Statistically inferred neuronal connections from observed spike train data are often skewed from ground truth by factors such as model mismatch, unobserved neurons, and limited data. Spike train covariances, sometimes referred to as “functional connections,” are often used as a proxy for the connections between pairs of neurons, but reflect statistical relationships between neurons, not anatomical connections. Moreover, covariances are not causal: spiking activity is correlated in both the past and the future, whereas neurons respond only to synaptic inputs in the past. Connections inferred by maximum likelihood inference, however, can be constrained to be causal. However, we show in this work that the inferred connections in spontaneously active networks modeled by stochastic leaky integrate-and-fire networks strongly correlate with the covariances between neurons, and may reflect noncausal relationships, when many neurons are unobserved or when neurons are weakly coupled. This phenomenon occurs across different network structures, including random networks and balanced excitatory-inhibitory networks. We use a combination of simulations and a mean-field analysis with fluctuation corrections to elucidate the relationships between spike train covariances, inferred synaptic filters, and ground-truth connections in partially observed networks.

An inclusive framework for joined Hamiltonian and dissipative dynamical systems that are thermodynamically consistent, i.e., preserve energy and produce entropy, is given. The dissipative dynamics of the framework is based on the metriplectic 4-bracket, a quantity like the Poisson bracket defined on phase space functions, but unlike the Poisson bracket has four slots with symmetries and properties motivated by Riemannian curvature. Metriplectic 4-bracket dynamics is generated using two generators, the Hamiltonian and the entropy, with the entropy being a Casimir of the Hamiltonian part of the system. The formalism includes known previous binary bracket theories for dissipation or relaxation as special cases. Rich geometrical significance of the formalism and methods for constructing metriplectic 4-brackets are explored. Many examples of both finite and infinite dimensions are given.

In this paper, we present a hybrid numerical scheme that couples the lattice Boltzmann method (LBM) with the finite difference method (FDM) to model micro-phase-change-material (MPCM) suspensions in a minichannel. Within this framework, the LBM was employed to solve the continuity, momentum, and energy equations for the fluid domain, while a Lagrangian scheme replicates the motion of MPCM particles. The LBM is coupled with an FDM solver which operates under the lumped capacitance assumption to address the phase-change phenomena within the microparticles. This hybrid coupling eliminates the necessity for any specific treatment in handling phase transitions and tracking phase interfaces. The proposed method is first evaluated on classic particle cases, demonstrating its ability to achieve four-way coupling. Furthermore, the current model effectively adapted viscosity changes when integrating the microparticles, obviating the need for homogenous viscosity models. Subsequently, the potential of this approach is demonstrated by examining the influence of the near-wall thermal interaction of MPCM particles considering three scenarios based on particle density: light $({\rho }_p<{\rho }_f)$, neutrally buoyant $({\rho }_p\approx {\rho }_f)$, and dense $({\rho }_p>{\rho }_f)$ microparticles. The hybrid approach further revealed insights into the impact of the volume fraction on the heat transfer coefficient as well as on the overall heat transfer coefficient and performance index from a Lagrangian perspective.

The network structure of densely packed chromatin within the nucleus of eukaryotic cells acts in concert with nonequilibrium processes. Using statistical physics simulations, we explore the control provided by transient crosslinking of the chromatin network by structural-maintenance-of-chromosome (SMC) proteins over (i) the physical properties of the chromatin network and (ii) condensate formation of embedded molecular species. We find that the density and lifetime of transient SMC crosslinks regulate structural relaxation modes and tune the sol-vs-gel state of the chromatin network, which imparts control over the kinetic pathway to condensate formation. Specifically, lower density, shorter-lived crosslinks induce sollike networks and a droplet-fusion pathway, whereas higher density, longer-lived crosslinks induce gellike networks and an Ostwald-ripening pathway.

In conventional site percolation, all lattice sites are occupied with the same probability. For a bipartite lattice, sublattice-selective percolation instead involves two independent occupation probabilities, depending on the sublattice to which a given site belongs. Here, we determine the corresponding phase diagram for the two-dimensional square and Lieb lattices from quantifying the parameter regime where a percolating cluster persists for sublattice-selective percolation. For this purpose, we present an adapted Newman-Ziff algorithm. We also consider the critical exponents at the percolation transition, confirming previous Monte Carlo and renormalization-group findings that suggest sublattice-selective percolation belongs to the same universality class as conventional site percolation. To further strengthen this conclusion, we finally treat sublattice-selective percolation on the Bethe lattice (infinite Cayley tree) by an exact solution.

