Related papers: Nonlinear non-extensive approach for identificatio…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
In this paper we develop a method for learning nonlinear systems with multiple outputs and inputs. We begin by modelling the errors of a nominal predictor of the system using a latent variable framework. Then using the maximum likelihood…
The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
When simultaneously reasoning with evidences about several different events it is necessary to separate the evidence according to event. These events should then be handled independently. However, when propositions of evidences are weakly…
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
In this paper we give some two-dimensional and some three-dimensional examples for the shape of the symmetric solution set of a linear complementarity problem where the given data are not explicitly known but can only be enclosed in…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
A special case of the satisfiability problem, in which the clauses have a hierarchical structure, is shown to be solvable in linear time, assuming that the clauses have been represented in a convenient way.
Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…
Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…
This paper compares and evaluates a set of non-parametric mutual information estimators with the goal of providing a novel toolset to progress in the analysis of the capacity of the nonlinear optical channel, which is currently an open…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena…
A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of…