Noise is ubiquitous and has been verified to play constructive roles in various systems, among which the inverse stochastic resonance (ISR) has aroused much attention in contrast to positive effects such as stochastic resonance. The ISR has been observed in both bistable and monostable systems for which the mechanisms are revealed as noise-induced biased switching and noise-enhanced stability, respectively. In this paper, we investigate the ISR phenomenon in the monostable and bistable Hindmarsh-Rose neurons within a unified framework of large deviation theory. The critical noise strengths for both cases can be obtained by matching the timescales between noise-induced boundary crossing and the limit cycle. Furthermore, different stages of ISR are revealed by the bursting frequency distribution, where the gradual increase of the peak bursting frequency can also be explained within the same framework. The perspective and results in this paper may shed some light on the understanding of the noise-induced complex phenomena in stochastic dynamical systems.Modeling, simulation, and analysis of interacting agent systems is a broad field of research, with existing approaches reaching from informal descriptions of interaction dynamics to more formal, mathematical models. In this paper, we study agent-based models (ABMs) given as continuous-time stochastic processes and their pathwise approximation by ordinary and stochastic differential equations (SDEs) for medium to large populations. By means of an appropriately adapted transfer operator approach, we study the behavior of the ABM process on long time scales. We show that, under certain conditions, the transfer operator approach allows us to bridge the gap between the pathwise results for large populations on finite timescales, i.e., the SDE limit model, and approaches built to study dynamical behavior on long time scales like large deviation theory. The latter provides a rigorous analysis of rare events including the associated asymptotic rates on timescales that scale exponentially with the population size. We demonstrate that it is possible to reveal metastable structures and timescales of rare events of the ABM process by finite-length trajectories of the SDE process for large enough populations. This approach has the potential to drastically reduce computational effort for the analysis of ABMs.Detecting the interactions in networks helps us to understand the collective behaviors of complex systems. However, doing so is challenging due to systemic noise, nonlinearity, and a lack of information. Very few researchers have attempted to reconstruct discrete-time dynamic networks. Recently, Shi et al. proposed resetting a random state variable to infer the interactions in a continuous-time dynamic network. In this paper, we introduce a random resetting method for discrete-time dynamic networks. The statistical characteristics of the method are investigated and verified with numerical simulations. In addition, this reconstruction method was evaluated for limited data and weak coupling and within multiple-attractor systems.Complex network theory yields a powerful approach to solve the difficulties arising in a major section of ecological systems, prey-predator interaction being one among them. A large variety of ecological systems have been successfully investigated employing the theory of complex networks, and one of the most significant advancements in this theory is the emerging field of multilayer networks.  https://www.selleckchem.com/products/b102-parp-hdac-in-1.html  The field of multilayer networks provides a natural framework to accommodate multiple layers of complexities emerging in ecosystems. In this article, we consider prey-predator patches communicating among themselves while being connected by distinct small-world dispersal topologies in two layers of the network. We scrutinize the robustness of the multilayer ecological network sustaining gradually over harvested patches. We thoroughly report the consequences of introducing asymmetries in both interlayer and intralayer dispersal strengths as well as the network topologies on the global persistence of species in the network. Besides numerical simulation, we analytically derive the critical point up to which the network can sustain species in the network. Apart from the results on a purely multiplex framework, we validate our claims for multilayer formalism in which the patches of the layers are different. Interestingly, we observe that due to the interaction between the two layers, species are recovered in the layer that we assume to be extinct initially. Moreover, we find similar results while considering two completely different prey-predator systems, which eventually attests that the outcomes are not model specific.Reservoir computing (RC) is an attractive area of research by virtue of its potential for hardware implementation and low training cost. An intriguing research direction in this field is to interpret the underlying dynamics of an RC model by analyzing its short-term memory property, which can be quantified by the global index memory capacity (MC). In this paper, the global MC of the RC whose reservoir network is specified as a directed acyclic network (DAN) is examined, and first we give that its global MC is theoretically bounded by the length of the longest path of the reservoir DAN. Since the global MC is technically influenced by the model hyperparameters, the dependency of the MC on the hyperparameters of this RC is then explored in detail. In the further study, we employ the improved conventional network embedding method (i.e., struc2vec) to mine the underlying memory community in the reservoir DAN, which can be regarded as the cluster of reservoir nodes with the same memory profile. Experimental results demonstrate that such a memory community structure can provide a concrete interpretation of the global MC of this RC. Finally, the clustered RC is proposed by exploiting the detected memory community structure of DAN, where its prediction performance is verified to be enhanced with lower training cost compared with other RC models on several chaotic time series benchmarks.