Related papers: Random weights, robust lattice rules and the geome…
We perform a global fit to the CKM unitarity triangle using the latest experimental and theoretical constraints. Our emphasis is on the hadronic weak matrix elements that enter the analysis, which must be computed using lattice QCD or other…
We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…
In recent years, locally repairable codes (LRCs) have attracted considerable attention owing to their pivotal role in distributed storage systems. Since binary linear locally repairable codes can significantly reduce the complexity of both…
We introduce a general framework of matrix-form combinatorial Riemann boundary value problem (cRBVP) to characterize the integrability of functional equations arising in lattice walk enumerations. A matrix cRBVP is defined as integrable if…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
This paper develops an algorithmic approach for obtaining approximate, numerical estimates of the sizes of subcodes of Reed-Muller (RM) codes, all of the codewords in which satisfy a given constraint. Our algorithm is based on a statistical…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
QMC rules are equal weight quadrature rules for approximating integrals over $[0,1]^s$. One line of research studies the integration error of functions in the unit ball of so-called Korobov spaces, which are Hilbert spaces of periodic…
Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where its entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number…
A lattice model is presented for investigating the fluctuations in static granular materials under gravitationally induced stress. The model is similar in spirit to the scalar q-model of Coppersmith et al., but ensures balance of all…
We present a method to non-perturbatively determine the parameters of the on-shell, $O(a)$-improved relativistic heavy quark action. These three parameters, $m_0$, $\zeta$, and $c_B=c_E$ are obtained by matching finite-volume, heavy-heavy…
In some studies requiring predictive and CPU-time consuming numerical models, the sampling design of the model input variables has to be chosen with caution. For this purpose, Latin hypercube sampling has a long history and has shown its…
Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…
In the analysis of using quasi-Monte Carlo (QMC) methods to approximate expectations of a linear functional of the solution of an elliptic PDE with random diffusion coefficient the sensitivity w.r.t. the parameters is often stated in terms…
Given a set C in R^d, let p(C) be the probability that a random d-dimensional unimodular lattice, chosen according to Haar measure on SL(d,Z)\SL(d,R), is disjoint from C\{0}. For special convex sets C we prove bounds on p(C) which are sharp…
We determine to order alpha^3 in the quenched approximation the so-called residual mass in the lattice regularisation of the Heavy Quark Effective Theory. We follow a gauge-invariant strategy which exploits the fact that this mass term…
Re-weighting is a useful tool that has been employed in Lattice QCD in different contexts including, tuning the strange quark mass, approaching the light quark mass regime, and simulating electromagnetic fields on top of QCD gauge…