Although temporal coding through spike-time patterns has long been of interest in neuroscience, the specific structures that could be useful for spike-time codes remain highly unclear. Here, we introduce an analytical approach, using techniques from discrete mathematics, to study spike-time codes. As an initial example, we focus on the phenomenon of “phase precession” in the rodent hippocampus. During navigation and learning on a physical track, specific cells in a rodent's brain form a highly structured pattern relative to the oscillation of population activity in this region. Studies of phase precession largely focus on its role in precisely ordering spike times for synaptic plasticity, as the role of phase precession in memory formation is well established. Comparatively less attention has been paid to the fact that phase precession represents one of the best candidates for a spike-time neural code. The precise nature of this code remains an open question. Here, we derive an analytical expression for a function mapping points in physical space to complex-valued spikes by representing individual spike times as complex numbers. The properties of this function make explicit a specific relationship between past and future in spike patterns of the hippocampus. Importantly, this mathematical approach generalizes beyond the specific phenomenon studied here, providing a technique to study the neural codes within precise spike-time sequences found during sensory coding and motor behavior. We then introduce a spike-based decoding algorithm, based on this function, that successfully decodes a simulated animal's trajectory using only the animal's initial position and a pattern of spike times. This decoder is robust to noise in spike times and works on a timescale almost an order of magnitude shorter than typically used with decoders that work on average firing rate. These results illustrate the utility of a discrete approach, based on the structure and symmetries in spike patterns across finite sets of cells, to provide insight into the structure and function of neural systems.

The coordinated movement of multiple swimmers is a crucial component of fish schools. Fish swimming in different formations, such as tandem, side-by-side, diamond, and phalanx, can achieve significant energetic advantages. However, the energetic benefits of nonstraight swimming behaviors, such as the collective motion of a milling pattern, are not well understood. To fill in this gap, we consider two swimmers in circular tracks, controlled by a PID approach to reach stable configurations. Our study finds that the optimal phase is affected by circumferential effects, and that substantial energy savings can result from both propulsion and turning. We also explore the radial effect in terms of energetic benefits. In a milling pattern, the inner swimmers can easily gain a certain energetic benefit ($-8\%$), while their peers on the outside must be close enough to the inner swimmer with a proper phase to gain the energetic benefit ($-14\%$). When the radial spacing becomes larger or is in an unmatched phase, the swimming of the outer swimmers becomes more laborious ($+16\%$). Our results indicate that swimmers who maintain a matched phase and minimum radial effect obtain the highest energetic benefits ($-26\%$). These findings highlight the energetic benefits of swimmers, even in a milling pattern, where the position difference dominates the extent of benefit.

The main objective of this work is to clarify the role that taper-shaped elongated molecules, i.e., molecules with one end wider than the other, can play in stabilizing orientational order. The focus is exclusively on entropy-driven self-organization induced by purely excluded volume interactions. Drawing an analogy to RM734 (4-[(4-nitrophenoxy)carbonyl]phenyl-2,4-dimethoxybenzoate), which is known to stabilize ferroelectric nematic (${\text{N}}_{\text{F}}$) and nematic splay (${\text{N}}_{\text{S}}$) phases, and assuming that molecular biaxiality is of secondary importance, we consider monodisperse systems composed of hard molecules. Each molecule is modeled using six collinear tangent spheres with linearly decreasing diameters. Through hard-particle, constant-pressure Monte Carlo simulations, we study the emergent phases as functions of the ratio between the smallest and largest diameters of the spheres (denoted as $d$) and the packing fraction ($\eta$). To analyze global and local molecular orderings, we examine molecular configurations in terms of nematic, smectic, and hexatic order parameters. Additionally, we investigate the radial pair distribution function, polarization correlation function, and the histogram of angles between molecular axes. The last characteristic is utilized to quantify local splay. The findings reveal that splay-induced deformations drive unusual long-range orientational order at relatively high packing fractions ($\eta >0.5$), corresponding to crystalline phases. When $\eta <0.5$, only short-range order is affected, and in addition to the isotropic liquid, only the standard nematic and smectic-A liquid crystalline phases are stabilized. However, for $\eta >0.5$, apart from the ordinary nonpolar hexagonal crystal, three additional frustrated crystalline polar blue phases with long-range splay modulation are observed: antiferroelectric splay crystal (${\text{Cr}}_{\text{S}}{\text{P}}_{\text{A}}$), antiferroelectric double-splay crystal (${\text{Cr}}_{\text{DS}}{\text{P}}_{\text{A}}$), and ferroelectric double-splay crystal (${\text{Cr}}_{\text{DS}}{\text{P}}_{\text{F}}$). Finally, we employ Onsager-Parsons-Lee local density functional theory to investigate whether any sterically induced (anti)ferroelectric nematic or smectic-A type of ordering is possible for our system, at least in a metastable regime.

