Search

Social balance theory describes allowable and forbidden configurations of thetopologies of signed directed social appraisal networks. In this paper, wepropose two discrete-time dynamical systems that explain how an appraisalnetwork \textcolor{blue}{converges to} social balance from an initiallyunbalanced configuration. These two models are based on two differentsocio-psychological mechanisms respectively: the homophily mechanism and theinfluence mechanism. Our main theoretical contribution is a comprehensiveanalysis for both models in three steps. First, we establish the well-posednessand bounded evolution of the interpersonal appraisals. Second, we fullycharacterize the set of equilibrium points; for both models, each equilibriumnetwork is composed by an arbitrary number of complete subgraphs satisfyingstructural balance. Third, we establish the equivalence among three distinctproperties: non-vanishing appraisals, convergence to all-to-all appraisalnetworks, and finite-time achievement of social balance. In addition totheoretical analysis, Monte Carlo validations illustrates how the non-vanishingappraisal condition holds for generic initial conditions in both models.Moreover, numerical comparison between the two models indicate that thehomophily-based model might be a more universal explanation for the formationof social balance. Finally, adopting the homophily-based model, we presentnumerical results on the mediation and globalization of local conflicts, thecompetition for allies, and the asymptotic formation of a single versus twofactions.

We propose a probabilistic enhancement of standard kernel Support VectorMachines for binary classification, in order to address the case when, alongwith given data sets, a description of uncertainty (e.g., error bounds) may beavailable on each datum. In the present paper, we specifically considerGaussian distributions to model uncertainty. Thereby, our data consist of pairs$(x_i,\Sigma_i)$, $i\in\{1,\ldots,N\}$, along with an indicator$y_i\in\{-1,1\}$ to declare membership in one of two categories for each pair.These pairs may be viewed to represent the mean and covariance, respectively,of random vectors $\xi_i$ taking values in a suitable linear space (typically$\mathbb R^n$). Thus, our setting may also be viewed as a modification ofSupport Vector Machines to classify distributions, albeit, at present, onlyGaussian ones. We outline the formalism that allows computing suitableclassifiers via a natural modification of the standard "kernel trick." The maincontribution of this work is to point out a suitable kernel function forapplying Support Vector techniques to the setting of uncertain data for which adetailed uncertainty description is also available (herein, "Gaussian points").

This paper proposes models of learning process in teams of individuals whocollectively execute a sequence of tasks and whose actions are determined byindividual skill levels and networks of interpersonal appraisals and influence.The closely-related proposed models have increasing complexity, starting with acentralized manager-based assignment and learning model, and finishing with asocial model of interpersonal appraisal, assignments, learning, and influences.We show how rational optimal behavior arises along the task sequence for eachmodel, and discuss conditions of suboptimality. Our models are grounded inreplicator dynamics from evolutionary games, influence networks frommathematical sociology, and transactive memory systems from organizationscience.

This paper proposes models of learning process in teams of individuals whocollectively execute a sequence of tasks and whose actions are determined byindividual skill levels and networks of interpersonal appraisals and influence.The closely-related proposed models have increasing complexity, starting with acentralized manager-based assignment and learning model, and finishing with asocial model of interpersonal appraisal, assignments, learning, and influences.We show how rational optimal behavior arises along the task sequence for eachmodel, and discuss conditions of suboptimality. Our models are grounded inreplicator dynamics from evolutionary games, influence networks frommathematical sociology, and transactive memory systems from organizationscience.