We investigate and solve the weak noise theory for the semidiscrete O'Connell-Yor directed polymer. In the large deviation regime, the most probable evolution of the partition function obeys a classical nonlinear system which is a nonstandard discretization of the nonlinear Schrödinger equation with mixed initial-final conditions. We show that this system is integrable and find its general solution through an inverse scattering method and a non-standard Fredholm determinant framework that we develop. This allows us to obtain the large deviation rate function of the free energy of the polymer model from its conserved quantities and to study its convergence to the large deviations of the Kardar-Parisi-Zhang equation. Our model also degenerates to the classical Toda chain, which further substantiates the applicability of our Fredholm framework.

The temperature below which the homogeneous liquid state of a mixture is not thermodynamically stable is called the liquidus temperature. This temperature varies with composition, and its composition dependence is represented by the liquidus curve. This curve provides fundamental reference points on the composition-temperature plane for characterizing the behavior of liquids, glasses, and crystals. In this paper, using molecular dynamics simulations, we determine the liquidus curve of the Wahnström mixture, which consists of large and small atoms interacting via the Lennard-Jones potential. Since this system is one of the standard models used to study the behavior of liquids and glasses, the liquidus curve presented in this work will contribute to a deeper understanding of disordered materials in general.

We propose a data-driven framework to describe spatiotemporal climate variability in terms of a few entities and their causal linkages. Given a high-dimensional climate field, the methodology first reduces its dimensionality into a set of regionally constrained patterns. Causal relations among such patterns are then inferred in the interventional sense through the fluctuation-response formalism. To distinguish between true and spurious responses, we propose an analytical null model for the fluctuation-dissipation relation, therefore allowing us for uncertainty estimation at a given confidence level. We showcase the methodology on the sea surface temperature field from a state-of-the-art climate model. The usefulness of the proposed framework for spatiotemporal climate data is demonstrated in several ways. First, we focus on the correct identification of known causal relations across tropical basins. Second, we show how the methodology allows us to visualize the cumulative response of the whole system to climate variability in a few selected regions. Finally, each pattern is ranked in terms of its causal strength, quantifying its relative ability to influence the system's dynamics. We argue that the methodology allows us to explore and characterize causal relations in spatiotemporal fields in a rigorous and interpretable way.

Sawtooth structures are observed in tunneling probabilities with changing Planck's constant for a periodically perturbed rounded-rectangular potential with a sufficiently wide width for which instanton tunneling is substantially prohibited. The sawtooth structure is a manifestation of the essential nature of multiquanta absorption tunneling. Namely, the periodic perturbation creates an energy ladder of harmonic channels at $E_n=E_I+n\hslash \omega$, where $E_I$ is an incident energy and $\omega$ is an angular frequency of the perturbation. The harmonic channel that absorbs the minimum amount of quanta of $n=\overline{n}$, such that $V_0<E_{\overline{n}}\le V_0+\hslash \omega$, makes a dominant contribution to the tunneling process, where $V_0$ is the height of the static potential and $V_0-E_I\gg \hslash \omega$. At each steep slope part of the sawtooth structure, replacement of the dominant harmonic channel, i.e., $E_{\overline{n}}\to E_{\overline{n}+1}$, occurs and the tunneling probability suddenly drops with increasing $1/\hslash$. Due to the flatness of the potential top, resonance eigenstates exist just above the potential and the first resonance state appears as the peak of each edge of the sawtooth structure for the tunneling probability in the potential region. Sawtooth structures are also observed with changing the perturbation frequency. We introduce an effective formula to characterize the basic profile of those sawtooth structures.

