Friedman, Joel 1962
Overview
Works:  23 works in 61 publications in 1 language and 661 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA193, 512.9436 
Publication Timeline
.
Most widely held works by
Joel Friedman
A proof of Alon's second eigenvalue conjecture and related problems by
Joel Friedman(
Book
)
10 editions published in 2008 in English and held by 226 WorldCat member libraries worldwide
10 editions published in 2008 in English and held by 226 WorldCat member libraries worldwide
Expanding graphs : proceedings of a DIMACS workshop, May 1114, 1992 by Dimacs Workshop on Expander Graphs(
Book
)
9 editions published in 1993 in English and held by 155 WorldCat member libraries worldwide
9 editions published in 1993 in English and held by 155 WorldCat member libraries worldwide
Sheaves on graphs, their homological invariants, and a proof of the Hanna Neumann conjecture by
Joel Friedman(
Book
)
15 editions published between 2014 and 2015 in English and held by 90 WorldCat member libraries worldwide
In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture
15 editions published between 2014 and 2015 in English and held by 90 WorldCat member libraries worldwide
In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture
The decision method for real algebra: is it practical? by
Joel Friedman(
Book
)
2 editions published in 1966 in English and held by 22 WorldCat member libraries worldwide
This memorandum deals with the practicality of Tarski's decision procedure for the mathematical theory of Real Algebra. The procedure is presented in a modified form. It is reduced to three basic methods. Each method processes a basic kind of formula of Real Algebra. The efficiency of each of these methods is discussed. Finally, an alternative to the third method, invented by Hamblin, is presented. Its efficiency is also discussed. For each of these methods, only a partial measure of efficiency is offered. This partial measure is itself not determined exactly, but rather to within certain bounds. The general impracticality of both the third method and its alternative is then inferred from this partial measure of efficiency. Hence the general impracticality of the whole decision procedure follows. (Author)
2 editions published in 1966 in English and held by 22 WorldCat member libraries worldwide
This memorandum deals with the practicality of Tarski's decision procedure for the mathematical theory of Real Algebra. The procedure is presented in a modified form. It is reduced to three basic methods. Each method processes a basic kind of formula of Real Algebra. The efficiency of each of these methods is discussed. Finally, an alternative to the third method, invented by Hamblin, is presented. Its efficiency is also discussed. For each of these methods, only a partial measure of efficiency is offered. This partial measure is itself not determined exactly, but rather to within certain bounds. The general impracticality of both the third method and its alternative is then inferred from this partial measure of efficiency. Hence the general impracticality of the whole decision procedure follows. (Author)
Emerging applications of number theory by
Dennis A Hejhal(
Book
)
3 editions published in 1999 in English and held by 11 WorldCat member libraries worldwide
Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging  providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern numbertheoretical techniques
3 editions published in 1999 in English and held by 11 WorldCat member libraries worldwide
Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging  providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern numbertheoretical techniques
On the second eigenvalue of hypergraphs by
Joel Friedman(
Book
)
4 editions published between 1989 and 1992 in English and held by 7 WorldCat member libraries worldwide
4 editions published between 1989 and 1992 in English and held by 7 WorldCat member libraries worldwide
On Newton's method by
Joel Friedman(
)
2 editions published in 1987 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1987 in English and held by 5 WorldCat member libraries worldwide
A note on poset geometries by
Joel Friedman(
Book
)
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we describe how varying the geometric representation of a poset can be applied to 'poset balancing.' We show that the 1/3, 2/3 balancing property holds for a certain class of posets whose number of relations is sufficiently small, in a certain sense."
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we describe how varying the geometric representation of a poset can be applied to 'poset balancing.' We show that the 1/3, 2/3 balancing property holds for a certain class of posets whose number of relations is sufficiently small, in a certain sense."
The spectra of infinite hypertrees by
Joel Friedman(
Book
)
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We develop a model of regular, infinite hypertrees, to mimic for hypergraphs what infinite trees do for graphs. We then examine two notions of spectra or 'first eigenvalue' for the infinite tree, obtaining a precise value for the first notion and obtaining some estimates for the second. The results indicate agreement of the first eigenvalue of the infinite hypertree with the 'second eigenvalue' of a random hypergraph of the same degree, to within logarithmic factors, at least for the first notion of first eigenvalue."
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We develop a model of regular, infinite hypertrees, to mimic for hypergraphs what infinite trees do for graphs. We then examine two notions of spectra or 'first eigenvalue' for the infinite tree, obtaining a precise value for the first notion and obtaining some estimates for the second. The results indicate agreement of the first eigenvalue of the infinite hypertree with the 'second eigenvalue' of a random hypergraph of the same degree, to within logarithmic factors, at least for the first notion of first eigenvalue."
