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Generalized Uncertainty Relations:
, 1996
"... The quantummechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonicoscillator phase. We introduce a broader framework that allows us to derive quantummechanical limi ..."
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mechanical limits on the precision to which a parametere.g., elapsed timemay be determined via arbitrary data analysis of arbitrary measurements on N identically prepared quantum systems. The limits are expressed as generalized MandelstamTamm uncertainty relations, which involve the operator that generates
Generalized Uncertainty Relations: Theory, Examples,
, 1995
"... The quantummechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonicoscillator phase. We introduce a broader framework that allows us to derive quantummechanical limits ..."
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Cited by 19 (2 self)
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on the precision to which a parameter e.g., elapsed time may be determined via arbitrary data analysis of arbitrary measurements on N identically prepared quantum systems. The limits are expressed as generalized Mandelstam Tamm uncertainty relations, which involve the operator that generates displacements
Generalized Uncertainty Relations and Efficient Measurements in Quantum Systems
 Theoretical and Mathematical Physics
, 1976
"... Abstract. We consider two variants of a quantumstatistical generalization of the CramÃ©rRao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this inequality leads to a precise formulation of a general ..."
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Cited by 2 (1 self)
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generalized uncertainty principle for arbitrary states, in contrast to Helstromâ€™s variant [1] in which these relations are obtained only for pure states. A notion of canonical states is introduced and the lower mean square error bound is found for estimating of the parameters of canonical states
Generalized uncertainty relations and coherent and squeezed states
, 2000
"... Characteristic uncertainty relations and their related squeezed states are briefly reviewed and compared in accordance with the generalizations of three equivalent definitions of the canonical coherent states. The standard SU(1,1) coherent states are shown to be the unique states that minimize the S ..."
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Cited by 1 (0 self)
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Characteristic uncertainty relations and their related squeezed states are briefly reviewed and compared in accordance with the generalizations of three equivalent definitions of the canonical coherent states. The standard SU(1,1) coherent states are shown to be the unique states that minimize
Generalized Uncertainty Relations,Fundamental Length and Density Matrix
, 2002
"... states, mix states It was shown that if in Quantum Theory a fundamental length exists and a wellknown measurement procedure is used, then in this case there are not pure states in conventional sense. Moreover, density matrix at the Planck scale cannot be defined in the usual way, because in this ca ..."
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Cited by 2 (1 self)
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states, mix states It was shown that if in Quantum Theory a fundamental length exists and a wellknown measurement procedure is used, then in this case there are not pure states in conventional sense. Moreover, density matrix at the Planck scale cannot be defined in the usual way, because in this case density matrix trace is strongly less than one. Density matrix must be changed by a progenitrix or as we call it throughout this paper, density promatrix. This promatrix is a deformed density matrix, which at low energy limit turns to usual one. Below the explicit form of the deformation is described. Implications of obtained results are summarized as well as their application to the interpretation of Information Paradox on the Black Holes.
SupportLimited Generalized Uncertainty Relations on Fractional Fourier Transform
"... This paper investigates the generalized uncertainty principles of fractional Fourier transform (FRFT) for concentrated data in limited supports. The continuous and discrete generalized uncertainty relations, whose bounds are related to FRFT parameters and signal lengths, were derived in theory. The ..."
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This paper investigates the generalized uncertainty principles of fractional Fourier transform (FRFT) for concentrated data in limited supports. The continuous and discrete generalized uncertainty relations, whose bounds are related to FRFT parameters and signal lengths, were derived in theory
Generalized Autoregressive Conditional Heteroskedasticity
 JOURNAL OF ECONOMETRICS
, 1986
"... A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametri ..."
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Cited by 2288 (31 self)
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of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.
Uncertainty principles and ideal atomic decomposition
 IEEE Transactions on Information Theory
, 2001
"... Suppose a discretetime signal S(t), 0 t<N, is a superposition of atoms taken from a combined time/frequency dictionary made of spike sequences 1ft = g and sinusoids expf2 iwt=N) = p N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every d ..."
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Cited by 588 (19 self)
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discretetime signal can be represented as a superposition of spikes alone, or as a superposition of sinusoids alone, there is no unique way of writing S as a sum of spikes and sinusoids in general. We prove that if S is representable as a highly sparse superposition of atoms from this time
Learning probabilistic relational models
 In IJCAI
, 1999
"... A large portion of realworld data is stored in commercial relational database systems. In contrast, most statistical learning methods work only with "flat " data representations. Thus, to apply these methods, we are forced to convert our data into a flat form, thereby losing much ..."
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Cited by 619 (31 self)
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A large portion of realworld data is stored in commercial relational database systems. In contrast, most statistical learning methods work only with "flat " data representations. Thus, to apply these methods, we are forced to convert our data into a flat form, thereby losing much
Results 1  10
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