Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm

NASA Technical Reports Server (NTRS)

Brenner, Martin J.; Prazenica, Chad

2006-01-01

This report investigates the utility of the Hilbert Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this report is to demonstrate the potential applications of the Hilbert Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F-18 Active Aeroelastic Wing airplane, an Aerostructures Test Wing, and pitch plunge simulation.

Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm

NASA Technical Reports Server (NTRS)

Brenner, Marty; Prazenica, Chad

2005-01-01

This paper investigates the utility of the Hilbert-Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert-Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert-Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this paper is to demonstrate the potential applications of the Hilbert-Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized/online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F/A-18 Active Aeroelastic Wing aircraft, an Aerostructures Test Wing, and pitch-plunge simulation.

On Nth roots of positive operators

NASA Technical Reports Server (NTRS)

Brown, D. R.; Omalley, M. J.

1978-01-01

A bounded operator A on a Hilbert space H was positive. These operators were symmetric, and as such constitute a natural generalization of nonnegative real diagonal matrices. The following result is thus both well known and not surprising: A positive operator has a unique positive square root (under operator composition).

Characterizing resonant component in speech: A different view of tracking fundamental frequency

NASA Astrophysics Data System (ADS)

Dong, Bin

2017-05-01

Inspired by the nonlinearity and nonstationarity and the modulations in speech, Hilbert-Huang Transform and cyclostationarity analysis are employed to investigate the speech resonance in vowel in sequence. Cyclostationarity analysis is not directly manipulated on the target vowel, but on its intrinsic mode functions one by one. Thanks to the equivalence between the fundamental frequency in speech and the cyclic frequency in cyclostationarity analysis, the modulation intensity distributions of the intrinsic mode functions provide much information for the estimation of the fundamental frequency. To highlight the relationship between frequency and time, the pseudo-Hilbert spectrum is proposed to replace the Hilbert spectrum here. After contrasting the pseudo-Hilbert spectra of and the modulation intensity distributions of the intrinsic mode functions, it finds that there is usually one intrinsic mode function which works as the fundamental component of the vowel. Furthermore, the fundamental frequency of the vowel can be determined by tracing the pseudo-Hilbert spectrum of its fundamental component along the time axis. The later method is more robust to estimate the fundamental frequency, when meeting nonlinear components. Two vowels [a] and [i], picked up from a speech database FAU Aibo Emotion Corpus, are applied to validate the above findings.

Cohomologie des Groupes Localement Compacts et Produits Tensoriels Continus de Representations

ERIC Educational Resources Information Center

Guichardet, A.

1976-01-01

Contains few and sometimes incomplete proofs on continuous tensor products of Hilbert spaces and of group representations, and on the irreducibility of the latter. Theory of continuous tensor products of Hilbert Spaces is closely related to that of conditionally positive definite functions; it relies on the technique of symmetric Hilbert spaces,…

Robust Magnetotelluric Impedance Estimation

NASA Astrophysics Data System (ADS)

Sutarno, D.

2010-12-01

Robust magnetotelluric (MT) response function estimators are now in standard use by the induction community. Properly devised and applied, these have ability to reduce the influence of unusual data (outliers). The estimators always yield impedance estimates which are better than the conventional least square (LS) estimation because the `real' MT data almost never satisfy the statistical assumptions of Gaussian distribution and stationary upon which normal spectral analysis is based. This paper discuses the development and application of robust estimation procedures which can be classified as M-estimators to MT data. Starting with the description of the estimators, special attention is addressed to the recent development of a bounded-influence robust estimation, including utilization of the Hilbert Transform (HT) operation on causal MT impedance functions. The resulting robust performances are illustrated using synthetic as well as real MT data.

Device-Independent Tests of Classical and Quantum Dimensions

NASA Astrophysics Data System (ADS)

Gallego, Rodrigo; Brunner, Nicolas; Hadley, Christopher; Acín, Antonio

2010-12-01

We address the problem of testing the dimensionality of classical and quantum systems in a “black-box” scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension necessary to reproduce given measurement data. Furthermore, we generalize the concept of quantum dimension witnesses to arbitrary quantum systems, allowing one to place a lower bound on the Hilbert space dimension necessary to reproduce certain data. Illustrating these ideas, we provide simple examples of classical and quantum dimension witnesses.

