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Dyck paths are classical Catalan objects. The peak distribution of Dyck paths is an important topic of combinatorics, and further the representation of symmetric groups.
Abstract: In the recent paper [Chru\'{s}ci\'{n}ski and Wudarski, arXiv:1105.4821], it was conjectured that the entanglement witnesses arising from some generalized Choi maps are optimal. We show that ...
Abstract: In the context of the geometrical analysis of weakly non Gaussian CMB maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments ex...
Abstract: We study equivariant maps corresponding to the classical Skyrme model and the Adkins-Nappi model, for which we prove global existence and scattering in critical Sobolev-Besov spaces.
Graded Hopf Maps and Fuzzy Superspheres     Graded Hopf Maps  Fuzzy Superspheres  High Energy Physics - Theory       font style='font-size:12px;'> 2011/7/28
Abstract: We argue supersymmetric generalizations of fuzzy two- and four-spheres based on the unitary-orthosymplectic algebras, $UOSp(N|2)$ and $UOSp(N|4)$, respectively. Supersymmetric version of Sch...
Abstract: Let $D$ be a space of $2\times n$ matrices. Then the face of the cone of all completely positive maps from $M_2$ into $M_n$ given by $D$ is an exposed face of the bigger cone of all decompos...
Abstract: We consider the O(n) loop model on tetravalent maps and show how to rephrase it into a model of bipartite maps without loops. This follows from a combinatorial decomposition that consists in...
Abstract: We consider the O(n) loop model on tetravalent maps and show how to rephrase it into a model of bipartite maps without loops. This follows from a combinatorial decomposition that consists in...
Abstract: A construction of multidimensional parametric Yang-Baxter maps is presented. The corresponding Lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the Skl...
The operator-sum decomposition (OS) of a mapping from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides...
Dynamical A and B maps have been employed extensively by Sudarshan and co-workers to investigate open system evolution of quantum systems. A canonical structure of the A-map is introduced here. It is ...
The goal of the present paper is three-fold. First is to clarify the connection between the dominant energy condition and hyperbolicity properties of Lagrangian field theories.
Entanglement evolution of non-trace-preserving maps      Entanglement evolution  non-trace-preserving maps        font style='font-size:12px;'> 2010/10/21
By solving the Schrodinger equation one obtains the whole energy spectrum, both the bound and the continuum states. If the Hamiltonian depends on a set of parameters, these could be tuned to a trans...
For a system of globally coupled chaotic maps with bistable behaviour we relate the rate function for large deviations in the system size at finite time to dynamical properties of the self consistent ...
Irreversibility in quantum maps with decoherence     quantum maps  decoherence       font style='font-size:12px;'> 2010/4/6
The Bolztmann echo (BE) is a measure of irreversibility and sensitivity to perturbations for non-isolated systems. Recently, different regimes of this quantity were described for chaotic systems. Ther...

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