相关论文: Factored Notation for Interval I/O

This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…

A critical challenge for modern system design is meeting the overwhelming performance, storage, and communication bandwidth demand of emerging applications within a tightly bound power budget. As both the time and power, hence the energy,…

This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…

In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced…

Ideally, the time that an incremental algorithm uses to process a change should be a function of the size of the change rather than, say, the size of the entire current input. Based on a formalization of ``the set of things changed'' by an…

We consider the challenge of preference elicitation in systems that help users discover the most desirable item(s) within a given database. Past work on preference elicitation focused on structured models that provide a factored…

The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…

Big array analytics is becoming indispensable in answering important scientific and business questions. Most analysis tasks consist of multiple steps, each making one or multiple passes over the arrays to be analyzed and generating…

Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval…

This work investigates the factorization of finite lattices to implode selected intervals while preserving the remaining order structure. We examine how complete congruence relations and complete tolerance relations can be utilized for this…

In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…

In functional programming languages, the classic form of annotation is a single type constraint on a term. Intersection types add complications: a single term may have to be checked several times against different types, in different…

A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced…

In this paper we discuss how semantic annotations can be used to introduce mathematical algorithmic information of the underlying imperative code to enable compilers to produce code transformations that will enable better performance. By…

The article describes prime intervals into the prime factorization of the middle binomial coefficient. Prime factors and prime powers are distributed in layers. Each layer consists of non-repeated prime numbers which are chosen (not…

Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated…

In many applications it will be useful to know those patterns that occur with a balanced interval, e.g., a certain combination of phone numbers are called almost every Friday or a group of products are sold a lot on Tuesday and Thursday. In…

Structured prediction can be considered as a generalization of many standard supervised learning tasks, and is usually thought as a simultaneous prediction of multiple labels. One standard approach is to maximize a score function on the…

We investigate a weighted variant of the interval stabbing problem, where the goal is to design an efficient data structure for a given set $\mathcal{I}$ of weighted intervals such that, for a query point $q$ and an integer $k>0$, we can…

Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…