Related papers: Simplifying Multiple Sums in Difference Fields
Graph generation and enumeration problems often require handling equivalent graphs -- those that differ only in vertex labeling. We study how to extend SAT Modulo Symmetries (SMS), a framework for eliminating such redundant graphs, to…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…
Sampling methods that choose a subset of the data proportional to its diversity in the feature space are popular for data summarization. However, recent studies have noted the occurrence of bias (under- or over-representation of a certain…
A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…
We give an extension of Sister Celine's method of proving hypergeometric sum identities that allows it to handle a larger variety of input summands. We then apply this to several problems. Some give new results, and some reprove already…
Multiple harmonic sums are iterated generalizations of harmonic sums. Recently Dilcher has considered congruences involving q-analogs of these sums in depth one. In this paper we shall study the homogeneous case for arbitrary depth by using…
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops.…
We present two novel applications of symmetries for mixed-integer linear programming. First we propose two variants of a new heuristic to improve the objective value of a feasible solution using symmetries. These heuristics can use either…
Quantum corrections significantly influence the quantities observed in modern particle physics. The corresponding theoretical computations are usually quite lengthy which makes their automation mandatory. This review reports on the current…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to…
We present a new interface called FeynHelpers that connects FeynCalc, a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and calculations in quantum field theory (QFT) to Package-X and FIRE. The former provides…
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
The software package developed in the MS thesis research implements functions for the intelligent guessing of polynomial sequence formulas based on user-defined expected sequence factors of the input coefficients. We present a specialized…
Given a set (or multiset) S of n numbers and a target number t, the subset sum problem is to decide if there is a subset of S that sums up to t. There are several methods for solving this problem, including exhaustive search,…
Solving mathematical word problems (MWPs) automatically is challenging, primarily due to the semantic gap between human-readable words and machine-understandable logics. Despite the long history dated back to the1960s, MWPs have regained…
Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…
In this paper we give a systematized treatment to some coincidence situations for multiple summing multilinear mappings which extend, generalize and simplify the methods and results obtained thus far. The application of our general results…