Adaptive strategy for joint measurements

NASA Astrophysics Data System (ADS)

Uola, Roope; Luoma, Kimmo; Moroder, Tobias; Heinosaari, Teiko

2016-08-01

We develop a technique to find simultaneous measurements for noisy quantum observables in finite-dimensional Hilbert spaces. We use the method to derive lower bounds for the noise needed to make incompatible measurements jointly measurable. Using our strategy together with recent developments in the field of one-sided quantum information processing we show that the attained lower bounds are tight for various symmetric sets of quantum measurements. We use this characterisation to prove the existence of so called 4-Specker sets, i.e. sets of four incompatible observables with compatible subsets in the qubit case.

Application of the Hilbert-Huang Transform to Financial Data

NASA Technical Reports Server (NTRS)

Huang, Norden

2005-01-01

A paper discusses the application of the Hilbert-Huang transform (HHT) method to time-series financial-market data. The method was described, variously without and with the HHT name, in several prior NASA Tech Briefs articles and supporting documents. To recapitulate: The method is especially suitable for analyzing time-series data that represent nonstationary and nonlinear phenomena including physical phenomena and, in the present case, financial-market processes. The method involves the empirical mode decomposition (EMD), in which a complicated signal is decomposed into a finite number of functions, called "intrinsic mode functions" (IMFs), that admit well-behaved Hilbert transforms. The HHT consists of the combination of EMD and Hilbert spectral analysis. The local energies and the instantaneous frequencies derived from the IMFs through Hilbert transforms can be used to construct an energy-frequency-time distribution, denoted a Hilbert spectrum. The instant paper begins with a discussion of prior approaches to quantification of market volatility, summarizes the HHT method, then describes the application of the method in performing time-frequency analysis of mortgage-market data from the years 1972 through 2000. Filtering by use of the EMD is shown to be useful for quantifying market volatility.

Clifford coherent state transforms on spheres

NASA Astrophysics Data System (ADS)

Dang, Pei; Mourão, José; Nunes, João P.; Qian, Tao

2018-01-01

We introduce a one-parameter family of transforms, U(m)t , t > 0, from the Hilbert space of Clifford algebra valued square integrable functions on the m-dimensional sphere, L2(Sm , dσm) ⊗Cm+1, to the Hilbert spaces, ML2(R m + 1 ∖ { 0 } , dμt) , of solutions of the Euclidean Dirac equation on R m + 1 ∖ { 0 } which are square integrable with respect to appropriate measures, dμt. We prove that these transforms are unitary isomorphisms of the Hilbert spaces and are extensions of the Segal-Bargman coherent state transform, U(1) :L2(S1 , dσ1) ⟶ HL2(C ∖ { 0 } , dμ) , to higher dimensional spheres in the context of Clifford analysis. In Clifford analysis it is natural to replace the analytic continuation from Sm to SCm as in (Hall, 1994; Stenzel, 1999; Hall and Mitchell, 2002) by the Cauchy-Kowalewski extension from Sm to R m + 1 ∖ { 0 } . One then obtains a unitary isomorphism from an L2-Hilbert space to a Hilbert space of solutions of the Dirac equation, that is to a Hilbert space of monogenic functions.

Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2009-08-01

One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H ≠ H† is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our recent paper on bound states [Znojil M., SIGMA 5 (2009), 001, 19 pages, arXiv:0901.0700] is complemented by the text on scattering. An elementary example illustrates the feasibility of the resulting innovative theoretical recipe. A new family of the so called quasilocal inner products in Hilbert space is found to exist. Constructively, these products are all described in terms of certain non-equivalent short-range metric operators Θ ≠ I represented, in Runge-Kutta approximation, by (2R-1)-diagonal matrices.

High-speed spectral calibration by complex FIR filter in phase-sensitive optical coherence tomography.

