Related papers: Complexity reduction for path categories
Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the…
We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.
CAT(0) metric spaces constitute a far-reaching common generalization of Euclidean and hyperbolic spaces and simple polygons: any two points x and y of a CAT(0) metric space are connected by a unique shortest path {\gamma}(x,y). In this…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies.…
We present the `Basic S*' algorithm for computing shortest path through a metric simplicial complex. In particular, given a metric graph, $G$, which is constructed as a discrete representation of an underlying configuration space (a larger…
The pseudoparticle approach is a numerical technique to compute path integrals without discretizing spacetime. The basic idea is to integrate over those field configurations, which can be represented by a sum of a fixed number of localized…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
In a $k$-critical bifiltration, every simplex enters along a staircase with at most $k$ steps. Examples with $k>1$ include degree-Rips bifiltrations and models of the multicover bifiltration. We consider the problem of converting a…
The pseudoparticle approach is a numerical method to compute path integrals without discretizing spacetime. The basic idea is to consider only those field configurations, which can be represented as a linear superposition of a small number…
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that…
Inspired by work of Fr\"oberg (1990), and Eagon and Reiner (1998), we define the \emph{total $k$-cut complex} of a graph $G$ to be the simplicial complex whose facets are the complements of independent sets of size $k$ in $G$. We study the…
We formalise, in Coq, the opening sections of Parity Complexes [Street1991] up to and including the all important excision of extremals algorithm. Parity complexes describe the essential combinatorial structure exhibited by simplexes, cubes…
We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial…
We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x2013}$ in particular, the coherent state path integral. We…
The method of partial derivatives is one of the most successful lower bound methods for arithmetic circuits. It uses as a complexity measure the dimension of the span of the partial derivatives of a polynomial. In this paper, we consider…
In this paper, we introduce the notion of an admissible partition of a simplicial polyhedral fan and define the category of a partitioned fan as a generalisation of the $\tau$-cluster morphism category of a finite-dimensional algebra. This…
A circular Pascal array is a periodization of the familiar Pascal's triangle. Using simple operators defined on periodic sequences, we find a direct relationship between the ranges of the circular Pascal arrays and numbers of certain…
The performance of particle advection-based flow visualization techniques is complex, since computational work can vary based on many factors, including number of particles, duration, and mesh type. Further, while many approaches have been…