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Transformations of two cryptographic problems in terms of matrices 用矩阵表示两个密码问题的变换
SIGSAM Bull. Pub Date : 2005-12-01 DOI: 10.1145/1140378.1140384
E. Laskari, G. Meletiou, D. Tasoulis, M. Vrahatis
{"title":"Transformations of two cryptographic problems in terms of matrices","authors":"E. Laskari, G. Meletiou, D. Tasoulis, M. Vrahatis","doi":"10.1145/1140378.1140384","DOIUrl":"https://doi.org/10.1145/1140378.1140384","url":null,"abstract":"The Discrete Logarithm and the Diffie-Hellman are two hard computational problems, closely related to cryptography and its applications. The computational equivalence of these problems has been proved only for some special cases. In this study, using LU-decomposition to Vandermonde matrices, we are able to transform the two problems in terms of matrices, thus giving a new perspective to their equivalence. A first study on matrix transformations for the Double and Multiple Discrete Logarithms is also presented.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127470520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Jordan algebras arising from intermolecular recombination 由分子间重组产生的约当代数
SIGSAM Bull. Pub Date : 2005-12-01 DOI: 10.1145/1140378.1140380
M. Bremner
{"title":"Jordan algebras arising from intermolecular recombination","authors":"M. Bremner","doi":"10.1145/1140378.1140380","DOIUrl":"https://doi.org/10.1145/1140378.1140380","url":null,"abstract":"We use computer algebra to show that a linearization of the operation of intermolecular recombination from theoretical genetics satisfies a nonassociative polynomial identity of degree 4 which implies the Jordan identity. We use the representation theory of the symmetric group to decompose this new identity into its irreducible components. We show that this new identity implies all the identities of degree ≤ 6 satisfied by intermolecular recombination.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124418849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Extension of expansion base algorithm for multivariate analytic factorization including the case of singular leading coefficient 多元解析分解的扩展基算法的推广，包括奇异先导系数的情况
SIGSAM Bull. Pub Date : 2005-12-01 DOI: 10.1145/1140378.1140383
Maki Iwami
{"title":"Extension of expansion base algorithm for multivariate analytic factorization including the case of singular leading coefficient","authors":"Maki Iwami","doi":"10.1145/1140378.1140383","DOIUrl":"https://doi.org/10.1145/1140378.1140383","url":null,"abstract":"The expansion base algorithm, which was devised by Abhyankar, Kuo and McCallum is very efficient for analytic factorization of bivariate polynomials. The author had extended it to more than two variables but it was only for polynomials with non-vanishing leading coefficient at the expansion point. We improve it to be able to apply to polynomials including the case of vanishing leading coefficient, that is, singular leading coefficient, which comes to a specific problem only for more than two variables.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129592717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Stability of expanding homographic configurations: 3D case 膨胀单形构型的稳定性:三维情况
SIGSAM Bull. Pub Date : 2005-12-01 DOI: 10.1145/1140378.1140386
A. Mylläri
{"title":"Stability of expanding homographic configurations: 3D case","authors":"A. Mylläri","doi":"10.1145/1140378.1140386","DOIUrl":"https://doi.org/10.1145/1140378.1140386","url":null,"abstract":"Stability of expanding homographic configurations formed by bodies of equal masses placed at the vertices of regular polyhedrons is considered in linear approximation. Perturbations growing faster than the general expansion of the system are considered to be unstable. These instabilities are studied in detail. Different ways to visualize 3D structure of unstable modes are discussed.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125840232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Apollonius circle conflict 阿波罗尼乌斯圈冲突
SIGSAM Bull. Pub Date : 2005-12-01 DOI: 10.1145/1140378.1140388
George M. Tzoumas, I. Emiris
{"title":"Apollonius circle conflict","authors":"George M. Tzoumas, I. Emiris","doi":"10.1145/1140378.1140388","DOIUrl":"https://doi.org/10.1145/1140378.1140388","url":null,"abstract":"What does a query ellipse do (outside, intersects or tangent) with respect to the Apollonius circle of the three black ellipses?","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114918536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Root finding and approximation approaches through neural networks 通过神经网络的寻根和逼近方法
SIGSAM Bull. Pub Date : 2005-12-01 DOI: 10.1145/1140378.1140382
M. Epitropakis, M. Vrahatis
{"title":"Root finding and approximation approaches through neural networks","authors":"M. Epitropakis, M. Vrahatis","doi":"10.1145/1140378.1140382","DOIUrl":"https://doi.org/10.1145/1140378.1140382","url":null,"abstract":"In this paper, we propose two approaches to approximate high order multivariate polynomials and to estimate the number of roots of high order univariate polynomials. We employ high order neural networks such as Ridge Polynomial Networks and Pi -- Sigma Networks, respectively. To train the networks efficiently and effectively, we recommend the application of stochastic global optimization techniques. Finally, we propose a two step neural network based technique, to estimate the number of roots of a high order univariate polynomial.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122329066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On the visualization of the DNA sequence and its nucleotide content 关于DNA序列及其核苷酸含量的可视化
