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The transition from individual to collective motion plays a significant role in many biological processes. While the implications of different types of particle-particle interactions for the emergence of particular modes of collective motion have been well studied, it is unclear how particular types of individual migration patterns influence collective motion. Here, motivated by swarming bacteria Myxococcus xanthus, we investigate the combined effects of the individual pattern of migration and of particle-particle interactions, on the emergence of collective migration. We analyze the effects of a feature of individual pattern migration, the persistence of motion, on the collective properties of the system that emerge from interactions among individuals; in particular, when nematic velocity alignment interaction mediates collective dynamics. We find, through computer simulations and mathematical analysis, that an initially disordered migratory state can become globally ordered by increasing either, the particle-particle alignment interaction strength or the persistence of individual migration. In contrast, we find that persistence prevents the emergence of global nematic order when both persistence and nematic alignment are comparatively high. We conclude that behavior at the population level does not only depend on interactions between individuals but also on the individuals' own intrinsic behavior.

Solving the three-dimensional (3D) Bratu equation is highly challenging due to the presence of multiple and sharp solutions. Research on this equation began in the late 1990s, but there are no satisfactory results to date. To address this issue, we introduce a symmetric finite difference method (SFDM) which embeds the symmetry properties of the solutions into a finite difference method (FDM). This SFDM is primarily used to obtain more accurate solutions and bifurcation diagrams for the 3D Bratu equation. Additionally, we propose modifying the Bratu equation by incorporating a new constraint that facilitates the construction of bifurcation diagrams and simplifies handling the turning points. The proposed method, combined with the use of sparse matrix representation, successfully solves the 3D Bratu equation on grids of up to $301^3$ points. The results demonstrate that SFDM outperforms all previously employed methods for the 3D Bratu equation. Furthermore, we provide bifurcation diagrams for the 1D, 2D, 4D, and 5D cases, and accurately identify the first turning points in all dimensions. All simulations indicate that the bifurcation diagrams of the Bratu equation on the cube domains closely resemble the well-established behavior on the ball domains described by Joseph and Lundgren [1]. Furthermore, when SFDM is applied to linear stability analysis, it yields the same largest real eigenvalue as the standard FDM despite having fewer equations and variables in the nonlinear system., Comment: Accepted for publication in Applied Mathematics and Computation

Decision making is the cognitive process of selecting a course of action among multiple alternatives. As the decision maker belongs to a complex microenvironment (which contains multiple decision makers), has to make a decision where multiple options are present which often leads to a phenomenon known as the "paradox of choices". The latter refers to the case where too many options can lead to negative outcomes, such as increased uncertainty, decision paralysis, and frustration. Here, we employ an entropy driven mechanism within a statistical physics framework to explain the premises of the paradox. In turn, we focus on the emergence of a collective "paradox of choice", in the case of interacting decision-making agents, quantified as the decision synchronization time. Our findings reveal a trade-off between synchronization time and the sensing radius, indicating the optimal conditions for information transfer among group members, which significantly depends the individual sensitivity parameters. Interestingly, when agents sense their microenvironment in a biased way or their decisions are influenced by their past choices, then the collective "paradox of choice" does not occur. In a nutshell, our theory offers a low-dimensional and unified statistical explanation of the "paradox of choice" at the individual and at the collective level., Comment: 20 pages, 8 figures

We introduce a novel lattice-gas cellular automaton (LGCA) for compressible vectorial active matter with polar and nematic velocity alignment. Interactions are, by construction, zero-range. For polar alignment, we show the system undergoes a phase transition that promotes aggregation with strong resemblance to the classic zero-range process. We find that above a critical point, the states of a macroscopic fraction of the particles in the system coalesce into the same state, sharing the same position and momentum (polar condensate). For nematic alignment, the system also exhibits condensation, but there exist fundamental differences: a macroscopic fraction of the particles in the system collapses into a filament, where particles possess only two possible momenta. Furthermore, we derive hydrodynamic equations for the active LGCA model to understand the phase transitions and condensation that undergoes the system. We also show that generically the discrete lattice symmetries -- e.g. of a square or hexagonal lattice -- affect drastically the emergent large-scale properties of on-lattice active systems. The study puts in evidence that aligning active matter on the lattice displays new behavior, including phase transitions to states that share similarities to condensation models.

Learning is a fundamental characteristic of living systems, enabling them to comprehend their environments and make informed decisions. These decision-making processes are inherently influenced by available information about their surroundings and specific objectives. An intriguing perspective is that each process could be optimal under a given set of conditions. Here, a geometric method is introduced for analytically exploring such a perspective. The probability distribution describing the state of the composite system of the environment, termed the information bath, and a decision-maker is discussed on the basis of the entropic concept. This enables one to study the system in analogy with thermodynamics. Learning processes are expressed as the changes of parameters contained in the distribution. For a geometric interpretation of the processes, the manifold endowed with the Fisher-Rao metric as the Riemannian metric is considered. This framework allows one to conceptualize the optimality of each process as a state change along a geodesic curve on the manifold, which is referred to here as geodesic learning. Then, the bivariate Gaussian model is presented for illustrating this approach, and its rigorous solution is obtained. There, the correspondence between learning and cooling is made manifest. Evolution of the entropy is evaluated for geodesic learning. The findings are then interpreted in the context of adaptation. Geodesic learning plays a role of the case of reference and may give novel insights into the mechanics of learning in living systems., Comment: 22 pages, no figures

Cell decision-making refers to the process by which cells gather information from their local microenvironment and regulate their internal states to create appropriate responses. Microenvironmental cell sensing plays a key role in this process. Our hypothesis is that cell decision-making regulation is dictated by Bayesian learning. In this article, we explore the implications of this hypothesis for internal state temporal evolution. By using a timescale separation between internal and external variables on the mesoscopic scale, we derive a hierarchical Fokker-Planck equation for cell-microenvironment dynamics. By combining this with the Bayesian learning hypothesis, we find that changes in microenvironmental entropy dominate cell state probability distribution. Finally, we use these ideas to understand how cell sensing impacts cell decision-making. Notably, our formalism allows us to understand cell state dynamics even without exact biochemical information about cell sensing processes by considering a few key parameters.

