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3,234,738
Determining Lyapunov Exponents from a Time Series
 Physica
, 1985
"... We present the first algorithms that allow the estimation of nonnegative 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 ..."
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Cited by 469 (1 self)
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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 longterm growth rate of small volume
Rendering of Surfaces from Volume Data
 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 ..."
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Cited by 863 (11 self)
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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”
, 1999
"... Largescale 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, wireless communications and Micro ElectroMechanical Systems (MEMS). Th ..."
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Cited by 615 (1 self)
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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 colocated within a small volume.
Illiquidity and Stock Returns: Crosssection and Timeseries Effects
 Journal of Financial Markets
, 2002
"... 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 crosssectional positive return–illiquidity relationship. Also, stock returns are n ..."
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Cited by 831 (8 self)
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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 affects more
System architecture directions for networked sensors
 IN ARCHITECTURAL SUPPORT FOR PROGRAMMING LANGUAGES AND OPERATING SYSTEMS
, 2000
"... Technological progress in integrated, lowpower, 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 ..."
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Cited by 1764 (58 self)
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Technological progress in integrated, lowpower, 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
 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 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 521 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau 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
 Wireless Personal Communications
, 1998
"... Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bitrates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multielement array (M ..."
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Cited by 2363 (14 self)
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Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bitrates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multielement array
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 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 ..."
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Cited by 1487 (20 self)
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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 weakℓp ball
The Capacity of LowDensity ParityCheck Codes Under MessagePassing Decoding
, 2001
"... In this paper, we present a general method for determining the capacity of lowdensity paritycheck (LDPC) codes under messagepassing decoding when used over any binaryinput memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly chos ..."
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Cited by 570 (9 self)
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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 DifferentialGeometry Operators for Triangulated 2Manifolds
, 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 ..."
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Cited by 445 (14 self)
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Voronoi cells and the mixed FiniteElement/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
Results 1  10
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