多项多因式相乘布尔函数的最小割集求取新算法

化简布尔函数的方法有许多种,有布尔代数法、行列法、矩阵法等。文中提出一种化简新算法,通过组合排除,可以化简基本事件较少、重复基本事件较多情况的多因式相乘的布尔函数。此法在求解时思路清晰,列表过程简单,大大提高了求解本类布尔函数的计算效率。

Linear Factorization of λ _polynomial Over Quaternionic Field

A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.

An Effective Multiple Model Least Squares Method in Tracking of a Maneuvering Target

A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent.

Polymorphisms of alcohol dehydrogenase 2 and aldehyde dehydrogenase 2 and colorectal cancer risk in Chinese males

AIM: To evaluate the relationship between drinking and polymorphisms of alcohol dehydrogenase 2 (ADH2) and/or aldehyde dehydrogenase 2 (ALDH2) for risk of colorectal cancer (CRC) in Chinese males. METHODS: A case-control study was conducted in 190 cases and 223 population-based controls. ADH2 Arg47His (G-A) and ALDH2 Glu487Lys (G-A)genotypes were identified by PCR and denaturing high-performance liquid chromatography (DHPLC). Information on smoking and drinking was collected and odds ratio (OR) was estimated. RESULTS: The ADH2 A/A and ALDH2 G/G genotypes showed moderately increased CRC risk. The age- and smoking-adjusted OR for ADH2 A/A relative to G/A and G/G was 1.60 (95% CI=1.08-2.36), and the adjusted OR for ALDH2 G/G relative to G/A and A/A was 1.79 (95% CI=1.19-2.69). Signif icant interactions between ADH2, ALDH2 and drinking were observed. As compared to the subjects with ADH2 G and ALDH2 A alleles, those with ADH2 A/A and ALDH2 G/G genotypes had a signif icantly increased OR (3.05, 95% CI= 1.67-5.57). The OR for CRC among drinkers with the ADH2 A/A genotype was increased to 3.44 (95% CI= 1.84-6.42) compared with non-drinkers with the ADH2 G allele. The OR for CRC among drinkers with the ALDH2 G/G genotype was also increased to 2.70 (95% CI= 1.57-4.66) compared with non-drinkers with the ALDH2 A allele. CONCLUSION: Polymorphisms of the ADH2 and ALDH2 genes are significantly associated with CRC risk. There are also signifi cant gene-gene and gene- environment interactions between drinking and ADH2 and ALDH2 polymorphisms regarding CRC risk in Chinese males.

Super number roots and factorizations for a kind of polynomial

It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 8212890625X=L and 1787109376Y=L, and obtained 4 (super number) roots of the equation2xx=. For progressing to wider conditions, with the way of exactly divisible and mutually orthogonal Latin squares, three attractive results are obtained: 1) A kind of polynomial 1()()niiPxxa==P-, ,1,2,,iain?KZ has and only has different n2 super number roots; 2) When n>2 and n 6, those n2 roots of the polynomial ()Px can be arranged in an n-order square matrix, of which n roots of every row and every column satisfy Vieta Formula of roots and coefficients; 3) In *Z ring of super number, the polynomial1()()niiPxxa==P-, ,1,2,,iain?KZ has n! different factorizations.

A novel hybrid algorithm based on a harmony search and artificial bee colony for solving a portfolio optimization problem using a mean-semi variance approach

Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk factor in drawing up an efficient frontier and the optimal portfolio. Since semi-variance offers a better estimation of the actual risk portfolio, it was used as a measure to approximate the risk of investment in this work. The optimal portfolio selection is one of the non-deterministic polynomial(NP)-hard problems that have not been presented in an exact algorithm, which can solve this problem in a polynomial time. Meta-heuristic algorithms are usually used to solve such problems. A novel hybrid harmony search and artificial bee colony algorithm and its application were introduced in order to draw efficient frontier portfolios. Computational results show that this algorithm is more successful than the harmony search method and genetic algorithm. In addition, it is more accurate in finding optimal solutions at all levels of risk and return.

MinK gene G112A polymorphisms and atrial fibrillation:a Meta-analysis

Atrial fibrillation (AF) is the most common arrhythmia with multi-factorial pathogenesis. A number of studies of genetic epidemiology have assessed the association of G112A (G38S) single nucleotide polymorphisms (SNPs) in Mink gene with AF in different populations. However, the results are inconsistent and inconclusive. We performed a Meta-analysis of the association between G112A polymorphisms of MinK gene and AF to estimate the magnitude of the gene effect. Six case-control studies with a combined 854 cases and 1079 controls were summarized. Subgroups in different races were separately analyzed. Heterogeneity and publication bias were also explored. When all groups were pooled, the individuals with G allele had an over 40% higher risk of AF compared with individuals with the A allele. The GG genotype (versus AA genotype) was found to be significant association with increased AF risk. The significant associations were also found in both dominant and recessive genetic model. For subgroup analysis, the results were consistent with above, except that the pooled OR for Chinese population was not significant in a recessive genetic model. In conclusion, G112A polymorphisms in Mink gene may have an important effect on the pathogenesis of AF. This warrants further investigation in large multi-center studies with precise design.

Analytic Solutions of a Polynomial-Like Iterative Functional Equation near Resonance

In this paper existence of local analytic solutions of a polynomial-like iterative functional equation is studied. As well as in previous work, we reduce this problem with the SchrSder transformation to finding analytic solutions of a functional equation without iteration of the unknown function f. For technical reasons, in previous work the constant α given in the Schroder transformation, i.e., the eigenvalue of the linearized f at its fixed point O, is required to fulfill that α is off the unit circle S^1 or lies on the circle with the Diophantine condition. In this paper, we obtain results of analytic solutions in the case of α at resonance, i.e., at a root of the unity and the case of α near resonance under the Brjuno condition.

