Related papers: Approximating the parallel transport of an induced…
This paper investigates the projectivization of real vector bundles over small covers. We first give a necessary and sufficient condition for such a projectivization to be a small cover. Then associated with moment-angle manifolds, we…
A quantum algorithm for approximating efficiently 3--manifold topological invariants in the framework of SU(2) Chern-Simons-Witten (CSW) topological quantum field theory at finite values of the coupling constant k is provided. The model of…
Tractors and Twistors bundles both provide natural conformally covariant calculi on $4D$-Riemannian manifolds. They have different origins but are closely related, and usually constructed bottom-up through prolongation of defining…
A numerical method for the direct numerical simulation of incompressible wall turbulence in rectangular and cylindrical geometries is presented. The distinctive feature resides in its design being targeted towards an efficient…
This paper introduces a parallel and distributed extension to the alternating direction method of multipliers (ADMM) for solving convex problem: minimize $\sum_{i=1}^N f_i(x_i)$ subject to $\sum_{i=1}^N A_i x_i=c, x_i\in \mathcal{X}_i$. The…
Parallel transport is a fundamental tool to perform statistics on Rie-mannian manifolds. Since closed formulae don't exist in general, practitioners often have to resort to numerical schemes. Ladder methods are a popular class of algorithms…
We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
We present a new multiscale algorithm for solving regularized Optimal Transport problems on the GPU, with a linear memory footprint. Relying on Sinkhorn divergences which are convex, smooth and positive definite loss functions, this method…
Tractors and Twistors bundles both provide natural conformally covariant calculi on $4D$-Riemannian manifolds. They have different origins but are closely related, and usually constructed bottom-up from prolongation of defining differential…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, which is closely related to iterated Runge-Kutta methods…
A wide range of physical phenomena exhibit auxiliary admissibility criteria, such as conservation of entropy or various energies, which arise implicitly under exact solution of their governing PDEs. However, standard temporal schemes, such…
Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient…
Computations on a manifold often involve constructing an operator on the tangent space and computing its inverse, which can be time-consuming in many applications. In order to reduce the computational costs and preserve the benign…
We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number…
In this work, we propose a novel approach for subgraph matching, the problem of finding a given query graph in a large source graph, based on the fused Gromov-Wasserstein distance. We formulate the subgraph matching problem as a partial…
Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge--Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher-order…
There are two methods to study families of conformal theories in the operator formalism. In the first method we begin with a theory and a family of deformed theories is defined in the state space of the original theory. In the other there…
We study finite dimensional vector spaces over fields of elliptic functions equipped with two commuting aotomorphisms \sigma and \tau induced by isogenies of relatively prime orders. We give a structure theorem for such objects, that…