SIGSAM Bull. Pub Date : 2005-12-01 DOI: 10.1145/1140378.1140385
A. Mylläri, T. Salakoski, A. Pasechnik
{"title":"On the visualization of the DNA sequence and its nucleotide content","authors":"A. Mylläri, T. Salakoski, A. Pasechnik","doi":"10.1145/1140378.1140385","DOIUrl":"https://doi.org/10.1145/1140378.1140385","url":null,"abstract":"Visual inspection can help reveal patterns that would be computationally rather difficult to reveal. We consider three different algorithms for visualizations of a DNA sequence and its nucleotide content: random walk, fractal and visualization based on the entropy-like parameters calculated using a sliding window. We present a program that uses these three methods and visualizes either the whole of a given sequence, or specified fragments. It also provides facilities to compare visualizations obtained for different sequences/fragments. Random walk visualization considers the sequence symbol-by-symbol; the other two methods also take into account how well nucleotides are \"mixed\" in the sequence. It allows an easy visualization of repeated patterns, segments with a high/low content of some nucleotides, such as CG-islands, etc. The program also helps to identify regions of interest for further study.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"292 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114129553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Application of CAS to constructing schemes of superhigh order of accuracy for heat conduction equation CAS在热传导方程超高阶精度格式构建中的应用
SIGSAM Bull. Pub Date : 2005-12-01 DOI: 10.1145/1140378.1140387
V. Shapeev
{"title":"Application of CAS to constructing schemes of superhigh order of accuracy for heat conduction equation","authors":"V. Shapeev","doi":"10.1145/1140378.1140387","DOIUrl":"https://doi.org/10.1145/1140378.1140387","url":null,"abstract":"The algorithm of indeterminate coefficients method for constructing difference schemes and its implementation in a computer algebra system (CAS) are described. The set of two-layer schemes with high order of convergence are constructed for the one-dimensional heat conduction equation. The conclusions are proved by numerical experiments.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121279550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The nearest polynomial with a given zero, revisited 有给定零的最接近的多项式
SIGSAM Bull. Pub Date : 2005-09-01 DOI: 10.1145/1113439.1113442
N. Rezvani, Robert M Corless
{"title":"The nearest polynomial with a given zero, revisited","authors":"N. Rezvani, Robert M Corless","doi":"10.1145/1113439.1113442","DOIUrl":"https://doi.org/10.1145/1113439.1113442","url":null,"abstract":"In his 1999 SIGSAM BULLETIN paper [7], H. J. Stetter gave an explicit formula for finding the nearest polynomial with a given zero. This present paper revisits the issue, correcting a minor omission from Stetter's formula and explicitly extending the results to different polynomial bases.Experiments with our implementation demonstrate that the formula may not after all, fully solve the problem, and we discuss some outstanding issues: first, that the nearest polynomial with the given zero may be identically zero (which might be surprising), and, second, that the problem of finding the nearest polynomial of the same degree with a given zero may not, in fact, have a solution. A third variant of the problem, namely to find the nearest monic polynomial (given a monic polynomial initially) with a given zero, a problem that makes sense in some polynomial bases but not others, can also be solved with Stetter's formula, and this may be more satisfactory in some circumstances. This last can be generalized to the case where some coefficients are intrinsic and not to be changed, whereas others are empiric and may safely be changed. Of course, this minor generalization is implicit in [7]; This paper simply makes it explicit.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115053819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 28
Finite fans, actions of tori and D-modules 有限的风扇，tori和d模块的动作
SIGSAM Bull. Pub Date : 2005-09-01 DOI: 10.1145/1113439.1113450
Sonia L. Rueda
{"title":"Finite fans, actions of tori and D-modules","authors":"Sonia L. Rueda","doi":"10.1145/1113439.1113450","DOIUrl":"https://doi.org/10.1145/1113439.1113450","url":null,"abstract":"Let <i>G</i> be a finite dimensional torus acting diagonally on the smooth affine variety <i>X</i> = <i>k</i><sup><i>r</i></sup> x (<i>k</i><sup><i>x</i></sup>)<sup><i>s</i></sup>, with <i>k</i> an algebraically closed field <i>k</i> of characteristic 0. We denote the ring of regular functions on <i>X</i> by <i>O</i>(<i>X</i>) and the ring of differential operators by <i>D</i>(<i>X</i>). Let <i>D</i>(<i>X</i>)<sup><i>G</i></sup> be the subring of <i>D</i>(<i>X</i>) of invariants under the action of <i>G</i>.The goal of this poster is to show how finite fans of cones can be used to study <i>D</i>(<i>X</i>)<sup><i>G</i></sup>-modules. We associate a finite fan of cones to the action of <i>G</i> on <i>X</i>, in such a way that the study of the fan will allow us to get conclusions about the finite dimensional <i>D</i>(<i>X</i>)<sup><i>G</i></sup>-modules. We describe next the basic ingredients of our construction.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"26 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132900329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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