265 research outputs found
Memory functions and Correlations in Additive Binary Markov Chains
A theory of additive Markov chains with long-range memory, proposed earlier
in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical
properties of long-range correlated systems. The convenient characteristics of
such systems, a memory function, and its relation to the correlation properties
of the systems are examined. Various methods for finding the memory function
via the correlation function are proposed. The inverse problem (calculation of
the correlation function by means of the prescribed memory function) is also
solved. This is demonstrated for the analytically solvable model of the system
with a step-wise memory function.Comment: 11 pages, 5 figure
Thomas Decomposition and Nonlinear Control Systems
This paper applies the Thomas decomposition technique to nonlinear control
systems, in particular to the study of the dependence of the system behavior on
parameters. Thomas' algorithm is a symbolic method which splits a given system
of nonlinear partial differential equations into a finite family of so-called
simple systems which are formally integrable and define a partition of the
solution set of the original differential system. Different simple systems of a
Thomas decomposition describe different structural behavior of the control
system in general. The paper gives an introduction to the Thomas decomposition
method and shows how notions such as invertibility, observability and flat
outputs can be studied. A Maple implementation of Thomas' algorithm is used to
illustrate the techniques on explicit examples
Hierarchical Models in the Brain
This paper describes a general model that subsumes many parametric models for
continuous data. The model comprises hidden layers of state-space or dynamic
causal models, arranged so that the output of one provides input to another. The
ensuing hierarchy furnishes a model for many types of data, of arbitrary
complexity. Special cases range from the general linear model for static data to
generalised convolution models, with system noise, for nonlinear time-series
analysis. Crucially, all of these models can be inverted using exactly the same
scheme, namely, dynamic expectation maximization. This means that a single model
and optimisation scheme can be used to invert a wide range of models. We present
the model and a brief review of its inversion to disclose the relationships
among, apparently, diverse generative models of empirical data. We then show
that this inversion can be formulated as a simple neural network and may provide
a useful metaphor for inference and learning in the brain
Algebraic estimation in partial derivatives systems: parameters and differentiation problems
International audienceTwo goals are sought in this paper: namely, to provide a succinct overview on algebraic techniques for numerical differentiation and parameter estimation for linear systems and to present novel algebraic methods in the case of several variables. The state-of-art in the introduction is followed by a brief description of the methodology in the subsequent sections. Our new algebraic methods are illustrated by two examples in the multidimensional case. Some algebraic preliminaries are given in the appendix
S-D logic-informed customer engagement: Integrative framework, revised fundamental propositions, and application to CRM
Advance online in 2016</p
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