Low-rank tensor methods for large Markov chains and forward feature selection methods

In the first part of this thesis, we present and compare several approaches for the determination of the steady-state of large-scale Markov chains with an underlying low-rank tensor structure. Such structure is, in our context of interest, associated with the existence of interacting processes. The state space grows exponentially with the number of processes. This type of problems arises, for instance, in queueing theory, in chemical reaction networks, or in telecommunications. As the number of degrees of freedom of the problem grows exponentially with the number of processes, the so-called \textit{curse of dimensionality} severely impairs the use of standard methods for the numerical analysis of such Markov chains. We drastically reduce the number of degrees of freedom by assuming a low-rank tensor structure of the solution. We develop different approaches, all considering a formulation of the problem where all involved structures are considered in their low-rank representations in \textit{tensor train} format. The first approaches that we will consider are associated with iterative solvers, in particular focusing on solving a minimization problem that is equivalent to the original problem of finding the desired steady state. We later also consider tensorized multigrid techniques as main solvers, using different operators for restriction and interpolation. For instance, aggregation/disaggregation operators, which have been extensively used in this field, are applied. In the second part of this thesis, we focus on methods for feature selection. More concretely, since, among the various classes of methods, sequential feature selection methods based on mutual information have become very popular and are widely used in practice, we focus on this particular type of methods. This type of problems arises, for instance, in microarray analysis, in clinical prediction, or in text categorization. Comparative evaluations of these methods have been limited by being based on specific datasets and classifiers. We develop a theoretical framework that allows evaluating the methods based on their theoretical properties. Our framework is based on the properties of the target objective function that the methods try to approximate, and on a novel categorization of features, according to their contribution to the explanation of the class; we derive upper and lower bounds for the target objective function and relate these bounds with the feature types. Then, we characterize the types of approximations made by the methods, and analyse how these approximations cope with the good properties of the target objective function. We also develop a distributional setting designed to illustrate the various deficiencies of the methods, and provide several examples of wrong feature selections. In the context of this setting, we use the minimum Bayes risk as performance measure of the methods

Statistical physics approaches to the complex Earth system

Global warming, extreme climate events, earthquakes and their accompanying socioeconomic disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, multiple interactions and complex structures of the Earth system, the understanding and, in particular, the prediction of such disruptive events represent formidable challenges to both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge of the Earth system, including climate extreme events, earthquakes and geological relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as critical phenomena, network theory, percolation, tipping points analysis, and entropy can be applied to complex Earth systems. Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics concepts and theories can be useful in the field of Earth system science

Statistical physics approaches to the complex Earth system

Global climate change, extreme climate events, earthquakes and their accompanying natural disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, strategic interactions and complex structure of the Earth system, the understanding and in particular the predicting of such disruptive events represent formidable challenges for both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge for a better understanding of the Earth system, including climate extreme events, earthquakes and Earth geometric relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as, critical phenomena, network theory, percolation, tipping points analysis, as well as entropy can be applied to complex Earth systems (climate, earthquakes, etc.). Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics approaches can be useful in the field of Earth system science

Product form steady-state distribution for Stochastic Automata Networks with Domino Synchronizations

International audienceWe present a new kind of synchronization which allows Continuous Time Stochastic Automata Networks (SAN) to have a product form steady-state distribution. Unlike previous models on SAN with product form solutions, our model allows synchronization between three automata but functional rates are not allowed. The synchronization is not the usual "Rendez-Vous" but an ordered list of transitions. Each transition may fail. When a transition fails, the synchronization ends but all the transitions already executed are kept. This synchronization is related to the triggered customer movement between queues in a network and this class of SAN is a generalization of Gelenbe's networks with triggered customer movement

Telecommunications Networks

This book guides readers through the basics of rapidly emerging networks to more advanced concepts and future expectations of Telecommunications Networks. It identifies and examines the most pressing research issues in Telecommunications and it contains chapters written by leading researchers, academics and industry professionals. Telecommunications Networks - Current Status and Future Trends covers surveys of recent publications that investigate key areas of interest such as: IMS, eTOM, 3G/4G, optimization problems, modeling, simulation, quality of service, etc. This book, that is suitable for both PhD and master students, is organized into six sections: New Generation Networks, Quality of Services, Sensor Networks, Telecommunications, Traffic Engineering and Routing

A Control-Theoretic Methodology for Adaptive Structured Parallel Computations

Adaptivity for distributed parallel applications is an essential feature whose impor- tance has been assessed in many research fields (e.g. scientific computations, large- scale real-time simulation systems and emergency management applications). Especially for high-performance computing, this feature is of special interest in order to properly and promptly respond to time-varying QoS requirements, to react to uncontrollable environ- mental effects influencing the underlying execution platform and to efficiently deal with highly irregular parallel problems. In this scenario the Structured Parallel Programming paradigm is a cornerstone for expressing adaptive parallel programs: the high-degree of composability of parallelization schemes, their QoS predictability formally expressed by performance models, are basic tools in order to introduce dynamic reconfiguration processes of adaptive applications. These reconfigurations are not only limited to imple- mentation aspects (e.g. parallelism degree modifications), but also parallel versions with different structures can be expressed for the same computation, featuring different levels of performance, memory utilization, energy consumption, and exploitation of the memory hierarchies. Over the last decade several programming models and research frameworks have been developed aimed at the definition of tools and strategies for expressing adaptive parallel applications. Notwithstanding this notable research effort, properties like the optimal- ity of the application execution and the stability of control decisions are not sufficiently studied in the existing work. For this reason this thesis exploits a pioneer research in the context of providing formal theoretical tools founded on Control Theory and Game Theory techniques. Based on these approaches, we introduce a formal model for control- ling distributed parallel applications represented by computational graphs of structured parallelism schemes (also called skeleton-based parallelism). Starting out from the performance predictability of structured parallelism schemes, in this thesis we provide a formalization of the concept of adaptive parallel module per- forming structured parallel computations. The module behavior is described in terms of a Hybrid System abstraction and reconfigurations are driven by a Predictive Control ap- proach. Experimental results show the effectiveness of this work, in terms of execution cost reduction as well as the stability degree of a system reconfiguration: i.e. how long a reconfiguration choice is useful for targeting the required QoS levels. This thesis also faces with the issue of controlling large-scale distributed applications composed of several interacting adaptive components. After a panoramic view of the existing control-theoretic approaches (e.g. based on decentralized, distributed or hierar- chical structures of controllers), we introduce a methodology for the distributed predictive control. For controlling computational graphs, the overall control problem consists in a set of coupled control sub-problems for each application module. The decomposition is- sue has a twofold nature: first of all we need to model the coupling relationships between control sub-problems, furthermore we need to introduce proper notions of negotiation and convergence in the control decisions collectively taken by the parallel modules of the application graph. This thesis provides a formalization through basic concepts of Non-cooperative Games and Cooperative Optimization. In the notable context of the dis- tributed control of performance and resource utilization, we exploit a formal description of the control problem providing results for equilibrium point existence and the compari- son of the control optimality with different adaptation strategies and interaction protocols. Discussions and a first validation of the proposed techniques are exploited through exper- iments performed in a simulation environment