PubMed

Kim, Sangmin; Raphael, Patrick D; Oghalai, John S; Applegate, Brian E

2016-04-01

Swept-laser sources offer a number of advantages for Phase-sensitive Optical Coherence Tomography (PhOCT). However, inter- and intra-sweep variability leads to calibration errors that adversely affect phase sensitivity. While there are several approaches to overcoming this problem, our preferred method is to simply calibrate every sweep of the laser. This approach offers high accuracy and phase stability at the expense of a substantial processing burden. In this approach, the Hilbert phase of the interferogram from a reference interferometer provides the instantaneous wavenumber of the laser, but is computationally expensive. Fortunately, the Hilbert transform may be approximated by a Finite Impulse-Response (FIR) filter. Here we explore the use of several FIR filter based Hilbert transforms for calibration, explicitly considering the impact of filter choice on phase sensitivity and OCT image quality. Our results indicate that the complex FIR filter approach is the most robust and accurate among those considered. It provides similar image quality and slightly better phase sensitivity than the traditional FFT-IFFT based Hilbert transform while consuming fewer resources in an FPGA implementation. We also explored utilizing the Hilbert magnitude of the reference interferogram to calculate an ideal window function for spectral amplitude calibration. The ideal window function is designed to carefully control sidelobes on the axial point spread function. We found that after a simple chromatic correction, calculating the window function using the complex FIR filter and the reference interferometer gave similar results to window functions calculated using a mirror sample and the FFT-IFFT Hilbert transform. Hence, the complex FIR filter can enable accurate and high-speed calibration of the magnitude and phase of spectral interferograms.

High-speed spectral calibration by complex FIR filter in phase-sensitive optical coherence tomography

PubMed Central

Kim, Sangmin; Raphael, Patrick D.; Oghalai, John S.; Applegate, Brian E.

2016-01-01

Swept-laser sources offer a number of advantages for Phase-sensitive Optical Coherence Tomography (PhOCT). However, inter- and intra-sweep variability leads to calibration errors that adversely affect phase sensitivity. While there are several approaches to overcoming this problem, our preferred method is to simply calibrate every sweep of the laser. This approach offers high accuracy and phase stability at the expense of a substantial processing burden. In this approach, the Hilbert phase of the interferogram from a reference interferometer provides the instantaneous wavenumber of the laser, but is computationally expensive. Fortunately, the Hilbert transform may be approximated by a Finite Impulse-Response (FIR) filter. Here we explore the use of several FIR filter based Hilbert transforms for calibration, explicitly considering the impact of filter choice on phase sensitivity and OCT image quality. Our results indicate that the complex FIR filter approach is the most robust and accurate among those considered. It provides similar image quality and slightly better phase sensitivity than the traditional FFT-IFFT based Hilbert transform while consuming fewer resources in an FPGA implementation. We also explored utilizing the Hilbert magnitude of the reference interferogram to calculate an ideal window function for spectral amplitude calibration. The ideal window function is designed to carefully control sidelobes on the axial point spread function. We found that after a simple chromatic correction, calculating the window function using the complex FIR filter and the reference interferometer gave similar results to window functions calculated using a mirror sample and the FFT-IFFT Hilbert transform. Hence, the complex FIR filter can enable accurate and high-speed calibration of the magnitude and phase of spectral interferograms. PMID:27446666

Instantaneous frequency time analysis of physiology signals: The application of pregnant women’s radial artery pulse signals

NASA Astrophysics Data System (ADS)

Su, Zhi-Yuan; Wang, Chuan-Chen; Wu, Tzuyin; Wang, Yeng-Tseng; Tang, Feng-Cheng

2008-01-01

This study used the Hilbert-Huang transform, a recently developed, instantaneous frequency-time analysis, to analyze radial artery pulse signals taken from women in their 36th week of pregnancy and after pregnancy. The acquired instantaneous frequency-time spectrum (Hilbert spectrum) is further compared with the Morlet wavelet spectrum. Results indicate that the Hilbert spectrum is especially suitable for analyzing the time series of non-stationary radial artery pulse signals since, in the Hilbert-Huang transform, signals are decomposed into different mode functions in accordance with signal’s local time scale. Therefore, the Hilbert spectrum contains more detailed information than the Morlet wavelet spectrum. From the Hilbert spectrum, we can see that radial artery pulse signals taken from women in their 36th week of pregnancy and after pregnancy have different patterns. This approach could be applied to facilitate non-invasive diagnosis of fetus’ physiological signals in the future.

On the Computation of Optimal Designs for Certain Time Series Models with Applications to Optimal Quantile Selection for Location or Scale Parameter Estimation.

