相关论文: Factored Notation for Interval I/O

In a general fractional factorial design, the $n$-levels of a factor are coded by the $n$-th roots of the unity. This device allows a full generalization to mixed-level designs of the theory of the polynomial indicator function which has…

As the field of recommender systems has developed, authors have used a myriad of notations for describing the mathematical workings of recommendation algorithms. These notations ap-pear in research papers, books, lecture notes, blog posts,…

We study the problem of invariance of indices of thematic factorizations. Such factorizations were introduced in [PY1] for studying superoptimal approximation by bounded analytic matrix functions. As shown in [PY1], the indices may depend…

This paper attempts a more formal approach to the legibility of text based programming languages, presenting, with proof, minimum possible ways of representing structure in text interleaved with information. This presumes that a minimalist…

Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…

In this paper, we obtain several new factorization results for certain classes of polynomials having integer coefficients. In doing so, we use the information about prime factorization of the value taken up by such polynomials and their…

Interval approaches for the reachability analysis of initial value problems for sets of classical ordinary differential equations have been investigated and implemented by many researchers during the last decades. However, there exist…

Factor importance measures the impact of each feature on output prediction accuracy. Many existing works focus on the model-based importance, but an important feature in one learning algorithm may hold little significance in another model.…

The interval poset of a permutation catalogues the intervals that appear in its one-line notation, according to set inclusion. We study this poset, describing its structural, characterizing, and enumerative properties.

This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…

In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…

The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…

Certain new inequalities for the sums of factorials are presented.

This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter…

Orthogonal Arrays allow us to test various levels of each factor and balance the different factors so that we can estimate interactions as well as first order effects. There is a trade-off between how well we can sample different levels of…

Network Utility Maximization (NUM) provides a key conceptual framework to study reward allocation amongst a collection of users/entities across disciplines as diverse as economics, law and engineering. In network engineering, this framework…

The ISI-Impact Factors suffer from a number of drawbacks, among them the statistics-why should one use the mean and not the median?-and the incomparability among fields of science because of systematic differences in citation behavior among…

We consider a MapReduce-like distributed computing system. We derive a lower bound on the communication cost for any given storage and computation costs. This lower bound matches the achievable bound we proposed recently. As a result, we…

This paper addresses the tradeoffs which need to be considered in reasoning using probabilistic network representations, such as Influence Diagrams (IDs). In particular, we examine the tradeoffs entailed in using Temporal Influence Diagrams…

We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…