Coalescent approximation for structured populations in a stationary random environment

We establish convergence to the Kingman coalescent for the genealogy of a geographically - or otherwise - structured version of the Wright-Fisher population model with fast migration. The new feature is that migration probabilities may change in a random fashion. This brings a novel formula for the coalescent effective population size (EPS). We call it a quenched EPS to emphasize the key feature of our model - random environment. The quenched EPS is compared with an annealed (mean-field) EPS which describes the case of constant migration probabilities obtained by averaging the random migration probabilities over possible environments

Distributed Probabilistic Synchronization Algorithms for Communication Networks

In this paper, we present a probabilistic synchronization algorithm whose convergence properties are examined using tools of rowstochastic matrices. The proposed algorithm is particularly well suited for wireless sensor network applications, where connectivity is not guaranteed at all times, and energy efficiency is an important design consideration. The tradeoff between the convergence speed and the energy use is studied

Deconvolution of Quantized-Input Linear Systems: An Information-Theoretic Approach

The deconvolution problem has been drawing the attention of mathematicians, physicists and engineers since the early sixties. Ubiquitous in the applications, it consists in recovering the unknown input of a convolution system from noisy measurements of the output. It is a typical instance of inverse, ill-posed problem: the existence and uniqueness of the solution are not assured and even small perturbations in the data may cause large deviations in the solution. In the last fifty years, a large amount of estimation techniques have been proposed by different research communities to tackle deconvolution, each technique being related to a peculiar engineering application or mathematical set. In many occurrences, the unknown input presents some known features, which can be exploited to develop ad hoc algorithms. For example, prior information about regularity and smoothness of the input function are often considered, as well as the knowledge of a probabilistic distribution on the input source: the estimation techniques arising in different scenarios are strongly diverse. Less effort has been dedicated to the case where the input is known to be affected by discontinuities and switches, which is becoming an important issue in modern technologies. In fact, quantized signals, that is, piecewise constant functions that can assume only a finite number of values, are nowadays widespread in the applications, given the ongoing process of digitization concerning most of information and communication systems. Moreover, hybrid systems are often encountered, which are characterized by the introduction of quantized signals into physical, analog communication channels. Motivated by such consideration, this dissertation is devoted to the study of the deconvolution of continuous systems with quantized input; in particular, our attention will be focused on linear systems. Given the discrete nature of the input, we will show that the whole problem can be interpreted as a paradigmatic digital transmission problem and we will undertake an Information-theoretic approach to tackle it. The aim of this dissertation is to develop suitable deconvolution algorithms for quantized-input linear systems, which will be derived from known decoding procedures, and to test them in different scenarios. Much consideration will be given to the theoretical analysis of these algorithms, whose performance will be rigorously described in mathematical terms

Deconvolution of Quantized-Input Linear Systems : an Information-Theoretic Approach

The deconvolution problem has been drawing the attention of mathematicians, physicists and engineers since the early sixties. Ubiquitous in the applications, it consists in recovering the unknown input of a convolution system from noisy measurements of the output. It is a typical instance of inverse, ill-posed problem: the existence and uniqueness of the solution are not assured and even small perturbations in the data may cause large deviations in the solution. In the last fifty years, a large amount of estimation techniques have been proposed by di fferent research communities to tackle deconvolution, each technique being related to a peculiar engineering application or mathematical set. In many occurrences, the unknown input presents some known features, which can be exploited to develop ad hoc algorithms. For example, prior information about regularity and smoothness of the input function are often considered, as well as the knowledge of a probabilistic distribution on the input source: the estimation techniques arising in diff erent scenarios are strongly diverse. Less eff ort has been dedicated to the case where the input is known to be aff ected by discontinuities and switches, which is becoming an important issue in modern technologies. In fact, quantized signals, that is, piecewise constant functions that can assume only a fi nite number of values, are nowadays widespread in the applications, given the ongoing process of digitization concerning most of information and communication systems. Moreover, hybrid systems are often encountered, which are characterized by the introduction of quantized signals into physical, analog communication channels. Motivated by such consideration, this dissertation is devoted to the study of the deconvolution of continuous systems with quantized input; in particular, our attention will be focused on linear systems. Given the discrete nature of the input, we will show that the whole problem can be interpreted as a paradigmatic digital transmission problem and we will undertake an Information-theoretic approach to tackle it. The aim of this dissertation is to develop suitable deconvolution algorithms for quantized-input linear systems, which will be derived from known decoding procedures, and to test them in diff erent scenarios. Much consideration will be given to the theoretical analysis of these algorithms, whose performance will be rigorously described in mathematical terms