As said by Mareš and Mesiar, necessity of aggregation of complex real inputs appears almost in any field dealing with observed (measured) real quantities (see the citation below). For aggregation of probability distributions Sklar designed his copulas as early as in 1959. But surprisingly, since that time only a very few literature have appeared dealing with possibility to aggregate several different pairwise dependencies into one multivariate copula. In the present paper this problem is tackled using the well known Iterative Proportional Fitting Procedure. The proposed solution is not an exact mathematical solution of a marginal problem but just its approximation applicable in many practical situations like Monte Carlo sampling. This is why the authors deal not only with the consistent case, when the iterative procedure converges, but also with the inconsistent non-converging case. In the latter situation, the IPF procedure tends to cycle (when combining three pairwise dependencies the procedure creates three convergent subsequences), and thus the authors propose some heuristics yielding a "solution'' of the problem even for inconsistent pairwise dependence relations.
The physiological control system of the heart produces a highly complex pattern of cardiac rhythmicity which is reflected in the variability of heart rate. The aim of this study was to analyse the effects of posture and breathing frequency on the cardiac control system by various noninvasive techniques. Seven healthy subjects (24 ±5 years, mean age ± S.D.) were studied in the supine and sitting positions while breathing spontaneously or at a fixed rate (3, 6, 12, 24, 48, 60 breaths.min-1). Time series of instantaneous beat-to-beat heart rates were evaluated by spectral analysis and by the dimensionless approximate entropy parameter. The total spectral power as well as the low (<0.05 Hz) and mid frequency (0.05-0.12 Hz) spectral components were higher in the sitting position. Mean approximate entropy (± S.D.) (0.85 ±0.15 in sitting and 0.87±0.16 in lying subjects) was unaffected by postural changes or breathing frequencies higher than 6 breaths.min-1. Analysis in the frequency domain revealed that the activity of the autonomic components controlling heart rate was modified by ventilation and postural changes, whereas approximate entropy, a unique measure of the complexity and integrity of the cardiac control system, was almost unaffected by respiration and posture.
The paper deals with a model for water freezing in a deformable elastoplastic container. The mathematical problem consists of a system of one parabolic equation for temperature, one integrodifferential equation with a hysteresis operator for local volume increment, and one differential inclusion for the water content. The problem is shown to admit a unique global uniformly bounded weak solution.
In my previous papers ([18], [19]) the entropy of fuzzy partitions had been defined. The concept of the entropy of a fuzzy partition was used to define the entropy of a fuzzy dynamical system and to propose an ergodic theory for fuzzy dynamical systems ([19], [20]). In this paper, using my previous results related to the entropy of fuzzy partitions, a measure of average mutual information of fuzzy partitions is defined. Some properties concerning this measure are proved. It is shown that the entropy of fuzzy partitions can be considered as a special case of their mutual information. We obtain that subadditivity and additivity of entropy of fuzzy partitions are simple consequences of these properties. The suggested measures can be applied whenever it is need to know the amount of information that we obtain by realization of experiments, the results of which are fuzzy events.
{Graphical models provide an undirected graph representation of relations between the components of a random vector. In the Gaussian case such an undirected graph is used to describe conditional independence relations among such components. In this paper, we consider a continuous-time Gaussian model which is accessible to observations only at time T. We introduce the concept of infinitesimal conditional independence for such a model. Then, we address the corresponding graphical model selection problem, i. e. the problem to estimate the graphical model from data. Finally, simulation studies are proposed to test the effectiveness of the graphical model selection procedure.}
This paper deals with the concept of the "size" or "extent" of the information in the sense of measuring the improvement of our knowledge after obtaining a message. Standard approaches are based on the probabilistic parameters of the considered information source. Here we deal with situations when the unknown probabilities are subjectively or vaguely estimated. For the considered fuzzy quantities valued probabilities we introduce and discuss information theoretical concepts.
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.
We show that the typical coordinate-wise encoding of multivariate ergodic source into prescribed alphabets has the entropy profile close to the convolution of the entropy profile of the source and the modular polymatroid that is determined by the cardinalities of the output alphabets. We show that the proportion of the exceptional encodings that are not close to the convolution goes to zero doubly exponentially. The result holds for a class of multivariate sources that satisfy asymptotic equipartition property described via the mean fluctuation of the information functions. This class covers asymptotically mean stationary processes with ergodic mean, ergodic processes, irreducible Markov chains with an arbitrary initial distribution. We also proved that typical encodings yield the asymptotic equipartition property for the output variables. These asymptotic results are based on an explicit lower bound of the proportion of encodings that transform a multivariate random variable into a variable with the entropy profile close to the suitable convolution.
The paper deals with the problem of affected flow series in non-homogeneous conditions. The impact on water resources utilization is also discussed. The investigation has been based on the assumption that it is impossible to obtain ''pure'' homogeneous flow series by means of elimination or ''purification'' of anthropogenic factors. This is a good reason for application of maximum entropy, which is a suitable tool for the expression of maximum uncertainty due to affected flow series. A case study presents the results of the investigation of water reservoir function under the influence of anthropogenic factors. and Studie zkoumá problematiku ovlivněných průtokových řad v nehomogenních podmínkách a jejich dopady na využití vodních zdrojů. Vychází z předpokladu, že očištěním řad od antropogenních faktorů se nemusí vždy získat zcela neovlivněná a homogenní řada, protože nebyly k dispozici potřebné podklady. Využívá se princip maximální entropie, který za jistých podmínek připouští v dané náhodné řadě největší míru neurčitosti v rozložení pravděpodobnosti. Studie uvádí výsledky srovnávací analýzy dopadů různých modelů ovlivnění na zásobení funkcí nádrží.
The second part of the study deals with the best suitable structure of the linear regression stochastic model of the mean monthly flows in the Šance profil on the Ostravice River. This part compares the transmission measure method with the traditional autocorrelation analysis. The first part of the study was published in 2/2003 of the JHH. and Tato část studie zkoumá nejvhodnější strukturu lineárního regresního stochastického modelu průměrných měsíčních průtoků v profilu Šance na Ostravici metodou střední vzájemné informace a porovnává ji s metodou mnohorozměrné regrese s minimem reziduálního rozptylu. Navazuje na první část, publikovanou v č. 2/2003 Vodohospodářského časopisu.