DTIC Science & Technology

1981-07-01

process is observed over all of (0,1], the reproducing kernel Hilbert space (RKHS) techniques developed by Parzen (1961a, 1961b) 2 may be used to construct...covariance kernel,R, for the process (1.1) is the reproducing kernel for a reproducing kernel Hilbert space (RKHS) which will be denoted as H(R) (c.f...2.6), it is known that (c.f. Eubank, Smith and Smith (1981a, 1981b)), i) H(R) is a Hilbert function space consisting of functions which satisfy for fEH

Optical nonlinearities of excitonic states in atomically thin 2D transition metal dichalcogenides

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soh, Daniel Beom Soo

We calculated the optical nonlinearities of the atomically thin monolayer transition metal dichalcogenide material (particularly MoS 2), particularly for those linear and nonlinear transition processes that utilize the bound exciton states. We adopted the bound and the unbound exciton states as the basis for the Hilbert space, and derived all the dynamical density matrices that provides the induced current density, from which the nonlinear susceptibilities can be drawn order-by-order via perturbative calculations. We provide the nonlinear susceptibilities for the linear, the second-harmonic, the third-harmonic, and the kerr-type two-photon processes.

Scaled lattice fermion fields, stability bounds, and regularity

NASA Astrophysics Data System (ADS)

O'Carroll, Michael; Faria da Veiga, Paulo A.

2018-02-01

We consider locally gauge-invariant lattice quantum field theory models with locally scaled Wilson-Fermi fields in d = 1, 2, 3, 4 spacetime dimensions. The use of scaled fermions preserves Osterwalder-Seiler positivity and the spectral content of the models (the decay rates of correlations are unchanged in the infinite lattice). In addition, it also results in less singular, more regular behavior in the continuum limit. Precisely, we treat general fermionic gauge and purely fermionic lattice models in an imaginary-time functional integral formulation. Starting with a hypercubic finite lattice Λ ⊂(aZ ) d, a ∈ (0, 1], and considering the partition function of non-Abelian and Abelian gauge models (the free fermion case is included) neglecting the pure gauge interactions, we obtain stability bounds uniformly in the lattice spacing a ∈ (0, 1]. These bounds imply, at least in the subsequential sense, the existence of the thermodynamic (Λ ↗ (aZ ) d) and the continuum (a ↘ 0) limits. Specializing to the U(1) gauge group, the known non-intersecting loop expansion for the d = 2 partition function is extended to d = 3 and the thermodynamic limit of the free energy is shown to exist with a bound independent of a ∈ (0, 1]. In the case of scaled free Fermi fields (corresponding to a trivial gauge group with only the identity element), spectral representations are obtained for the partition function, free energy, and correlations. The thermodynamic and continuum limits of the free fermion free energy are shown to exist. The thermodynamic limit of n-point correlations also exist with bounds independent of the point locations and a ∈ (0, 1], and with no n! dependence. Also, a time-zero Hilbert-Fock space is constructed, as well as time-zero, spatially pointwise scaled fermion creation operators which are shown to be norm bounded uniformly in a ∈ (0, 1]. The use of our scaled fields since the beginning allows us to extract and isolate the singularities of the free energy when a ↘ 0.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

The Spectrum of the Billiard Laplacian of a Family of Random Billiards

NASA Astrophysics Data System (ADS)

Feres, Renato; Zhang, Hong-Kun

2010-12-01

Random billiards are billiard dynamical systems for which the reflection law giving the post-collision direction of a billiard particle as a function of the pre-collision direction is specified by a Markov (scattering) operator P. Billiards with microstructure are random billiards whose Markov operator is derived from a "microscopic surface structure" on the boundary of the billiard table. The microstructure in turn is defined in terms of what we call a billiard cellQ, the shape of which completely determines the operator P. This operator, defined on an appropriate Hilbert space, is bounded self-adjoint and, for the examples considered here, a Hilbert-Schmidt operator. A central problem in the statistical theory of such random billiards is to relate the geometric characteristics of Q and the spectrum of P. We show, for a particular family of billiard cell shapes parametrized by a scale invariant curvature K (Fig. 2), that the billiard Laplacian P- I is closely related to the ordinary spherical Laplacian, and indicate, by partly analytical and partly numerical means, how this provides asymptotic information about the spectrum of P for small values of K. It is shown, in particular, that the second moment of scattering about the incidence angle closely approximates the spectral gap of P.

