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The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations (RDPDEs). Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas, A. Mielke: Modeling of chemical reactions systems with detailed balance using gradient structures. J. Stat. Phys. (181), 2257-2303 (2020)] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.

We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering toward a weighted average heading. We consider the class of so-called p p -alignment hydrodynamics, based on 2 p 2p -Laplacians and weighted by a general family of symmetric communication kernels. The main new aspect here is the long-time emergence behavior for a general class of pressure tensors without a closure assumption, beyond the mere requirement that they form an energy dissipative process. We refer to such pressure laws as “entropic”, and prove the flocking of p p -alignment hydrodynamics, driven by singular kernels with a general class of entropic pressure tensors. These results indicate the rigidity of alignment in driving long-time flocking behavior despite the lack of thermodynamic closure.

Coherence resonance (CR), stochastic synchronization (SS), and spike-timing-dependent plasticity (STDP) are ubiquitous dynamical processes in biological neural networks. Whether there exists an optimal network and STDP configuration at which CR and SS are both pronounced is a fundamental question of interest that is still elusive. We expect such a configuration to enable the brain to make synergistic and optimal use of these phenomena to process information efficiently. This paper considers a small-world network of excitable Hodgkin-Huxley neurons driven by channel noise and STDP with an asymmetric Hebbian time window. Numerical results indicate specific network topology and STDP parameter intervals in which CR and SS can be simultaneously enhanced. Our results imply that an optimally tuned inherent background noise, STDP rule, and network topology can play a constructive role in enhancing both the time precision of firing and the synchronization in neural systems., 17 pages, 12 figures, 71 references

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales in very different systems and scientific disciplines, from physics, materials science and robotics to biology, geophysics andastronomy. Recent research has highlighted how self-organisation can be both mediated and controlled by confinement. Confinement is an action over a system that limits its units’ translational and rotational degrees of freedom, thus also influencing the system’s phase space probability density; it can functionas either a catalyst or inhibitor of self-organisation. Confinement can then become a means to actively steer the emergence or suppression of collective phenomena in space and time. Here, to provide a common framework and perspective for future research, we examine the role of confinement in the self-organisation of soft-matter systems and identify overarching scientific challenges that need to be addressed to harness its full scientific and technological potential in soft matter and related fields.By drawing analogies with other disciplines, this framework will accelerate a common deeper understanding of self-organisation and trigger the development of innovative strategies to steer it using confinement, with impact on, e.g., the design of smarter materials, tissue engineering for biomedicineand in guiding active matter.

A nonlinear electronic circuit comprising of three nodes with a feedback loop is analyzed. The system has two stable states, a uniform state and a sinusoidal oscillating state, and it transitions from one to another by means of a Hopf bifurcation. The stability of this system is analyzed with nonlinear equations derived from a repressilator-like transistor circuit. The apparatus is simple and inexpensive, and the experiment demonstrates aspects of nonlinear dynamical systems in an advanced undergraduate laboratory setting.

A living cell uses long tubular appendages for locomotion and sensory purposes. Hence, assembling and maintaining a protrusion of correct length is crucial for its survival and overall performance. Usually the protrusions lack the machinery for the synthesis of building blocks and imports them from the cell body. What are the unique features of the transport logistics which facilitate the exchange of these building blocks between the cell and the protrusion? What kind of `rulers' and `timers' does the cell use for constructing its appendages of correct length on time? How do the multiple appendages coordinate and communicate among themselves during different stages of their existence? How frequently do the fluctuations drive the length of these dynamic protrusions out of the acceptable bounds? These questions are addressed from a broad perspective in this review which is organized in three parts. In part-I the list of all known cell protrusions is followed by a comprehensive list of the mechanisms of length control of cell protrusions reported in the literature. We review not only the dynamics of the genesis of the protrusions, but also their resorption and regrowth as well as regeneration after amputation. As a case study in part-II, the specific cell protrusion that has been discussed in detail is eukaryotic flagellum (also known as cilium); this choice was dictated by the fact that flagellar length control mechanisms have been studied most extensively over more than half a century in cells with two or more flagella. Although limited in scope, brief discussions on a few non-flagellar cell protrusions in part-III of this review is intended to provide a glimpse of the uncharted territories and challenging frontiers of research on subcellular length control phenomena that awaits vigorous investigations., Preprint of a Review Article; comments are welcome

The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions take place. Hence, we replace the classical coupling law with a very general coupling function involving higher-order terms. Furthermore, we allow for multiple populations of oscillators interacting with each other through a very general law. In our analysis, we focus on the characteristic system and the mean-field limit of this generalized class of Kuramoto models. While there are several works studying particular aspects of our program, we propose a general framework to work with all three aspects (higher-order, multi-population, and mean-field) simultaneously. Assuming identical oscillators in each population, we derive equations for the evolution of oscillator populations in the mean-field limit. First, we clarify existence and uniqueness of our set of characteristic equations, which are formulated in the space of probability measures together with the bounded-Lipschitz metric. Then, we investigate dynamical properties within the framework of the characteristic system. We identify invariant subspaces and stability of the state, in which all oscillators are synchronized within each population. Even though it turns out that this so called all-synchronized state is never asymptotically stable, under some conditions and with a suitable definition of stability, the all-synchronized state can be proven to be at least locally stable. In summary, our work provides a rigorous mathematical framework upon which the further study of multi-population higher-order coupled particle systems can be based., 35 pages, 0 figures

