Related papers: Advanced Determinant Calculus
This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described…
We present here a new method for evaluating determinants -- the reduction method. Firstly, in the section 2, we apply it to third-order determinants and after, in the section 3, we generalize it to higher-order determinants. In the section…
This article evaluates the determinants of two classes of special matrices, which are both from a number theory problem. Applications of the evaluated determinants can be found in [arXiv:math.NT/0509523]. Note that the two determinants are…
This paper presents a method for expressing the determinant of an N {\times} N complex block matrix in terms of its constituent blocks. The result allows one to reduce the determinant of a matrix with N^2 blocks to the product of the…
Main purposes of the paper are followings: 1) To show examples of the calculations in domain of QFT via ``derivative rules'' of an expert system; 2) To consider advantages and disadvantage that technology of the calculations; 3) To reflect…
The purpose of this paper is to report on the most recent developments in our ongoing investigation of the representation and manipulation of uncertainty in automated reasoning systems. In our earlier studies (Tong and Shapiro, 1985) we…
Based on geometric intuition, in this paper we are trying to give an idea and visualize the meaning of the determinants for the cubic-matrix. In this paper we have analyzed the possibilities of developing the concept of determinant of…
The goal of this thesis is threefold: first, to provide a general semantic setting for reasoning about incremental computation. Second, to establish and clarify the connection between derivatives in the incremental sense and derivatives in…
The roles played by decision factors in making complex subject are decisions are characterized by how these factors affect the overall decision. Evidence that partially matches a factor is evaluated, and then effective computational rules…
This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.
We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results…
The aim of this paper is to study determinants of matrices related to the Pascal triangle.
We present an overview of the existing methods for computing functional determinants, and outline a possible way forward for Hamiltonians of higher dimensions without radial symmetry.
The purpose of this book is to provide an overview of AI research, ranging from basic work to interfaces and applications, with as much emphasis on results as on current issues. It is aimed at an audience of master students and Ph.D.…
AI-driven outcomes can be challenging for end-users to understand. Explanations can address two key questions: "Why this outcome?" (factual) and "Why not another?" (counterfactual). While substantial efforts have been made to formalize…
This position paper suggests that progress with automatic summarising demands a better research methodology and a carefully focussed research strategy. In order to develop effective procedures it is necessary to identify and respond to the…
The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval.The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics…
This volume is a collection of six papers on the use of auxiliary information and 'a priori' values in construction of improved estimators. The work included here will be of immense application for researchers and students who emply…
Multicriteria decision analysis aims at supporting a person facing a decision problem involving conflicting criteria. We consider an additive utility model which provides robust conclusions based on preferences elicited from the decision…
This article introduces the Multidimensional Research Assessment Matrix of scientific output. Its base notion holds that the choice of metrics to be applied in a research assessment process depends upon the unit of assessment, the research…