Self complementary topologies and preorders

A topology on a set X is self complementary if there is a homeomorphic copy on the same set that is a complement in the lattice of topologies on X. The problem of characterizing finite self complementary topologies leads us to redefine the problem in terms of preorders (i.e. reflexive, transitive relations). A preorder P on a set X is self complementary if there is an isomorphic copy P of P on X that is arc disjoint to P (except for loops) and with the property that PP is strongly connected. We characterize here self complementary finite partial orders and self complementary finite equivalence relations.     

分布矩阵与随机变量独立性的判定

利用离散型随机变量的联合分布矩阵,得到了离散型随机变量独立性的一种判别方法,并用实例给出了一定的应用。     

随机幂级数的亏函数

研究了十分一般的随机幂级数,并证明了有限级的随机幂级数几乎必然没有亏函数．     

随机连接广义合作网络模型

本文提出了一个项目参与者数T是随机变量的广义合作网络模型,新节点与随机选择的节点合作,通过节点度演化所满足的马尔可夫性,利用马．尔可夫链的方法和技巧得到了度分布的精确解析表达式．并说,明了此广义合作网络不是无标度网络．     

A Brauerian representation of split preorders

Split preorders are preordering relations on a domain whose composition is defined in a particular way by splitting the domain into two disjoint subsets. These relations and the associated composition arise in categorial proof theory in connection with coherence theorems. Here split preorders are represented isomorphically in the category whose arrows are binary relations and whose composition is defined in the usual way. This representation is related to a classical result of representation theory due to Richard Brauer. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

连续型指数差分布

本文提出了一个连续型随机变量的概率分布:指数差分布。讨论了该分布的极值、拐点、数学期望和方差,推导了参数的矩估计公式,探讨了该分布与指数分布的关系,给出了该分布在药代动力学中的应用。     

Finite preorders and topological descent II: étale descent

It is known that every effective (global-) descent morphism of topological spaces is an effective étale-descent morphism. On the other hand, in the predecessor of this paper we gave examples of:

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a descent morphism that is not an effective étale-descent morphism;

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an effective étale-descent morphism that is not a descent morphism.

Both of the examples in fact involved only finite topological spaces, i.e. just finite preorders, and now we characterize the effective étale-descent morphisms of preorders/finite topological spaces completely.     

二维随机变量条件分布函数教学的思考

本文利用条件概率的定义,由随机变量分布函数的性质,给出一般情形下随机变量条件分布函数的定义,以帮助学生更好地理解随机变量的条件分布函数的概念.     

Fuzzy preorders: conditional extensions,extensions and their representations

The crisp literature provides characterizations of the preorders that admit a total preorder extension when some pairwise order comparisons are imposed on the extended relation. It is also known that every preorder is the intersection of a collection of total preorders. In this contribution we generalize both approaches to the fuzzy case. We appeal to a construction for deriving the strict preference and the indifference relations from a weak preference relation, that allows to obtain full characterizations in the conditional extension problem. This improves the performance of the construction via generators studied earlier.     

Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances

Let Ω^Ω be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of Ω^Ω, then we write U≈V if there exists a finite subset F of Ω^Ω such that the subsemigroup generated by U and F equals that generated by V and F. The relative rank of U in Ω^Ω is the least cardinality of a subset A of Ω^Ω such that the union of U and A generates Ω^Ω. In this paper we study the notions of relative rank and the equivalence ≈ for semigroups of endomorphisms of binary relations on Ω.The semigroups of endomorphisms of preorders, bipartite graphs, and tolerances on Ω are shown to lie in two equivalence classes under ≈. Moreover such semigroups have relative rank 0, 1, 2, or d in Ω^Ω where d is the minimum cardinality of a dominating family for N^N. We give examples of preorders, bipartite graphs, and tolerances on Ω where the relative ranks of their endomorphism semigroups in Ω^Ω are 0, 1, 2, and d.We show that the endomorphism semigroups of graphs, in general, fall into at least four classes under ≈ and that there exist graphs where the relative rank of the endomorphism semigroup is 2^ℵ₀.     