Within a kinetic theory, the linear magnetic response of uniaxial single-domain particles suspended in a fluid is analyzed. The main qualitatively different types of frequency dependence of the longitudinal dynamic magnetic susceptibility of such particles are described. It is shown that superparamagnetic (related to orientation thermal fluctuations of the magnetic moment inside a particle) peculiarities of the response of a particle to a probing magnetic field are not fully determined by the ratio of anisotropy energy to thermal energy when a stationary bias field is applied. For a case where the indicated ratio is much greater than one, a simple approximate expression for the dynamic magnetic susceptibility of a particle is proposed. The developed approach is extended to polydisperse suspensions of noninteracting uniaxial nanoparticles. It is shown that polydispersity does not vanish away specific superparamagnetic features in the dynamic magnetic response of such systems. Quantitative estimates of the corresponding effects are performed in different frequency ranges of the applied field. It is demonstrated that under certain restrictions on the disperse composition of a suspension, the internal diffusion of the magnetic moment can lead to a splitting of the absorption spectrum of the system. The significant role of the bias field is revealed. In particular, it can cause an additional absorption maximum provided the particle-size distribution meets the outlined condition. Also, it enables one to assess how important it is to take into account superparamagnetism of particles: the effect of the biasing is stronger for particles with smaller anisotropy and thereby more pronounced superparamagnetic properties. A qualitative agreement of some of the inferences with the experimental data is briefly discussed.

In recent work it was shown that elasticity theory can break down in amorphous solids subjected to nonuniform static loads. The elastic fields are screened by geometric dipoles; these stem from gradients of the quadrupole field associated with plastic responses. Here we study the dynamical responses induced by oscillatory loads. The required modification to classical elasticity is described. Exact solutions for the displacement field in circular geometry are presented, demonstrating that dipole screening results in essential departures from the expected predictions of classical elasticity theory. Numerical simulations are conducted to validate the theoretical predictions and to delineate their range of validity.

We numerically explore the two-dimensional, incompressible, isothermal flow through a wavy channel, with a focus on how the channel geometry affects the routes to chaos at Reynolds numbers between 150 and 1000. We find that (i) the period-doubling route arises in a symmetric channel, (ii) the Ruelle-Takens-Newhouse route arises in an asymmetric channel, and (iii) the type-II intermittency route arises in both asymmetric and semiwavy channels. We also find that the flow through the semiwavy channel evolves from a quasiperiodic torus to an unstable invariant set (chaotic saddle), before eventually settling on a period-1 limit-cycle attractor. This study reveals that laminar channel flow at elevated Reynolds numbers can exhibit a variety of nonlinear dynamics. Specifically, it highlights how breaking the symmetry of a wavy channel can not only influence the critical Reynolds number at which chaos emerges, but also diversify the types of bifurcation encountered en route to chaos itself.

Entropy production and dynamical activity are two complementary aspects in nonequilibrium physics. The asymmetry of cross-correlation, serving as a distinctive feature of nonequilibrium, also finds widespread utility. In this Letter, we establish two thermodynamic bounds on the normalized asymmetry of cross-correlation in terms of dynamical activity and entropy production rate. These bounds demonstrate broad applicability and offer experimental testability.

We investigate the thermodynamic characteristics of unified quantum statistics, a framework exhibiting a crossover between Bose-Einstein and Fermi-Dirac statistics by varying a generalization parameter $\delta$. An intrinsic statistical interaction becomes attractive for $\delta \le 0.5$, maintaining positive thermodynamic curvature across the entire physical range. In the range $0.5<\delta <1$, the system predominantly displays Fermi-like behavior at high temperatures. Conversely, at low temperatures, the thermodynamic curvature is positive, resembling bosonic behavior. Further temperature reduction induces a transition into the condensate phase. We introduce a critical fugacity ($z=Z^{*}$) at which the thermodynamic curvature changes sign. Below ($z<Z^{*}$) and above ($z>Z^{*}$) this critical point, the statistical behavior mimics fermions and bosons, respectively. We explore the system's statistical behavior for various $\delta$ values with respect to temperature, determining the critical fugacity and temperature-dependent condensation. Finally, we analyze specific heat as a function of temperature and condensation phase transition temperature for different $\delta$ values in various dimensions.

Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external reservoirs, a range of behaviors is possible, including transition to a new equilibrium state, a nonequilibrium state, or indefinite growth. This study shows that slowly driven CRNs are governed by the conserved quantities of the closed system, which are generally far fewer in number than the species. Considering both deterministic and stochastic dynamics, a universal slow-dynamics equation is derived with singular perturbation methods and is shown to be thermodynamically consistent. The slow dynamics is highly robust against microscopic details of the network, which may be unknown in practical situations. In particular, nonequilibrium states of realistic large CRNs can be sought without knowledge of bulk reaction rates. The framework is successfully tested against a suite of networks of increasing complexity and argued to be relevant in the treatment of open CRNs as chemical machines.

The origin of the uniform Dzyaloshinskii-Moriya interaction (DMI), which is responsible for the creation of chiral magnetism, has been the subject of extensive research. Recently, modern technology has allowed for its production and utilization in a modulated form. Not only can magnetic phases of spin chains be enriched by the presence of such a potential as detailed in Japaridze et al. [Phys. Rev. E 104, 014134 (2021)], but the capacity of such systems for information transmission is also greatly enhanced. The current paper examines the impact of a staggered pattern of DMI (STDMI) on a chain with a substrate XX Heisenberg interaction. It is demonstrated how enhancing the intensity of this coupling improves the propagation of an entangled quantum state. Additionally, as our analysis has shown, the initial condition over the system's state has a profound effect on the speed at which entanglement spreads. The aberrant behavior of the entanglement's speed profile in response to fine-tuning of the phase factor which adjusts the initial state is the focus of this paper. This anomalous behavior is characterized by dramatic drops in speed for certain phase factor values. We have also shown that, using wave interference principles, we can predict exactly why these phenomena occur. This research will pave the way for additional studies on STDMI and its potential applications in the field of quantum information.

We present a simple model to predict network activity at the edge level by extending a known approximation method to compute betweenness centrality with a repulsive mechanism to prevent unphysical densities. By taking into account the strong interaction effects often observed in real phenomena, we aim to obtain an improved measure of edge usage during rush hours as traffic congestion patterns emerge in urban networks. In this approach, the network is iteratively populated by agents following dynamically evolving fastest paths who are progressively attracted towards uncongested parts of the network as the global traffic volume increases. Following the transition of the network state from empty to saturated, we study the emergence of congestion and the progressive disruption of global connectivity due to a relatively small fraction of crowded edges. We assess the predictive power of our model by comparing the speed distribution against a large experimental data set for the London area with remarkable results, which also translate into a qualitative similarity of the congestion maps. Also, percolation analysis confirms the quantitative agreement of the model with the real data for London. We perform simulations for seven other topologically different cities to obtain the Fisher critical exponent $\tau$ that shows no common functional dependence on the traffic level. The critical exponent $\gamma$, studied to assess the power-law decay of spatial correlation, is found to be inversely proportional to the number of vehicles for both real and simulated traffic. This simulation approach seems particularly fit to describe qualitative and quantitative properties of the network loading process, culminating in peak-hour congestion, by using only topological and geographical network features.

In the face of the stupefying complexity of the human brain, network analysis is a most useful tool that allows one to greatly simplify the problem, typically by approximating the billions of neurons making up the brain by means of a coarse-grained picture with a practicable number of nodes. But even such relatively small and coarse networks, such as the human connectome with its 100–1000 nodes, may present challenges for some computationally demanding analyses that are incapable of handling networks with more than a handful of nodes. With such applications in mind, we set out to study the extent to which dynamical behavior and critical phenomena in the brain may be preserved following a severe coarse-graining procedure. Thus we proceeded to further coarse grain the human connectome by taking a modularity-based approach, the goal being to produce a network of a relatively small number of modules. After finding that the qualitative dynamical behavior of the coarse-grained networks reflected that of the original networks, albeit to a less pronounced extent, we then formulated a hypothesis based on the coarse-grained networks in the context of criticality in the Wilson-Cowan and Ising models, and we verified the hypothesis, which connected a transition value of the former with the critical temperature of the latter, using the original networks. This preservation of dynamical and critical behavior following a severe coarse-graining procedure, in principle, allows for the drawing of similar qualitative conclusions by analyzing much smaller networks, which opens the door for studying the human connectome in contexts typically regarded as computationally intractable, such as Integrated Information Theory and quantum models of the human brain.