Related papers: Dimensionality Reduction in Stochastic Complex Dyn…

With the recent surge in big data analytics for hyper-dimensional data there is a renewed interest in dimensionality reduction techniques for machine learning applications. In order for these methods to improve performance gains and…

Current dynamic networks and dynamic pruning methods have shown their promising capability in reducing theoretical computation complexity. However, dynamic sparse patterns on convolutional filters fail to achieve actual acceleration in…

In this paper, a new computational framework based on the topology derivative concept is presented for evaluating stochastic topological sensitivities of complex systems. The proposed framework, designed for dealing with high dimensional…

Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to…

We study the effect of stochastic wireless channel models on the connectivity of ad hoc networks. Unlike in the deterministic geometric disk model where nodes connect if they are within a certain distance from each other, stochastic models…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Real-world network systems are inherently dynamic, with network topologies undergoing continuous changes over time. Previous works often focus on static networks or rely on complete prior knowledge of evolving topologies, whereas real-world…

Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order…

We study the properties of linear and non-linear determining functionals for dissipative dynamical systems generated by PDEs. The main attention is payed to the lower bounds for the number of such functionals. In contradiction to the common…

A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…

Estimation of parameters is a crucial part of model development. When models are deterministic, one can minimise the fitting error; for stochastic systems one must be more careful. Broadly parameterisation methods for stochastic dynamical…

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…

Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…

Dimensionality reduction methods are an essential tool for multidimensional data analysis, and many interesting processes can be studied as time-dependent multivariate datasets. There are, however, few studies and proposals that leverage on…

Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from…

When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…

Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…

Solutions of symbolic regression problems are expressions that are composed of input variables and operators from a finite set of function symbols. One measure for evaluating symbolic regression algorithms is their ability to recover…

Selecting the appropriate dimensionality reduction (DR) technique and determining its optimal hyperparameter settings that maximize the accuracy of the output projections typically involves extensive trial and error, often resulting in…