Reconstruction of microstructure in granular porous media, which can be viewed as granular assemblies, is crucial for studying their characteristics and physical properties in various fields concerned with the behavior of such media, including petroleum geology and computational materials science. In spite of the fact that many existing studies have investigated grain reconstruction, most of them treat grains as simplified individuals for discrete reconstruction, which cannot replicate the complex geometrical shapes and natural interactions between grains. In this work, a hybrid generative model based on a deep-learning algorithm is proposed for high-quality three-dimensional (3D) microstructure reconstruction of granular porous media from a single two-dimensional (2D) slice image. The method extracts 2D prior information from the given image and generates the grain set as a whole. Both a self-attention module and effective pattern loss are introduced in a bid to enhance the reconstruction ability of the model. Samples with grains of varied geometrical shapes are utilized for the validation of our method, and experimental results demonstrate that our proposed approach can accurately reproduce the complex morphology and spatial distribution of grains without any artificiality. Furthermore, once the model training is complete, rapid end-to-end generation of diverse 3D realizations from a single 2D image can be achieved.

The out-of-time-ordered correlator (OTOC) has emerged as an interesting object in both classical and quantum systems for probing the spatial spread and temporal growth of initially local perturbations in spatially extended chaotic systems. Here, we study the (classical) OTOC and its “light cone” in the nonlinear Kuramoto-Sivashinsky (KS) equation, using extensive numerical simulations. We also show that the linearized KS equation exhibits a qualitatively similar OTOC and light cone, which can be understood via a saddle-point analysis of the linearly unstable modes. Given the deep connection between the KS (deterministic) and the Kardar-Parisi-Zhang (KPZ, which is stochastic) equations, we also explore the OTOC in the KPZ equation. While our numerical results in the KS case are expected to hold in the continuum limit, for the KPZ case it is valid in a discretized version of the KPZ equation. More broadly, our work unravels the intrinsic interplay between noise/instability, nonlinearity, and dissipation in partial differential equations (deterministic or stochastic) through the lens of OTOC.

The renewal process is a point process where an interevent time between successive renewals is an independent and identically distributed random variable. Alternating renewal process is a dichotomous process and a slight generalization of the renewal process, where the interevent time distribution alternates between two distributions. We investigate statistical properties of the number of renewals and occupation times for one of the two states in alternating renewal processes. When both means of the interevent times are finite, the alternating renewal process can reach an equilibrium. On the other hand, an alternating renewal process shows aging when one of the means diverges. We provide analytical calculations for the moments of the number of renewals, occupation time statistics, and the correlation function for several case studies in the interevent-time distributions. We show anomalous fluctuations for the number of renewals and occupation times when the second moment of interevent time diverges. When the mean interevent time diverges, distributional limit theorems for the number of events and occupation times are shown analytically. These are known as the Mittag-Leffler distribution and the generalized arcsine law in probability theory.