The Riemann-Hilbert problem for nonsymmetric systems

NASA Astrophysics Data System (ADS)

Greenberg, W.; Zweifel, P. F.; Paveri-Fontana, S.

1991-12-01

A comparison of the Riemann-Hilbert problem and the Wiener-Hopf factorization problem arising in the solution of half-space singular integral equations is presented. Emphasis is on the factorization of functions lacking the reflection symmetry usual in transport theory.

Least square regularized regression in sum space.

PubMed

Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

2013-04-01

This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

On the definition of the time evolution operator for time-independent Hamiltonians in non-relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.

2017-09-01

The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.

Employing the Hilbert-Huang Transform to analyze observed natural complex signals: Calm wind meandering cases

NASA Astrophysics Data System (ADS)

Martins, Luis Gustavo Nogueira; Stefanello, Michel Baptistella; Degrazia, Gervásio Annes; Acevedo, Otávio Costa; Puhales, Franciano Scremin; Demarco, Giuliano; Mortarini, Luca; Anfossi, Domenico; Roberti, Débora Regina; Costa, Felipe Denardin; Maldaner, Silvana

2016-11-01

In this study we analyze natural complex signals employing the Hilbert-Huang spectral analysis. Specifically, low wind meandering meteorological data are decomposed into turbulent and non turbulent components. These non turbulent movements, responsible for the absence of a preferential direction of the horizontal wind, provoke negative lobes in the meandering autocorrelation functions. The meandering characteristic time scales (meandering periods) are determined from the spectral peak provided by the Hilbert-Huang marginal spectrum. The magnitudes of the temperature and horizontal wind meandering period obtained agree with the results found from the best fit of the heuristic meandering autocorrelation functions. Therefore, the new method represents a new procedure to evaluate meandering periods that does not employ mathematical expressions to represent observed meandering autocorrelation functions.

Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter.

PubMed

Zhuang, Leimeng; Khan, Muhammad Rezaul; Beeker, Willem; Leinse, Arne; Heideman, René; Roeloffzen, Chris

2012-11-19

We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance analysis in both frequency and time domain validates that the proposed implementation provides a good approximation to an ideal fractional Hilbert transformer. This is also experimentally verified by an electrical S₂₁ response characterization performed on a waveguide realization of a ring resonator. The waveguide-based structure allows the proposed Hilbert transformer to be integrated together with other building blocks on a photonic integrated circuit to create various system-level functionalities for on-chip microwave photonic signal processors. As an example, a circuit consisting of a splitter and a ring resonator has been realized which can perform on-chip phase control of microwave signals generated by means of optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range. For these functionalities, this simple and on-chip solution is considered to be practical, particularly when operating together with a dual-frequency laser. To our best knowledge, this is the first-time on-chip demonstration where ring resonators are employed to perform phase control functionalities for optical generation of microwave signals by means of optical heterodyning.

Terahertz bandwidth photonic Hilbert transformers based on synthesized planar Bragg grating fabrication.

PubMed

Sima, Chaotan; Gates, J C; Holmes, C; Mennea, P L; Zervas, M N; Smith, P G R

2013-09-01

Terahertz bandwidth photonic Hilbert transformers are proposed and experimentally demonstrated. The integrated device is fabricated via a direct UV grating writing technique in a silica-on-silicon platform. The photonic Hilbert transformer operates at bandwidths of up to 2 THz (~16 nm) in the telecom band, a 10-fold greater bandwidth than any previously reported experimental approaches. Achieving this performance requires detailed knowledge of the system transfer function of the direct UV grating writing technique; this allows improved linearity and yields terahertz bandwidth Bragg gratings with improved spectral quality. By incorporating a flat-top reflector and Hilbert grating with a waveguide coupler, an ultrawideband all-optical single-sideband filter is demonstrated.

Constraint-Free Theories of Gravitation

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.; Robinson, R. Steve; Wahlquist, Hugo D.

1998-01-01

Lovelock actions (more precisely, extended Gauss-Bonnet forms) when varied as Cartan forms on subspaces of higher dimensional flat Riemannian manifolds, generate well set, causal exterior differential systems. In particular, the Einstein- Hilbert action 4-form, varied on a 4 dimensional subspace of E(sub 10) yields a well set generalized theory of gravity having no constraints. Rcci-flat solutions are selected by initial conditions on a bounding 3-space.

