Related papers: Fast n-point correlation functions and three-point…
We developed the functional form of the two-point correlation function under the approximation of fixed particle number density n(bar). We solved the quasi-linear partial differential equation (PDE) through the method of characteristics to…
We describe an explicit algorithm to factorize an even antisymmetric N^2 matrix into triangular and trivial factors. This allows for a straight forward computation of Pfaffians (including their signs) at the cost of N^3/3 flops.
We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erd\H{o}s-R\'enyi graphs $\mathcal{G}(n,q)$ whose edges are…
Visibility information is critical in game AI applications, but the computational cost of raycasting-based methods poses a challenge for real-time systems. To address this challenge, we propose a novel method that represents a partitioned…
A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph…
We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$ nodes.…
We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation -- the…
Free-streaming of cosmic neutrinos affects the distribution and growth of cosmic structures on small scales. This enables the sum of neutrino masses $M_\nu$ to be constrained from clustering studies. We investigate the possibility of…
We present a fast and accurate solution to the perspective $n$-points problem, by way of a new approach to the n=4 case. Our solution hinges on a novel separation of variables: given four 3D points and four corresponding 2D points on the…
This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a…
Computation of correlation functions is a key operation in Lattice quantum chromodynamics (LQCD) simulations to extract nuclear physics observables. These functions involve many binary batch tensor contractions, each tensor possibly…
We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix $M\in{\mathbb R}^{n\times n}$ can be decomposed as $M=\Phi U +…
This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of $n$ points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help…
We study the exact counting problem for all lattice rectangles contained in the square $[0,n)\times[0,n)$, including non-axis-parallel ones. Starting from the standard parametrization by a primitive direction $(u,v)$ and two side lengths,…
The three-point current correlation function in Euclidean spacetime for a strongly coupled system with non-Abelian global symmetry, $\langle J^a_i(x)J^b_j(y)J^c_k(z)\rangle$, is calculated from the weakly coupled AdS dual. The contribution…
Rigidity Percolation is a crucial framework for describing rigidity transitions in amorphous systems. We present a new, efficient algorithm to study central-force Rigidity Percolation in two dimensions. This algorithm combines the Pebble…
In the non-negative matrix factorization (NMF) problem, the input is an $m\times n$ matrix $M$ with non-negative entries and the goal is to factorize it as $M\approx AW$. The $m\times k$ matrix $A$ and the $k\times n$ matrix $W$ are both…
We propose fast, exact and efficient algorithms for the convolution of two arbitrary functions on the sphere which speed up computations by a factor \order{\sqrt{N}} compared to present methods where $N$ is the number of pixels. No…
Given the recent progress in computing three-point functions in N=4 SYM via integrability, I provide here a novel direct calculation of some structure constants at weak coupling. The main focus is on correlators involving more than one…
An algorithm is developed for finding a close to optimal junction tree of a given graph G. The algorithm has a worst case complexity O(c^k n^a) where a and c are constants, n is the number of vertices, and k is the size of the largest…