Social Shaping for Multi-Agent Systems

Multi-agent systems have gained attention due to advances in automation, technology, and AI. In these systems, intelligent agents collaborate through networks to achieve goals. Despite successes, multi-agent systems pose social challenges. Problems include agents finding resource prices unacceptable due to efficient allocation, interactions being cooperative/competitive, leading to varying outcomes, and sensitive data being at risk due to sharing. Problems are: 1. Price Acceptance; 2. Agent Cooperation and Competition; 3. Privacy Risks. For Price Acceptance, we address decentralized resource allocation systems as markets. We solve price acceptance in static systems with quadratic utility functions by defining allowed quadratic ranges. For dynamic systems, we present dynamic competitive equilibrium computation and propose a horizon strategy for smoothing dynamic pricing. Concerning Agent Cooperation and Competition, we study the well-known Regional Integrated Climate-Economy model (RICE). It's a dynamic game. We analyze cooperative and competitive solutions, showing impact on negotiations and consensus for regional climate action. Regarding Privacy Risks, we infer network structures from linear-quadratic game best-response dynamics to reveal agent vulnerabilities. We prove network identifiability tied to controllability conditions. A stable, sparse system identification algorithm learns network structures despite noise. Lastly, we contribute privacy-aware algorithms. We address network games where agents aggregate under differential privacy. Extending to network games, we propose a Laplace linear-quadratic functional perturbation algorithm. A tutorial example demonstrates meeting privacy needs through tuning. In summary, this thesis solves social challenges in multi-agent systems: Price Acceptance, Agent Cooperation and Competition, and Privacy Risks

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described