Neural coding tools, based on Information Theory, applied to discrete time series: from electrophysiology to neuroethology

This work is supported by Brazilian agencies Fapesp, CAPES and CNPq

Performance Evaluation of Material Flow Systems in Discrete Time

Im folgenden Beitrag werden zeitdiskrete analytische Methoden vorgestellt, mit Hilfe derer Informations- und Materialflüsse in logistischen Systemen analysiert und bewertet werden können. Bestehende zeitdiskrete Verfahren sind jedoch auf die Bearbeitung und Weitergabe in immer gleichen Mengen („One Piece Flow“) beschränkt. Vor allem in Materialflusssystemen kommt es, bedingt durch die Zusammenfassung von Aufträgen, durch Transporte und durch Sortiervorgänge, zur Bildung von Batches. Daher wurden analytische Methoden entwickelt, die es ermöglichen, verschiedene Sammelprozesse, Batchankünfte an Ressourcen, Batchbearbeitung und Sortieren von Batches analytisch abzubilden und Leistungskenngrößen zu deren Bewertung zu bestimmen. Die im Rahmen der Entwicklungsarbeiten entstandene Software-Lösung „Logistic Analyzer“ ermöglicht eine einfache Modellierung und Analyse von praktischen Problemen. Der Beitrag schließt mit einem numerischen Beispiel.

On the Velocity and Acceleration Estimation from Discrete Time-Position Sensors

In this work is addressed the topic of estimation of velocity and acceleration from digital position data. It is presented a review of several classic methods and implemented with real position data from a low cost digital sensor of a hydraulic linear actuator. The results are analyzed and compared. It is shown that static methods have a limited bandwidth application, and that the performance of some methods may be enhanced by adapting its parameters according to the current state.

Convergence analysis of a discrete-time single-unit gradient ICA algorithm

We revisit the one-unit gradient ICA algorithm derived from the kurtosis function. By carefully studying properties of the stationary points of the discrete-time one-unit gradient ICA algorithm, with suitable condition on the learning rate, convergence can be proved. The condition on the learning rate helps alleviate the guesswork that accompanies the problem of choosing suitable learning rate in practical computation. These results may be useful to extract independent source signals on-line.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

On the Extinction Probability for Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration

Марусия Н. Славчова-Божкова - В настоящата работа се обобщава една гранична теорема за докритичен многомерен разклоняващ се процес, зависещ от възрастта на частиците с два типа имиграция. Целта е да се обобщи аналогичен резултат в едномерния случай като се прилагат “coupling” метода, теория на възстановяването и регенериращи процеси.

An edge-based matching kernel through discrete-time quantum walks

In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Large Deviations and Branching Processes

These lecture notes are devoted to present several uses of Large Deviation asymptotics in Branching Processes.