相关论文: Local and global robustness at steady state

Perfect adaptation is a well-studied biochemical homeostatic behavior lying at the core of biochemical regulation. While the concepts of homeostasis and perfect adaptation are not new, their underlying mechanisms and associated biochemical…

DC microgrids have promising applications in renewable integration due to their better energy efficiency when connecting DC components. However, they might be unstable since many loads in a DC microgrid are regulated as constant power loads…

Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs)…

We study local, analytic solutions for a class of initial value problems for singular ODEs. We prove existence and uniqueness of such solutions under a certain non-resonance condition. Our proof translates the singular initial value problem…

Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size…

Chemical reaction networks (CRNs) are foundational models for describing complex biochemical processes. We study noncompetitive CRNs, a class of networks whose static states are rate-independent, and that can implement ReLU neural networks.…

This paper investigates the fundamental mechanisms driving plasticity loss in deep reinforcement learning (RL), a critical challenge where neural networks lose their ability to adapt to non-stationary environments. While existing research…

We study cardinality-constrained optimization problems (CCOP) in general position, i. e. those optimization-related properties that are fulfilled for a dense and open subset of their defining functions. We show that the well-known…

A general scheme, which includes constructions of coarse-grained (CG) models, weighted ensemble dynamics (WED) simulations and cluster analyses (CA) of stable states, is presented to detect dynamical and thermodynamical properties in…

We have obtained a criterion for spherically symmetric and static structures under hydrostatic equilibrium in general relativity (GR), which states that for a given value of $\sigma \equiv (P_0/E_0) \equiv $ the ratio of central pressure to…

This paper introduces a hybrid attention and autoencoder (AE) model for unsupervised online anomaly detection in time series. The autoencoder captures local structural patterns in short embeddings, while the attention model learns long-term…

We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow…

Topological edge states arise at the interface of two topologically-distinct structures and have two distinct features: they are localized and robust against symmetry protecting disorder. On the other hand, conventional transport in one…

This work considers the transition to unsteadiness in the wake of 2D slender bodies, and questions the relevance of the generally accepted scenario involving a region of absolute instability within the near wake. The case of a thin plate at…

We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of…

Bifunctional enzymes, which catalyze both the forward and reverse steps of a substrate modification reaction, arise naturally in bacterial two-component signaling systems and metabolic regulation. Beyond their well-known role in conferring…

A new cellular automaton (CA) model is presented for the self-organized criticality (SOC) in recurrent bursts of soft gamma repeaters (SGRs), which are interpreted as avalanches of reconnection in the magnetosphere of neutron stars. The…

We study asynchronous dynamics in a network of interacting agents updating their binary states according to a time-varying threshold rule. Specifically, agents revise their state asynchronously by comparing the weighted average of the…

Robust adversarial reinforcement learning has emerged as an effective paradigm for training agents to handle uncertain disturbance in real environments, with critical applications in sequential decision-making domains such as autonomous…

Well-posedness in $L_\infty$ of the nonlocal Gray-Scott model is studied for integrable kernels, along with the stability of the semi-trivial spatially homogeneous steady state. In addition, it is shown that the solutions to the nonlocal…