相关论文: Source-only realizations, weakly reversible defici…

In a stochastic reaction network setting we consider the problem of tracking the fate of individual molecules. We show that using the classical large volume limit results, we may approximate the dynamics of a single tracked molecule in a…

Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has…

This work concerns the development of deep networks that are certifiably robust to adversarial attacks. Joint robust classification-detection was recently introduced as a certified defense mechanism, where adversarial examples are either…

Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology,…

Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…

The spatially distributed reaction networks are indispensable for the understanding of many important phenomena concerning the development of organisms, coordinated cell behavior, and pattern formation. The purpose of this brief discussion…

Living organisms must respond to environmental changes. Generally, accurate and rapid responses are provided by simple, unidirectional networks that connect inputs with outputs. Besides accuracy and speed, biological responses should also…

Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at…

It is common knowledge that a key dynamical characteristic of a network is its spectrum (the collection of all eigenvalues of the network's weighted adjacency matrix). In \cite{BW10} we demonstrated that it is possible to reduce a network,…

Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…

To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however,…

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…

Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or…

Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…

It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on…

Reaction networks are mainly used to model the time-evolution of molecules of interacting chemical species. Stochastic models are typically used when the counts of the molecules are low, whereas deterministic models are used when the counts…

A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…

When studying a complex system it is often useful to think of the system as a network of interacting units. One can then ask if some properties of the entire network are already explained by a small part of the network - a network motif. A…

We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh--Nagumo oscillators. For a large range of within- and between-network couplings, the…