Physical review. E最新文献

From cytoskeletal networks to tissues, many biological systems behave as active materials. Their composition and stress generation is affected by chemical reaction networks. In such systems, the coupling between mechanics and chemistry enables self-organization, for example, into waves. Recently, contractile mechanochemical systems have been shown to be able to spontaneously develop localized spatial patterns. Here, we show that these localized patterns can present intrinsic spatiotemporal dynamics, including oscillations and chaotic-like dynamics. We discuss their physical origin and bifurcation structure.

Network systems can exhibit memory effects in which the interactions between different pairs of nodes adapt in time, leading to the emergence of preferred connections, patterns, and subnetworks. To a first approximation, this memory can be modeled through a "plastic" Hebbian or homophily mechanism, in which edges get reinforced proportionally to the amount of information flowing through them. However, recent studies on glia-neuron networks have highlighted how memory can evolve due to more complex dynamics, including multilevel network structures and "metaplastic" effects that modulate reinforcement. Inspired by those systems, here we develop a simple and general model for the dynamics of an adaptive network with an additional metaplastic mechanism that varies the rate of Hebbian strengthening of its edge connections. The metaplastic term acts on a second network level in which edges are grouped together, simulating local, longer timescale effects. Specifically, we consider a biased random walk on a cyclic feed-forward network. The random walk chooses its steps according to the weights of the network edges. The weights evolve through a Hebbian mechanism modulated by a metaplastic reinforcement, biasing the walker to prefer edges that have been already explored. We study the dynamical emergence (memorization) of preferred paths and their retrieval and identify three regimes: one dominated by the Hebbian term, one in which the metareinforcement drives memory formation, and a balanced one. We show that, in the latter two regimes, metareinforcement allows the retrieval of a previously stored path even after the weights have been reset to zero to erase Hebbian memory.

In this paper, using hydrodynamic entropy, we quantify multiscale disorder in Euler and hydrodynamic turbulence. These examples illustrate that the hydrodynamic entropy is not extensive because it is not proportional to the system size. Consequently, we cannot add hydrodynamic and thermodynamic entropies, which measure disorder at macroscopic and microscopic scales, respectively. In this paper, we also discuss the hydrodynamic entropy for the time-dependent Ginzburg-Landau equation and Ising spins.

One of the key predictions of Parisi's broken replica symmetry theory of spin glasses is the existence of a phase transition in an applied field to a state with broken replica symmetry. This transition takes place at the de Almeida-Thouless (AT) line in the h-T plane. We have studied this line in the power-law diluted Heisenberg spin glass in which the probability that two spins separated by a distance r interact with each other falls as 1/r^{2σ}. In the presence of a random vector field of variance h_{r}^{2} the phase transition is in the universality class of the Ising spin glass in a field. Tuning σ is equivalent to changing the dimension d of the short-range system, with the relation being d=2/(2σ-1) for σ<2/3. We have found by numerical simulations that h_{AT}^{2}∼(2/3-σ) implying that the AT line does not exist below six dimensions and that the Parisi scheme is not appropriate for spin glasses in three dimensions.

We examine the conditions for the emergence of self-organized criticality in the Olami-Feder-Christensen model by introducing a single defect under periodic boundary conditions. Our findings reveal that strong localized energy dissipation is crucial for self-organized criticality emergence, while weak localized or global energy dissipation leads to its disappearance in this model. Furthermore, slight dissipation perturbations to a system in a self-organized criticality reveal a novel state characterized by a limit cycle of distinct configurations. This newly discovered state offers significant insights into the fundamental mechanisms governing the emergence of self-organized criticality.

The thermodynamic relations for a Brownian particle moving in a discrete ratchet potential coupled with quadratically decreasing temperature are explored as a function of time. We show that this thermal arrangement leads to a higher velocity (lower efficiency) compared to a Brownian particle operating between hot and cold baths, and a heat bath where the temperature linearly decreases along with the reaction coordinate. The results obtained in this study indicate that if the goal is to design a fast-moving motor, the quadratic thermal arrangement is more advantageous than the other two thermal arrangements. In contrast, the entropy, entropy production rate, and entropy extraction rate are significantly larger in the case of a quadratically decreasing temperature compared to the linearly decreasing temperature case and piecewise constant temperature case. Furthermore, the thermodynamic features of a system consisting of several Brownian ratchets arranged in a complex network are explored. The theoretical findings exhibit that as the network size increases, the entropy, entropy production, and entropy extraction of the system also increase, showing that these thermodynamic quantities exhibit extensive property. As a result, as the number of lattice sizes increases, thermodynamic relations such as entropy, entropy production, and entropy extraction also step up, confirming that these complex networks cannot be reduced to a corresponding one-dimensional lattice. However, in the long time limit, thermodynamic relations such as velocity, entropy production rate, and entropy extraction rate become independent of the network size. These results are also confirmed via a continuum Fokker-Planck model for the overdamped case.

