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Determining Lyapunov Exponents from a Time Series

by Alan Wolf, Jack B. Swift, Harry L. Swinney, John A. Vastano - Physica , 1985
"... We present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of n ..."
Abstract - Cited by 495 (1 self) - Add to MetaCart
of nearby orbits in phase space. A system with one or more positive Lyapunov exponents is defined to be chaotic. Our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems: we monitor the long-term growth rate of small volume

Rendering of Surfaces from Volume Data

by Marc Levoy - IEEE COMPUTER GRAPHICS AND APPLICATIONS , 1988
"... The application of volume rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions is explored. Fitting of geometric primitives to the sampled data is not required. Images are formed by directly shading each sample and projecting it onto the picture ..."
Abstract - Cited by 875 (12 self) - Add to MetaCart
The application of volume rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions is explored. Fitting of geometric primitives to the sampled data is not required. Images are formed by directly shading each sample and projecting it onto

Next Century Challenges: Mobile Networking for “Smart Dust”

by J. M. Kahn, R. H. Katz , K. S. J. Pister , 1999
"... Large-scale networks of wireless sensors are becoming an active topic of research. Advances in hardware technology and engineering design have led to dramatic reductions in size, power consumption and cost for digital circuitry, wire-less communications and Micro ElectroMechanical Systems (MEMS). Th ..."
Abstract - Cited by 625 (1 self) - Add to MetaCart
the key elements of the emergent technology of “Smart Dust ” and outline the research challenges they present to the mobile networking and systems community, which must provide coherent connectivity to large numbers of mobile network nodes co-located within a small volume.

Illiquidity and stock returns: cross-section and time-series effects,

by Yakov Amihud - Journal of Financial Markets , 2002
"... Abstract This paper shows that over time, expected market illiquidity positively affects ex ante stock excess return, suggesting that expected stock excess return partly represents an illiquidity premium. This complements the cross-sectional positive return-illiquidity relationship. Also, stock ret ..."
Abstract - Cited by 864 (9 self) - Add to MetaCart
returns are negatively related over time to contemporaneous unexpected illiquidity. The illiquidity measure here is the average across stocks of the daily ratio of absolute stock return to dollar volume, which is easily obtained from daily stock data for long time series in most stock markets. Illiquidity

System architecture directions for networked sensors

by Jason Hill, Robert Szewczyk, Alec Woo, Seth Hollar, David Culler, Kristofer Pister - IN ARCHITECTURAL SUPPORT FOR PROGRAMMING LANGUAGES AND OPERATING SYSTEMS , 2000
"... Technological progress in integrated, low-power, CMOS communication devices and sensors makes a rich design space of networked sensors viable. They can be deeply embedded in the physical world or spread throughout our environment. The missing elements are an overall system architecture and a methodo ..."
Abstract - Cited by 1789 (58 self) - Add to MetaCart
Technological progress in integrated, low-power, CMOS communication devices and sensors makes a rich design space of networked sensors viable. They can be deeply embedded in the physical world or spread throughout our environment. The missing elements are an overall system architecture and a

Homological Algebra of Mirror Symmetry

by Maxim Kontsevich - in Proceedings of the International Congress of Mathematicians , 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
Abstract - Cited by 523 (3 self) - Add to MetaCart
Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual

On limits of wireless communications in a fading environment when using multiple antennas

by G. J. Foschini, M. J. Gans - Wireless Personal Communications , 1998
"... Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (M ..."
Abstract - Cited by 2426 (14 self) - Add to MetaCart
Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array

Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?

by Emmanuel J. Candès , Terence Tao , 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
Abstract - Cited by 1513 (20 self) - Add to MetaCart
-law), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude |f | (1) ≥ |f | (2) ≥... ≥ |f | (N), and define the weak-ℓp ball

The Capacity of Low-Density Parity-Check Codes Under Message-Passing Decoding

by Thomas J. Richardson, Rüdiger L. Urbanke , 2001
"... In this paper, we present a general method for determining the capacity of low-density parity-check (LDPC) codes under message-passing decoding when used over any binary-input memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly chos ..."
Abstract - Cited by 574 (9 self) - Add to MetaCart
chosen element of the given ensemble will achieve an arbitrarily small target probability of error with a probability that approaches one exponentially fast in the length of the code. (By concatenating with an appropriate outer code one can achieve a probability of error that approaches zero

Discrete Differential-Geometry Operators for Triangulated 2-Manifolds

by Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr , 2002
"... This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Vorono ..."
Abstract - Cited by 449 (14 self) - Add to MetaCart
Voronoi cells and the mixed Finite-Element/FiniteVolume method, and compare them to existing formulations. Building upon previous work in discrete geometry, these new operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting
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