Search results for "Probability."
showing 10 items of 3396 documents
SPATIAL MULTIFRACTALITY OF ELECTRONIC STATES AND THE METAL-INSULATOR TRANSITION IN DISORDERED SYSTEMS
1993
For the investigation of the spatial behavior of electronic wave functions in disordered systems, we employ the Anderson model of localization. The eigenstates of the corresponding Hamiltonian are calculated numerically by means of the Lanczos algorithm and are analyzed with respect to their spatial multifractal properties. We find that the wave functions show spatial multifractality for all parameter cases not too far away from the metal-insulator transition (MIT) which separates localized from extended states in this model. Exactly at the MIT, multifractality is expected to exist on all length scales larger than the lattice spacing. It is found that the corresponding singularity spectrum…
Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range co…
2017
Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of …
Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique
2010
We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected acc…
Didactical note: probabilistic conditionality in a Boolean algebra
1996
This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling ``If-then" propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem will be only considered, with the Material Conditional Operation, on a Boolean Algebra endowed with a finite probability and in three different cases: with the Internal-Conditional Probability, with th…
On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
2023
In this paper we investigate canonical extensions of conditional probabilities to Boolean algebras of conditionals. Before entering into the probabilistic setting, we first prove that the lattice order relation of every Boolean algebra of conditionals can be characterized in terms of the well-known order relation given by Goodman and Nguyen. Then, as an interesting methodological tool, we show that canonical extensions behave well with respect to conditional subalgebras. As a consequence, we prove that a canonical extension and its original conditional probability agree on basic conditionals. Moreover, we verify that the probability of conjunctions and disjunctions of conditionals in a rece…
On utilizing dependence-based information to enhance micro-aggregation for secure statistical databases
2011
Published version of an article in the journal: Pattern Analysis and Applications. Also available from the publisher at: http://dx.doi.org/10.1007/s10044-011-0199-9 We consider the micro-aggregation problem which involves partitioning a set of individual records in a micro-data file into a number of mutually exclusive and exhaustive groups. This problem, which seeks for the best partition of the micro-data file, is known to be NP-hard, and has been tackled using many heuristic solutions. In this paper, we would like to demonstrate that in the process of developing micro-aggregation techniques (MATs), it is expedient to incorporate information about the dependence between the random variable…
CATs: whither and whence
2000
TAI: Hacia dónde y de dónde. En este trabajo esbozo el estado de la
 cuestión que dio lugar a los test adaptativos, centrando la discusión en el
 avance de los TAI y en particular en las expectativas que expresara Bert
 Green sobre las ventajas de esta tecnología. Se usan datos de la primera
 década donde los TAI fueron operativos, para comparar lo que ocurrió con
 aquello que se esperaba que ocurriera. Encuentro que algunas de las metas
 de TAI expresadas por Green están próximas a cumplirse, aunque la
 mayoría de ellas quedan para el futuro.
Conservation Laws and Asymptotic Behavior of a Model of Social Dynamics
2008
Abstract A conservative social dynamics model is developed within a discrete kinetic framework for active particles, which has been proposed in [M.L. Bertotti, L. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Mod. Meth. Appl. Sci. 14 (2004) 1061–1084]. The model concerns a society in which individuals, distinguished by a scalar variable (the activity) which expresses their social state, undergo competitive and/or cooperative interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear ordinary differential equations. The asymptotic trend of their solutions…
Numerical propagator method solutions for the linear parabolic initial boundary-value problems
2007
On the base of our numerical propagator method a new finite volume difference scheme is proposed for solution of linear initial-boundary value problems. Stability of the scheme is investigated taking into account the obtained analytical solution of the initial-boundary value problems. It is shown that stability restrictions for the propagator scheme become weaker in comparison to traditional semi-implicit difference schemes. There are some regions of coefficients, for which the elaborated propagator difference scheme becomes absolutely stable. It is proven that the scheme is unconditionally monotonic. Analytical solutions, which are consistent with solubility conditions of the problem are f…
Unitary Space–Time Constellation Design Based on the Chernoff Bound of the Pairwise Error Probability
2008
Unitary space-time constellation design is considered for noncoherent multiple-antenna communications, where neither the transmitter nor the receiver knows the fading coefficients of the channel. By employing the Clarke's subdifferential theorem of the sum of the kappa largest singular values of a unitary matrix, we present a numerical optimization procedure for finding unitary space-time signal constellations of any dimension. The Chernoff bound of the pairwise error probability is used directly as a design criterion. The constellations are found by performing gradient descent search on a family ldquosurrogaterdquo functions that converge to the maximum pairwise error probability. The comp…