Results 1  10
of
4,242
Caps on Classical Varieties and Their Projections
 European Journal of Combinatorics
, 1999
"... A family of caps constructed by Ebert, Metsch and T. Szonyi [8] results from projecting a Veronesian or a Grasmannian to a suitable lowerdimensional space. We improve on this construction by projecting to a space of much smaller dimension. More precisely we partition PG(3r \Gamma 1; q) into a (2r ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
A family of caps constructed by Ebert, Metsch and T. Szonyi [8] results from projecting a Veronesian or a Grasmannian to a suitable lowerdimensional space. We improve on this construction by projecting to a space of much smaller dimension. More precisely we partition PG(3r \Gamma 1; q) into a (2r \Gamma 1)\Gammaspace, an (r \Gamma 1)\Gammaspace and q r \Gamma 1 cyclic caps, each of size (q 2r \Gamma 1)(q \Gamma 1): We also decide when one of 1 our caps can be extended by a point from the (2r \Gamma 1)\Gammaspace or the (r \Gamma 1)\Gammaspace. The proof of the results uses several ingredients, most notably hyperelliptic curves. 1 Introduction Let PG(N; q) be the projective space of dimension N over the finite field GF (q). A kcap K in PG(N; q) is a set of k points, no three of which are collinear [13], and a kcap is complete if it is maximal with respect to inclusion. The maximum value of k for which there exists a kcap in PG(N; q) is denoted by m 2 (N; q). The number m...
Classical varieties, codes and combinatorics
 in: Proceedings of the 15th International Conference on Formal Power Series and Algebraic Combinatorics
, 2003
"... For over two decades, the theory of linear (error correcting) codes has extensive and fruitful interaction with the theory of algebraic curves. The study of linear codes associated to higher dimensional algebraic varieties over finite fields is relatively new. However, given the richness ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
For over two decades, the theory of linear (error correcting) codes has extensive and fruitful interaction with the theory of algebraic curves. The study of linear codes associated to higher dimensional algebraic varieties over finite fields is relatively new. However, given the richness
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
Abstract

Cited by 547 (12 self)
 Add to MetaCart
We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
Abstract

Cited by 506 (2 self)
 Add to MetaCart
~ (1, and then the result is classical. A simple proof appears in EnriquesChisini [E, vol. 3, chap. 3], based on analyzing the totality of coverings of p1 of degree n, with a fixed number d of ordinary branch points. This method has been extended to char. p by William Fulton [F], using specializations
MATRIX FACTORIZATION TECHNIQUES FOR RECOMMENDER SYSTEMS
 IEEE COMPUTER
, 2009
"... As the Netflix Prize competition has demonstrated, matrix factorization models are superior to classic nearestneighbor techniques for producing product recommendations, allowing the incorporation of additional information such as implicit feedback, temporal effects, and confidence levels. Modern co ..."
Abstract

Cited by 593 (4 self)
 Add to MetaCart
As the Netflix Prize competition has demonstrated, matrix factorization models are superior to classic nearestneighbor techniques for producing product recommendations, allowing the incorporation of additional information such as implicit feedback, temporal effects, and confidence levels. Modern
Tabu Search  Part I
, 1989
"... This paper presents the fundamental principles underlying tabu search as a strategy for combinatorial optimization problems. Tabu search has achieved impressive practical successes in applications ranging from scheduling and computer channel balancing to cluster analysis and space planning, and more ..."
Abstract

Cited by 680 (11 self)
 Add to MetaCart
, and more recently has demonstrated its value in treating classical problems such as the traveling salesman and graph coloring problems. Nevertheless, the approach is still in its infancy, and a good deal remains to be discovered about its most effective forms of implementation and about the range
From Data Mining to Knowledge Discovery in Databases.
 AI Magazine,
, 1996
"... ■ Data mining and knowledge discovery in databases have been attracting a significant amount of research, industry, and media attention of late. What is all the excitement about? This article provides an overview of this emerging field, clarifying how data mining and knowledge discovery in database ..."
Abstract

Cited by 538 (0 self)
 Add to MetaCart
research directions in the field. A cross a wide variety of fields, data are being collected and accumulated at a dramatic pace. There is an urgent need for a new generation of computational theories and tools to assist humans in extracting useful information (knowledge) from the rapidly growing volumes
Results 1  10
of
4,242