Deep learning models have achieved high performance in a wide range of applications. Recently, however, there have been increasing concerns about the fragility of many of those models to adversarial approaches and out-of-distribution inputs. A way to investigate and potentially address model fragility is to develop the ability to provide interpretability to model predictions. To this end, input attribution approaches such as Grad-CAM and integrated gradients have been introduced to address model interpretability. Here, we combine adversarial and input attribution approaches in order to achieve two goals. The first is to investigate the impact of adversarial approaches on input attribution. The second is to benchmark competing input attribution approaches. In the context of the image classification task, we find that models trained with adversarial approaches yield dramatically different input attribution matrices from those obtained using standard techniques for all considered input attribution approaches. Additionally, by evaluating the signal-(typical input attribution of the foreground)-to-noise (typical input attribution of the background) ratio and correlating it to model confidence, we are able to identify the most reliable input attribution approaches and demonstrate that adversarial training does increase prediction robustness. Our approach can be easily extended to contexts other than the image classification task and enables users to increase their confidence in the reliability of deep learning models.

We study the fluctuational behavior of overdamped elastic filaments (e.g., strings or rods) driven by active matter which induces irreversibility. The statistics of discrete normal modes are translated into the continuum of the position representation which allows discernment of the spatial structure of dissipation and fluctuational work done by the active forces. The mapping of force statistics onto filament statistics leads to a generalized fluctuation-dissipation relation which predicts the components of the stochastic area tensor and its spatial proxy, the irreversibility field. We illustrate the general theory with explicit results for a tensioned string between two fixed endpoints. Plots of the stochastic area tensor components in the discrete plane of mode pairs reveal how the active forces induce spatial correlations of displacement along the filament. The irreversibility field provides additional quantitative insight into the relative spatial distributions of fluctuational work and dissipative response.

The cross-entropy loss function is widely used in machine learning to measure the performance of a classification model. Interestingly, our study find that this function has scaling behavior when deep neural networks are used to investigate percolation models. Specifically, we use convolutional neural networks with different pooling methods to study the site percolation on square lattices under two labeling methods (labeling based on spanning cluster and the exact solution of the critical point). Subsequently, graph convolutional neural networks (GCNs) with different pooling methods are utilized to do the same kind of experiment. Finally, the GCN with different pooling methods is used to study the percolation phase transitions on the Erdős-Rényi (ER) networks under labeling based on the critical point. The reliability of the classifiers is detected by the values of the critical point p_{c} and critical exponent ν which are obtained by the scaling behaviors of the percolation probability. The results demonstrate that the scaling exponent of cross-entropy ψ/ν depends on the labeling and pooling methods. Labeling based on critical points, which is equivalent to labeling based on spanning clusters in infinite systems, can be used to investigate the critical behaviors in finite systems. SAGPooling-Mean is an effective pooling method to study the scaling behavior of cross-entropy loss on two-dimensional square lattices and ER networks.

Thermal resonance, that is, the heat flux obtained by means of a periodic external driving, offers the possibility of controlling heat flux in nanoscale devices suitable for power generation, cooling, and thermoelectrics, among others. In this work we study the effect of the onsite potential period on the thermal resonance phenomenon present in a one-dimensional system composed of two dissimilar Frenkel-Kontorova lattices connected by a time-modulated coupling and in contact with two heat reservoirs operating at different temperature by means of molecular dynamics simulations. When the periods of the onsite potential on both sides of the system are equal, the maximum resonance is obtained for the lowest considered value of the period. For highly structurally asymmetric lattices, the heat flux toward the cold reservoir is maximized, and asymmetric periods of the onsite potential afford an extra way to control the magnitude of the heat fluxes in each side of the system. Our results highlight the importance of the substrate structure on thermal resonance and could inspire further developments in designing thermal devices.