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Evolutionary Models of Color Categorization based on Discrimination
 Invited Presentation. UCLA Marschak Colloquium & UCI Human Sciences and Social Complexity Colloquium. Video Stream interaction with UCI, UCSD, UCR, UCSB and UCLA. May 4
, 2007
"... Specifying the factors that contribute to the universality of color categorization across individuals and cultures is a longstanding and still controversial issue in psychology, linguistics, and anthropology. The present article approaches this issue through the simulated evolution of color lexicons ..."
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Cited by 15 (5 self)
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Specifying the factors that contribute to the universality of color categorization across individuals and cultures is a longstanding and still controversial issue in psychology, linguistics, and anthropology. The present article approaches this issue through the simulated evolution of color lexicons. It is shown that the combination of a minimal perceptual psychology of discrimination, simple pragmatic constraints involving communication, and simple learning rules are enough to evolve color naming systems. Implications of this result for psychological theories of color categorization and the evolution of color naming systems in human societies are discussed. 1
On the mathematics of learning
, 2001
"... Abstract. We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking the ..."
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Cited by 3 (3 self)
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Abstract. We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots uniformly at random in the interval [0, 1], although our results extend to other distributions). This, in turn, requires the study of the statistical behavior of the harmonic mean of random variables as above, which leads us to delicate question of the rate of convergence to stable laws and tail estimates for stable laws. The reader can find the proofs of most of the results announced here in [KR2001a]. The original motivation for the work in this paper was provided by the firstnamed author’s research in learning theory, specifically in various models of language acquisition (see [KNN2001, NKN2001, KN2001]) and more specifically yet by the analysis of the speed of convergence
THE PERFORMANCE OF THE BATCH LEARNING ALGORITHM
, 2002
"... Abstract. We analyze completely the convergence speed of the batch learning algorithm, and compare its speed to that of the memoryless learning algorithm and of learning with memory (as analyzed in [KR2001b]). We show that the batch learning algorithm is never worse than the memoryless learning algo ..."
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Abstract. We analyze completely the convergence speed of the batch learning algorithm, and compare its speed to that of the memoryless learning algorithm and of learning with memory (as analyzed in [KR2001b]). We show that the batch learning algorithm is never worse than the memoryless learning algorithm (at least asymptotically). Its performance visavis learning with full memory is less clearcut, and depends on certain probabilistic assumptions.
www.elsevier.com/locate/jmp Evolutionary models of color categorization based on discrimination
, 2007
"... Specifying the factors that contribute to the universality of color categorization across individuals and cultures is a longstanding and still controversial issue in psychology, linguistics, and anthropology. This article approaches this issue through the simulated evolution of color lexicons. It is ..."
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Specifying the factors that contribute to the universality of color categorization across individuals and cultures is a longstanding and still controversial issue in psychology, linguistics, and anthropology. This article approaches this issue through the simulated evolution of color lexicons. It is shown that the combination of a minimal perceptual psychology of discrimination, simple pragmatic constraints involving communication, and simple learning rules is enough to evolve colornaming systems. Implications of this result for psychological theories of color categorization and the evolution of colornaming systems in human societies are discussed. r 2007 Elsevier Inc. All rights reserved. 1.
THE MOMENT ZETA FUNCTION AND APPLICATIONS
, 2002
"... Abstract. Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the moment zeta function of a probability distribution, and study in depth some asymptotic properties of the moment zeta function of those distributions suppo ..."
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Abstract. Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the moment zeta function of a probability distribution, and study in depth some asymptotic properties of the moment zeta function of those distributions supported in the interval [0, 1]. One example of such zeta functions is Riemann’s zeta function (which is the moment zeta function of the uniform distribution in [0, 1]. For Riemann’s zeta function we are able to show particularly sharp versions of our results.
ZEROS, CRITICAL POINTS, AND COEFFICIENTS OF RANDOM FUNCTIONS
"... It has been a long journey almost half a decade and this journey would not have been possible without some truly exceptional and amazing people! I would first like to thank my advisor, Robin Pemantle, for guiding me through my years at Penn. He’s been incredibly helpful and encouraging and I’ve le ..."
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It has been a long journey almost half a decade and this journey would not have been possible without some truly exceptional and amazing people! I would first like to thank my advisor, Robin Pemantle, for guiding me through my years at Penn. He’s been incredibly helpful and encouraging and I’ve learnt a lot from him. Apart from being a prolific mathematician, he’s also an amazing human being, and it has been a great privilege to work with him. I was lucky to have Andreea Nicoara, Tony Pantev, Stephen Shatz, J. Michael Steele (Statistics) instruct me in courses that have formed strong foundations. I want to thank Philip Gressman and Andreaa Nicoara for stimulating discussions and helpful suggestions that changed the way I was thinking about my very first research problem and led to my first ever Eureka! moment. Also, I’m grateful to Andreea Nicoara and J. Michael Steele for serving on my orals ’ committee, and Jerry Kazdan and J. Michael Steele for being a part of my defense committee. In my second year at Penn, I was a teaching assistant to Jerry Kazdan and Nakia Rimmer and learnt a lot from them about teaching mathematics.
Higher Order, Polar and Sz.Nagy’s Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circle
, 2014
"... Abstract. For random polynomials with i.i.d. (independent and identically distributed) zeros following any common probability distribution µ with support contained in the unit circle, the empirical measures of the zeros of their first and higher order derivatives will be proved to converge weakly ..."
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Abstract. For random polynomials with i.i.d. (independent and identically distributed) zeros following any common probability distribution µ with support contained in the unit circle, the empirical measures of the zeros of their first and higher order derivatives will be proved to converge weakly to µ a.s. (almost sure(ly)). This, in particular, completes a recent work of Subramanian on the first order derivative case where µ was assumed to be nonuniform. The same a.s. weak convergence will also be shown for polar and Sz.Nagy’s generalized derivatives, on some mild conditions. 1