Exact Bivariate Polynomial Factorization over Q by Approximation of Roots

Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C++ and J++,do not support symbolic computation directly.Hence,it leads to difficulties in applying factorization in engineering fields.In this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients.The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library.In addition,the numerical computation part often only requires double precision and is easily parallelizable.

THE MATRIX ITERATION ALGORITHM SOLVING AN ENUMERATION PROBLEM ON BACTERIAL COMPLETE GENOMES

Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any string in B as their substrings.From the fact that a string in the language is equivalent to a path in the corresponding graph,we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.

A note on semidefinite programming relaxations for polynomial optimization over a single sphere

We study two instances of polynomial optimization problem over a single sphere. The first problem is to compute the best rank-1 tensor approximation. We show the equivalence between two recent semidefinite relaxations methods. The other one arises from Bose-Einstein condensates(BEC), whose objective function is a summation of a probably nonconvex quadratic function and a quartic term. These two polynomial optimization problems are closely connected since the BEC problem can be viewed as a structured fourth-order best rank-1 tensor approximation. We show that the BEC problem is NP-hard and propose a semidefinite relaxation with both deterministic and randomized rounding procedures. Explicit approximation ratios for these rounding procedures are presented. The performance of these semidefinite relaxations are illustrated on a few preliminary numerical experiments.

Effect of polypeptide 2B1 on condition of dampness pattern in rats in terms of Traditional Chinese Medicine

OBJECTIVE： This study investigated how polypeptide 2B1 is involved in regulating and governing dampness in rat models with dampness pattern defined in terms of Traditional Chinese Medicine. METHODS： We randomly divided 48 SPF 10-week-old male Sprague-Dawley （SD） rats into a normal group, normal ＋ Aristolochic acid I （AA-I） for 5 min group, normal ＋ AA-I for 60 min group, dampness pattern group （DS-Group）, dampness pattern ＋ AA-I for 5 rain tern ＋ AA-I for 60 min group, and dampness pat- group. Groups were then treated accordingly. We took out the lung, stom- ach, liver, spleen, kidney, large intestine, and small intestine tissues to detect gene and protein expres- sion of organic anion transporter polypeptide 2B1 （OATP2B1）. RESULTS= Gene expression of OATP2B1 in spleen, kidney, and small intestine of rats with dampness pattern was lower than that in normal rats （P〈0.05）. The gene expressions of OATP2B1 in liver, stomach, large intestine, and small intestine were lower than that in control rats at different time points after being stimulated by AA-I （P〈0.05）. CONCLUSION There is coordination among multiple viscera in handling the condition of dampness, and the mechanism underlying the action may rely on regulating the expression of OATP2B1.

Sparse bivariate polynomial factorization

Motivated by Sasaki＇s work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting, which takes advantage of sparsity, for factoring bivariate polynomial over the rational number field. Another feature of the factorization algorithm presented in this article is a new recombination method, which can solve the extraneous factor problem before lifting based on numerical linear algebra. Both theoretical analysis and experimental data show that the algorithm is etIicient, especially for sparse bivariate polynomials.

Association among lifestyle, clinical examination, polymorphisms in CDH1 gene and Traditional Chinese Medicine syndrome differentiation of gastric cancer

OBJECTIVE:To explore the association among lifestyle,clinical examination,polymorphisms in CDH1 gene and Traditional Chinese Medicine(TCM)syndrome differentiation of gastric cancer(GC). METHODS:A hospital-based population of 387 GC patients was investigated in Jiangsu province.Relevant information regarding lifestyle and clinical examination were collected by a standard questionnaire.Four known single nucleotide polymorphisms(SNPs)in CDH1 were investigated by polymerase chain reaction-ligation detection reaction methods.Statistical analysis was conducted by SPSS 16.0 software.RESULTS:The results showed that meal duration and the status of glutamic pyruvic transaminase were significantly associated with TCM syndrome differentiation of GC(both P<0.05).None of the four SNPs in the E-cadherin(CDH1)gene achieved significant differences in their distributions among the nine syndrome types of GC(both P>0.05).However,significant differences were observed in rs13689 genotype distributions between several pairs of syndrome types of GC,suggesting that rs13689 is correlated with the syndrome differentiation of GC.CONCLUSION:Integrated analysis of lifestyle,clinical examination and CDH1 gene polymorphisms can contribute to a better understanding of the GC syndrome types and may improve the efficacy of interventions by stratifying disease according to TCM criteria.

ON FUNCTIONAL DECOMPOSITION OF MULTIVARIATE POLYNOMIALS WITH DIFFERENTIATION AND HOMOGENIZATION

This paper gives a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which were proposed by Ye, Dai, and Lam （1999） and were developed by Faugere, Perret （2006, 2008, 2009）. The authors show that a degree proper functional decomposition for a set of randomly decomposable quartic homoge- nous polynomials can be computed using the algorithm with high probability. This solves a conjecture proposed by Ye, Dal, and Lam （1999）. The authors also propose a conjecture which asserts that the decomposition for a set of polynomials can be computed from that of its homogenization and show that the conjecture is valid with high probability for quartic polynomials. Finally, the authors prove that the right decomposition factors for a set of polynomials can be computed from its right decomposition factor space.