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223,263
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 456 (1 self)
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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
Singularity Detection And Processing With Wavelets
 IEEE Transactions on Information Theory
, 1992
"... Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavele ..."
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Cited by 590 (13 self)
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Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales
Timing Attacks on Implementations of DiffieHellman, RSA, DSS, and Other Systems
, 1996
"... By carefully measuring the amount of time required to perform private key operations, attackers may be able to find fixed DiffieHellman exponents, factor RSA keys, and break other cryptosystems. Against a vulnerable system, the attack is computationally inexpensive and often requires only known cip ..."
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Cited by 644 (3 self)
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By carefully measuring the amount of time required to perform private key operations, attackers may be able to find fixed DiffieHellman exponents, factor RSA keys, and break other cryptosystems. Against a vulnerable system, the attack is computationally inexpensive and often requires only known
Capacity of multiantenna Gaussian channels
 EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS
, 1999
"... We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such form ..."
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Cited by 2878 (6 self)
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We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate
Survey on Independent Component Analysis
 NEURAL COMPUTING SURVEYS
, 1999
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
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Cited by 2241 (104 self)
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of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes
Recovering High Dynamic Range Radiance Maps from Photographs
"... We present a method of recovering high dynamic range radiance maps from photographs taken with conventional imaging equipment. In our method, multiple photographs of the scene are taken with different amounts of exposure. Our algorithm uses these differently exposed photographs to recover the respon ..."
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Cited by 856 (15 self)
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the response function of the imaging process, up to factor of scale, using the assumption of reciprocity. With the known response function, the algorithm can fuse the multiple photographs into a single, high dynamic range radiance map whose pixel values are proportional to the true radiance values in the scene
Powerlaw distributions in empirical data
 ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111
, 2009
"... Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the t ..."
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Cited by 589 (7 self)
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in the tail of the distribution. In particular, standard methods such as leastsquares fitting are known to produce systematically biased estimates of parameters for powerlaw distributions and should not be used in most circumstances. Here we describe statistical techniques for making accurate parameter
Diversity and Multiplexing: A Fundamental Tradeoff in Multiple Antenna Channels
 IEEE Trans. Inform. Theory
, 2002
"... Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. In this paper, we propose the point of view that both types of gains can be simultaneously obtained for a given multiple antenna channel, but there is a fund ..."
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Cited by 1143 (20 self)
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Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. In this paper, we propose the point of view that both types of gains can be simultaneously obtained for a given multiple antenna channel, but there is a fundamental tradeo# between how much of each any coding scheme can get. For the richly scattered Rayleigh fading channel, we give a simple characterization of the optimal tradeo# curve and use it to evaluate the performance of existing multiple antenna schemes.
Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 534 (48 self)
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How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in and outdegree distributions, communities, smallworld phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) orO(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification, requires very few parameters (like the “flammability” of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.
A public key cryptosystem and a signature scheme based on discrete logarithms
 Adv. in Cryptology, SpringerVerlag
, 1985
"... AbstractA new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. I. ..."
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Cited by 1520 (0 self)
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AbstractA new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. I.
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