Non-pharmacological interventions (NPIs), and in particular social distancing, in conjunction with the advent of effective vaccines at the end of 2020, aspired for the development of a protective immunity shield against the spread of SARS-CoV-2. The main question rose is related to the deployment strategy of the two doses with respect to the imposed NPIs and population age. In this study, an extended (SEIR) agent-based model on small-world networks was employed to identify the optimal policies against Covid 19 pandemic, including social distancing measures and mass vaccination. To achieve this, a new methodology is proposed to solve the inverse problem of calibrating an agent's infection rate with respect to vaccination efficacy. The results show that deploying the first vaccine dose across the whole population is sufficient to control the epidemic, with respect to deaths, even for low number of social contacts. Moreover, for the same range of social contacts, we found that there is an optimum ratio of vaccinating ages > 65 over the younger ones of 4/5., Comment: 14 pages, 9 figures

Countries around the world implement nonpharmaceutical interventions (NPIs) to mitigate the spread of COVID-19. Design of efficient NPIs requires identification of the structure of the disease transmission network. We here identify the key parameters of the COVID-19 transmission network for time periods before, during, and after the application of strict NPIs for the first wave of COVID-19 infections in Germany combining Bayesian parameter inference with an agent-based epidemiological model. We assume a Watts-Strogatz small-world network which allows to distinguish contacts within clustered cliques and unclustered, random contacts in the population, which have been shown to be crucial in sustaining the epidemic. In contrast to other works, which use coarse-grained network structures from anonymized data, like cell phone data, we consider the contacts of individual agents explicitly. We show that NPIs drastically reduced random contacts in the transmission network, increased network clustering, and resulted in a change from an exponential to a constant regime of newcases. In this regime, the disease spreads like a wave with a finite wave speed that depends on the number of contacts in a nonlinear fashion, which we can predict by mean field theory. Our analysis indicates that besides the well-known transitionbetween exponential increase and exponential decrease in the number of new cases, NPIs can induce a transition to another, previously unappreciated regime of constant new cases.

Cellular decision making allows cells to assume functionally different phenotypes in response to microenvironmental cues, without genetic change. It is an open question, how individual cell decisions influence the dynamics at the tissue level. Here, we study spatio-temporal pattern formation in a population of cells exhibiting phenotypic plasticity, which is a paradigm of cell decision making. We focus on the migration/resting and the migration/proliferation plasticity which underly the epithelial-mesenchymal transition (EMT) and the go or grow dichotomy. We assume that cells change their phenotype in order to minimize their microenvironmental entropy (LEUP: Least microEnvironmental Uncertainty Principle) and study the impact of the LEUP-driven migration/resting and migration/proliferation plasticity on the corresponding multicellular spatio-temporal dynamics with a stochastic cell-based mathematical model for the spatio-temporal dynamics of the cell phenotypes. In the case of the go or rest plasticity, a corresponding mean-field approximation allows to identify a bistable switching mechanism between a diffusive (fluid) and an epithelial (solid) tissue phase which depends on the sensitivity of the phenotypes to the environment. For the go or grow plasticity, we show the possibility of Turing pattern formation for the "solid" tissue phase and its relation with the parameters of the LEUP-driven cell decisions.

Multipotent differentiation, where cells adopt one of several cell fates, is a determinate and orchestrated procedure that often incorporates stochastic mechanisms in order to diversify cell types. How these stochastic phenomena interact to govern cell fate are poorly understood. Nonetheless, cell fate decision making procedure is mainly regulated through the activation of differentiation waves and associated signaling pathways. In the current work, we focus on the Notch/Delta signaling pathway which is not only known to trigger such waves but also is used to achieve the principle of lateral inhibition, i.e. a competition for exclusive fates through cross-signaling between neighboring cells. Such a process ensures unambiguous stochastic decisions influenced by intrinsic noise sources, e.g.~as ones found in the regulation of signaling pathways, and extrinsic stochastic fluctuations, attributed to micro-environmental factors. However, the effect of intrinsic and extrinsic noise on cell fate determination is an open problem. Our goal is to elucidate how the induction of extrinsic noise affects cell fate specification in a lateral inhibition mechanism. Using a stochastic Cellular Automaton with continuous state space, we show that extrinsic noise results in the emergence of steady-state furrow patterns of cells in a "frustrated/transient" phenotypic state.

Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly crystalline photoreceptor patterns of some fish and reptiles. Birds are highly visual animals with five different cone photoreceptor subtypes, yet their photoreceptor patterns are not perfectly regular. By analyzing the chicken cone photoreceptor system consisting of five different cell types using a variety of sensitive microstructural descriptors, we find that the disordered photoreceptor patterns are ``hyperuniform'' (exhibiting vanishing infinite-wavelength density fluctuations), a property that had heretofore been identified in a unique subset of physical systems, but had never been observed in any living organism. Remarkably, the photoreceptor patterns of both the total population and the individual cell types are simultaneously hyperuniform. We term such patterns ``multi-hyperuniform'' because multiple distinct subsets of the overall point pattern are themselves hyperuniform. We have devised a unique multiscale cell packing model in two dimensions that suggests that photoreceptor types interact with both short- and long-ranged repulsive forces and that the resultant competition between the types gives rise to the aforementioned singular spatial features characterizing the system, including multi-hyperuniformity., Comment: 31 pages, 12 figures