A class of evolution equations with nonlocal diffusion is considered in this work. These are integro-differential equations arising as models of propagation phenomena in continuum media with nonlocal interactions including neural tissue, porous media flow, peridynamics, models with fractional diffusion, as well as continuum limits of interacting dynamical systems. The principal challenge of numerical integration of nonlocal systems stems from the lack of spatial regularity of the data and solutions intrinsic to nonlocal models. To overcome this problem we propose a semidiscrete numerical scheme based on the combination of sparse Monte Carlo and discontinuous Galerkin methods. An important feature of our method is sparsity. Sparse sampling of points in the Monte Carlo approximation of the nonlocal term allows to use fewer discretization points without compromising the accuracy. We prove convergence of the numerical method and estimate the rate of convergence. There are two principal ingredients in the error of the numerical method related to the use of Monte Calro and Galerkin approximations respectively. We analyze both errors. Two representative examples of discontinuous kernels are presented. The first example features a kernel with a singularity, while the kernel in the second example experiences jump discontinuity. We show how the information about the singularity in the former case and the geometry of the discontinuity set in the latter translate into the rate of convergence of the numerical procedure. In addition, we illustrate the rate of convergence estimate with a numerical example of an initial value problem, for which an explicit analytic solution is available. Numerical results are consistent with analytical estimates.

We demonstrate how the pitchfork, transcritical and saddle-node bifurcations of steady states observed in dynamical systems with a finite number of isolated equilibrium points occur in systems with lines of equilibria. The exploration is carried out by using the numerical simulation and linear stability analysis applied to a model of a memristor-based oscillator. First, all the discussed bifurcation scenarios are considered in the context of systems including Chua's memristor with a piecewise-smooth characteristic. Then the memristor characteristic is changed to a function that is smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration. The presented results are obtained for electronic circuit models, but the considered bifurcation phenomena can be exhibited by systems with a line of equilibria of any nature., Comment: 7 pages, 4 figures

A primary challenge in understanding collective behavior is characterizing the spatiotemporal dynamics of the group. We employ topological data analysis to explore the structure of honeybee aggregations that form during trophallaxis, which is the direct exchange of food among nestmates. From the positions of individual bees, we build topological summaries called CROCKER matrices to track the morphology of the group as a function of scale and time. Each column of a CROCKER matrix records the number of topological features, such as the number of components or holes, that exist in the data for a range of analysis scales at a given point in time. To detect important changes in the morphology of the group from this information, we first apply dimensionality reduction techniques to these matrices and then use classic clustering and change-point detection algorithms on the resulting scalar data. A test of this methodology on synthetic data from an agent-based model of honeybees and their trophallaxis behavior shows two distinct phases: a dispersed phase that occurs before food is introduced, followed by a food-exchange phase during which aggregations form. We then move to laboratory data, successfully detecting the same two phases across multiple experiments. Interestingly, our method reveals an additional phase change towards the end of the experiments, suggesting the possibility of another dispersed phase that follows the food-exchange phase.

Network synchronization of lasers is critical for reaching high-power levels and for effective optical computing. Yet, the role of network topology for the frequency synchronization of lasers is not well understood. Here, we report our significant progress toward solving this critical problem for networks of heterogeneous laser model oscillators with repulsive coupling. We discover a general approximate principle for predicting the onset of frequency synchronization from the spectral knowledge of a complex matrix representing a combination of the signless Laplacian induced by repulsive coupling and a matrix associated with intrinsic frequency detuning. We show that the gap between the two smallest eigenvalues of the complex matrix generally controls the coupling threshold for frequency synchronization. In stark contrast with Laplacian networks, we demonstrate that local rings and all-to-all networks prevent frequency synchronization, whereas full bipartite networks have optimal synchronization properties. Beyond laser models, we show that, with a few exceptions, the spectral principle can be applied to repulsive Kuramoto networks. Our results may provide guidelines for optimal designs of scalable laser networks capable of achieving reliable synchronization.

Microbial populations generally evolve in volatile environments, under conditions fluctuating between harsh and mild, e.g. as the result of sudden changes in toxin concentration or nutrient abundance. Environmental variability thus shapes the population long-time dynamics, notably by influencing the ability of different strains of microorganisms to coexist. Inspired by the evolution of antimicrobial resistance, we study the dynamics of a community consisting of two competing strains subject to twofold environmental variability. The level of toxin varies in time, favouring the growth of one strain under low levels and the other strain when the toxin level is high. We also model time-changing resource abundance by a randomly switching carrying capacity that drives the fluctuating size of the community. While one strain dominates in a static environment, we show that species coexistence is possible in the presence of environmental variability. By computational and analytical means, we determine the environmental conditions under which long-lived coexistence is possible and when it is almost certain. Notably, we study the circumstances under which environmental and demographic fluctuations promote, or hinder, the strains coexistence. We also determine how the make-up of the coexistence phase and the average abundance of each strain depend on the environmental variability., 15 pages + appendix of 10 pages (Supplementary Material); Figshare resources: https://doi.org/10.6084/m9.figshare.23553066

Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real world applications, the latter are not static but do evolve in time, in this paper we thus discuss the impact of the time-varying nature of high-order structures in the emergence of global synchronization. To achieve this goal we extend the master stability formalism to account, in a general way, for the additional contributions arising from the time evolution of the higher-order structure supporting the dynamical systems. The theory is successfully challenged against two illustrative examples, the Stuart-Landau nonlinear oscillator and the Lorenz chaotic oscillator.