Bell-correlated activable bound entanglement in multiqubit systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bandyopadhyay, Somshubhro; Chattopadhyay, Indrani; Roychowdhury, Vwani

2005-06-15

We show that the Hilbert space of even number ({>=}4) of qubits can always be decomposed as a direct sum of four orthogonal subspaces such that the normalized projectors onto the subspaces are activable bound entangled (ABE) states. These states also show a surprising recursive relation in the sense that the states belonging to 2N+2 qubits are Bell correlated to the states of 2N qubits; hence, we refer to these states as Bell-correlated ABE (BCABE) states. We also study the properties of noisy BCABE states and show that they are very similar to that of two qubit Bell-diagonal states.

Noncommuting observables in quantum detection and estimation theory

NASA Technical Reports Server (NTRS)

Helstrom, C. W.

1972-01-01

Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a larger Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.

Quantum theory of the generalised uncertainty principle

NASA Astrophysics Data System (ADS)

Bruneton, Jean-Philippe; Larena, Julien

2017-04-01

We extend significantly previous works on the Hilbert space representations of the generalized uncertainty principle (GUP) in 3 + 1 dimensions of the form [X_i,P_j] = i F_{ij} where F_{ij} = f({{P}}^2) δ _{ij} + g({{P}}^2) P_i P_j for any functions f. However, we restrict our study to the case of commuting X's. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heisenberg algebra of operators and an aquadratic Hamiltonian, provided the boost sector of the symmetries is modified accordingly. The theory can also be mapped to a completely standard Quantum Mechanics with standard symmetries, but with momentum dependent position operators. Next, we investigate the Hilbert space representations of these algebraically equivalent models, and focus specifically on whether they exhibit a minimal length. We carry the functional analysis of the various operators involved, and show that the appearance of a minimal length critically depends on the relationship between the generators of translations and the physical momenta. In particular, because this relationship is preserved by the algebraic mapping presented in this paper, when a minimal length is present in the standard GUP, it is also present in the corresponding Aquadratic Hamiltonian formulation, despite the perfectly standard algebra of this model. In general, a minimal length requires bounded generators of translations, i.e. a specific kind of quantization of space, and this depends on the precise shape of the function f defined previously. This result provides an elegant and unambiguous classification of which universal quantum gravity corrections lead to the emergence of a minimal length.

Hilbert transform evaluation for electron-phonon self-energies

NASA Astrophysics Data System (ADS)

Bevilacqua, Giuseppe; Menichetti, Guido; Pastori Parravicini, Giuseppe

2016-01-01

The electron tunneling current through nanostructures is considered in the presence of the electron-phonon interactions. In the Keldysh nonequilibrium formalism, the lesser, greater, advanced and retarded self-energies components are expressed by means of appropriate Langreth rules. We discuss the key role played by the entailed Hilbert transforms, and provide an analytic way for their evaluation. Particular attention is given to the current-conserving lowest-order-expansion for the treament of the electron-phonon interaction; by means of an appropriate elaboration of the analytic properties and pole structure of the Green's functions and of the Fermi functions, we arrive at a surprising simple, elegant, fully analytic and easy-to-use expression of the Hilbert transforms and involved integrals in the energy domain.

Rational Solutions of the Painlevé-II Equation Revisited

NASA Astrophysics Data System (ADS)

Miller, Peter D.; Sheng, Yue

2017-08-01

The rational solutions of the Painlevé-II equation appear in several applications and are known to have many remarkable algebraic and analytic properties. They also have several different representations, useful in different ways for establishing these properties. In particular, Riemann-Hilbert representations have proven to be useful for extracting the asymptotic behavior of the rational solutions in the limit of large degree (equivalently the large-parameter limit). We review the elementary properties of the rational Painlevé-II functions, and then we describe three different Riemann-Hilbert representations of them that have appeared in the literature: a representation by means of the isomonodromy theory of the Flaschka-Newell Lax pair, a second representation by means of the isomonodromy theory of the Jimbo-Miwa Lax pair, and a third representation found by Bertola and Bothner related to pseudo-orthogonal polynomials. We prove that the Flaschka-Newell and Bertola-Bothner Riemann-Hilbert representations of the rational Painlevé-II functions are explicitly connected to each other. Finally, we review recent results describing the asymptotic behavior of the rational Painlevé-II functions obtained from these Riemann-Hilbert representations by means of the steepest descent method.