We study the nonequilibrium dynamics of an isolated bipartite quantum system, the sunburst quantum Ising model, under interaction quench. The prequench limit of this model is two noninteracting integrable systems, namely a transverse Ising chain and finite number of isolated qubits. As a function of interaction strength, the spectral fluctuation property goes from Poisson to Wigner-Dyson statistics. We chose entanglement entropy as a probe to study the approach to thermalization or lack of it in postquench dynamics. In the near-integrable limit, as expected, the linear entropy displays oscillatory behavior, while in the chaotic limit it saturates. Along with the chaotic nature of the time evolution generator, we show the importance of the role played by the coherence of the initial state in deciding the nature of thermalization. We further show that these findings are general by replacing the Ising ring with a disordered $XXZ$ model with disorder strength putting it in the many-body localized phase.

In a predator-prey metapopulation, two traits are adversely related: synchronization and persistence. A decrease in synchrony apparently leads to an increase in persistence and, therefore, necessitates the study of desynchrony in a metapopulation. In this article, we study predator-prey patches that communicate with one another while being interconnected through distinct dispersal structures in the layers of a three-layer multiplex network. We investigate the synchronization phenomenon among the patches of the outer layers by introducing higher-order interactions (specifically three-body interactions) in the middle layer. We observe a decrease in the synchronous behavior or, alternatively, an increase in desynchrony due to the inclusion of group interactions among the patches of the middle layer. The advancement of desynchrony becomes more prominent with increasing strength and numbers of three-way interactions in the middle layer. We analytically validate our numerical results by performing a stability analysis of the referred synchronous solution using the master stability function approach. Additionally, we verify our findings by taking into account two distinct predator-prey models and dispersal topologies, which ultimately supports that the findings are generalizable across various models and dispersal structures.

Diversity is omnipresent in natural and synthetic extended systems, the phenomenon of diversity-induced resonance (DIR), wherein a moderate degree of the diversity can provoke an optimal collective response, provides researchers a brand-new strategy to amplify and utilize the weak signal. As yet the relevant advances focus mostly on the ideal situations where the interactions among elements are uncorrelated with the physical proximity of agents. Such a consideration overlooks interactions mediated by the motion of agents in space. Here, we investigate the signal response of an ensemble of spatial mobile heterogeneous bistable oscillators with two canonical interacting modes: dynamic and preset. The oscillators are considered as mass points and perform random walks in a two-dimensional square plane. Under the dynamic scheme, the oscillators can only interact with other oscillators within a fixed vision radius. For the preset circumstance, the interaction among oscillators occurs only when all of them are in a predefined region at the same moment. We find that the DIR can be obtained in both situations. Additionally, the strength of resonance nonmonotonically rises with respect to the increase of moving speed, and the optimal resonance is acquired by an intermediate magnitude of speed. Finally, we propose reduced equations to guarantee the occurrence of such mobility-optimized DIR on the basis of the fast switching approximation theory and also examine the robustness of such phenomenon through the excitable FitzHugh-Nagumo model and a different spatial motion mechanism. Our results reveal for the first time that the DIR can be optimized by the spatial mobility and thus has promising potential application in the communication of mobile agents.

We present a systematic investigation of the short-range spectral fluctuation properties of three non-Hermitian spin-chain Hamiltonians using complex spacing ratios (CSRs). Specifically, we focus on the non-Hermitian variants of the standard one-dimensional anisotropic XY model having intrinsic rotation-time ($\mathcal{RT}$) symmetry that has been explored analytically by Zhang and Song [Phys. Rev. A 87, 012114 (2013)]. The corresponding Hermitian counterpart is also exactly solvable and has been widely employed as a toy model in several condensed matter physics problems. We show that the presence of a random field along the $x$ direction together with the one along the $z$ direction facilitates integrability and $\mathcal{RT}$-symmetry breaking, leading to the emergence of quantum chaotic behavior. This is evidenced by a spectral crossover closely resembling the transition from Poissonian to Ginibre unitary ensemble (GinUE) statistics of random matrix theory. Additionally, we consider two phenomenological random matrix models in this paper to examine 1D Poisson to GinUE and 2D Poisson to GinUE crossovers and the associated signatures in CSRs. Here 1D and 2D Poisson correspond to real and complex uncorrelated levels, respectively. These crossovers reasonably capture spectral fluctuations observed in the spin-chain systems within a certain range of parameters.

