This thesis presents a dynamical system approach to learning forward and inverse models in associative recurrent neural networks. Ambiguous inverse models are represented by multi-stable dynamics. Random projection networks, i.e. reservoirs, together with a rigorous regularization methodology enable robust and efficient training of multi-stable dynamics with application to flexible movement con...

This article describes how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by means of backfitting or more general algorithms, like the alternating conditional expectation value one. The method is illustrated by numerically generated data. As an application, the example o...

‎In this text we prove that in generalized shift dynamical system $(X^Gamma,sigma_varphi)$‎ ‎for finite discrete $X$ with at least two elements‎, ‎infinite countable set $Gamma$ and‎ ‎arbitrary map $varphi:GammatoGamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(X^Gamma,sigma_varphi)$ is‎ Li-Yorke chaotic;‎ - the dynamical system $(X^Gamma,sigma_varphi)$ has‎ an scr...

This paper discusses a general approach to qualitative modeling based on fuzzy logic. The method of qualitative modeling is divided into two parts: fuzzy modeling and linguistic approximation. It proposes to use a fuzzy clustering method (fuzzy c-means method) to identify the structure of a fuzzy model. To clarify the advantages of the proposed method, it also shows some examples of modeling, a...

This paper is concerned with the study of fuzzy dynamical systems. Let (XM ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map dened on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.

How can we model influence between individuals in a social system? How can we use influence to model and predict observations from social systems? In this article, we explain the recent advances of the influence model, a Bayesian network approach for modeling social influence from observations of individuals. We review the development of the influence model in the literature. We also introduce ...

nonlinear, black box model, behavioral model, input-output model, time-series, embedology This technical report describes the groundwork for our nonlinear modeling technologies. Future technical reports will go into detail about the specific solutions we are developing to build accurate models for nonlinear electronic devices from input-output measurements for possible use in CAD simulators suc...

The development of mathematical tools for describing dynamical systems has made it possible to characterize forms of behavior that could not be characterized before. This represents progress, but the enterprise runs the risk of being nothing more than curve fitting if investigators fail to identify the physical, biological, or psychological mechanisms which are common to systems that follow the...

Recent studies have employed simple linear dynamical systems to model trial-by-trial dynamics in various sensorimotor learning tasks. Here we explore the theoretical and practical considerations that arise when employing the general class of linear dynamical systems (LDS) as a model for sensorimotor learning. In this framework, the state of the system is a set of parameters that define the curr...