people adapt their decisions over time, in light of how effective their strategies have proven to be. A crucial quantity in respective models is the strength of selection. This quantity regulates how likely individuals switch to a better strategy when given the choice. The larger the selection strength, the more biased is the learning process in favor of strategies with large payoffs. Therefore, this quantity is often interpreted as a measure of rationality. Traditionally, most models take selection strength to be a fixed parameter. Instead, here we allow the individuals' strategies and their selection strength to co-evolve. The endpoints of this co-evolutionary process depend on the strategic interaction in place. In many prisoner's dilemmas, selection strength increases indefinitely, as one may expect. However, in snowdrift or stag-hunt games, it can either converge to a finite value, or we observe evolutionary branching altogether - such that different individuals arrive at different selection strengths. Overall, this work sheds light on how evolution might shape learning mechanisms for social behavior. It suggests that boundedly rational learning is not only a by-product of cognitive constraints. Instead it might also evolve as a means to gain strategic advantages.

We present a strong theoretical foundation that frames a well-defined family of outer-totalistic network automaton models as a topological generalisation of binary outer-totalistic cellular automata, of which the Game of Life is one notable particular case. These "Life-like network automata" are quantitatively described by expressing their genotype (the mean field curve and Derrida curve) and phenotype (the evolution of the state and defect averages). After demonstrating that the genotype and phenotype are correlated, we illustrate the utility of these essential metrics by tackling the firing squad synchronisation problem in a bottom-up fashion, with results that exceed a 90% success rate.

While information-theoretic quantities, such as transfer entropy, have been widely adopted to infer causal relationships in collective systems, a critical gap exists: the absence of quantitative evidence directly linking information-theoretic quantities to a physically defined influence. This letter addresses this gap by proposing a modified Vicsek model that enables the calculation of a physically interpretable influence grounded in the angular interactions between particles. Averaged pairwise influences can serve as new order parameters to indicate collective phase transitions. We reveal quantitative relations between information, represented by transfer entropy, and average influence in pairwise and collective interactions. We test three typical methods of partial information decomposition and find that the method based on intrinsic mutual information gives the most appropriate interpretation. Overall, this work provides a model system for quantitative studies of influence and information in complex systems.

Inspired by the growth dynamics of the protist \textit{Physarum polycephalum}, we use a formalism that describes adaptive incompressible Hagen-Poiseuille flows on channel networks to identify graphs connecting different nodes within Euclidean space. These graphs are either suboptimal or optimal in terms of their length. Occasionally, we obtain graph tree configurations that are topologically equivalent to Steiner trees. This approach is employed to design communication systems, such as railway networks, motorways, or fibre webs. As a proof of concept, we explicitly apply this framework to the Portuguese railway network.

St. Francis of Assisi (1181/82-1226) famously called money the devil's dung, and indeed money is often associated with greed, inequality, and corruption. Drawing on Nowak's five rules for the evolution of cooperation, we argue here that money promotes the formation of circuits of generalized reciprocity across human groups that are fundamental to social evolution. In an evolutionary tournament, we show that money exchange is an evolutionary stable strategy that promotes cooperation without relying on the cognitive demands of direct reciprocity or reputation mechanisms. However, we also find that excessive liquidity can be detrimental because it can distort the informational value of money as a signal of past cooperation, making defection more profitable. Our results suggest that, in addition to institutions that promoted trust and punishment, the emergence of institutions that regulated the money supply was key to maintaining generalized reciprocity within and across human groups.

In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network theory addresses this by considering variables defined on nodes, links, triangles, and higher-order simplices, called topological signals (or cochains). Moreover, topological signals of different dimensions can interact through the Dirac-Bianconi operator, which allows coupling between topological signals defined, for example, on nodes and links. Such interactions can induce various dynamical behaviors, for example, periodic oscillations. The oscillating system consists of topological signals on nodes and links whose dynamics are driven by the Dirac-Bianconi coupling, hence, which we call it Dirac-Bianconi driven oscillator. Using the phase reduction method, we obtain a phase description of this system and apply it to the study of synchronization between two such oscillators. This approach offers a way to analyze oscillatory behaviors in higher-order networks beyond the node-based paradigm, while providing a ductile modeling tool for node- and edge-signals.

Different collective behaviors emerging from the unknown have been examined in networks of mobile agents in recent years. Mobile systems, far from being limited to modeling and studying various natural and artificial systems in motion and interaction, offer versatile solutions across various domains, facilitating tasks ranging from navigation and communication to data collection and environmental monitoring. We examine the relative mobility between clusters, each composed of different elements in a multi-clusters network-a system composed of clusters interconnected to form a larger network of mobile oscillators. Each mobile oscillator exhibits both external (i.e., position in a 2D space) and internal dynamics (i.e., phase oscillations). Studying the mutual influence between external and internal dynamics, often leads the system towards a state of synchronization within and between clusters. We show that synchronization between clusters is affected by their spatial closeness. The stability of complete synchronization observed within the clusters is demonstrated through analytical and numerical methods.