823 research outputs found
Quantifying the Evolutionary Self Structuring of Embodied Cognitive Networks
We outline a possible theoretical framework for the quantitative modeling of
networked embodied cognitive systems. We notice that: 1) information self
structuring through sensory-motor coordination does not deterministically occur
in Rn vector space, a generic multivariable space, but in SE(3), the group
structure of the possible motions of a body in space; 2) it happens in a
stochastic open ended environment. These observations may simplify, at the
price of a certain abstraction, the modeling and the design of self
organization processes based on the maximization of some informational
measures, such as mutual information. Furthermore, by providing closed form or
computationally lighter algorithms, it may significantly reduce the
computational burden of their implementation. We propose a modeling framework
which aims to give new tools for the design of networks of new artificial self
organizing, embodied and intelligent agents and the reverse engineering of
natural ones. At this point, it represents much a theoretical conjecture and it
has still to be experimentally verified whether this model will be useful in
practice.
Highly symmetric POVMs and their informational power
We discuss the dependence of the Shannon entropy of normalized finite rank-1
POVMs on the choice of the input state, looking for the states that minimize
this quantity. To distinguish the class of measurements where the problem can
be solved analytically, we introduce the notion of highly symmetric POVMs and
classify them in dimension two (for qubits). In this case we prove that the
entropy is minimal, and hence the relative entropy (informational power) is
maximal, if and only if the input state is orthogonal to one of the states
constituting a POVM. The method used in the proof, employing the Michel theory
of critical points for group action, the Hermite interpolation and the
structure of invariant polynomials for unitary-antiunitary groups, can also be
applied in higher dimensions and for other entropy-like functions. The links
between entropy minimization and entropic uncertainty relations, the Wehrl
entropy and the quantum dynamical entropy are described.Comment: 40 pages, 3 figure
Information dynamics: Temporal behavior of uncertainty measures
We carry out a systematic study of uncertainty measures that are generic to
dynamical processes of varied origins, provided they induce suitable continuous
probability distributions. The major technical tool are the information theory
methods and inequalities satisfied by Fisher and Shannon information measures.
We focus on a compatibility of these inequalities with the prescribed
(deterministic, random or quantum) temporal behavior of pertinent probability
densities.Comment: Incorporates cond-mat/0604538, title, abstract changed, text
modified, to appear in Cent. Eur. J. Phy
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