Highly Entangled, Non-random Subspaces of Tensor Products from Quantum Groups

NASA Astrophysics Data System (ADS)

Brannan, Michael; Collins, Benoît

2018-03-01

In this paper we describe a class of highly entangled subspaces of a tensor product of finite-dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values and obtain lower bounds for the minimum output entropy of the corresponding quantum channels. An application to the construction of d-positive maps on matrix algebras is also presented.

Chain of point-like potentials in Script R3 and infiniteness of the number of bound states

NASA Astrophysics Data System (ADS)

Boitsev, A. A.; Popov, I. Yu; Sokolov, O. V.

2014-10-01

Infinite chain of point-like potentials having the Hamiltonian with infinite number of eigenvalues below the continuous spectrum is constructed. The background of the model is the theory of self-adjoint extensions of symmetric operators in the Hilbert space. The analogous example of the Hamiltonian is obtained for the system of three-dimensional waveguides coupled through point-like windows.

Thermalization Time Bounds for Pauli Stabilizer Hamiltonians

NASA Astrophysics Data System (ADS)

Temme, Kristan

2017-03-01

We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.

Wavelet SVM in Reproducing Kernel Hilbert Space for hyperspectral remote sensing image classification

NASA Astrophysics Data System (ADS)

Du, Peijun; Tan, Kun; Xing, Xiaoshi

2010-12-01

Combining Support Vector Machine (SVM) with wavelet analysis, we constructed wavelet SVM (WSVM) classifier based on wavelet kernel functions in Reproducing Kernel Hilbert Space (RKHS). In conventional kernel theory, SVM is faced with the bottleneck of kernel parameter selection which further results in time-consuming and low classification accuracy. The wavelet kernel in RKHS is a kind of multidimensional wavelet function that can approximate arbitrary nonlinear functions. Implications on semiparametric estimation are proposed in this paper. Airborne Operational Modular Imaging Spectrometer II (OMIS II) hyperspectral remote sensing image with 64 bands and Reflective Optics System Imaging Spectrometer (ROSIS) data with 115 bands were used to experiment the performance and accuracy of the proposed WSVM classifier. The experimental results indicate that the WSVM classifier can obtain the highest accuracy when using the Coiflet Kernel function in wavelet transform. In contrast with some traditional classifiers, including Spectral Angle Mapping (SAM) and Minimum Distance Classification (MDC), and SVM classifier using Radial Basis Function kernel, the proposed wavelet SVM classifier using the wavelet kernel function in Reproducing Kernel Hilbert Space is capable of improving classification accuracy obviously.

Averaging of random walks and shift-invariant measures on a Hilbert space

NASA Astrophysics Data System (ADS)

Sakbaev, V. Zh.

2017-06-01

We study random walks in a Hilbert space H and representations using them of solutions of the Cauchy problem for differential equations whose initial conditions are numerical functions on H. We construct a finitely additive analogue of the Lebesgue measure: a nonnegative finitely additive measure λ that is defined on a minimal subset ring of an infinite-dimensional Hilbert space H containing all infinite-dimensional rectangles with absolutely converging products of the side lengths and is invariant under shifts and rotations in H. We define the Hilbert space H of equivalence classes of complex-valued functions on H that are square integrable with respect to a shift-invariant measure λ. Using averaging of the shift operator in H over random vectors in H with a distribution given by a one-parameter semigroup (with respect to convolution) of Gaussian measures on H, we define a one-parameter semigroup of contracting self-adjoint transformations on H, whose generator is called the diffusion operator. We obtain a representation of solutions of the Cauchy problem for the Schrödinger equation whose Hamiltonian is the diffusion operator.

Constraining the noncommutative spectral action via astrophysical observations.

PubMed

Nelson, William; Ochoa, Joseph; Sakellariadou, Mairi

2010-09-03

The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of particle physics in this setting, in addition to a modified version of Einstein-Hilbert gravity. In this Letter we use observations of pulsar timings, assuming that no deviation from general relativity has been observed, to constrain the gravitational sector of this theory. While the bounds on the coupling constants remain rather weak, they are comparable to existing bounds on deviations from general relativity in other settings and are likely to be further constrained by future observations.

