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Solving a linear system $Ax=b$ is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are…
This paper introduces a unified framework for stable matching, which nests the traditional definition of stable matching in finite markets and the continuum definition of stable matching from Azevedo and Leshno (2016) as special cases.…
Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with…
The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
In the Stable Roommates problem, we seek a stable matching of the agents into pairs, in which no two agents have an incentive to deviate from their assignment. It is well known that a stable matching is unlikely to exist, but a stable…
In the bounded confidence model the opinions of a set of agents evolve over discrete time steps. In each round an agent averages the opinion of all agents whose opinions are at most a certain threshold apart. Here we assume that the…
In this paper, we study a convergence condition for asynchronous consensus problems in multi-agent systems. The convergence in this context implies the asynchronous consensus value converges to the synchronous one and is unique. Although it…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
Algorithms for computing equilibria, optima, and fixed points in nonconvex problems often depend sensitively on practitioner-chosen initial conditions. When uniqueness of a solution is of interest, a common heuristic is to run such…
The notion of stability in a structured argumentation setup characterizes situations where the acceptance status associated with a given literal will not be impacted by any future evolution of this setup. In this paper, we abstract away…
For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…
Logics for resource-bounded agents have been getting more and more attention in recent years since they provide us with more realistic tools for modelling and reasoning about multi-agent systems. While many existing approaches are based on…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…
This paper addresses the problem of risk-aware fixed-time stabilization of a class of uncertain, output-feedback nonlinear systems modeled via stochastic differential equations. First, novel classes of certificate functions, namely…
Static stability in economic models means negative incentives for deviation from equilibrium strategies, which we expect to assure a return to equilibrium, i.e., dynamic stability, as long as agents respond to incentives. There have been…
We study a Stackelberg variant of the classical discrete-time Dynkin game, in which Player 1 (the leader) commits to a stopping strategy first and Player 2 (the follower) responds optimally. This leader-follower structure induces an optimal…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…