On the second eigenvalue and random walks in random dregular graphs by
Joel Friedman(
Book
)
1 edition published in 1988 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 3 WorldCat member libraries worldwide
A note on matrix rigidity by
Joel Friedman(
Book
)
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this paper we give an explicit construction of n X n matrices over finite fields which are somewhat rigid, in that if we change at most k entries in each row, its rank remains at least Cn(log[subscript q]k)/k, where q is the size of the field and C is an absolute constant. Our matrices satisfy a somewhat stronger property, we which explain and call 'strong rigidity.' We introduce and briefly discuss strong rigidity, because it is in a sense a simpler property and may be easier to use in giving explicit constructions."
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this paper we give an explicit construction of n X n matrices over finite fields which are somewhat rigid, in that if we change at most k entries in each row, its rank remains at least Cn(log[subscript q]k)/k, where q is the size of the field and C is an absolute constant. Our matrices satisfy a somewhat stronger property, we which explain and call 'strong rigidity.' We introduce and briefly discuss strong rigidity, because it is in a sense a simpler property and may be easier to use in giving explicit constructions."
Some graphs with small second eigenvalue by
Joel Friedman(
Book
)
1 edition published in 1989 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 3 WorldCat member libraries worldwide
A deterministic view of random sampling and its use in geometry by
B Chazelle(
Book
)
1 edition published in 1988 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 3 WorldCat member libraries worldwide
A density theorem for purely iterative zero finding methods by
Joel Friedman(
Book
)
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
On the bit extraction problem by
Joel Friedman(
Book
)
1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide
Abstract: "Consider a coloring of the ndimensional Boolean cube with c = 2[superscript s] colors in such a way that every kdimensional subcube is equicolored, i.e. each color occurs the same number of times. We show that for such a coloring we necessarily have (k1)/n [> or =] [theta][supscript c] = (c/2 1)/(c1). This resolves the 'bit extraction' or 'tresilient functions' problem in many cases, such as [formula], proving that XOR type colorings are optimal. We also study the problem of finding almost equicolored colorings when (k1)/n <[theta][subscript c], and of classifying all optimal colorings."
1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide
Abstract: "Consider a coloring of the ndimensional Boolean cube with c = 2[superscript s] colors in such a way that every kdimensional subcube is equicolored, i.e. each color occurs the same number of times. We show that for such a coloring we necessarily have (k1)/n [> or =] [theta][supscript c] = (c/2 1)/(c1). This resolves the 'bit extraction' or 'tresilient functions' problem in many cases, such as [formula], proving that XOR type colorings are optimal. We also study the problem of finding almost equicolored colorings when (k1)/n <[theta][subscript c], and of classifying all optimal colorings."
Random polynomials and approximate zeros of Newton's method by
Joel Friedman(
Book
)
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
Some geometric aspects of graphs and their eigenfunctions by
Joel Friedman(
Book
)
1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide
Abstract: "We study two mathematical notions, that of nodal regions for eigenfunctions of the Laplacian, and that of fiber products, in the context of graph theory. We formulate analogous notions and theorems for graphs and their eigenpairs. These techniques suggest new ways of studying problems related to spectral theory of graphs."
1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide
Abstract: "We study two mathematical notions, that of nodal regions for eigenfunctions of the Laplacian, and that of fiber products, in the context of graph theory. We formulate analogous notions and theorems for graphs and their eigenpairs. These techniques suggest new ways of studying problems related to spectral theory of graphs."
On the second eigenvalue of noisy boolean networks by
Craig Gotsman(
Book
)
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
Abstract: "We introduce the nprocessor boolean network model and examine its kinematic behavior in the presence of noise. We prove that if each processor has error probability [delta], the derivative of the network second eigenvalue at [delta] = 0 is highly concentrated around n. This, along with numerical results, seem to indicate that when [delta] = 1/poly(n), almost all network kinematics mix rapidly."
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
Abstract: "We introduce the nprocessor boolean network model and examine its kinematic behavior in the presence of noise. We prove that if each processor has error probability [delta], the derivative of the network second eigenvalue at [delta] = 0 is highly concentrated around n. This, along with numerical results, seem to indicate that when [delta] = 1/poly(n), almost all network kinematics mix rapidly."
Sheaves on graphs, their homological invariants, and a proof of the Hanna Neumann conjecture by
Joel Friedman(
)
1 edition published in 2014 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2014 in English and held by 0 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 DIMACS (Group)
 Dicks, Warren 1947 Author of introduction Collector
 Odlyzko, Andrew M. Editor
 Gutzwiller, M. C. (Martin C.) Editor
 Hejhal, Dennis A. Author Editor
 American Mathematical Society Editor
 Wigderson, Avi
 Chazelle, B. (Bernard) Author
 Wigderson, A.
 Dikun, Suyono
Associated Subjects
Algebra Boolean rings Coding theory Combinatorial analysis Combinatorial optimization Density altitude computers Eigenfunctions Eigenvalues Geometry Gödel's theorem Graph theory Hypergraphs Logic, Symbolic and mathematical Mathematics Matrices Neural networks (Computer science) Number theory Numerical analysis Partially ordered sets Polynomials Random walks (Mathematics) Sampling (Statistics) Sheaf theory Vector analysis Vector spaces