Search results for "Combinatorics"
showing 10 items of 1770 documents
Balanced Words Having Simple Burrows-Wheeler Transform
2009
The investigation of the "clustering effect" of the Burrows-Wheeler transform (BWT) leads to study the words having simple BWT , i.e. words w over an ordered alphabet $A=\{a_1,a_2,\ldots,a_k\}$, with $a_1 < a_2 < \ldots <a_k$, such that $bwt(w)$ is of the form $a_k^{n_k} a_{k-1}^{n_{k-1}} \cdots a_1^{n_1}$, for some non-negative integers $n_1, n_2, \ldots, n_k$. We remark that, in the case of binary alphabets, there is an equivalence between words having simple BWT, the family of (circular) balanced words and the conjugates of standard words. In the case of alphabets of size greater than two, there is no more equivalence between these notions. As a main result of this paper we prove that, u…
Conjugacy class numbers and π-subgroups
2021
Convex bodies and convexity on Grassmann cones
1962
Optimal Locations and Inner Products
1997
Abstract In a normed space X , we consider objective functions which depend on the distances between a variable point and the points of certain finite sets A . A point where such a function attains its minimum on X is generically called an optimal location. In this paper we obtain characterizations of inner product spaces with properties connecting optimal locations and the convex hull of A or barycenters of points of A with well chosen weights. We thus generalize several classical results about characterization of inner product spaces.
The Linear Ordering Polytope
2010
So far we developed a general integer programming approach for solving the LOP. It was based on the canonical IP formulation with equations and 3-dicycle inequalities which was then strengthened by generating mod-k-inequalities as cutting planes. In this chapter we will add further ingredients by looking for problem- specific inequalities. To this end we will study the convex hull of feasible solutions of the LOP: the so-called linear ordering polytope.
The simplex dispersion ordering and its application to the evaluation of human corneal endothelia
2009
A multivariate dispersion ordering based on random simplices is proposed in this paper. Given a R^d-valued random vector, we consider two random simplices determined by the convex hulls of two independent random samples of sizes d+1 of the vector. By means of the stochastic comparison of the Hausdorff distances between such simplices, a multivariate dispersion ordering is introduced. Main properties of the new ordering are studied. Relationships with other dispersion orderings are considered, placing emphasis on the univariate version. Some statistical tests for the new order are proposed. An application of such ordering to the clinical evaluation of human corneal endothelia is provided. Di…
A reconstruction algorithm for L-convex polyominoes
2006
AbstractWe give an algorithm that uniquely reconstruct an L-convex polyomino from the size of some special paths, called bordered L-paths.
Testing for selectivity in the dependence of random variables on external factors
2008
Random variables AA and BB, whose joint distribution depends on factors (x,y)(x,y), are selectively influenced by xx and yy, respectively, if AA and BB can be represented as functions of, respectively, (x,SA,C)(x,SA,C) and (y,SB,C)(y,SB,C), where SA,SB,CSA,SB,C are stochastically independent and do not depend on (x,y)(x,y). Selective influence implies selective dependence of marginal distributions on the respective factors: thus no parameter of AA may depend on yy. But parameters characterizing stochastic interdependence of AA and BB, such as their mixed moments, are generally functions of both xx and yy. We derive two simple necessary conditions for selective dependence of (A,B)(A,B) on (x…
Molecular Classification of N-Aryloxazolidinone-5-carboxamides as Human Immunodeficiency Virus Protease Inhibitors
2015
Algorithms for classification and taxonomy are proposed in this chapter based information entropy (IE) and its production. The 38 N- aryloxazolidinone-5-carboxamides (NCAs), for human immunodeficiency virus (HIV) protease (PR) inhibition, are classified using seven characteristic chemical properties of different moieties: R 1/2 , R 3–6 on different phenyls and R 7 . Many classification algorithms are based on IE. When applying some procedures to moderate-sized sets, excessive number of results appear compatible with the data and suffer combinatorial explosion. However, after the equipartition conjecture (EC), one has a selection criterion among different variants that results from classifi…