While much is written about the importance of sparse polynomials in computer algebra, much less is known about the complexity of advanced (i.e. anything more than multiplication!) algorithms for them. this is due to a...
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ISBN:
(纸本)9780769539645
While much is written about the importance of sparse polynomials in computer algebra, much less is known about the complexity of advanced (i.e. anything more than multiplication!) algorithms for them. this is due to a variety of factors, not least the problems posed by cyclotomic polynomials. In this paper we state a few of the challenges that sparse polynomials pose.
We present an algebraic framework to represent indefinite nested sums over hypergeometric expressions in difference rings. In order to accomplish this task, parts of Karr's difference field theory have been extend...
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ISBN:
(纸本)9781479984480
We present an algebraic framework to represent indefinite nested sums over hypergeometric 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.
We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate...
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ISBN:
(纸本)9781509057078
We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantage of this new approach.
It is known that one of the most disastrous forms of collective human behavior is the kind of crowd stampede induced by panic. this situation often leads to fatalities as people are crushed or trampled this problem ha...
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ISBN:
(纸本)0769524532
It is known that one of the most disastrous forms of collective human behavior is the kind of crowd stampede induced by panic. this situation often leads to fatalities as people are crushed or trampled this problem has been well researched from a socio-psychological point of view. In this paper we attempt to study and analyze the crowd behavior by using an Ant Colony Optimization (ACO) based computational framework. the initial simulations refer to a panic situation generated in a few connected cities of a war affected country.
this paper presents a novel method to perform regression on a finite sample of noisy data. the purpose is to obtain a mathematical model for data which is both reliable and valid, yet the analytical expression is not ...
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ISBN:
(纸本)0769524532
this paper presents a novel method to perform regression on a finite sample of noisy data. the purpose is to obtain a mathematical model for data which is both reliable and valid, yet the analytical expression is not restricted to any particular form. To obtain a statistical model of the noisy data set we use symbolic regression with pseudorandom number generators. We begin by describing symbolic regression and our implementation of this technique using genetic programming (GP) and gene expression programming (GEP). We present some results for symbolic regression on computer generated and real financial data sets in the final part of this paper.
We show that the reduced mesh root systems and mesh geometries of roots for each of the simply-laced Dynkin diagrams can be classified by applying symbolic computer algebra computations and numeric algorithmic computa...
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ISBN:
(纸本)9780769546308
We show that the reduced mesh root systems and mesh geometries of roots for each of the simply-laced Dynkin diagrams can be classified by applying symbolic computer algebra computations and numeric algorithmic computations in Maple, C++ and Linux. Results of our computing experiences are presented in a table of Section 2 and in Section 6.
After presenting the basic definition of spiking neural P systems (SN P systems), illustrated with two examples, we recall some results concerning the computing power and the size of universal SN P systems. We end thi...
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ISBN:
(纸本)9781479984480
After presenting the basic definition of spiking neural P systems (SN P systems), illustrated with two examples, we recall some results concerning the computing power and the size of universal SN P systems. We end this note with a couple of research topics.
We propose general preprocessing techniques to reshape dense multivariate polynomials over finite fields, in order to minimize the cost of memory accesses, while preserving sufficient parallelism, so as to reduce the ...
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ISBN:
(纸本)9781665465458
We propose general preprocessing techniques to reshape dense multivariate polynomials over finite fields, in order to minimize the cost of memory accesses, while preserving sufficient parallelism, so as to reduce the running time of polynomial multiplication in multi-threaded implementations.
In my PhD thesis 1965 and the subsequent publication 1970 in Aequationes Mathematicae, I introduced the notion of Grobner bases and proved a characterization theorem for Grobner bases on which an algorithm for constru...
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ISBN:
(纸本)9781538626269
In my PhD thesis 1965 and the subsequent publication 1970 in Aequationes Mathematicae, I introduced the notion of Grobner bases and proved a characterization theorem for Grobner bases on which an algorithm for constructing Grobner bases can be based. the main idea for the theorem and the algorithm was the notion of \"�S-polynomials\"�. Most of the subsequent work on the algorithmic theory of Grobner bases, including the implementation of the Grobner bases technology in mathematical software systems like Mathematica, Maple, etc. was based on this approach.
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