In this piece we study complexity science in the context of Heliophysics, describing it not as a discipline, but as a paradigm. In the context of Heliophysics, complexity science is the study of a star, interplanetary environment, magnetosphere, upper and terrestrial atmospheres, and planetary surface as interacting subsystems. Complexity science studies entities in a system (e.g., electrons in an atom, planets in a solar system, individuals in a society) and their interactions, and is the nature of what emerges from these interactions. It is a paradigm that employs systems approaches and is inherently multi- and cross-scale. Heliophysics processes span at least 15 orders of magnitude in space and another 15 in time, and its reaches go well beyond our own solar system and Earth's space environment to touch planetary, exoplanetary, and astrophysical domains. It is an uncommon domain within which to explore complexity science. After first outlining the dimensions of complexity science, the review proceeds in three epochal parts: 1) A pivotal year in the Complexity Heliophysics paradigm: 1996; 2) The transitional years that established foundations of the paradigm (1996-2010); and 3) The emergent literature largely beyond 2010. This review article excavates the lived and living history of complexity science in Heliophysics. The intention is to provide inspiration, help researchers think more coherently about ideas of complexity science in Heliophysics, and guide future research. It will be instructive to Heliophysics researchers, but also to any reader interested in or hoping to advance the frontier of systems and complexity science.

Synchronization, which is caused by mutual coupling, and turnover, which is the replacement of old components with new ones, are observed in various open systems consisting of many components. Although these phenomena can co-occur, the interplay of coupling and turnover has been overlooked. Here, we analyze coupled phase oscillators with turnover and reveal that two distinct transitions occur, depending on both coupling and turnover: desynchronization and what we name stochastic oscillation quenching. Importantly, the latter requires both the turnover and coupling to be sufficiently intense., Comment: 7 pages, 3 figures; typos corrected, references modified, acknowledgment added, author contribution added, abstract updated, and equations and figures displayed in a more readable manner

As artificial intelligence (AI) systems are increasingly embedded in our lives, their presence leads to interactions that shape our behaviour, decision-making, and social interactions. Existing theoretical research has primarily focused on human-to-human interactions, overlooking the unique dynamics triggered by the presence of AI. In this paper, resorting to methods from evolutionary game theory, we study how different forms of AI influence the evolution of cooperation in a human population playing the one-shot Prisoner's Dilemma game in both well-mixed and structured populations. We found that Samaritan AI agents that help everyone unconditionally, including defectors, can promote higher levels of cooperation in humans than Discriminatory AI that only help those considered worthy/cooperative, especially in slow-moving societies where change is viewed with caution or resistance (small intensities of selection). Intuitively, in fast-moving societies (high intensities of selection), Discriminatory AIs promote higher levels of cooperation than Samaritan AIs., This work is the result of the Complexity72h 2023 workshop

Global infrastructure robustness and local transport efficiency are critical requirements for transportation networks. However, since passengers often travel greedily to maximize their own benefit and trigger traffic jams, overall transportation performance can be heavily disrupted. We develop adaptation rules that leverage Optimal Transport theory to effectively route passengers along their shortest paths while also strategically tuning edge weights to optimize traffic. As a result, we enforce both global and local optimality of transport. We prove the efficacy of our approach on synthetic networks and on real data. Our findings on the International European highways reveal that our method results in an effective strategy to lower car-produced carbon emissions., 17 pages, 15 figures

The continuum limit of a system of interacting particles on a convergent family of graphs can be described by a nonlocal evolution equation in the limit as the number of particles goes to infinity. Given the continuum limit, the discrete model can be viewed as a Galerkin approximation of the limiting continuous equation. We estimate the speed of convergence of the Galerkin scheme for the model at hand on Euclidean and fractal domains. The latter are relevant when the underlying family of graphs approximates a fractal. Conversely, this paper proposes a Galerkin scheme for a nonlocal diffusion equation on self--similar domains and establishes its convergence rate. Convergence analysis is complemented with numerical integration results for a model problem on Sierpinski Triangle. The rate of convergence of numerical solutions of the model problem fits well the analytical estimate.

Complex adaptive learning is intelligent and crucial in living and inanimate complex systems. A complex system comprises many interacting individuals or units, shows hidden patterns as they interact, and widely occurs in almost every traditional discipline, from natural to social sciences. A recent study has demonstrated a so-called architected material capable of learning. It stimulates scientists to explore the mechanism of complex systems formulation. However, it is very challenging. Here the authors attempt to extract a universal rule or a law of complex adaptive learning subject to local dynamic equilibrium in complex systems from a trading volume-price probability wave equation and apply it to complex quantum systems as its application. It proves particles capable of intelligence-like properties in interactive coherence if the momentum force exerted on the complex quantum systems is non-localized. It is the cumulative probability of the moving particles observed in a time interval. Thus, it assumes that particles in complex quantum systems have a complex adaptive learning- or intelligence-like property in a reinforced coordinate, governed by the exact complex adaptive learning mechanism as that of traders in the complexity of the financial markets. With this assumption, the authors propose an innovative interpretation of entanglement in quantum mechanics. It concludes that quantum entanglement is not a state of the superposition of coherent states as the mainstream Copenhagen school of thought maintains. It is a coherent state in the interaction between two opposite, complementary, and variable forces. The authors look forward to the experimental results to examine its validity and further improve the theory until it is perfect, suggesting industrial production of entanglement resources in new technical routes available, 22 pages in total (double spaces and including a title page and a popular summary), 2 figures, and 20 references

