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Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 558 (0 self)
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] is a bounded interval in R, in modern language the original statement of the theorem was that L 2 ([a, b]) is complete and abstractly isomorphic to l 2. According to [Jah03, p. 385], the name “Hilbert space ” was first used in 1908 by A. Schönflies, apparently to refer to what we today call l 2. Von
A Learning Algorithm for Continually Running Fully Recurrent Neural Networks
, 1989
"... The exact form of a gradientfollowing learning algorithm for completely recurrent networks running in continually sampled time is derived and used as the basis for practical algorithms for temporal supervised learning tasks. These algorithms have: (1) the advantage that they do not require a precis ..."
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Cited by 534 (4 self)
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precisely defined training interval, operating while the network runs; and (2) the disadvantage that they require nonlocal communication in the network being trained and are computationally expensive. These algorithms are shown to allow networks having recurrent connections to learn complex tasks requiring
Tawards Credible Implementation of Inner Interval Operations
 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics. Volume 2 Numerical Mathematics
, 1997
"... This paper briefly outlines interval arithmetic, extended by four supplementary interval operations, discuss a source of numerical errors at the implementation of floatingpoint inner interval operations and shows different ways for their suppression. The goal is to make computations involving these ..."
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Cited by 1 (1 self)
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This paper briefly outlines interval arithmetic, extended by four supplementary interval operations, discuss a source of numerical errors at the implementation of floatingpoint inner interval operations and shows different ways for their suppression. The goal is to make computations involving
Interval Operations Involving NaNs
 Reliable Computing
, 1996
"... Ten years ago IEEE standard [1] for oatingpoint arithmetic became o cial. Each IEEE oatingpoint format supports: its own set of nite real numbers, 1, two distinguished values +0 and;0 and a set of special values called NaNs (NotaNumber). Arithmetic operations include operations on numeric, nonn ..."
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Cited by 11 (3 self)
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Ten years ago IEEE standard [1] for oatingpoint arithmetic became o cial. Each IEEE oatingpoint format supports: its own set of nite real numbers, 1, two distinguished values +0 and;0 and a set of special values called NaNs (NotaNumber). Arithmetic operations include operations on numeric, non
Capacity of a Mobile MultipleAntenna Communication Link in Rayleigh Flat Fading
"... We analyze a mobile wireless link comprising M transmitter and N receiver antennas operating in a Rayleigh flatfading environment. The propagation coefficients between every pair of transmitter and receiver antennas are statistically independent and unknown; they remain constant for a coherence int ..."
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Cited by 495 (22 self)
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We analyze a mobile wireless link comprising M transmitter and N receiver antennas operating in a Rayleigh flatfading environment. The propagation coefficients between every pair of transmitter and receiver antennas are statistically independent and unknown; they remain constant for a coherence
Software pipelining: An effective scheduling technique for VLIW machines
, 1988
"... This paper shows that software pipelining is an effective and viable scheduling technique for VLIW processors. In software pipelining, iterations of a loop in the source program are continuously initiated at constant intervals, before the preceding iterations complete. The advantage of software pipe ..."
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Cited by 581 (3 self)
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This paper shows that software pipelining is an effective and viable scheduling technique for VLIW processors. In software pipelining, iterations of a loop in the source program are continuously initiated at constant intervals, before the preceding iterations complete. The advantage of software
Polygonization of Nonmanifolds With the Aid of Interval Operators
, 2000
"... This paper introduces a general mechanism for finding the triangulated surface of nonmanifold implicit expressions, defined by boolean formulae, equations and inequalities. The approach is based on a simplicial subdivision scheme, combined with an interval operator approach. The algorithm simultane ..."
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Cited by 3 (0 self)
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This paper introduces a general mechanism for finding the triangulated surface of nonmanifold implicit expressions, defined by boolean formulae, equations and inequalities. The approach is based on a simplicial subdivision scheme, combined with an interval operator approach. The algorithm
Computation and Analysis of Multiple Structural Change Models.‖
 Journal of Applied Econometrics
, 2003
"... SUMMARY In a recent paper, Bai and Perron (1998) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the pro ..."
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Cited by 448 (6 self)
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of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This algorithm is based on the principle of dynamic programming and requires at most leastsquares operations of order O T 2 for any number
LevelSpacing Distributions and the Airy Kernel
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1994
"... Scaling levelspacing distribution functions in the "bulk of the spectrum" in random matrix models of N x N hermitian matrices and then going to the limit N — » oo leads to the Fredholm determinant of the sine kernel sinπ(x — y)/π(x — y). Similarly a scaling limit at the "edge o ..."
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Cited by 430 (24 self)
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single interval, of the Fredholm determinant in terms of a Painleve transcendent; the existence of a commuting differential operator; and the fact that this operator can be used in the derivation of asymptotics, for general n, of the probability that an interval contains precisely n eigenvalues.
Hierarchical Modelling and Analysis for Spatial Data. Chapman and Hall/CRC,
, 2004
"... Abstract Often, there are two streams in statistical research one developed by practitioners and other by main stream statisticians. Development of geostatistics is a very good example where pioneering work under realistic assumptions came from mining engineers whereas it is only now that statisti ..."
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Cited by 442 (45 self)
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in There is no doubt that the availability of cheap and powerful computers has increased the interest in ML applications. With spatially correlated data, the maximization of the likelihood requires considerable computer power mainly for two numerical operations: matrix inversion and maximization in multidimensional
Results 1  10
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6,858