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Mathematical Control Theory: Deterministic Finite Dimensional Systems
 of Texts in Applied Mathematics
, 1990
"... The title of this book gives a very good description of its contents and style, although I might have added “Introduction to ” at the beginning. The style is mathematical: precise, clear statements (i.e., theorems) are asserted, then carefully proved. The book covers many of the key topics in contro ..."
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Cited by 485 (121 self)
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The title of this book gives a very good description of its contents and style, although I might have added “Introduction to ” at the beginning. The style is mathematical: precise, clear statements (i.e., theorems) are asserted, then carefully proved. The book covers many of the key topics
A Simple Model of Capital Market Equilibrium with Incomplete Information
 JOURNAL OF FINANCE
, 1987
"... The sphere of modern financial economics encompases finance, micro investment theory and much of the economics of uncertainty. As is evident from its influence on other branches of economics including public finance, industrial organization and monetary theory, the boundaries of this sphere are both ..."
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Cited by 756 (2 self)
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are both permeable and flexible. The complex interactions of time and uncertainty guarantee intellectual challenge and intrinsic excitement to the study of financial economics. Indeed, the mathematics of the subject contain some of the most interesting applications of probability and optimization theory
Framing: toward clarification of a fractured paradigm’’,
 Journal of Communication
, 1993
"... In response to the proposition that communication lacks disciplinary status because of deficient core knowledge, I propose that we turn an ostensible weakness into a strength. We should identify our mission as bringing together insights and theories that would otherwise remain scattered in other di ..."
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Cited by 620 (1 self)
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in one location, communication can aspire to become a master discipline that synthesizes related theories and concepts and exposes them to the most rigorous, comprehensive statement and exploration. Reaching this goal would require a more selfconscious determination by communication scholars to plumb
On the Selfsimilar Nature of Ethernet Traffic (Extended Version)
, 1994
"... We demonstrate that Ethernet LAN traffic is statistically selfsimilar, that none of the commonly used traffic models is able to capture this fractallike behavior, that such behavior has serious implications for the design, control, and analysis of highspeed, cellbased networks, and that aggrega ..."
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Cited by 2213 (46 self)
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, and that aggregating streams of such traffic typically intensifies the selfsimilarity (“burstiness”) instead of smoothing it. Our conclusions are supported by a rigorous statistical analysis of hundreds of millions of high quality Ethernet traffic measurements collected between 1989 and 1992, coupled with a
A gentle tutorial on the EM algorithm and its application to parameter estimation for gaussian mixture and hidden markov models
, 1997
"... We describe the maximumlikelihood parameter estimation problem and how the Expectationform of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) fi ..."
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Cited by 693 (4 self)
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) finding the parameters of a hidden Markov model (HMM) (i.e., the BaumWelch algorithm) for both discrete and Gaussian mixture observation models. We derive the update equations in fairly explicit detail but we do not prove any convergence properties. We try to emphasize intuition rather than mathematical
Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex
 J. Neurosci
, 1982
"... The development of stimulus selectivity in the primary sensory cortex of higher vertebrates is considered in a general mathematical framework. A synaptic evolution scheme of a new kind is proposed in which incoming patterns rather than converging afferents compete. The change in the efficacy of a gi ..."
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Cited by 432 (20 self)
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The development of stimulus selectivity in the primary sensory cortex of higher vertebrates is considered in a general mathematical framework. A synaptic evolution scheme of a new kind is proposed in which incoming patterns rather than converging afferents compete. The change in the efficacy of a
A new method for nonparametric multivariate analysis of variance in ecology.
 Austral Ecology,
, 2001
"... Abstract Hypothesistesting methods for multivariate data are needed to make rigorous probability statements about the effects of factors and their interactions in experiments. Analysis of variance is particularly powerful for the analysis of univariate data. The traditional multivariate analogues, ..."
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Cited by 368 (4 self)
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Abstract Hypothesistesting methods for multivariate data are needed to make rigorous probability statements about the effects of factors and their interactions in experiments. Analysis of variance is particularly powerful for the analysis of univariate data. The traditional multivariate analogues
BraMBLe: A Bayesian MultipleBlob Tracker
, 2001
"... Blob trackers have become increasingly powerful in recent years largely due to the adoption of statistical appearance models which allow effective background subtraction and robust tracking of deforming foreground objects. It has been standard, however, to treat background and foreground modelling a ..."
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Cited by 313 (1 self)
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camera realtime surveillance applications. The first innovation is a multiblob likelihood function which assigns directly comparable likelihoods to hypotheses containing different numbers of objects. This likelihood function has a rigorous mathematical basis: it is adapted from the theory of Bayesian
Style and Rigor in Mathematics
"... One of the primary goals of my work in the history of mathematics is to make known the way in which Leopold Kronecker’s effort to base the mathematics of his and preceding generations on what he called “generalized arithmetic”—the algebra of polynomials with integer coefficients—was overruled at th ..."
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and presentation. I was encouraged by James Pierpont’s statement in his essay “Mathematical Rigor, Past and Present, ” [5] that “Personally [I] do not believe
Mathematical Objects and the Evolution of Rigor
"... ABSTRACT: In this paper we discuss the origins and the evolution of rigor in mathematics in relation to the creation of mathematical objects. We provide examples of key moments in the development of mathematics that support our thesis that the nature of mathematical objects is cosubstantia1 with th ..."
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ABSTRACT: In this paper we discuss the origins and the evolution of rigor in mathematics in relation to the creation of mathematical objects. We provide examples of key moments in the development of mathematics that support our thesis that the nature of mathematical objects is cosubstantia1
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