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect more than two nodes, have thus become a new paradigm in network science. Yet, we are still in lack of models linking network growth and hyperedge expansion, both of which are commonly observable in the real world. Here, we propose a generative hypergraph model by employing the preferential attachment mechanism in both nodes and hyperedge formation. The model can produce bi-heterogeneity, exhibiting scale-free distributions in both hyperdegree and hyperedge size. We provide a mean-field treatment that gives the expression of the two scaling exponents, which agree with the numerical simulations. Our model may help to understand the networked systems showing both types of heterogeneity and facilitate the study of complex dynamics thereon., 11 pages, 6 figures

The Kuramoto model is a versatile mathematical framework that explains phenomena resulting from interactions among phase oscillators. It finds applications in various scientific and engineering domains. In this study, we focused on a Y-shaped network, which serves as the fundamental unit of a tree network. By simulating oscillators on the network, we generated heat maps for different numbers of nodes and coupling strengths and demonstrated the occurrence of different phases. Our findings reveal transitions between synchronization, wave state, and chaos within the system.

We study numerically the effects of time delay in networks of delay-coupled excitable FitzHugh Nagumo systems with dissipation. The generation of periodic self-sustained oscillations and its threshold are analyzed depending on the dissipation of a single neuron, the delay time, and random initial conditions. The peculiarities of spatiotemporal dynamics of time-delayed bidirectional ring-structured FitzHugh-Nagumo neuronal systems are investigated in cases of local and nonlocal coupling topology between the nodes, and a first-order nonequilibrium phase transition to synchrony is established. It is shown that the emergence of oscillatory activity in delay-coupled FitzHugh-Nagumo neurons is observed for smaller values of the coupling strength as the dissipation parameter decreases. This can provide the possibility of controlling the spatiotemporal behavior of the considered neuronal networks. The observed effects are quantified by plotting distributions of the maximal Lyapunov exponent and the global order parameter in terms of delay and coupling strength., 14 pages, 17 figures

The U.S. DOE Office of Integrated Waste Management is planning for the eventual transportation, storage, and disposal of spent nuclear fuel (SNF) and high-level radioactive waste (HLW) from nuclear power plants and DOE sites. The Stakeholder Tool for Assessing Radioactive Transportation (START) is a web-based, geospatial decision-support tool developed for evaluating routing options and other aspects of transporting SNF and HLW, covering rail, truck, barge, and intermodal infrastructure and operations in the continental United States. The verification and validation (V&V) process is intended to independently assess START and provide confidence in the ability of START to accurately provide intended results. The V&V efforts included an independent analysis of select outputs through other geographic information system (GIS) programs including QGIS. The V&V efforts have focused primarily on the route buffer zone population values as well as the route lengths reported in START. The efforts include developing a V&V methodology for each output type that an independent user could replicate through the user interface for a small number of routes as well as more automated methodologies that reduce the number of interactions with the GIS user interfaces. Independent analysis of the routes showed excellent agreement between the START outputs for population within the route buffer zone and the length of the routes. Over 200 test routes were evaluated; in all cases, the percent difference in the population within the buffer region was less than +/- 5%, and most cases were below +/- 1%. The V&V work is ongoing and other START features that are undergoing independent analysis include population density within the route buffer zone as well as reported doses for the segments within the START code., Presented at PATRAM 2022 (June 11-15, 2023). arXiv admin note: text overlap with arXiv:2306.09901

Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse analytically and numerically the steady states of this theory in systems of arbitrary density and report the following. 1. We discover that all such dynamics almost certainly possess only one physical steady state, which may or may not satisfy detailed balance. 2. We show rigorously that, if a detailed balance solution is possible then it is unique. The above two results correct an erroneous conjecture in the literature. 3. We show rigorously that the detailed-balance solutions in very dense systems are globally stable, extending the local stability found for these solutions in the literature. 4. In view of recent experimental observations of robust detailed balance steady states in very dilute cyclically sheared systems, our results point to a self-organisation of process rates in dynamic granular systems., 6 pages, 3 figures, supplemental material. To appear in Journal of Physics A: Mathematical and Theoretical

Evolution is a fundamental process that shapes the biological world we inhabit, and reinforcement learning is a powerful tool used in artificial intelligence to develop intelligent agents that learn from their environment. In recent years, researchers have explored the connections between these two seemingly distinct fields, and have found compelling evidence that they are more closely related than previously thought. This paper examines these connections and their implications, highlighting the potential for reinforcement learning principles to enhance our understanding of evolution and the role of feedback in evolutionary systems.

The United States Department of Energy (U.S. DOE) is planning for the transportation, storage, and disposal of spent nuclear fuel (SNF) and high-level radioactive waste (HLW) from commercial nuclear power plants and other U.S. DOE sites. The Stakeholder Tool for Assessing Radioactive Transportation (START) is a web-based, geospatial decision-support tool developed for evaluating routing options and other aspects of transporting SNF and HLW via barge, train, truck, and intermodal surface transport in the continental United States. The verification and validation (V&V) effort is intended to independently assess START to provide confidence in the ability of the tool to accurately provide intended outputs. The results selected for the V&V effort of the START code include those identified as crucial outputs by subject matter experts. Outputs from START such as shape files and keyhole markup language (KML) files are analyzed using a geodesic computation using the WSG-84 ellipsoid model. Most of the V&V efforts are aimed towards examining and comparing the total length reported in the various files in the START tool. This work also focuses on the development of V&V methodologies for various outputs that could be replicated by the end user on a set of user-defined routes. Over 150 origin destination pairs were run as part of this effort to test the functionality of the START tool. In addition to presenting results using an independent geodesic computation, this work will provide a comparison of the total route lengths between START version 3.3 and the previous release of START (version 3.2.2)., Presented at PATRAM 2022 (June 11-15, 2023)