Integrable turbulence studies the complex dynamics of random waves for the nonlinear integrable systems, and it has become an important element in exploring the sophisticated turbulent phenomena. In the present work, based on the coupled nonlinear Schrödinger models, we have shown the coexistence of Gaussian and non-Gaussian single-point statistics in multiple wave components, which might be viewed as an exclusive feature for the vector integrable turbulence. This coexistent statistic can relate to different distributions of the vector solitonic excitations depending on the time-invariant nonlinear spectra. Our results are expected to shed light on a deeper understanding of the turbulent behaviors of vector waves and may motivate relevant experiments in the coupled optical or atomic systems.

We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately geometrically round cultures get a competitive advantage. We first analyze the model with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e., freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely, that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity, and the central European plain has less clear cultural borders.

Non-Euclidean origami is a promising technique for designing multistable deployable structures folded from nonplanar developable surfaces. The impossibility of flat foldability inherent to non-Euclidean origami results in two disconnected solution branches each with the same angular deficiency but opposite handedness. We show that these regions can be connected via “crease stretching,” wherein the creases exhibit extensibility in addition to torsional stiffness. We further reveal that crease stretching acts as an energy storage method capable of passive deployment and control. Specifically, we show that in a Miura-Ori system with a single stretchable crease, this is achieved via two unique, easy to realize, equilibrium folding pathways for a certain wide set of parameters. In particular, we demonstrate that this connection mostly preserves the stable states of the non-Euclidean system, while resulting in a third stable state enabled only by the interaction of crease torsion and stretching. Finally, we show that this simplified model can be used as an efficient and robust tool for inverse design of multistable origami based on closed-form predictions that yield the system parameters required to attain multiple, desired stable shapes. This facilitates the implementation of multistable origami for applications in architecture materials, robotics, and deployable structures.

We examine the momentum and thermal transport in the continuum breakdown regime of a mixing layer flow, which exhibits Kelvin-Helmholtz instability under ideal continuum conditions. The Grad 13 moment model is used as it provides an adequate description of the flow physics (second-order accurate in Knudsen number) in the transition regime. Analytical solutions are developed under breakdown conditions for two-dimensional, compressible, parallel shear flows. It is shown that the deviation of viscous stress and heat flux from the Navier-Stokes-Fourier system follows two different scaling regimes depending upon the Mach number. At low Mach numbers, the departure of all stress and heat-flux components depends only upon the Knudsen number. At high Mach number, the scaling of shear stress and transverse heat flux depends on the product of the Knudsen and Mach numbers. The normal stresses depend individually on the Knudsen and Mach number. The scaling results are verified against numerical simulations of compressible mixing layers performed using the unified gas kinetic scheme for various degrees of rarefaction.

Long-range interacting systems unavoidably relax through Poisson shot noise fluctuations generated by their finite number of particles, $N$. When driven by two-body correlations, i.e., $1/N$ effects, this long-term evolution is described by the inhomogeneous $1/N$ Balescu-Lenard equation. Yet, in one-dimensional systems with a monotonic frequency profile and only subject to 1:1 resonances, this kinetic equation exactly vanishes: this is a first-order full kinetic blocking. These systems' long-term evolution is then driven by three-body correlations, i.e., $1/N^2$ effects. In the limit of dynamically hot systems, this is described by the inhomogeneous $1/N^2$ Landau equation. We numerically investigate the long-term evolution of systems for which this second kinetic equation also exactly vanishes: this a second-order bare kinetic blocking. We demonstrate that these systems relax through the “leaking” contributions of dressed three-body interactions that are neglected in the inhomogeneous $1/N^2$ Landau equation. Finally, we argue that these never-vanishing contributions prevent four-body correlations, i.e., $1/N^3$ effects, from ever being the main driver of relaxation.

