this paper is about copying on artificial agents humans' perception of time and their ability to produce-condensed short stories out of large free texts. We propose a model intended to objectivize processes that h...
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ISBN:
(纸本)9781509057085
this paper is about copying on artificial agents humans' perception of time and their ability to produce-condensed short stories out of large free texts. We propose a model intended to objectivize processes that help to achieve this reasoning behaviour on machines.
In this talk, we present several algorithms for decomposing systems of multivariate polynomials into triangular systems of various kinds. the algorithms have been efficiently implemented and successfully applied to nu...
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In this talk, we present several algorithms for decomposing systems of multivariate polynomials into triangular systems of various kinds. the algorithms have been efficiently implemented and successfully applied to numerous problems of scientificcomputing, ranging over computational polynomial algebra, automated geometric reasoning, solving systems of nonlinear equations, qualitative analysis of biological systems, and computer aided geometric design. We discuss some of the applications with a number of illustrative examples.
In this paper we present efficient algorithmic techniques for identifying several types of sequence-related patterns. We consider two main problems: finding a maximum weight contiguous subsequence which has the struct...
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In this paper we present efficient algorithmic techniques for identifying several types of sequence-related patterns. We consider two main problems: finding a maximum weight contiguous subsequence which has the structure of a permutation with repetitions, and an online problem consisting of the constrained guessing of a secret sequence.
Automatic methods for discovering program runtime and proving program termination have always been a challenging problem in computer science. We present here a novel and systematic approach for calculating an upper bo...
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Automatic methods for discovering program runtime and proving program termination have always been a challenging problem in computer science. We present here a novel and systematic approach for calculating an upper bound of the maximum runtime of functions for a non-trivial class of programs. the proof is based on an induction over a tree of execution traces - a new mathematical data structure. As a consequence, this can also show termination for these functions. the approach uses symbolic-numericalgorithms over a novel mathematical data structure, and can systematically find the maximum runtime for a wide class of functions.
An important and challenging computational problem is to identify and include the missing compatibility (integrability) conditions for general systems of partial differential equations. the inclusion of such missing c...
An important and challenging computational problem is to identify and include the missing compatibility (integrability) conditions for general systems of partial differential equations. the inclusion of such missing conditions is executed by the application of differential-elimination algorithms. Differential equations arising during modeling generally contain both exactly known coefficients and coefficients known approximately from data. We focus on our recent work on approximate differential-elimination methods and in particular their application to the determination of approximate symmetries. We illustrate this with applications to a class of Schrödinger equations.
We present an algebraic framework to represent indefinite nested sums over hyper geometric expressions in difference rings. In order to accomplish this task, parts of Karr's difference field theory have been exten...
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We present an algebraic framework to represent indefinite nested sums over hyper geometric expressions in difference rings. In order to accomplish this task, parts of Karr's difference field theory have been extended to a ring theory in which also the alternating sign can be expressed. the underlying machinery relies on algorithmsthat compute all solutions of a given parameterized telescoping equation. As a consequence, we can solve the telescoping and creative telescoping problem in such difference rings.
algorithms which compute modulo triangular sets must respect zero divisors. We present Hensel lifting as a tool for resolving them. We give an application: a modular algorithm for computing gcds of univariate polynomi...
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ISBN:
(纸本)9781538626276
algorithms which compute modulo triangular sets must respect zero divisors. We present Hensel lifting as a tool for resolving them. We give an application: a modular algorithm for computing gcds of univariate polynomials with coefficients modulo a radical triangular set over the rational numbers. We have implemented our algorithm using Maple's RECDEN package. We compare our implementation withthe procedure RegularGcd in the RegularChains package.
Hybrid sets are generalizations of sets and multisets, in which the multiplicities of elements can take any integers. this construction was proposed by Whitney in 1933 in terms of characteristic functions. Hybrid sets...
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ISBN:
(纸本)9781509057085
Hybrid sets are generalizations of sets and multisets, in which the multiplicities of elements can take any integers. this construction was proposed by Whitney in 1933 in terms of characteristic functions. Hybrid sets have been used by combinatorists to give combinatorial interpretations for several generalizations of binomial coefficients and Stirling numbers and by computer scientists to design fast algorithms for symbolic domain decompositions. We present in this paper some combinatorial results on subsets and partitions of hybrid sets.
One of the most useful computer algebra used today is calgebra and its versions, e.g. stream calculus. In the paper I show that p-adic arithmetic can be regarded as one of the natural interpretation of stream calculus...
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One of the most useful computer algebra used today is calgebra and its versions, e.g. stream calculus. In the paper I show that p-adic arithmetic can be regarded as one of the natural interpretation of stream calculus on a finite set of positive integers. Further, I define probabilities on streams using bisimulation and construct probability logic with non-well-founded syntax and non-well-founded semantics.
In this paper we represent a class of queries that contain sub-formulas with universally quantified variables using views. the queries and views considered can contain input parameters. Both views and queries are expr...
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In this paper we represent a class of queries that contain sub-formulas with universally quantified variables using views. the queries and views considered can contain input parameters. Both views and queries are expressed as unions of conjunctive formulas, where the predicates of literals are views or database relations. the negation is allowed in body views or body queries. We study the equivalence of a query and one of its expansions.
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