778 research outputs found
Solution of polynomial Lyapunov and Sylvester equations
A two-variable polynomial approach to solve the one-variable polynomial Lyapunov and Sylvester equations is proposed. Lifting the problem from the one-variable to the two-variable context gives rise to associated lifted equations which live on finite-dimensional vector spaces. This allows for the design of an iterative solution method which is inspired by the method of Faddeev for the computation of matrix resolvents. The resulting algorithms are especially suitable for applications requiring symbolic or exact computation
Dynamics of the Fisher Information Metric
We present a method to generate probability distributions that correspond to
metrics obeying partial differential equations generated by extremizing a
functional , where is the
Fisher metric. We postulate that this functional of the dynamical variable
is stationary with respect to small variations of these
variables. Our approach enables a dynamical approach to Fisher information
metric. It allows to impose symmetries on a statistical system in a systematic
way. This work is mainly motivated by the entropy approach to nonmonotonic
reasoning.Comment: 11 page
Metric on a Statistical Space-Time
We introduce a concept of distance for a space-time where the notion of point
is replaced by the notion of physical states e.g. probability distributions. We
apply ideas of information theory and compute the Fisher information matrix on
such a space-time. This matrix is the metric on that manifold. We apply these
ideas to a simple model and show that the Lorentzian metric can be obtained if
we assumed that the probability distributions describing space-time
fluctuations have complex values. Such complex probability distributions appear
in non-Hermitian quantum mechanics.Comment: 7 page
Identifiability of generalised Randles circuit models
The Randles circuit (including a parallel resistor and capacitor in series
with another resistor) and its generalised topology have widely been employed
in electrochemical energy storage systems such as batteries, fuel cells and
supercapacitors, also in biomedical engineering, for example, to model the
electrode-tissue interface in electroencephalography and baroreceptor dynamics.
This paper studies identifiability of generalised Randles circuit models, that
is, whether the model parameters can be estimated uniquely from the
input-output data. It is shown that generalised Randles circuit models are
structurally locally identifiable. The condition that makes the model structure
globally identifiable is then discussed. Finally, the estimation accuracy is
evaluated through extensive simulations
Information geometric methods for complexity
Research on the use of information geometry (IG) in modern physics has
witnessed significant advances recently. In this review article, we report on
the utilization of IG methods to define measures of complexity in both
classical and, whenever available, quantum physical settings. A paradigmatic
example of a dramatic change in complexity is given by phase transitions (PTs).
Hence we review both global and local aspects of PTs described in terms of the
scalar curvature of the parameter manifold and the components of the metric
tensor, respectively. We also report on the behavior of geodesic paths on the
parameter manifold used to gain insight into the dynamics of PTs. Going
further, we survey measures of complexity arising in the geometric framework.
In particular, we quantify complexity of networks in terms of the Riemannian
volume of the parameter space of a statistical manifold associated with a given
network. We are also concerned with complexity measures that account for the
interactions of a given number of parts of a system that cannot be described in
terms of a smaller number of parts of the system. Finally, we investigate
complexity measures of entropic motion on curved statistical manifolds that
arise from a probabilistic description of physical systems in the presence of
limited information. The Kullback-Leibler divergence, the distance to an
exponential family and volumes of curved parameter manifolds, are examples of
essential IG notions exploited in our discussion of complexity. We conclude by
discussing strengths, limits, and possible future applications of IG methods to
the physics of complexity.Comment: review article, 60 pages, no figure
Three ways to look at mutually unbiased bases
This is a review of the problem of Mutually Unbiased Bases in finite
dimensional Hilbert spaces, real and complex. Also a geometric measure of
"mubness" is introduced, and applied to some recent calculations in six
dimensions (partly done by Bjorck and by Grassl). Although this does not yet
solve any problem, some appealing structures emerge.Comment: 18 pages. Talk at the Vaxjo Conference on Foundations of Probability
and Physics, June 200
Higher coordination with less control - A result of information maximization in the sensorimotor loop
This work presents a novel learning method in the context of embodied
artificial intelligence and self-organization, which has as few assumptions and
restrictions as possible about the world and the underlying model. The learning
rule is derived from the principle of maximizing the predictive information in
the sensorimotor loop. It is evaluated on robot chains of varying length with
individually controlled, non-communicating segments. The comparison of the
results shows that maximizing the predictive information per wheel leads to a
higher coordinated behavior of the physically connected robots compared to a
maximization per robot. Another focus of this paper is the analysis of the
effect of the robot chain length on the overall behavior of the robots. It will
be shown that longer chains with less capable controllers outperform those of
shorter length and more complex controllers. The reason is found and discussed
in the information-geometric interpretation of the learning process
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