4,768 research outputs found
Nonspecific Networking
A new model of strategic network formation is developed and analyzed, where an agent's investment in links is nonspecific. The model comprises a large class of games which are both potential and super- or submodular games. We obtain comparative statics results for Nash equilibria with respect to investment costs for supermodular as well as submodular networking games. We also study logit-perturbed best-response dynamics for supermodular games with potentials. We find that the associated set of stochastically stable states forms a sublattice of the lattice of Nash equilibria and derive comparative statics results for the smallest and the largest stochastically stable state. Finally, we provide a broad spectrum of applications from social interaction to industrial organization. Models of strategic network formation typically assume that each agent selects his direct links to other agents in which to invest. Nonspecific networking means that an agent cannot select a specific subset of feasible links which he wants to establish or strengthen. Rather, each agent chooses an effort level or intensity of networking. In the simplest case, the agent faces a binary choice: to network or not to network. If an agent increases his networking effort, all direct links to other agents are strengthened to various degrees. We assume that benefits accrue only from direct links. The set of agents or players is finite. Each agent has a finite strategy set consisting of the networking levels to choose from. For any pair of agents, their networking levels determine the individual benefits which they obtain from interacting with each other. An agent derives an aggregate benefit from the pairwise interactions with all others. In addition, the agent incurs networking costs, which are a function of the agent's own networking level. The agent's payoff is his aggregate benefit minus his cost.Network Formation, Potential Games, Supermodular Games
Efficient Relaxations for Dense CRFs with Sparse Higher Order Potentials
Dense conditional random fields (CRFs) have become a popular framework for
modelling several problems in computer vision such as stereo correspondence and
multi-class semantic segmentation. By modelling long-range interactions, dense
CRFs provide a labelling that captures finer detail than their sparse
counterparts. Currently, the state-of-the-art algorithm performs mean-field
inference using a filter-based method but fails to provide a strong theoretical
guarantee on the quality of the solution. A question naturally arises as to
whether it is possible to obtain a maximum a posteriori (MAP) estimate of a
dense CRF using a principled method. Within this paper, we show that this is
indeed possible. We will show that, by using a filter-based method, continuous
relaxations of the MAP problem can be optimised efficiently using
state-of-the-art algorithms. Specifically, we will solve a quadratic
programming (QP) relaxation using the Frank-Wolfe algorithm and a linear
programming (LP) relaxation by developing a proximal minimisation framework. By
exploiting labelling consistency in the higher-order potentials and utilising
the filter-based method, we are able to formulate the above algorithms such
that each iteration has a complexity linear in the number of classes and random
variables. The presented algorithms can be applied to any labelling problem
using a dense CRF with sparse higher-order potentials. In this paper, we use
semantic segmentation as an example application as it demonstrates the ability
of the algorithm to scale to dense CRFs with large dimensions. We perform
experiments on the Pascal dataset to indicate that the presented algorithms are
able to attain lower energies than the mean-field inference method
Multi-marginal optimal transport: theory and applications
Over the past five years, multi-marginal optimal transport, a generalization
of the well known optimal transport problem of Monge and Kantorovich, has begun
to attract considerable attention, due in part to a wide variety of emerging
applications. Here, we survey this problem, addressing fundamental theoretical
questions including the uniqueness and structure of solutions. The (partial)
answers to these questions uncover a surprising divergence from the classical
two marginal setting, and reflect a delicate dependence on the cost function.
We go one to describe two applications of the multi-marginal problem.Comment: Typos corrected and minor changes to presentatio
Symmetry Breaking for Answer Set Programming
In the context of answer set programming, this work investigates symmetry
detection and symmetry breaking to eliminate symmetric parts of the search
space and, thereby, simplify the solution process. We contribute a reduction of
symmetry detection to a graph automorphism problem which allows to extract
symmetries of a logic program from the symmetries of the constructed coloured
graph. We also propose an encoding of symmetry-breaking constraints in terms of
permutation cycles and use only generators in this process which implicitly
represent symmetries and always with exponential compression. These ideas are
formulated as preprocessing and implemented in a completely automated flow that
first detects symmetries from a given answer set program, adds
symmetry-breaking constraints, and can be applied to any existing answer set
solver. We demonstrate computational impact on benchmarks versus direct
application of the solver.
Furthermore, we explore symmetry breaking for answer set programming in two
domains: first, constraint answer set programming as a novel approach to
represent and solve constraint satisfaction problems, and second, distributed
nonmonotonic multi-context systems. In particular, we formulate a
translation-based approach to constraint answer set solving which allows for
the application of our symmetry detection and symmetry breaking methods. To
compare their performance with a-priori symmetry breaking techniques, we also
contribute a decomposition of the global value precedence constraint that
enforces domain consistency on the original constraint via the unit-propagation
of an answer set solver. We evaluate both options in an empirical analysis. In
the context of distributed nonmonotonic multi-context system, we develop an
algorithm for distributed symmetry detection and also carry over
symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201
Modularity bounds for clusters located by leading eigenvectors of the normalized modularity matrix
Nodal theorems for generalized modularity matrices ensure that the cluster
located by the positive entries of the leading eigenvector of various
modularity matrices induces a connected subgraph. In this paper we obtain lower
bounds for the modularity of that set of nodes showing that, under certain
conditions, the nodal domains induced by eigenvectors corresponding to highly
positive eigenvalues of the normalized modularity matrix have indeed positive
modularity, that is they can be recognized as modules inside the network.
Moreover we establish Cheeger-type inequalities for the cut-modularity of the
graph, providing a theoretical support to the common understanding that highly
positive eigenvalues of modularity matrices are related with the possibility of
subdividing a network into communities
There and back again: detecting regularity in human encounter communities
Detecting communities that recur over time is a challenging problem due to the potential sparsity of encounter events at an individual scale and inherent uncertainty in human behavior. Existing methods for community detection in mobile human encounter networks ignore the presence of temporal patterns that lead to periodic components in the network. Daily and weekly routine are prevalent in human behavior and can serve as rich context for applications that rely on person-to-person encounters, such as mobile routing protocols and intelligent digital personal assistants. In this article, we present the design, implementation, and evaluation of an approach to decentralized periodic community detection that is robust to uncertainty and computationally efficient. This alternative approach has a novel periodicity detection method inspired by a neural synchrony measure used in the field of neurophysiology. We evaluate our approach and investigate human periodic encounter patterns using empirical datasets of inferred and direct-sensed encounters
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