Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

DECENTRALIZED ALGORITHMS FOR NASH EQUILIBRIUM PROBLEMS – APPLICATIONS TO MULTI-AGENT NETWORK INTERDICTION GAMES AND BEYOND

Nash equilibrium problems (NEPs) have gained popularity in recent years in the engineering community due to their ready applicability to a wide variety of practical problems ranging from communication network design to power market analysis. There are strong links between the tools used to analyze NEPs and the classical techniques of nonlinear and combinatorial optimization. However, there remain significant challenges in both the theoretical and algorithmic analysis of NEPs. This dissertation studies certain special classes of NEPs, with the overall purpose of analyzing theoretical properties such as existence and uniqueness, while at the same time proposing decentralized algorithms that provably converge to solutions. The subclasses are motivated by relevant application examples

Selfish versus coordinated routing in network games

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.Includes bibliographical references (p. 159-170) and index.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.A common assumption in network optimization models is that a central authority controls the whole system. However, in some applications there are independent users, and assuming that they will follow directions given by an authority is not realistic. Individuals will only accept directives if they are in their own interest or if there are incentives that encourage them to do so. Actually, it would be much easier to let users make their own decisions hoping that the outcome will be close to the authority's goals. Our main contribution is to show that, in static networks subject to congestion, users' selfish decisions drive the system close to optimality with respect to various common objectives. This connection to individual decision making proves fruitful; not only does it provide us with insights and additional understanding of network problems, but it also allows us to design approximation algorithms for computationally difficult problems. More specifically, the conflicting objectives of the users prompt the definition of a network game in which they minimize their own latencies. We show that the so-called price of anarchy is small in a quite general setting. Namely, for networks with side constraints and non-convex, non-differentiable, and even discontinuous latency functions, we show that although an arbitrary equilibrium need not be efficient, the total latency of the best equilibrium is close to that of an optimal solution. In addition, when the measure of the solution quality is the maximum latency, equilibria in networks without constraints are also near-optimal. We provide the first analysis of the problem of minimizing that objective in static networks with congestion.(cont.) As this problem is NP-hard, computing an equilibrium represents a constant-factor approximation algorithm. In some situations, the network authority might still want to do better than in equilibrium. We propose to use a solution that minimizes the total latency, subject to constraints designed to improve the solution's fairness. For several real-world instances, we compute traffic assignments of notably smaller total latency than an equilibrium, yet of similar fairness. Furthermore, we provide theoretical results that explain the conclusions derived from the computational study.by Nicolás E. Stier-Moses.Ph.D

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Computation and Consistent Estimation of Stationary Optimal Transport Plans

Informally, the optimal transport (OT) problem is to align, or couple, two distributions of interest as best as possible with respect to some prespecified cost. A coupling that achieves the minimum cost among all couplings is referred to as an OT plan; the cost of the OT plan is referred to as the OT cost. Researchers in statistics and machine learning have expended a great deal of effort to understand the properties of OT plans and costs. The motivation for this work stems partly from the fact that, unlike many other divergence measures and metrics between distributions, OT plans and costs describe relationships between distributions in a manner that respects the geometry of the underlying space (by way of the specified cost). However, this advantage does not necessarily carry over when standard OT techniques are applied to distributions with specific structure. In the case that the two distributions describe stationary stochastic processes, the OT problem may ignore the differences in the sequential dependence of either process. One must find a way to make the OT problem account for the stationary dependence of the marginal processes. In this thesis, we study OT for stationary processes, a field that we refer to as stationary optimal transport. Through example and theory, we argue that when applying OT to stationary processes, one should incorporate the stationarity into the problem directly -- constraining the set of allowed transport plans to those that are stationary themselves. In this way, we only consider transport plans that respect the dependence structure of the marginal processes. We study this constrained OT problem from statistical and computational perspectives, with an eye toward applications in machine learning and data science. In particular, we develop algorithms for computing stationary OT plans of Markov chains, extend these tools for Markov OT to the alignment and comparison of weighted graphs, and propose estimates of stationary OT plans based on finite sequences of observations. We build upon existing techniques in OT as well as draw from a variety of fields including Markov decision processes, graph theory, and ergodic theory. In doing this, we uncover new perspectives on OT and pave the way for additional applications and approaches in future work.Doctor of Philosoph