External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical reaction networks? Here, we analyze transitions giving rise to complex behavior in random reaction networks subject to external driving forces. In the absence of driving, we characterize the uniqueness of the steady state and identify the percolation of a giant connected component in these networks as the number of reactions increases. When subject to chemical driving (influx and outflux of chemical species), the steady state can undergo bifurcations, leading to multistability or oscillatory dynamics. By quantifying the prevalence of these bifurcations, we show how chemical driving and network sparsity tend to promote the emergence of these complex dynamics and increased rates of entropy production. We show that catalysis also plays an important role in the emergence of complexity, strongly correlating with the prevalence of bifurcations. Our results suggest that coupling a minimal number of chemical signatures with external driving can lead to features present in biochemical processes and abiogenesis., 12 pages, 4 figures

Phase transitions, characterized by abrupt shifts between macroscopic patterns of organization, are ubiquitous in complex systems. Despite considerable research in the physical and natural sciences, the empirical study of this phenomenon in societal systems is relatively underdeveloped. The goal of this study is to explore whether the dynamics of collective civil unrest can be plausibly characterized as a sequence of recurrent phase shifts, with each phase having measurable and identifiable latent characteristics. We introduce a macro-level statistical model of civil unrest and evaluate its plausibility using a comprehensive dataset of civil unrest events in 170 countries from 1946 to 2017. Our findings demonstrate that the macro-level phase model effectively captures the characteristics of civil unrest data from diverse countries globally and that universal mechanisms may underlie certain aspects of the dynamics of civil unrest. We also introduce a new scale to quantify a country's long-term unrest per unit of time and show that civil unrest events tend to cluster geographically, with the magnitude of civil unrest concentrated in specific regions. Our approach has the potential to identify and measure phase transitions in various collective human phenomena beyond civil unrest, contributing to a better understanding of complex social systems., Main paper (38 pages) and Supporting Information (138 pages)

Populations of heterogeneous phase oscillators with frustrated random interactions exhibit a quasi-glassy state in which the distribution of local fields is volcano-shaped. In a recent work [Phys. Rev. Lett. 120, 264102 (2018)] the volcano transition was replicated in a solvable model using a low-rank, random coupling matrix $\mathbf M$. We extend here that model including tunable nonreciprocal interactions, i.e. ${\mathbf M}^T\ne \mathbf M$. More specifically, we formulate two different solvable models. In both of them the volcano transition persists if matrix elements $M_{jk}$ and $M_{kj}$ are enough correlated. Our numerical simulations fully confirm the analytical results. To put our work in a wider context, we also investigate numerically the volcano transition in the analogous model with a full-rank random coupling matrix.

Control studies in ecological models of networks involving invasive plants can offer tangible management strategies. Framing control policies to tackle problems posed by invasive plants on indigenous plant diversity under the sustainable developmental goals framework is the main motivation of this paper. Based on the reported experimental and theoretical observations, we propose minimal ecological models of direct interactions of \textit{Lantana camara} with other entitites e.g. other indigenous plants (denoted by Control-plant) and soil microbes. The species' abundance variables represented by the nodes in the model networks follow generalized Lotka-Volterra dynamics and input signals are incorporated at appropriate driver nodes to control the \textit{Lantana camara} outgrowth. Analysis with Lie algebra and controllability criteria showed that our model systems are controllable with minimum of two control input signals. Analytical results of our model equations indicated that successive interventions are required to increase the abundance of control-plant, the microbes and suppress \textit{Lantana camara}. We observed from the numerical analysis with LQR algorithm that the number of interventions to be taken to control the \textit{Lantana camara} outgrowth depends on the choice of various important parameters such as intervention time, effort and penalty etc. Further, the increase in nonlinear terms contributed from self-loops in the network model shows the persistence of \textit{L. camara} and how it drives the coexistence of the species. We propose that parameters we have identified in our study needed to be considered and analyzed extensively for designing sustainable policies to control invasive species in an ecosystem., 11 Figures, 30 pages

The essential ingredient for studying the phenomena of emergence is the ability to generate and manipulate emergent systems that span large scales. Cellular automata are the model class particularly known for their effective scalability but are also typically constrained by fixed local rules. In this paper, we propose a new model class of adaptive cellular automata that allows for the generation of scalable and expressive models. We show how to implement computation-effective adaptation by coupling the update rule of the cellular automaton with itself and the system state in a localized way. To demonstrate the applications of this approach, we implement two different emergent models: a self-organizing Ising model and two types of plastic neural networks, a rate and spiking model. With the Ising model, we show how coupling local/global temperatures to local/global measurements can tune the model to stay in the vicinity of the critical temperature. With the neural models, we reproduce a classical balanced state in large recurrent neuronal networks with excitatory and inhibitory neurons and various plasticity mechanisms. Our study opens multiple directions for studying collective behavior and emergence.

