Related papers: Stable Relationships
We initiate the study of external manipulations in Stable Marriage by considering several manipulative actions as well as several manipulation goals. For instance, one goal is to make sure that a given pair of agents is matched in a stable…
We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
How can we model influence between individuals in a social system, even when the network of interactions is unknown? In this article, we review the literature on the "influence model," which utilizes independent time series to estimate how…
Some aspects of the problem of stable marriage are discussed. There are two distinguished marriage plans: the fully transferable case, where money can be transferred between the participants, and the fully non transferable case where each…
The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of…
The personal network of relationships is structured in circles of friendships, that go from the most intense relationships to the least intense ones. While this is a well established result, little is known about the stability of those…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley[GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…
We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…
Coalition forming is investigated among countries, which are coupled with short range interactions, under the influence of external fields produced by the existence of global alliances. The model rests on the natural model of coalition…
Emotional disorders and psychological flourishing are the result of complex interactions between positive and negative affects that depend on external events and the subject's internal representations. Based on psychological data, we…
We study control problems in the context of matching under preferences: We examine how a central authority, called the controller, can manipulate an instance of the Stable Marriage or Stable Roommates problems in order to achieve certain…
A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
A class of polynomial dynamical systems called complex-balanced are locally stable and conjectured to be globally stable. In general, complex-balancing is not a robust property, i.e., small changes in parameter values may result in the loss…
We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
We analyze a mathematical model to understand the dynamics of bullying in schools. The model considers a population divided into four groups: susceptible individuals, bullies, individuals exposed to bullying, and violent individuals.…