Related papers: Compactified Webs and Domain Wall Partition Functi…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
T-duality is one of the essential elements of string theory. Recently, Hull has developed a formalism where the dimension of the target space is doubled so as to make T-duality manifest. This is then supplemented with a constraint equation…
Optimization of thin-walled structures like an aircraft wing, aircraft fuselage or submarine hull often involves dividing the shell surface into numerous localized panels, each characterized by its own set of design variables. The process…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also…
We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries…
The topological vertex formalism for 5d $\mathcal{N}=1$ gauge theories is not only a convenient tool to compute the instanton partition function of these theories, but it is also accompanied by a nice algebraic structure that reveals…
Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the…
Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology…
We discuss algorithms for domain wall fermions focussing on accelerating Hybrid Monte Carlo sampling of gauge configurations. Firstly a new multigrid algorithm for domain wall solvers and secondly a domain decomposed hybrid monte carlo…
A window function is a generalization of the aggregation operation. Unlike aggregation, the cardinality of its output is always the same as the cardinality of input. That is, the semantics of this operator imply computing values for extra…
We show how the topological string partition function, which is known to capture the degeneracies of a gas of BPS spinning M2-branes in M-theory compactified to 5 dimensions, is related to a 4-dimensional D-brane system that consists of…
We show that the solitonic contribution of compactified strings corresponds to the quantum statistical partition function of a free particle living on higher dimensional spaces. In the simplest case of a compactification in a circle, the…
We perform the calculation of the partition function of the Poisson-sigma model on the world sheet with the topology of a two-dimensional disc. Considering the special case of a linear Poisson structure we recover the partition function of…
We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse…
Important illustration to the principle ``partition functions in string theory are $\tau$-functions of integrable equations'' is the fact that the (dual) partition functions of $4d$ $\mathcal{N}=2$ gauge theories solve Painlev\'e equations.…
In this paper we present a new algorithm for multivariate interpolation of scattered data sets lying in convex domains $\Omega \subseteq \RR^N$, for any $N \geq 2$. To organize the points in a multidimensional space, we build a $kd$-tree…
In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We then used this correspondence to give a geometric proof of the…
There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical…
Simplicial, piecewise-flat discretizations of manifolds provide a clear path towards curvature analysis on discrete geometries and for solutions of PDE's on manifolds of complex topologies. In this manuscript we review and expand on…