On some multivariate density estimates and empirical Bayes problems

This paper consider estimates of multidimensional density functions and their derivatives. The asymptotic unbiasedness and the convergence properties of these estimates are established.Some applications to empirical Bayes problems are considered.     

A note on asymptotic inference in a class of non-stationary processes

In this note some problems of asymptotic inference in a class of non-stationary stochastic processes are considered. In particular, it is shown that no criterion based on the existence of uniformly most powerful tests over a local neighborhood can be used in this situation.     

Phase diagram of the Ising Model on a Cayley tree in the presence of competing interactions and magnetic field

We study the phase diagram for the Ising Model on a Cayley tree with competing nearest-neighbor interactionsJ ₁ and next-nearest-neighbor interactionsJ ₂ andJ ₃ in the presence of an external magnetic field. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular cases, previous works by Vannimenus and by Inawashiroet al. At vanishing temperature, the phase diagram is fully determined, for all values and signs ofJ ₂/J ₁ andJ ₃/J ₂; in particular, we verify that values ofJ ₃/J ₂ high enough favor the paramagnetic phase. At finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into two disconnected pieces, etc.) are exhibited for typical values ofJ ₂/J ₁ andJ ₃/J ₂.Partially supported by the Brazilian Agencies CNPq and FINEP.     

Successive Proportional Additive Numeration Using Fuzzy Linguistic Labels (Fuzzy Linguistic SPAN)

The SPAN (Successive Proportional Additive Numeration or Social Participatory Allocation Network) is a procedure that converts individual judgments into a group decision. The procedure is based on a voting design by which individual experts allocate their votes iteratively between their preferred options and other experts. The process ends when all the votes are allocated to options, and the one with the highest number of votes is selected. The method requires the experts to specify an exact allocation of votes to both options and other experts. The Fuzzy Linguistic SPAN allows experts to allocate their votes using linguistic labels such as “most of” or “a few”, and determine the preferred option. This method is demonstrated using the Max–Min aggregation function used to develop a proportional representation of the option and member voting schemes. The method is also demonstrated using the LOWA aggregation function. The Fuzzy Linguistic SPAN method is beneficial since the linguistic voting process is easier for the experts and significantly reduces the computational process compared to the traditional SPAN. The paper presents the method and two examples with comparisons to the numerical SPAN method.     

Classifying G-protein coupled receptors with bagging classification tree

G-protein coupled receptors (GPCRs) play a key role in different biological processes, such as regulation of growth, death and metabolism of cells. They are major therapeutic targets of numerous prescribed drugs. However, the ligand specificity of many receptors is unknown and there is little structural information available. Bioinformatics may offer one approach to bridge the gap between sequence data and functional knowledge of a receptor. In this paper, we use a bagging classification tree algorithm to predict the type of the receptor based on its amino acid composition. The prediction is performed for GPCR at the sub-family and sub-sub-family level. In a cross-validation test, we achieved an overall predictive accuracy of 91.1% for GPCR sub-family classification, and 82.4% for sub-sub-family classification. These results demonstrate the applicability of this relative simple method and its potential for improving prediction accuracy.     

On Gibbs measures of P-adic Potts model on the cayley tree

We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ? _p) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ? p and p ≥ 3 (resp. q ? 2², p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ? p if p ≥ 3 and q ? 2² if p = 2.     

Trees, parking functions, syzygies, and deformations of monomial ideals

For a graph , we construct two algebras whose dimensions are both equal to the number of spanning trees of . One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis elements correspond to -parking functions that naturally came up in the abelian sandpile model. These ideals are instances of the general class of monotone monomial ideals and their deformations. We show that the Hilbert series of a monotone monomial ideal is always bounded by the Hilbert series of its deformation. Then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals. In some cases these resolutions coincide with Scarf resolutions. We prove several formulas for Hilbert series of monotone monomial ideals and investigate when they are equal to Hilbert series of deformations. In the appendix we discuss the abelian sandpile model.

     

A Complete Solution to a Conjecture on the β-Polynomials of Graphs

In 1990, Gutman and Mizoguchi conjectured that all roots of the -polynomial (G,C,x) of a graph G are real. Since then, there has been some literature intending to solve this conjecture. However, in all existing literature, only classes of graphs were found to show that the conjecture is true; for example, monocyclic graphs, bicyclic graphs, graphs such that no two circuits share a common edge, graphs without 3-matchings, etc, supporting the conjecture in some sense. Yet, no complete solution has been given. In this paper, we show that the conjecture is true for all graphs, and therefore completely solve this conjecture.     

瓶罐玻璃行业企业绩效评价

笔者依据所能获得的资料———《瓶罐玻璃行业企业经济信息汇编》[6],建立了一套经济实用的瓶罐玻璃行业企业绩效评价指标体系;提供了一种科学评价方法和计算机化的评价技术;能适时地对该行业内各企业绩效进行评价和比较分析;及时获得各企业在全行业内竞争位次;及时发现影响企业绩效的主要因素;为高层管理者制定和调整企业管理决策提供了参考依据。     

The Topology of Algebra: Combinatorics of Squaring

We study the graph each of whose edges connects an element of a given ring with the square of itself. For a finite commutative group (e.g., for the multiplicative group of coprime residue classes modulo a positive integer), we describe this graph explicitly: each of its connected components is an oriented attracting cycle equipped with identical -vertex rooted trees of special form whose roots reside on the cycle. We also compute the graphs of permutation groups on not too many elements and of the subgroups of even permutations; the connected components of these graphs are also uniformly equipped cycles.