The Kuramoto model, describing the synchronization dynamics of coupled oscillators, has been generalized in many ways over the past years. One recent extension of the model replaces the oscillators, originally characterized by a single phase, by particles with $D-1$ internal phases, represented by a point on the surface of the unit D-sphere. Particles are then more easily represented by $D$-dimensional unit vectors than by $D-1$ spherical angles. However, numerical integration of the state equations should ensure that the propagated vectors remain unit, avoiding artifacts that change their norm. Euler's method, for instance, displaces the particles in the direction of the tangent velocity field, moving them away from the sphere. The state vectors, therefore, must be manually projected back onto the surface after each integration step. As discussed in [1], this procedure produces a small rotation of the particles over the sphere, but with the wrong angle. Although higher order integration methods, such as forth order Runge-Kutta, do provide accurate results even requiring projection of vectors back to the sphere, integration can be safely performed by doing a sequence of direct small rotations, as dictated by the equations of motion. This keeps the particles on the sphere at all times and ensure exact norm preservation, as proposed in [1]. In this work I propose an alternative way to do such integration by rotations in 3D that can be generalized to more dimensions using Cayley-Hamilton's theorem. Explicit formulas are provided for 2, 3 and 4 dimensions., 17 pages, 3 figures

We explore numerically the impact of additive Gaussian noise on the spatio-temporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the Henon map. 2D distributions of the probability of observing chimera states are constructed in terms of the coupling strength and the noise intensity and for several choices of the local dynamics parameters. It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance., 15 pages, 14 figures; typos corrected, references added

We attempt to achieve isochronal synchronization between a drive system unidirectionally coupled to a response system, under the assumption that limited knowledge on the states of the drive is available at the response. Machine learning techniques have been previously implemented to estimate the states of a dynamical system from limited measurements. We consider situations in which knowledge of the non-measurable states of the drive system is needed in order for the response system to synchronize with the drive. We use a reservoir computer to estimate the non-measurable states of the drive system from its measured states and then employ these measured states to synchronize the response system with the drive.

The United States Department of Energy has long term goals to develop solutions for managing the nations spent nuclear fuel and high-level waste inventory. The Integrated Waste Management program is employing system-level engineering and analysis principles to inform potential future waste management system architectures. Managing the SNF requires the use of system-level analysis software that considers waste generation, on-site (centralized storage), transportation infrastructure, and long-term disposal. The Next Generation System Analysis Model is an agent-based model that was developed to simulate the transportation and storage of SNF and HLW. NGSAM has the capability to detail the interaction and movement of individual components and groups, such as rail cars and casks. The SNF inventory from commercial nuclear reactors is currently in temporary storage at multiple locations spread across the US. Shipping of SNF from these locations relies on one of three transportation modes: rail, heavy-haul truck, or barge. Rail is the most preferred due to the size of the canisters and casks the SNF would be shipped in. Under some scenarios, a rail route might not be available to a reactor site or improving the rail infrastructure at shutdown sites might be too cost-prohibitive for utilities to opt for a direct rail transfer. Under such scenarios, using a barge or heavy haul truck to de-inventory the site and transfer the SNF to a nearby intermodal transfer site with adequate rail infrastructure where the payload could be transferred to a rail car might prove to be an attractive option. This work presents the various intermodal transportation options to move SNF from reactor sites to rail cars. Next, the operational steps in each of these modes to move the SNF from a reactor site and transfer it to a rail car is explored. The ideology, assumptions, and future steps are presented., American Nuclear Society 2022 International High-Level Radioactive Waste Management Conference (https://www.ans.org/pubs/proceedings/article-52728/)

The presence of undesirable large-amplitude self-sustained oscillations in combustors resulting from thermoacoustic instability can lead to performance loss and structural damage to components of gas turbine and rocket engines. Traditional feedback controls to mitigate thermoacoustic instability possess electromechanical components, which are expensive to maintain regularly and unreliable in the harsh environments of combustors. In this study, we demonstrate the quenching of thermoacoustic instability through self-coupling -- a method wherein a hollow tube is used to provide acoustic self-feedback to a thermoacoustic system. Through experiments and modeling, we identify the optimal coupling conditions for attaining amplitude death, i.e., complete suppression of thermoacoustic instabilities, in a horizontal Rijke tube. We examine the effect of both system and coupling parameters on the occurrence of amplitude death. We thereby show that the parametric regions of amplitude death occur when the coupling tube length is close to an odd multiple of the length of the Rijke tube. The optimal location of the coupling tube for achieving amplitude death is near the anti-node of the acoustic standing wave in the Rijke tube. Furthermore, we find that self-coupling mitigates thermoacoustic instability in a Rijke tube more effectively than mutual coupling of two identical Rijke tubes. Thus, we believe that self-coupling can prove to be a simple, cost-effective solution for mitigating thermoacoustic instability in gas turbine combustors., Comment: 12 pages, 8 figures

Designing feasible control strategies for opinion dynamics in complex social systems has never been an easy task. It requires a control protocol which 1) is not enforced on all individuals in the society, and 2) does not exclusively rely on specific opinion values shared by the social system. Thanks to the recent studies on noise-induced consensus in opinion dynamics, the noise-based intervention strategy has emerged as the only one meeting both of the above requirements, yet its underlying general theory is still lacking. In this paper, we perform rigorous theoretical analysis and simulations of a noise-based control strategy for opinion formation in which only a fraction of individuals is affected by randomly generated noise. We found that irrespective of the number of noise-driven individuals, including the case of only one single noise-affected individual, the system can attain a quasi-consensus in finite time, and the critical noise strength can be obtained. Our results highlight the efficiency of noise-driven mechanisms for the control of complex social dynamics., arXiv admin note: text overlap with arXiv:1711.01432

We examine adaptive strategies adopted by vehicles for route selection en-route in transportation networks. By studying a model of two-dimensional cellular automata, we model vehicles characterized by a parameter called path-greediness, which corresponds to the tendency for them to travel to their destinations via the shortest path. The path-greediness of each individual vehicle is updated based on the local traffic conditions, to either keep the vehicle travels via a shorter path in an un-congested region or to explore longer diverted paths in a congested region. We found that the optimal number of steps to trigger an update of path-greediness is dependent on the density of vehicles, and the magnitude of path-greediness increment affects the macroscopic traffic conditions of the system. To better coordinate vehicles in denser networks, the update on the tendency for vehicles to travel via the shorter paths should be gradual and less frequent.

