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9,368
Complete discrete 2D Gabor transforms by neural networks for image analysis and compression
, 1988
"... A threelayered neural network is described for transforming twodimensional discrete signals into generalized nonorthogonal 2D “Gabor” representations for image analysis, segmentation, and compression. These transforms are conjoint spatial/spectral representations [lo], [15], which provide a comp ..."
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Cited by 478 (8 self)
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that the auxiliary orthogonalizing functions are nonlocal infinite series. In the present “neural network” approach, based
Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions
 J. MOL. BIOL
, 1997
"... We explore the ability of a simple simulated annealing procedure to assemble nativelike structures from fragments of unrelated protein structures with similar local sequences using Bayesian scoring functions. Environment and residue pair specific contributions to the scoring functions appear as the ..."
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Cited by 393 (70 self)
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as the first two terms in a series expansion for the residue probability distributions in the protein database; the decoupling of the distance and environment dependencies of the distributions resolves the major problems with current databasederived scoring functions noted by Thomas and Dill. The simulated
Long memory relationships and the aggregation of dynamic models
 Journal of Econometrics
, 1980
"... By aggregating simple. possibly dependent, dynamic microrelationships, it is shown that the aggregate series may have univariate longmemory models and obey integrated, or infinite length transfer function relationships. A longmemory time series model is one having spectrum or order 6 ” for small ..."
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Cited by 356 (2 self)
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By aggregating simple. possibly dependent, dynamic microrelationships, it is shown that the aggregate series may have univariate longmemory models and obey integrated, or infinite length transfer function relationships. A longmemory time series model is one having spectrum or order 6 ” for small
New Expansion and Infinite Series
"... Copyright c © 2014 Daiyuan Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Different from the Taylor polynomials, a new formul ..."
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formula for function expansion is proposed where the terms are not polynomials. A new infinite series based on the new formula is also proposed, and the new infinite series can keep some important properties of the original functions. Some forms of remainder are also presented for analysis
Series and Infinite Products Related to Binary Expansion of Integers
, 1992
"... Various problems related to the binary expansion of integers are investigated. The ThueMorse sequence, which gives the parity of the number of 1's in the binary expansion of an integer, appears in several identities and constants. We illustrate techniques, based on Dirichlet series or elementar ..."
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Cited by 2 (0 self)
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Various problems related to the binary expansion of integers are investigated. The ThueMorse sequence, which gives the parity of the number of 1's in the binary expansion of an integer, appears in several identities and constants. We illustrate techniques, based on Dirichlet series
On Series Expansions of Capparelli’s Infinite Product
, 2003
"... Using Lie theory, Stefano Capparelli conjectured an interesting RogersRamanujan type partition identity in his 1988 Rutgers Ph.D. thesis. The first proof was given by George Andrews, using combinatorial methods. Later, Capparelli was able to provide a Lie theoretic proof. Most combinatorial Rogers ..."
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Cited by 2 (1 self)
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Ramanujan type identities (e.g. the GöllnitzGordon identities, Gordon’s combinatorial generalization of the RogersRamanujan identities, etc.) have an analytic counterpart. The main purpose of this paper is to provide two new series representations for the infinite product associated with Capparelli’s
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remar ..."
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Cited by 211 (52 self)
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associated with the trapezoidal rule and thus helps bound it. The greatest difficulty is approximately calculating the infinite series obtained from the inversion integral. Within this framework, lattice cdf's can be calculated from generating functions by finite sums without truncation. For other cdf
An Infinite Family of Engel Expansions of RogersRamanujan Type
 ADV. IN APPL. MATH
, 2000
"... The Extended Engel Expansion is an algorithm that leads to unique series expansions of qseries. Various examples related to classical partition theorems, including the RogersRamanujan identities, have been given recently. The object of this paper is to show that the new and elegant RogersRamanuja ..."
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Cited by 23 (6 self)
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The Extended Engel Expansion is an algorithm that leads to unique series expansions of qseries. Various examples related to classical partition theorems, including the RogersRamanujan identities, have been given recently. The object of this paper is to show that the new and elegant Rogers
A Generalized Representer Theorem
 In Proceedings of the Annual Conference on Computational Learning Theory
, 2001
"... Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in terms of the training examples. We generalize the theorem to a larger class of regularizers and ..."
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Cited by 222 (17 self)
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Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in terms of the training examples. We generalize the theorem to a larger class of regularizers
Results 1  10
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