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  1. We investigate questions related to the time evolution of discrete graph dynamical systems where each node has a state from {0,1}. The configuration of a system at any time instant is a Boolean vector that specifies the state of each node at that instant. We say that two configurations are similar if the Hamming distance between them is small. Also, a predecessor of a configuration B is a configuration A such that B can be reached in one step from A. We study problems related to the similarity of predecessor configurations from which two similar configurations can be reached inmore »one time step. We address these problems both analytically and experimentally. Our analytical results point out that the level of similarity between predecessors of two similar configurations depends on the local functions of the dynamical system. Our experimental results, which consider random graphs as well as small world networks, rely on the fact that the problem of finding predecessors can be reduced to the Boolean Satisfiability problem (SAT).« less
  2. Using a discrete dynamical system model for a networked social system, we consider the problem of learning a class of local interaction functions in such networks. Our focus is on learning local functions which are based on pairwise disjoint coalitions formed from the neighborhood of each node. Our work considers both active query and PAC learning models. We establish bounds on the number of queries needed to learn the local functions under both models.We also establish a complexity result regarding efficient consistent learners for such functions. Our experimental results on synthetic and real social networks demonstrate how the number ofmore »queries depends on the structure of the underlying network and number of coalitions.« less
  3. Discrete graphical dynamical systems serve as effective formal models in many contexts, including simulations of agent-based models, propagation of contagions in social networks and study of biological phenomena. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used as a good model of certain biological phenomena. Motivated by these biological applications, we study a variety of analysis problems for synchronous graphical dynamical systems (SyDSs) over the Boolean domain, where each local function is an NCF. Each analysis problem involves testing whether the phase space of a given SyDS satisfies a certain property. We present intractability results formore »some properties as well as efficient algorithms for others. In several cases, our results clearly delineate intractable and efficiently solvable versions of problems« less
  4. Nested canalyzing functions (NCFs) are a class of Boolean functions which are used to model certain biological phenomena. We derive a complete characterization of NCFs with the largest average sensitivity, expressed in terms of a simple structural property of the NCF. This characterization provides an alternate, but elementary, proof of the tight upper bound on the average sensitivity of any NCF established by Klotz et al. (2013). We also utilize the characterization to derive a closed form expression for the number of NCFs that have the largest average sensitivity.