We report a detailed analysis on the emergence of bursting in a recently developed neural mass model that includes short-term synaptic plasticity. Neural mass models can mimic the collective dynamics of large-scale neuronal populations in terms of a few macroscopic variables like mean membrane potential and firing rate. The present one is particularly important, as it represents an exact meanfield limit of synaptically coupled quadratic integrate and fire (QIF) neurons. Without synaptic dynamics, a periodic external current with slow frequency$$\varepsilon $$εcan lead to burst-like dynamics. The firing patterns can be understood using singular perturbation theory, specifically slow–fast dissection. With synaptic dynamics, timescale separation leads to a variety of slow–fast phenomena and their role for bursting becomes inordinately more intricate. Canards are crucial to understand the route to bursting. They describe trajectories evolving nearby repelling locally invariant sets of the system and exist at the transition between subthreshold dynamics and bursting. Near the singular limit$$\varepsilon = 0$$ε=0, we report peculiarjump-on canards, which block a continuous transition to bursting. In the biologically more plausible$$\varepsilon $$ε-regime, this transition becomes continuous and bursts emerge via consecutive spike-adding transitions. The onset of bursting is complex and involvesmixed-type-like torus canards, which form the very first spikes of the burst and follow fast-subsystem repelling limit cycles. We numerically evidence the same mechanisms to be responsible for bursting emergence in the QIF network with plastic synapses. The main conclusions apply for the network, owing to the exactness of the meanfield limit.

The emergence of order in nature manifests in different phenomena, with synchronization being one of the most representative examples. Understanding the role played by the interactions between the constituting parts of a complex system in synchronization has become a pivotal research question bridging network science and dynamical systems. Particular attention has been paid to the emergence of chimera states, where subsets of synchronized oscillations coexist with asynchronous ones. Such coexistence of coherence and incoherence is a perfect example where order and disorder can persist in a long-lasting regime. Although considerable progress has been made in recent years to understand such coherent and (coexisting) incoherent states, how they manifest in real-world networks remains to be addressed. Based on a symmetry-breaking mechanism, in this paper, we shed light on the role that non-normality, a ubiquitous structural property of real networks, has in the emergence of several diverse dynamical phenomena, e.g., amplitude chimeras or oscillon patterns. Specifically, we demonstrate that the prevalence of source or leader nodes in networks leads to the manifestation of phase chimera states. Throughout the paper, we emphasize that non-normality poses ongoing challenges to global synchronization and is instrumental in the emergence of chimera states.

We experimentally investigate the role of illumination on the collective dynamics of a large school (ca. 50 individuals) of Hemigrammus rhodostomus. The structure of the group, defined using two order parameters, is quantified while progressively altering the visual range of the fish through controlled cycles of ambient light intensity. We show that, at low light levels, the individuals within the group are unable to form a cohesive group, while at higher illuminance the degree of alignment of the school correlates with the light intensity. When increasing the illuminance, the school structure is successively characterized by a polarized state followed by a highly regular and stable rotational configuration (milling). Our study shows that vision is necessary to achieve cohesive collective motion for free swimming fish schools, while the short-range lateral line sensing is insufficient in this situation. The present experiment therefore provides new insights into the interaction mechanisms that govern the emergence and intensity of collective motion in biological systems.

Transport networks are crucial for the functioning of natural and technological systems. We study a mathematical model of vascular network adaptation, where the network structure dynamically adjusts to changes in blood flow and pressure. The model is based on local feedback mechanisms that occur on different time scales in the mammalian vasculature. The cost exponent $\gamma$ tunes the vessel growth in the adaptation rule, and we test the hypothesis that the cost exponent is $\gamma=1/2$ for vascular systems [Hu and Cai, Phys. Rev. Lett., Vol. 111(13) (2013)1 ]. We first perform a bifurcation analysis for a simple triangular network motif with fluctuating demand, and then conduct numerical simulations on network topologies extracted from perivascular networks of rodent brains. We compare the model predictions with experimental data and find that $\gamma$ is closer to 1 than to 1/2 for the model to be consistent with the data. Our study thus aims at addressing two questions: (i) Is a specific measured flow network consistent in terms of physical reality? (ii) Is the adaptive dynamic model consistent with measured network data? We conclude that the model can capture some aspects of vascular network formation and adaptation, but also suggest some limitations and directions for future research. Our findings contribute to a general understanding of the dynamics in adaptive transport networks, which is essential for studying mammalian vasculature and developing self-organizing piping systems.