In quantum thermodynamics, the two-projective-measurement (TPM) scheme provides a successful description of stochastic work only in the absence of initial quantum coherence. Extending the quantum work distribution to quasiprobability is a general way to characterize work fluctuation in the presence of initial coherence. However, among a large number of different definitions, there is no consensus on the most appropriate work quasiprobability. In this article, we list several physically reasonable requirements including the first law of thermodynamics, time-reversal symmetry, positivity of second-order moment, and a support condition for the work distribution. We prove that the only definition that satisfies all these requirements is the Margenau-Hill (MH) quasiprobability of work. In this sense, the MH quasiprobability of work shows its advantages over other definitions. As an illustration, we calculate the MH work distribution of a breathing harmonic oscillator with initial squeezed states and show the convergence to classical work distribution in the classical limit.

The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating drift and diffusion functions from inordinately large datasets through the use of incremental, online, updating statistics. I demonstrate the validity and utility of this method by analyzing three large, varied synthetic datasets, as well as an empirical turbulence dataset. This method will hopefully facilitate the analysis of complex systems from exceedingly large, “big data” scientific datasets, as well as real-time streamed data.

We consider a quantized version of the Sinai-Derrida model for “random walk in random environment.” The model is defined in terms of a Lindblad master equation. For a ring geometry (a chain with periodic boundary condition) it features a delocalization-transition as the bias in increased beyond a critical value, indicating that the relaxation becomes underdamped. Counterintuitively, the effective disorder is enhanced due to coherent hopping. We analyze in detail this enhancement and its dependence on the model parameters. The nonmonotonic dependence of the Lindbladian spectrum on the rate of the coherent transitions is highlighted.

Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In particular, percolation properties of correlation networks have been employed to identify early warning signals of critical transitions. In this work, we further investigate the corresponding potential of percolation measures for the anticipation of different types of sudden shifts in the state of coupled irregularly oscillating systems. As a paradigmatic model system, we study the dynamics of a ring of diffusively coupled noisy FitzHugh-Nagumo oscillators and show that, when the oscillators are nearly completely synchronized, the percolation-based precursors successfully provide very early warnings of the rapid switches between the two states of the system. We clarify the mechanisms behind the percolation transition by separating global trends given by the mean-field behavior from the synchronization of individual stochastic fluctuations. We then apply the same methodology to real-world data of sea surface temperature anomalies during different phases of the El Niño-Southern Oscillation. This leads to a better understanding of the factors that make percolation precursors effective as early warning indicators of incipient El Niño and La Niña events.

Understanding the homing dynamics of individual mesenchymal stem cells (MSCs) in physiologically relevant microenvironments is crucial for improving the efficacy of MSC-based therapies for therapeutic and targeting purposes. This study investigates the passive homing behavior of individual MSCs in micropores that mimic interendothelial clefts through predictive computational simulations informed by previous microfluidic experiments. Initially, we quantified the size-dependent behavior of MSCs in micropores and elucidated the underlying mechanisms. Subsequently, we analyzed the shape deformation and traversal dynamics of each MSC. In addition, we conducted a systematic investigation to understand how the mechanical properties of MSCs impact their traversal process. We considered geometric and mechanical parameters, such as reduced cell volume, cell-to-nucleus diameter ratio, and cytoskeletal prestress states. Furthermore, we quantified the changes in the MSC traversal process and identified the quantitative limits in their response to variations in micropore length. Taken together, the computational results indicate the complex dynamic behavior of individual MSCs in the confined microflow. This finding offers an objective way to evaluate the homing ability of MSCs in an interendothelial-slit-like microenvironment.