Related papers: System Network Analytics: Evolution and Stable Rul…
This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this…
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to…
Conditional Simple Temporal Network (CSTN) is a constraint-based graph-formalism for conditional temporal planning. It offers a more flexible formalism than the equivalent CSTP model of Tsamardinos, Vidal and Pollack, from which it was…
Static stability in economic models means negative incentives for deviation from equilibrium strategies, which we expect to assure a return to equilibrium, i.e., dynamic stability, as long as agents respond to incentives. There have been…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…
Trends change rapidly in today's world, prompting this key question: What is the mechanism behind the emergence of new trends? By representing real-world dynamic systems as complex networks, the emergence of new trends can be symbolized by…
The approximate master equation (AME) provides a highly accurate description of dynamical processes on networks, yet its steady states are generally analytically intractable. In this study, we develop an analytical framework to derive the…
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…
Evolutionarily stable strategy (ESS) is the defining concept of evolutionary game theory. It has a fairly unanimously accepted definition for the case of symmetric games which are played in a homogeneous population where all individuals are…
Temporal networks are an important type of network whose topological structure changes over time. Compared with methods on static networks, temporal network embedding (TNE) methods are facing three challenges: 1) it cannot describe the…
State estimation refers to determining the states of a dynamical system that starts from a noisy initial condition and evolves under process noise, based on noisy measurements and a known system model. For linear dynamical systems with…
We propose a stability analysis method for sampled-data switched linear systems with finite-level static quantizers. In the closed-loop system, information on the active mode of the plant is transmitted to the controller only at each…
During a financial crisis, the capital markets network frequently exhibits a high correlation between returns. We developed a network analysis framework based on daily returns from 42 countries to determine systemic stability. Our network…
We analyze a model of interacting agents (e.g. prebiotic chemical species) which are represended by nodes of a network, whereas their interactions are mapped onto directed links between these nodes. On a fast time scale, each agent follows…
Preserving the topology from being inferred by external adversaries has become a paramount security issue for network systems (NSs), and adding random noises to the nodal states provides a promising way. Nevertheless, recent works have…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies,…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…