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184
A New Kind of Science
, 2002
"... “Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplit ..."
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Cited by 496 (0 self)
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“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplitudes you told me about, they’re so complicated and absurd, what makes you think those are right? Maybe they aren’t right. ’ Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out.” —Richard Feynman [1, p.161]
Why a diagram is (sometimes) worth ten thousand words
 Cognitive Science
, 1987
"... We distinguish diagrammatic from sentential paperandpencil representationsof information by developing alternative models of informationprocessing systems that are informationally equivalent and that can be characterized as sentential or diagrammatic. Sentential representations are sequential, li ..."
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Cited by 492 (1 self)
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We distinguish diagrammatic from sentential paperandpencil representationsof information by developing alternative models of informationprocessing systems that are informationally equivalent and that can be characterized as sentential or diagrammatic. Sentential representations are sequential, like the propositions in a text. Dlogrammotlc representations ore indexed by location in a plane. Diogrommatic representations also typically display information that is only implicit in sententiol representations and that therefore has to be computed, sometimes at great cost, to make it explicit for use. We then contrast the computational efficiency of these representotions for solving several illustrative problems in mothematics and physics. When two representotions are informationally equivolent, their computational efficiency depends on the informationprocessing operators that act on them. Two sets of operators may differ in their copobilities for recognizing patterns, in the inferences they con carry out directly, and in their control strategies (in portitular. the control of search). Diogrommotic ond sentential representations sup
Cellular motions and thermal fluctuations: The Brownian ratchet
 Biophys. J
, 1993
"... this paper we describe several such processes and present simple formulas for the velocity and force they generate. We shall call these machines "Brownian Ratchets" (BR) because rectified Brownian motion is fundamental to their operation. ..."
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Cited by 67 (13 self)
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this paper we describe several such processes and present simple formulas for the velocity and force they generate. We shall call these machines "Brownian Ratchets" (BR) because rectified Brownian motion is fundamental to their operation.
Gödel's Theorem and Information
, 1982
"... Gödel's theorem may be demonstrated using arguments having an informationtheoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the tr ..."
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Cited by 52 (6 self)
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Gödel's theorem may be demonstrated using arguments having an informationtheoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.
Blind Inverse Gamma Correction
"... This paper presents a technique for blindly estimating the amount of gamma correction in the absence of any calibration information or knowledge of the imaging device. The basic approach exploits the fact that gamma correction introduces specific higherorder correlations in the frequency domain. ..."
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Cited by 35 (0 self)
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This paper presents a technique for blindly estimating the amount of gamma correction in the absence of any calibration information or knowledge of the imaging device. The basic approach exploits the fact that gamma correction introduces specific higherorder correlations in the frequency domain. These correlations can be detected using tools from polyspectral analysis. The amount of gamma correction is then estimated by minimizing these correlations
What do laboratory experiments tell us about the real world
 Journal of Economic Perspectives
"... An important question facing experimental economists is whether behavior inside the laboratory is a good indicator of behavior outside the laboratory. We begin with a model that assumes the choices that individuals make depend not just on financial implications, but also on the nature and extent of ..."
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Cited by 34 (1 self)
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An important question facing experimental economists is whether behavior inside the laboratory is a good indicator of behavior outside the laboratory. We begin with a model that assumes the choices that individuals make depend not just on financial implications, but also on the nature and extent of scrutiny by others, the particular context in which a decision is embedded, and the manner in which participants are selected. To the extent that lab and naturallyoccurring environments systematically differ on any of these dimensions, the results obtained inside and outside the lab need not correspond. Based on theory and empirical evidence, we argue that lab experiments are a useful tool for generating qualitative insights, but are not wellsuited for obtaining deep structural parameter estimates. We conclude that the sharp dichotomy sometimes drawn between lab experiments and data generated in natural settings is a false one. Each approach has strengths and weaknesses, and a combination of the two is likely to provide deeper insights than either in isolation.
Experimental quantum teleportation
 Nature
, 1997
"... Quantum entanglement lies at the heart of new proposals for quantum communication and computation. Here we describe the recent experimental realization of quantum teleportation. ..."
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Cited by 28 (1 self)
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Quantum entanglement lies at the heart of new proposals for quantum communication and computation. Here we describe the recent experimental realization of quantum teleportation.
Energy Functions for Early Vision and Analog Networks.
 Biological Cybernetics
, 1987
"... This paper describes attempts to model the modules of early vision in terms of minimizing energy functions, in particular energy functions allowing discontinuities in the solution. It examines the success of using Hopfieldstyle analog networks for solving such problems. Finally it discusses the ..."
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Cited by 23 (2 self)
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This paper describes attempts to model the modules of early vision in terms of minimizing energy functions, in particular energy functions allowing discontinuities in the solution. It examines the success of using Hopfieldstyle analog networks for solving such problems. Finally it discusses the limitations of the energy function approach.
Statistical Mechanics: A Selective Review Of Two Central Issues
 Rev. Mod. Phys
, 1999
"... I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These phenomena are emergent collective properties not discernible in ..."
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Cited by 21 (0 self)
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I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These phenomena are emergent collective properties not discernible in the behavior of individual atoms. They are given precise and elegant mathematical formulations when the ratio between macroscopic and microscopic scales becomes very large. 1. Introduction Nature has a hierarchical structure, with time, length and energy scales ranging from the submicroscopic to the supergalactic. Surprisingly it is possible and in many cases essential to discuss these levels independentlyquarks are irrelevant for understanding protein folding and atoms are a distraction when studying ocean currents. Nevertheless, it is a central lesson of science, very successful in the past three hundred years, that there are no new fundamental laws, only new phenomena, as one goes up...