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Jun 30, 2018
06/18

by
A. O. Smirnov; E. G. Semenova; V. Zinger; N. Zinger

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A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is investigated. An existence of a real smooth finite-gap solution of NLS equation with complex initial phase is proven. Degenerations of the constructed solution to one-phase traveling wave solution and solutions in the form of the plane waves are carried.

Topics: Mathematics, Nonlinear Sciences, Exactly Solvable and Integrable Systems, Mathematical Physics,...

Source: http://arxiv.org/abs/1407.7974

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3.0

Jun 30, 2018
06/18

by
Natasa Djurdjevac Conrad; Ralf Banisch; Christof Schütte

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The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarse-grained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important...

Topics: Physics, Mathematics, Computing Research Repository, Physics and Society, Probability, Social and...

Source: http://arxiv.org/abs/1407.8039

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6.0

Jun 30, 2018
06/18

by
Nicolas Juillet

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The (left-)curtain coupling, introduced by Beiglb\"ock and the author is an extreme element of the set of "martingale" couplings between two real probability measures in convex order. It enjoys remarkable properties with respect to order relations and a minimisation problem inspired by the theory of optimal transport. An explicit representation and a number of further noteworthy attributes have recently been established by Henry-Labord\`ere and Touzi. In the present paper we...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1407.8009

3
3.0

Jun 30, 2018
06/18

by
Noah Golowich; David Rolnick

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An acyclic set in a digraph is a set of vertices that induces an acyclic subgraph. In 2011, Harutyunyan conjectured that every planar digraph on $n$ vertices without directed 2-cycles possesses an acyclic set of size at least $3n/5$. We prove this conjecture for digraphs where every directed cycle has length at least 8. More generally, if $g$ is the length of the shortest directed cycle, we show that there exists an acyclic set of size at least $(1 - 3/g)n$.

Topics: Mathematics, Combinatorics

Source: http://arxiv.org/abs/1407.8045

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4.0

Jun 30, 2018
06/18

by
Takako Endo; Norio Konno; Etsuo Segawa; Masato Takei

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We consider a one-dimensional space-inhomogeneous discrete time quantum walk. This model is the Hadamard walk with one defect at the origin which is different from the model introduced by Wojcik et al. [14]. We obtain a stationary measure of the model by solving the eigenvalue problem and an asymptotic behaviour of the return probability by the path counting approach. Moreover, we get the time-averaged limit measure using the space-time generating function method. The measure is symmetric for...

Topics: Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1407.8103