Results 1 - 10 of 39,869

Fibonacci Heaps and Their Uses in Improved Network optimization algorithms

by Michael L. Fredman, Robert Endre Tarjan , 1987
"... In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in qlogn) amortized tim ..."
Abstract - Cited by 739 (18 self) - Add to MetaCart
matching), improved from O(nm log0dn+2)n); (4) O(mj3(m, n)) for the minimum spanning tree problem, improved from O(mloglo&,,.+2,n), where j3(m, n) = min {i 1 log % 5 m/n). Note that B(m, n) 5 log*n if m 2 n. Of these results, the improved bound for minimum spanning trees is the most striking, although

The fundamental properties of natural numbers

by Grzegorz Bancerek - Journal of Formalized Mathematics , 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
Abstract - Cited by 688 (73 self) - Add to MetaCart
.html The articles [4], [6], [1], [2], [5], and [3] provide the notation and terminology for this paper. A natural number is an element of N. For simplicity, we use the following convention: x is a real number, k, l, m, n are natural numbers, h, i, j are natural numbers, and X is a subset of R

The irreducibility of the space of curves of given genus

by P. Deligne, D. Mumford - 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
; for abelian varieties. This result was first proved independently in char. o by Grothendieck, using methods of etale cohomology (private correspondence with J. Tate), and by Mumford, applying the easy half of Theorem (2.5), to go from curves to abelian varieties (cf. [M2]). Grothendieck has recently

Formal Methods: State of the Art and Future Directions

by Edmund M. Clarke, Jeannette M. Wing - ACM Computing Surveys , 1996
"... ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, N ..."
Abstract - Cited by 425 (6 self) - Add to MetaCart
, NY 10036 USA, fax +1 (212) 869-0481, or permissions@acm.org. 2 \Delta E.M. Clarke and J.M. Wing About Programs---Mechanical verification, Specification techniques; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic---Mechanical theorem proving General Terms: Software engineering

On the bursty evolution of Blogspace

by Ravi Kumar, Jasmine Novak, Prabhakar Raghavan, Andrew Tomkins , 2003
"... O)( 1 #$ #+&PQ+&,0,/RP 2 ":9:0/ +%&P &.F0, )& ;)S O)( 1 #$ #+&PQ+&,0,/RP 2 ":9:0/ +% # O,<&7& =1 P &7"U;(Z ;>A@CB;D,[\D]K,D?^_ B`Bba]@C>Ac >AG8H$^2d)@C]E 9='0,*+82 &e " & Q (T0 U;Ub%&7*',#$ %& :3 Q ..."
Abstract - Cited by 365 (8 self) - Add to MetaCart
Q+ #$ f" L ;&Vg"L0 ,M' (Fhji_E KkI+H$^2D9" 0 O (` lV P gmA)fn i_E K/o3qpr%+N8%+*s&#$ V# t /M- &U5u 7*wv x)y z{V&.+L U; P| x)z}l P 3~10/)O&U; P)2 "; b" l P l*` 5)% U5u&0 =)7*& ( U; 28900-33320 3 &U;r82 U; 3!j" L8%=+*b

Submodular functions, matroids and certain polyhedra

by Jack Edmonds , 2003
"... The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts is that all ..."
Abstract - Cited by 355 (0 self) - Add to MetaCart
of linear programming. It turns out to be useful to regard “pure matroid theory”, which is only incidentally related to the aspects of algebra which it abstracts, as the study of certain classes of convex polyhedra. (1) A matroid M = (E,F) can be defined as a finite set E and a nonempty family F of so

Stereotype threat and women’s math performance

by Steven J. Spencer, Claude M. Steele, Diane M. Quinn - Journal of Experimental Social Psychology , 1999
"... When women perform math, unlike men, they risk being judged by the negative stereotype that women have weaker math ability. We call this predicament stereotype threat and hypothesize that the apprehension it causes may disrupt women’s math performance. In Study 1 we demonstrated that the pattern obs ..."
Abstract - Cited by 336 (7 self) - Add to MetaCart
of the effect. The implication that stereotype threat may underlie gender differences in advanced math performance, even This paper was based on a doctoral dissertation completed by Steven J. Spencer under the direction of Claude M. Steele. This research was supported by a National Institute of Mental Health

On Projection Algorithms for Solving Convex Feasibility Problems

by Heinz H. Bauschke, Jonathan M. Borwein , 1996
"... Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of the ..."
Abstract - Cited by 331 (43 self) - Add to MetaCart
09, 49M45, 65-02, 65J05, 90C25; Secondary 26B25, 41A65, 46C99, 46N10, 47N10, 52A05, 52A41, 65F10, 65K05, 90C90, 92C55. Key words and phrases. Angle between two subspaces, averaged mapping, Cimmino's method, computerized tomography, convex feasibility problem, convex function, convex

Performance persistence

by Gerald G. Brown, Robert F. Dell - Journal of Finance , 1995
"... Most optimization-based decision support systems are used repeatedly with only modest changes to input data from scenario to scenario. Unfortunately, optimization (mathematical programming) has a well-deserved reputation for amplifying small input changes into drastically different solutions. A prev ..."
Abstract - Cited by 325 (12 self) - Add to MetaCart
-Therefore, all progress depends on the unrea- j • M I J •- n * j i sonable man dominantly employed as follows; A model is used to produce a plan, the plan is pub-

A Theorem on Boolean Matrices

by Stephen Warshall - JOURNAL OF THE ACM , 1962
"... Given two boolean matrices A and B, we define the boolean product A AND B as that matrix whose (i, j)th entry is OR_k(a_ik AND b_kj). We define the boolean sum A OR B as that matrix whose (i, j)th entry is a_ij OR b_ij. The use of boolean matrices to represent program topology (Prosser [1], and Mari ..."
Abstract - Cited by 306 (1 self) - Add to MetaCart
Given two boolean matrices A and B, we define the boolean product A AND B as that matrix whose (i, j)th entry is OR_k(a_ik AND b_kj). We define the boolean sum A OR B as that matrix whose (i, j)th entry is a_ij OR b_ij. The use of boolean matrices to represent program topology (Prosser [1
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