Friedman, Joel 1962
Overview
Works:  20 works in 35 publications in 1 language and 442 library holdings 

Genres:  Conference 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
)
9 editions published in 2008 in English and held by 228 WorldCat member libraries worldwide
9 editions published in 2008 in English and held by 228 WorldCat member libraries worldwide
Expanding graphs : proceedings of a DIMACS workshop, May 1114, 1992 by DIMACS workshop on expander graphs(
Book
)
7 editions published in 1993 in English and held by 151 WorldCat member libraries worldwide
7 editions published in 1993 in English and held by 151 WorldCat member libraries worldwide
The decision method for real algebra: is it practical? by
Joel Friedman(
Book
)
1 edition published in 1966 in English and held by 21 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 21 WorldCat member libraries worldwide
Sheaves on graphs, their homological invariants, and a proof of the Hanna Neumann conjecture by
Joel Friedman(
)
2 editions published in 2015 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 2015 in English and held by 7 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 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."
On the second eigenvalue of hypergraphs 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
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."
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
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
On Newton's method by
Joel Friedman(
)
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
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
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 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
Expanding graphs(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
On the second eigenvalue of noisy boolean networks by
Craig Gotsman(
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library 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."
1 edition published in 1990 in English and held by 1 WorldCat member library 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."
Probabilistic spaces of boolean functions of a given complexity : generalities and random kSAT coefficients by
Joel Friedman(
Book
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
Abstract: "In this paper, we develop an approach to studying probabilistic spaces of boolean functions, namely recovering exact formulas for the event probabilities in terms of the moments. While this involves analyzing a large number of moments, there are situations in which this seems feasible to do; for the mfold AND of a probability space of functions, there is a formula involving coefficients with a geometric intepretation (and which is otherwise quite simple). We investigate the coefficients involved in the kSAT problem, where we give a formula for the 1SAT coefficients and are able to understand a few of the 2SAT coefficients."
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
Abstract: "In this paper, we develop an approach to studying probabilistic spaces of boolean functions, namely recovering exact formulas for the event probabilities in terms of the moments. While this involves analyzing a large number of moments, there are situations in which this seems feasible to do; for the mfold AND of a probability space of functions, there is a formula involving coefficients with a geometric intepretation (and which is otherwise quite simple). We investigate the coefficients involved in the kSAT problem, where we give a formula for the 1SAT coefficients and are able to understand a few of the 2SAT coefficients."
The decision method for real algebra: is it practical(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library 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)
1 edition published in 1966 in English and held by 1 WorldCat member library 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)
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Associated Subjects
Algebra Algebraic topology Boolean rings Coding theory Combinatorial optimization Density altitude computers Eigenfunctions Eigenvalues Geometry Gödel's theorem Graph theory Hypergraphs Logic, Symbolic and mathematical Matrices Neural networks (Computer science) Numerical analysis Partially ordered sets Polynomials Random walks (Mathematics) Sampling (Statistics) Sheaf theory Vector analysis Vector spaces