We employ the circular cumulant approach to construct a low dimensional description of the macroscopic dynamics of populations of phase oscillators (elements) subject to non-Gaussian white noise. Two-cumulant reduction equations for alpha-stable noises are derived. The implementation of the approach is demonstrated for the case of the Kuramoto ensemble with non-Gaussian noise. The results of direct numerical simulation of the ensemble of N=1500 oscillators and the "exact" numeric solution for the fractional Fokker-Planck equation in the Fourier space are found to be in good agreement with the analytical solutions for two feasible circular cumulant model reductions., 7 pages, 2 figures

A firm cognitive subject or ``individual'' is presupposed for the emergence of mind. However, with the development of recent information technology, the ``individual'' has become more dispersed in society and the cognitive subject has become increasingly unstable and adaptive, necessitating an update in our understanding of the ``individual''. Autopoiesis serves as a model of the cognitive subject, which is unstable and requires effort to maintain itself to adapt to the environment. In this study, we evaluated adaptivity for a highly extensible multi-particle system model Particle Lenia through the response perturbation. As a result, we found that Particle Lenia has a particle configuration that is both temporally unstable and has multiple stable states. This result suggests that Particle Lenia can express adaptive characteristics and is expected to be used as a computational model toward building an autopoietic cognitive agent., This paper has been accepted for ALIFE 2023

When a founder cell and its progeny divide with incomplete cytokinesis, a network forms in which each intercellular bridge corresponds to a past mitotic event. Networks built in this manner are required for gamete production in many animals, and different species have evolved very different final network topologies. While mechanisms regulating network assembly have been identified in particular organisms, we lack a quantitative framework to understand network assembly and inter-species variability. Motivated by cell networks responsible for oocyte production in invertebrates, where the final topology is typically invariant within each species, we devise a mathematical model for generating cell networks: each node is an oscillator, and after a full cycle, the node produces a daughter to which it remains connected. These cell cycle oscillations on the nodes are transient and coupled via diffusion over the network's edges. By variation of three biologically motivated parameters, our model generates nearly all such networks currently reported across invertebrates. Furthermore, small parameter variations can rationalize cases of within-species variation. Because cell networks outside of the ovary often form less deterministically, we propose generalizations of our model to account for different sources of stochasticity.

Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order interdependencies constitute a powerful resource that is, however, challenging to harness and can be readily disrupted. In this paper we contest this perspective by demonstrating that high-order interdependencies can not only exhibit robustness to stochastic perturbations, but can in fact be enhanced by them. Using elementary cellular automata as a general testbed, our results unveil the capacity of dynamical noise to enhance the statistical regularities between agents and, intriguingly, even alter the prevailing character of their interdependencies. Furthermore, our results show that these effects are related to the high-order structure of the local rules, which affect the system's susceptibility to noise and characteristic times-scales. These results deepen our understanding of how high-order interdependencies may spontaneously emerge within distributed systems interacting with stochastic environments, thus providing an initial step towards elucidating their origin and function in complex systems like the human brain., 8 pages, 4 figures, 2 tables

This paper proposes a framework for optimising the adaptation and attunement of a Complex Adaptive System (CAS) with its environments. The tendency towards stability can be explained by minimising free energy but high variability, noise, and over-specialized rigidity can lead to a "stuck state" in a CAS. Without perturbation (increasing free energy), the system remains stuck and unable to adapt to changing circumstances. The paper introduces the concept of 'psychotic' Markov blankets to understand and specify factors contributing to maladjustment conditions moving away from the minimum stuck state. The paper offers directions for optimising adaptation and attunement to be applied to real-world problems, from cells to behaviour, societies and ecosystems.

Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid. If such processes are Markov, then their probability distribution is governed by the Kramers-Moyal (KM) equation, a partial differential equation that involves an infinite number of coefficients, which depend on the state variable. The KM coefficients must be evaluated based on measured time series for a data-driven reconstruction of the governing equations for the stochastic dynamics. We present an accurate method of computing the KM coefficients, which relies on computing the coefficients' conditional moments based on the statistical moments of the time series. The method's advantages over state-of-the-art approaches are demonstrated by investigating prototypical stochastic processes with well-known properties., 20 pages, 9 figures, 1 table, 5 appendices

In physics, I noticed subjects not explained by formulas were often not studied, like how uncontrolled growth systems changed form. Weather, businesses, societies, environments, communities, cultures, groups, relationships, lives, and livelihoods all do it following some variation of an 'S' curve. It is a slow-fast-slow process of self-animated contextual energy system development. Making working systems, they seem to develop by "find and connect" in three stages, starting small to first A) freely build designs of growing power, then B) diversify, adapt, respond, and harmonize with others, then C) take on one or more roles in their climax environments. It is a life curve of tremendous syntropic success that then ends with decline. Life is particularly risky for small start-ups, but many do succeed. Many powerful civilizations have emerged, some never growing up but growing as endless startups, only to become fragile, fail, and vanish. That looks like a choice., 14 pages, 7 figures, 2023 pending SRBS review

Climate changes may affect ecosystems destabilising relationships among species. We investigate the spatial rock-paper-scissors models with a regional unevenness that reduces the selection capacity of organisms of one species. Our results show that the regionally weak species predominates in the local ecosystem, while spiral patterns appear far from the region, where individuals of every species play the rock-paper-scissors game with the same strength. Because the weak species controls all local territory, it is attractive for the other species to enter the local ecosystem to conquer the territory. However, our stochastic simulations show that the transitory waves formed when organisms of the strong species reach the region are quickly destroyed because of local strength unbalance in the selection game rules. Computing the effect of the topology on population dynamics, we find that the prevalence of the weak species becomes more significant if the transition of the selection capacity to the area of uneven rock-paper-scissors rules is smooth. Finally, our findings show that the biodiversity loss due to the arising of regional unevenness is minimised if the transition to the region where the cyclic game is unbalanced is abrupt. Our results may be helpful to biologists in comprehending the consequences of changes in the environmental conditions on species coexistence and spatial patterns in complex systems., 17 pages, 7 figures