Results 1  10
of
224,727
A Question from a Famous Paper of Erdős
 DISCRETE COMPUT GEOM (2013) 50:253–261
, 2013
"... Given a convex body K, consider the smallest number N so that there is a point P ∈ ∂ K such that every circle centred at P intersects ∂ K in at most N points. In 1946 Erdős conjectured that N = 2 for all K, but there are convex bodies for which this is not the case. As far as we know there is no k ..."
Abstract
 Add to MetaCart
Given a convex body K, consider the smallest number N so that there is a point P ∈ ∂ K such that every circle centred at P intersects ∂ K in at most N points. In 1946 Erdős conjectured that N = 2 for all K, but there are convex bodies for which this is not the case. As far as we know there is no known global upper bound. We show that no convex body has N =∞and that there are convex bodies for which N = 6.
An Introduction to the Kalman Filter
 UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
, 1995
"... In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discretedata linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area o ..."
Abstract

Cited by 1155 (13 self)
 Add to MetaCart
In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discretedata linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
Abstract

Cited by 553 (21 self)
 Add to MetaCart
of recovering a large matrix from a small subset of its entries (the famous Netflix problem). Offtheshelf algorithms such as interior point methods are not directly amenable to large problems of this kind with over a million unknown entries. This paper develops a simple firstorder and easy
Tracking People with Twists and Exponential Maps
, 1998
"... This paper demonstrates a new visual motion estimation technique that is able to recover high degreeoffreedom articulated human body configurations in complex video sequences. We introduce the use of a novel mathematical technique, the product of exponential maps and twist motions, and its integra ..."
Abstract

Cited by 445 (5 self)
 Add to MetaCart
This paper demonstrates a new visual motion estimation technique that is able to recover high degreeoffreedom articulated human body configurations in complex video sequences. We introduce the use of a novel mathematical technique, the product of exponential maps and twist motions, and its
The Power of Convex Relaxation: NearOptimal Matrix Completion
, 2009
"... This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering. In ..."
Abstract

Cited by 356 (7 self)
 Add to MetaCart
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
Abstract

Cited by 357 (6 self)
 Add to MetaCart
In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied
How algebraic Bethe ansatz works for integrable model
 In: Symétries quantiques (Les Houches
, 1996
"... In my Les–Houches lectures of 1982 I described the inverse scattering method of solving the integrable field–theoretical models in 1+1 dimensional space–time. Both classical case, stemming from the famous paper by Gardner, Green, Kruskal and Miura of 1967 on KdV equation, and its quantum counterpart ..."
Abstract

Cited by 270 (4 self)
 Add to MetaCart
In my Les–Houches lectures of 1982 I described the inverse scattering method of solving the integrable field–theoretical models in 1+1 dimensional space–time. Both classical case, stemming from the famous paper by Gardner, Green, Kruskal and Miura of 1967 on KdV equation, and its quantum
3D Sound for Virtual Reality and Multimedia
, 2000
"... This paper gives HRTF magnitude data in numerical form for 43 frequencies between 0.212 kHz, the average of 12 studies representing 100 different subjects. However, no phase data is included in the tables; group delay simulation would need to be included in order to account for ITD. In 3D sound ..."
Abstract

Cited by 288 (5 self)
 Add to MetaCart
This paper gives HRTF magnitude data in numerical form for 43 frequencies between 0.212 kHz, the average of 12 studies representing 100 different subjects. However, no phase data is included in the tables; group delay simulation would need to be included in order to account for ITD. In 3D sound
Famous trails to Paul Erdős
 MATHEMATICAL INTELLIGENCER
, 1999
"... The notion of Erdős number has floated around the mathematical research community for more than thirty years, as a way to quantify the common knowledge that mathematical and scientific research has become a very collaborative process in the twentieth century, not an activity engaged in solely by ..."
Abstract

Cited by 24 (0 self)
 Add to MetaCart
by isolated individuals. In this paper we explore some (fairly short) collaboration paths that one can follow from Paul Erdős to researchers inside and outside of mathematics. In particular, we find that all the Fields Medalists up through 1998 have Erdős numbers less than 6, and that over 60 Nobel Prize
The Catalan numbers are the famous sequence
"... Dedicated to my friend Dennis Stanton Abstract. L. Shapiro found an elegant formula for the selfconvolution of the even subscrtipted terms in the Catalan sequence. This paper provides a natural qanalog of Shapiro’s formula together with three proofs, one of which ..."
Abstract
 Add to MetaCart
Dedicated to my friend Dennis Stanton Abstract. L. Shapiro found an elegant formula for the selfconvolution of the even subscrtipted terms in the Catalan sequence. This paper provides a natural qanalog of Shapiro’s formula together with three proofs, one of which
Results 1  10
of
224,727