In the remainder, we call such a variety a convex symplectic variety. A convex symplectic variety has been studied in [K-V], [Ka 1] and [G-K]. One of main difficulties we meet is the fact that tangent objects TX and T 1 Y are not finite dimensional, since Y may possibly have non-isolated singularities; hence the usual deformation theory does not work well. Instead, in [K-V], [G-K], they introdu...

Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebra A together with a Lie algebra L mapped into the derivations of A. A bicomplex (with both Hochschild and Chevalley-Eilenberg cohomologies) is essential. The importance of Poisson algebras in classical mechanics makes it useful to have a...

Stein's method is used to prove approximations in total variation to the distributions of integer valued random variables by (possibly signed) compound Poisson measures. For sums of independent random variables, the results obtained are very explicit, and improve upon earlier work of Kruopis (1983) and Cekanavicius (1997); coupling methods are used to derive concrete expressions for the error b...

The Poisson Problem, ∇ · ∇x = b, is a sparse linear system of equations that arises, for example, in scientific computing. For this project, I describe a parallel Successive Over-Relaxation (SOR) algorithm for solving the Poisson problem and implement it in a C library using Message Passing Interface (MPI). I evaluate the performance of my implementation on a single multicore machine and in a c...

Semiclassical limits of generic multiparameter quantized coordinate rings A = Oq(k ) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric matrix whose entries generate a torsionfree subgroup of k. A semiclassical limit of A is a Poisson algebra structure on the corresponding classical coordinate ring...

SUMMARY We propose a parametric model, HiCNorm, to remove systematic biases in the raw Hi-C contact maps, resulting in a simple, fast, yet accurate normalization procedure. Compared with the existing Hi-C normalization method developed by Yaffe and Tanay, HiCNorm has fewer parameters, runs >1000 times faster and achieves higher reproducibility. AVAILABILITY Freely available on the web at: htt...

In the remainder, we call such a variety a convex symplectic variety. A convex symplectic variety has been studied in [K-V], [Ka 1] and [G-K]. One of main difficulties we meet is the fact that tangent objects TX and T 1 Y are not finite dimensional, since Y may possibly have non-isolated singularities; hence the usual deformation theory does not work well. Instead, in [K-V], [G-K], they introdu...

Notwithstanding known obstructions to this idea, we formulate an attempt to turn quantization into a functorial procedure. We define a category Poisson of Poisson manifolds, whose objects are integrable Poisson manifolds and whose arrows are isomorphism classes of regular Weinstein dual pairs; it follows that identity arrows are symplectic groupoids, and that two objects are isomorphic in Poiss...

We continue the study of the Poisson-Sigma model over Poisson-Lie groups. Firstly, we solve the models with targets G and G∗ (the dual group of the Poisson-Lie group G) corresponding to a triangular r-matrix and show that the model over G∗ is always equivalent to BF-theory. Then, given an arbitrary r-matrix, we address the problem of finding D-branes preserving the duality between the models. W...