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161.
G. Richomme 《Discrete Applied Mathematics》2007,155(15):2001-2016
A challenging problem is to find an algorithm to decide whether a morphism is k-power-free. When k?3, we provide such an algorithm for uniform morphisms showing that in such a case, contrarily to the general case, there exist finite test-sets for k-power-freeness. 相似文献
162.
Dominique Fourdrinier William E. Strawderman Martin T. Wells 《Annals of the Institute of Statistical Mathematics》2006,58(1):73-92
In this article we consider estimating a location parameter of a spherically symmetric distribution under restrictions on
the parameter. First we consider a general theory for estimation on polyhedral cones which includes examples such as ordered
parameters and general linear inequality restrictions. Next, we extend the theory to cones with piecewise smooth boundaries.
Finally we consider shrinkage toward a closed convex set K where one has vague prior information that θ is in K but where θ is not restricted to be in K. In this latter case we give estimators which improve on the usual unbiased estimator while in the restricted parameter case
we give estimators which improve on the projection onto the cone of the unbiased estimator. The class of estimators is somewhat
non-standard as the nature of the constraint set may preclude weakly differentiable shrinkage functions. The technique of
proof is novel in the sense that we first deduce the improvement results for the normal location problem and then extend them
to the general spherically symmetric case by combining arguments about uniform distributions on the spheres, conditioning
and completeness. 相似文献
163.
John Irving 《Journal of Combinatorial Theory, Series A》2006,113(7):1549-1554
We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic means, extending recent work of Biane. We deduce from our result a remarkable formula of Poulalhon and Schaeffer that was previously derived through an intricate combinatorial argument. 相似文献
164.
The asymmetric travelling salesman problem with replenishment arcs (RATSP), arising from work related to aircraft routing, is a generalisation of the well-known ATSP. In this paper, we introduce a polynomial size mixed-integer linear programming (MILP) formulation for the RATSP, and improve an existing exponential size ILP formulation of Zhu [The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994] by proposing two classes of stronger cuts. We present results that under certain conditions, these two classes of stronger cuts are facet-defining for the RATS polytope, and that ATSP facets can be lifted, to give RATSP facets. We implement our polyhedral findings and develop a Lagrangean relaxation (LR)-based branch-and-bound (BNB) algorithm for the RATSP, and compare this method with solving the polynomial size formulation using ILOG Cplex 9.0, using both randomly generated problems and aircraft routing problems. Finally we compare our methods with the existing method of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408-427]. It turns out that both of our methods are much faster than that of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408-427], and that the LR-based BNB method is more efficient for problems that resemble the aircraft rotation problems. 相似文献
165.
166.
We investigate discrete structures and combinatoric modeling of weighted prefix trees for managing and analyzing DNA microarray data. We describe the algorithms to construct the weighted trees for
these data. Using these weighted trees with our algorithms, we propose methods to compute the appearance probability of a DNA microarray, to compare the informational distances in the expression of genes between the DNA microarrays, to search
the characteristic microarrays and the group of candidate genes suggestive of a pathology. 相似文献
167.
L. da F. Costa L. E.C. da Rocha 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):237-242
This work describes how the
formalization of complex network concepts in terms of discrete
mathematics, especially mathematical morphology, allows a series
of generalizations and important results ranging from new
measurements of the network topology to new network growth models.
First, the concepts of node degree and clustering coefficient are
extended in order to characterize not only specific nodes, but any
generic subnetwork. Second, the consideration of distance
transform and rings are used to further extend those concepts in
order to obtain a signature, instead of a single scalar
measurement, ranging from the single node to whole graph scales.
The enhanced discriminative potential of such extended
measurements is illustrated with respect to the identification of
correspondence between nodes in two complex networks, namely a
protein-protein interaction network and a perturbed version of it. 相似文献
168.
We address a class of particularly hard-to-solve combinatorial optimization problems, namely that of multicommodity network optimization when the link cost functions are discontinuous step increasing. Unlike usual approaches consisting in the development of relaxations for such problems (in an equivalent form of a large scale mixed integer linear programming problem) in order to derive lower bounds, our d.c.(difference of convex functions) approach deals with the original continuous version and provides upper bounds. More precisely we approximate step increasing functions as closely as desired by differences of polyhedral convex functions and then apply DCA (difference of convex function algorithm) to the resulting approximate polyhedral d.c. programs. Preliminary computational experiments are presented on a series of test problems with structures similar to those encountered in telecommunication networks. They show that the d.c. approach and DCA provide feasible multicommodity flows x
* such that the relative differences between upper bounds (computed by DCA) and simple lower bounds r:=(f(x*)-LB)/{f(x*)} lies in the range [4.2 %, 16.5 %] with an average of 11.5 %, where f is the cost function of the problem and LB is a lower bound obtained by solving the linearized program (that is built from the original problem by replacing step increasing cost functions with simple affine minorizations). It seems that for the first time so good upper bounds have been obtained. 相似文献
169.
170.
Bharath Sriraman 《The Journal of Mathematical Behavior》2004,23(2):205-222
In mathematics, generalizations are the end result of an inductive zigzag path of trial and error, that begin with the construction of examples, within which plausible patterns are detected and lead to the formulation of theorems. This paper examines whether it is possible for high school students to discover and formulate generalizations similar to ways professional mathematicians do. What are the experiences that allow students to become adept at generalization? In this paper, the mathematical experiences of a ninth grade student, which lead to the discovery and the formulation of a mathematical generalization are described, qualitatively analyzed and interpreted using the notion of uniframes. It is found that reflecting on the solutions of a class of seemingly different problem-situations over a prolonged time period facilitates the abstraction of structural similarities in the problems and results in the formulation of mathematical generalizations. 相似文献