引入随机利率的养老保险破产问题

考虑带随机利率，负索赔是随机变量的复合二项养老保险模型。通过引入调节系数，得出破产概率的上界。进一步分析了破产前盈余分布和破产持续时间概率，并获得了递推公式。     

Mass spectra alignments and their significance

Mass Spectrometry has become one of the most popular analysis techniques in Genomics and Systems Biology. We investigate a general framework that allows the alignment (or matching) of any two mass spectra. In particular, we examine the alignment of a reference mass spectrum generated in silico from a database, with a measured sample mass spectrum. In this context, we assess the significance of alignment scores for character-specific cleavage experiments, such as tryptic digestion of amino acids. We present an efficient approach to estimate this significance, with runtime linear in the number of detected peaks. In this context, we investigate the probability that a random string over a weighted alphabet contains a substring of some given weight.     

Merging covering arrays and compressing multiple sequence alignments

Covering arrays have been extensively studied, in part because of their applications in testing interacting software components. In this setting, fast and flexible methods are needed to construct covering arrays of close-to-minimum size. However testing scenarios often impose additional structure on the tests that can be selected. We extend a greedy method to construct test suites for complex systems that have a hierarchical structure in which components combine to form subsystems, which in turn form larger subsystems, until the entire system is formed. The algorithm for merging covering arrays that we propose is then shown to have further potential application in the compression of multiple sequence alignments of genomic data.     

Continuous optimization methods for structure alignments

Structural Alignment is an important tool for fold identification of proteins, structural screening on ligand databases, pharmacophore identification and other applications. In the general case, the optimization problem of superimposing two structures is nonsmooth and nonconvex, so that most popular methods are heuristic and do not employ derivative information. Usually, these methods do not admit convergence theories of practical significance. In this work it is shown that the optimization of the superposition of two structures may be addressed using continuous smooth minimization. It is proved that, using a Low Order-Value Optimization approach, the nonsmoothness may be essentially ignored and classical optimization algorithms may be used. Within this context, a Gauss–Newton method is introduced for structural alignments incorporating (or not) transformations (as flexibility) on the structures. Convergence theorems are provided and practical aspects of implementation are described. Numerical experiments suggest that the Gauss–Newton methodology is competitive with state-of-the-art algorithms for protein alignment both in terms of quality and speed. Additional experiments on binding site identification, ligand and cofactor alignments illustrate the generality of this approach. The softwares containing the methods presented here are available at http://www.ime.unicamp.br/∼martinez/lovoalign. This work was supported by PRONEX-Optimization 76.79.1008-00, FAPESP (Grants 01-04597-4 - 02-14203-6 and 05-56773-1) and CNPq     

On the number of countable models of complete theories with finite Rudin-Keisler preorders

The aim of this article is to generalize the classification of complete theories with finitely many countable models with respect to two principal characteristics, Rudin-Keisler preorders and the distribution functions of the number of limit models, to an arbitrary case with a finite Rudin-Keisler preorder. We establish that the same characteristics play a crucial role in the case we consider. We prove the compatibility of arbitrary finite Rudin-Keisler preorders with arbitrary distribution functions f satisfying the condition rang f?ω∪{ω, 2^ω}.     

随机模糊集与随机集

本文研究了三个方面的工作：一是定义了一种模糊集上的可测结构，从而定义了随机模糊集，这些定义都与论域Ｘ上的拓扑结构无关。将通常意义下的集合看成特殊模糊集得到的通常集合上的超可测结构与文（３）中的定义一致；二是给出了随机模糊集、随机集的一些等价条件；三是研究了随机模糊集、随机集的分布与其有限维落影族的关系。     

Lower bounds for optimal alignments of binary sequences

In parametric sequence alignment, optimal alignments of two sequences are computed as a function of matches, mismatches and spaces, producing many different optimal alignments. In the two-parameter case, Gusfield et al shows that the number of distinct optimal alignment summaries for a pair of sequences is O(n^2/3). Here we construct binary sequences of length n with 3/(2^7/3π^2/3)n^2/3+O(n^1/3logn) distinct optimal alignment summaries. This shows that the upper bound given by Gusfield et al. is tight over all alphabets, thereby disproving the “ conjecture”. Thus the maximum number of distinct optimal alignment summaries over all pairs of length n sequences is Θ(n^2/3).