111,322 research outputs found
Solution space heterogeneity of the random K-satisfiability problem: Theory and simulations
The random K-satisfiability (K-SAT) problem is an important problem for
studying typical-case complexity of NP-complete combinatorial satisfaction; it
is also a representative model of finite-connectivity spin-glasses. In this
paper we review our recent efforts on the solution space fine structures of the
random K-SAT problem. A heterogeneity transition is predicted to occur in the
solution space as the constraint density alpha reaches a critical value
alpha_cm. This transition marks the emergency of exponentially many solution
communities in the solution space. After the heterogeneity transition the
solution space is still ergodic until alpha reaches a larger threshold value
alpha_d, at which the solution communities disconnect from each other to become
different solution clusters (ergodicity-breaking). The existence of solution
communities in the solution space is confirmed by numerical simulations of
solution space random walking, and the effect of solution space heterogeneity
on a stochastic local search algorithm SEQSAT, which performs a random walk of
single-spin flips, is investigated. The relevance of this work to glassy
dynamics studies is briefly mentioned.Comment: 11 pages, 4 figures. Final version as will appear in Journal of
Physics: Conference Series (Proceedings of the International Workshop on
Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japan
A Deep Siamese Network for Scene Detection in Broadcast Videos
We present a model that automatically divides broadcast videos into coherent
scenes by learning a distance measure between shots. Experiments are performed
to demonstrate the effectiveness of our approach by comparing our algorithm
against recent proposals for automatic scene segmentation. We also propose an
improved performance measure that aims to reduce the gap between numerical
evaluation and expected results, and propose and release a new benchmark
dataset.Comment: ACM Multimedia 201
Comments on Higher Rank Wilson Loops in
For theory with gauge group we evaluate expectation
values of Wilson loops in representations described by a rectangular Young
tableau with rows and columns. The evaluation reduces to a two-matrix
model and we explain, using a combination of numerical and analytical
techniques, the general properties of the eigenvalue distributions in various
regimes of parameters where is the 't Hooft
coupling. In the large limit we present analytic results for the leading
and sub-leading contributions. In the particular cases of only one row or one
column we reproduce previously known results for the totally symmetry and
totally antisymmetric representations. We also extensively discusss the limit of the theory. While establishing these connections
we clarify aspects of various orders of limits and how to relax them; we also
find it useful to explicitly address details of the genus expansion. As a
result, for the totally symmetric Wilson loop we find new contributions that
improve the comparison with the dual holographic computation at one loop order
in the appropriate regime.Comment: 28 pages, 4 figures. v2: References added. v3: More references, JHEP
versio
Efficiency of Truthful and Symmetric Mechanisms in One-sided Matching
We study the efficiency (in terms of social welfare) of truthful and
symmetric mechanisms in one-sided matching problems with {\em dichotomous
preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are
particularly interested in the well-known {\em Random Serial Dictatorship}
mechanism. For dichotomous preferences, we first show that truthful, symmetric
and optimal mechanisms exist if intractable mechanisms are allowed. We then
provide a connection to online bipartite matching. Using this connection, it is
possible to design truthful, symmetric and tractable mechanisms that extract
0.69 of the maximum social welfare, which works under assumption that agents
are not adversarial. Without this assumption, we show that Random Serial
Dictatorship always returns an assignment in which the expected social welfare
is at least a third of the maximum social welfare. For normalized von
Neumann-Morgenstern preferences, we show that Random Serial Dictatorship always
returns an assignment in which the expected social welfare is at least
\frac{1}{e}\frac{\nu(\opt)^2}{n}, where \nu(\opt) is the maximum social
welfare and is the number of both agents and items. On the hardness side,
we show that no truthful mechanism can achieve a social welfare better than
\frac{\nu(\opt)^2}{n}.Comment: 13 pages, 1 figur
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