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A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
Abstract

Cited by 507 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 then almost surely all components in such graphs are small. We can apply these results to G n;p ; G n;M , and other wellknown models of random graphs. There are also applications related to the chromatic number of sparse random graphs.
CRITICAL POINT
"... Many people have inspired, guided, and helped me during my tenure as a doctoral student, and I would like to thank them all for a great graduate school experience. First and foremost I would like to thank my advisor, Dr. John Hegseth, for his supervision as my advisor throughout the time it took me ..."
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Many people have inspired, guided, and helped me during my tenure as a doctoral student, and I would like to thank them all for a great graduate school experience. First and foremost I would like to thank my advisor, Dr. John Hegseth, for his supervision as my advisor throughout the time it took me to complete this research and write the dissertation. He challenged my thinking, writing and research skills and served as a teaching mentor and a role model. Without his insightful direction, many of the results presented here would not have been possible. My dissertation committee deserves recognition for their time, valuable suggestions and support: Dr. Juliette Ioup for her continuous support and her willingness to read and make constructive suggestions during my research on this dissertation. I am grateful to her for that, for all the hours of consultation, suggestions enthusiasm and professionalism; Dr. Dimitrios Charalampidis for generously giving his time and expertise to better my work; Dr. Joseph Murphy for his insight and sound advise through this entire research; Dr. Jinke Tang for his kind
Eigenfunctions With Few Critical Points
, 1999
"... . We construct a sequence of eigenfunctions on T 2 with a bounded number of critical points. S. T. Yau raised a question about the number and distribution of critical points of eigenfunctions of the Laplacian on a Riemannian manifold ([4, # 76], [5, # 43]). In [6] he investigated this problem in t ..."
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Cited by 17 (1 self)
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. We construct a sequence of eigenfunctions on T 2 with a bounded number of critical points. S. T. Yau raised a question about the number and distribution of critical points of eigenfunctions of the Laplacian on a Riemannian manifold ([4, # 76], [5, # 43]). In [6] he investigated this problem
Crashes as Critical Points
 International Journal of Theoretical and Applied Finance
, 2000
"... We study a rational expectation model of bubbles and crashes. The model has two components: (1) our key assumption is that a crash may be caused by local selfreinforcing imitation between noise traders. If the tendency for noise traders to imitate their nearest neighbors increases up to a certain p ..."
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Cited by 62 (24 self)
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point called the “critical ” point, all noise traders may place the same order (sell) at the same time, thus causing a crash. The interplay between the progressive strengthening of imitation and the ubiquity of noise is characterized by the hazard rate, i.e. the probability per unit time that the crash
Critical Points Of Polynomial Metaballs
 Implicit Surface’98 Proc
, 1998
"... Maintaining a triangle mesh on a changing implicit surface provides an amortized method for e#ciently polygonizing an implicit surface animation. Such maintenance requires special attention to the triangular mesh, including mesh reconnection when the implicit surface changes topological type, and o ..."
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Cited by 15 (1 self)
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, and optimization to ensure the triangles are well shaped. For added e#ciency, piecewise polynomial metaballs are often used, but introduce special problems in #nding the critical points necessary to determine topological type. There are numerous details important to implementing such techniques on piecewise
IDEAS IN CRITICAL POINT THEORY
"... Abstract. We present some basic tools in critical point theory. We first define the notion of differentiability and then introduce the PalaisSmale condition. Using this, we state a very important result called the deformation lemma in which the level sets of a function play an fundamental role. We ..."
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Abstract. We present some basic tools in critical point theory. We first define the notion of differentiability and then introduce the PalaisSmale condition. Using this, we state a very important result called the deformation lemma in which the level sets of a function play an fundamental role. We
Results 1  10
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1,218,227