Results 1  10
of
519,535
The BrunnMinkowski inequality
 Bull. Amer. Math. Soc. (N.S
, 2002
"... Abstract. In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The BrunnMinkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of R n, and deserves to be better known. This guide explains ..."
Abstract

Cited by 184 (9 self)
 Add to MetaCart
Abstract. In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The BrunnMinkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of R n, and deserves to be better known. This guide
The BrunnMinkowski Inequality: Work In Progress
"... . According to the MathSciNet search engine, approximately 100 papers and books pertaining to the BrunnMinkowski inequality have appeared since Das Gupta's 1980 article BrunnMinkowski and its aftermath [56]. An attempt is made here to present an uptodate survey. 1. Introduction About a ..."
Abstract
 Add to MetaCart
. According to the MathSciNet search engine, approximately 100 papers and books pertaining to the BrunnMinkowski inequality have appeared since Das Gupta's 1980 article BrunnMinkowski and its aftermath [56]. An attempt is made here to present an uptodate survey. 1. Introduction About
THE BRUNNMINKOWSKI INEQUALITY AND SOME CONSEQUENCES
"... Our first question may not seem very deep: What is a circle? An equivalent definition to the usual one is given by the following nontrivial fact: among all simple1 closed plane curves of a given length L, the circle of circumference L encloses ..."
Abstract
 Add to MetaCart
Our first question may not seem very deep: What is a circle? An equivalent definition to the usual one is given by the following nontrivial fact: among all simple1 closed plane curves of a given length L, the circle of circumference L encloses
A BrunnMinkowski inequality for the integer lattice
 Trans. Amer. Math. Soc
"... Abstract. A close discrete analog of the classical BrunnMinkowksi inequality that holds for finite subsets of the integer lattice is obtained. This is applied to obtain strong new lower bounds for the cardinality of the sum of two finite sets, one of which has full dimension, and, in fact, a method ..."
Abstract

Cited by 23 (3 self)
 Add to MetaCart
Abstract. A close discrete analog of the classical BrunnMinkowksi inequality that holds for finite subsets of the integer lattice is obtained. This is applied to obtain strong new lower bounds for the cardinality of the sum of two finite sets, one of which has full dimension, and, in fact, a
Fuchsian convex bodies: basics of Brunn–Minkowski theory
, 1112
"... The hyperbolic space Hd can be defined as a pseudosphere in the pd ` 1q Minkowski spacetime. In this paper, a Fuchsian group Γ is a group of linear isometries of the Minkowski space such that Hd{Γ is a compact manifold. We introduce Fuchsian convex bodies, which are closed convex sets in Minkowski ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
Brunn–Minkowski theory. For example, support functions can be defined, as functions on a compact hyperbolic manifold instead of the sphere. The main result is the convexity of the associated volume (it is log concave in the classical setting). This implies analogs of Alexandrov–Fenchel and Brunn–Minkowski
Identification of programmed cell death in situ via specific labeling of nuclear DNA fragmentation
 J. Cell
, 1992
"... Abstract. Programmed cell death (PCD) plays a key role in developmental biology and in maintenance of the steady state in continuously renewing tissues. Currently, its existence is inferred mainly from gel electrophoresis of a pooled DNA extract as PCD was shown to be associated with DNA fragmentati ..."
Abstract

Cited by 656 (0 self)
 Add to MetaCart
Abstract. Programmed cell death (PCD) plays a key role in developmental biology and in maintenance of the steady state in continuously renewing tissues. Currently, its existence is inferred mainly from gel electrophoresis of a pooled DNA extract as PCD was shown to be associated with DNA fragmentation. Based on this observation, we describe here the development of a method for the in situ visualization of PCD at the singlecell level, while preserving tissue architecture. Conventional histological sections, pretreated with protease, were nick end labeled with biotinylated poly dU, introduced by terminal deoxyp iaOGrtAMMED cell death 0~D) 1 is a selective process of physiological cell deletion (Wyllie, 1981; Umansky,
From BrunnMinkowski To BrascampLieb And To Logarithmic Sobolev Inequalities
 Geom. Funct. Anal
"... .  We develop several applications of the BrunnMinkowki inequality in the Pr'ekopaLeindler form. In particular, we show that an argument of B. Maurey may be adapted to deduce from the Pr'ekopaLeindler inequality the BrascampLieb inequality for stricly convex potentials. We deduce sim ..."
Abstract

Cited by 79 (2 self)
 Add to MetaCart
'ekopaLeinder inequality is a functional form of the geometric BrunnMinkowski inequality which indicates that whenever t; s ? 0, t + s = 1, and u, v, w are nonnegative measurable functions on R n such that for all x; y 2 R n , w \Gamma tx + sy) u(x) t v(y) s ; then Z wdx `Z udx ' t `Z vdx &apos
An extensive empirical study of feature selection metrics for text classification
 J. of Machine Learning Research
, 2003
"... Machine learning for text classification is the cornerstone of document categorization, news filtering, document routing, and personalization. In text domains, effective feature selection is essential to make the learning task efficient and more accurate. This paper presents an empirical comparison ..."
Abstract

Cited by 483 (15 self)
 Add to MetaCart
Machine learning for text classification is the cornerstone of document categorization, news filtering, document routing, and personalization. In text domains, effective feature selection is essential to make the learning task efficient and more accurate. This paper presents an empirical comparison of twelve feature selection methods (e.g. Information Gain) evaluated on a benchmark of 229 text classification problem instances that were gathered from Reuters, TREC, OHSUMED, etc. The results are analyzed from multiple goal perspectives—accuracy, Fmeasure, precision, and recall—since each is appropriate in different situations. The results reveal that a new feature selection metric we call ‘BiNormal Separation ’ (BNS), outperformed the others by a substantial margin in most situations. This margin widened in tasks with high class skew, which is rampant in text classification problems and is particularly challenging for induction algorithms. A new evaluation methodology is offered that focuses on the needs of the data mining practitioner faced with a single dataset who seeks to choose one (or a pair of) metrics that are most likely to yield the best performance. From this perspective, BNS was the top single choice for all goals except precision, for which Information Gain yielded the best result most often. This analysis also revealed, for example, that Information Gain and ChiSquared have correlated failures, and so they work poorly together. When choosing optimal pairs of metrics for each of the four performance goals, BNS is consistently a member of the pair—e.g., for greatest recall, the pair BNS + F1measure yielded the best performance on the greatest number of tasks by a considerable margin.
Results 1  10
of
519,535