相关论文: Magic number 7 $\pm$ 2 in networks of threshold dy…

The prevalence of Milnor attractors has recently been reported in a class of high-dimensional dynamical systems. We study how this prevalence depends on the number of degrees of freedom by using a globally coupled map and show that the…

Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely…

Universal intermittent dynamics in a random catalytic reaction network, induced by smallness in the molecule number is reported. Stochastic simulations for a random catalytic reaction network subject to a flow of chemicals show that the…

Magic is the resource that quantifies the amount of beyond-Clifford operations necessary for universal quantum computing. It bounds the cost of classically simulating quantum systems via stabilizer circuits central to quantum error…

Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information…

Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…

In a previous report we have evaluated analytically the mutual information between the firing rates of N independent units and a set of continuous+discrete stimuli, for finite N and in the limit of large noise. Here, we extend the analysis…

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme…

We have known that most sequences in $\mathcal{M}=\{1,2,\dots, M\}$ with length $n$ will miss $Me^{-\lambda}$ of the total numbers of $\{1,2,\dots,M\}$ as the ratio $n/M$ tends to $\lambda$. Now we consider a more general case where the…

Critical transitions are observed in many complex systems. This includes the onset of synchronization in a network of coupled oscillators or the emergence an epidemic state within a population. "Explosive" first-order transitions have…

In formal languages and automata theory, the magic number problem can be formulated as follows: for a given integer n, is it possible to find a number d in the range [n,2^n] such that there is no minimal deterministic finite automaton with…

Triggered by a controversy surrounding a universal behaviour of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral…

In a previous report we have evaluated analytically the mutual information between the firing rates of N independent units and a set of multi-dimensional continuous+discrete stimuli, for a finite population size and in the limit of large…

Two dimensional condensed matter is realised in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic…

Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates…

We investigate the topological structure of the decimal expansions of the three famous naturally occurring irrational numbers, $\pi$, $e$, and golden ratio, by explicitly calculating the diversity of the pair distributions of the ten digits…

A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how…

We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an…

We propose a general method for the construction and analysis of unweighted $\epsilon$ - recurrence networks from chaotic time series. The selection of the critical threshold $\epsilon_c$ in our scheme is done empirically and we show that…

Several studies have identified a significant amount of redundancy in the network traffic. For example, it is demonstrated that there is a great amount of redundancy within the content of a server over time. This redundancy can be leveraged…