Empirical mode decomposition for analyzing acoustical signals

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2005-01-01

The present invention discloses a computer implemented signal analysis method through the Hilbert-Huang Transformation (HHT) for analyzing acoustical signals, which are assumed to be nonlinear and nonstationary. The Empirical Decomposition Method (EMD) and the Hilbert Spectral Analysis (HSA) are used to obtain the HHT. Essentially, the acoustical signal will be decomposed into the Intrinsic Mode Function Components (IMFs). Once the invention decomposes the acoustic signal into its constituting components, all operations such as analyzing, identifying, and removing unwanted signals can be performed on these components. Upon transforming the IMFs into Hilbert spectrum, the acoustical signal may be compared with other acoustical signals.

The Baker-Akhiezer Function and Factorization of the Chebotarev-Khrapkov Matrix

NASA Astrophysics Data System (ADS)

Antipov, Yuri A.

2014-10-01

A new technique is proposed for the solution of the Riemann-Hilbert problem with the Chebotarev-Khrapkov matrix coefficient {G(t) = α1(t)I + α2(t)Q(t)} , {α1(t), α2(t) in H(L)} , I = diag{1, 1}, Q(t) is a {2×2} zero-trace polynomial matrix. This problem has numerous applications in elasticity and diffraction theory. The main feature of the method is the removal of essential singularities of the solution to the associated homogeneous scalar Riemann-Hilbert problem on the hyperelliptic surface of an algebraic function by means of the Baker-Akhiezer function. The consequent application of this function for the derivation of the general solution to the vector Riemann-Hilbert problem requires the finding of the {ρ} zeros of the Baker-Akhiezer function ({ρ} is the genus of the surface). These zeros are recovered through the solution to the associated Jacobi problem of inversion of abelian integrals or, equivalently, the determination of the zeros of the associated degree-{ρ} polynomial and solution of a certain linear algebraic system of {ρ} equations.

The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

NASA Astrophysics Data System (ADS)

Borzov, V. V.; Damaskinsky, E. V.

2014-10-01

In the previous works of Borzov and Damaskinsky ["Chebyshev-Koornwinder oscillator," Theor. Math. Phys. 175(3), 765-772 (2013)] and ["Ladder operators for Chebyshev-Koornwinder oscillator," in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.

Quantum one-way permutation over the finite field of two elements

NASA Astrophysics Data System (ADS)

de Castro, Alexandre

2017-06-01

In quantum cryptography, a one-way permutation is a bounded unitary operator U:{H} → {H} on a Hilbert space {H} that is easy to compute on every input, but hard to invert given the image of a random input. Levin (Probl Inf Transm 39(1):92-103, 2003) has conjectured that the unitary transformation g(a,x)=(a,f(x)+ax), where f is any length-preserving function and a,x \\in {GF}_{{2}^{\\Vert x\\Vert }}, is an information-theoretically secure operator within a polynomial factor. Here, we show that Levin's one-way permutation is provably secure because its output values are four maximally entangled two-qubit states, and whose probability of factoring them approaches zero faster than the multiplicative inverse of any positive polynomial poly( x) over the Boolean ring of all subsets of x. Our results demonstrate through well-known theorems that existence of classical one-way functions implies existence of a universal quantum one-way permutation that cannot be inverted in subexponential time in the worst case.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Borzov, V. V., E-mail: borzov.vadim@yandex.ru; Damaskinsky, E. V., E-mail: evd@pdmi.ras.ru

In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which ismore » bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.« less

Strong majorization entropic uncertainty relations

NASA Astrophysics Data System (ADS)

Rudnicki, Łukasz; Puchała, Zbigniew; Życzkowski, Karol

2014-05-01

We analyze entropic uncertainty relations in a finite-dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the recent bounds by Coles and Piani [P. Coles and M. Piani, Phys. Rev. A 89, 022112 (2014), 10.1103/PhysRevA.89.022112], which are known to be stronger than the well-known result of Maassen and Uffink [H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. 60, 1103 (1988), 10.1103/PhysRevLett.60.1103]. Furthermore, we find a bound based on majorization techniques, which also happens to be stronger than the recent results involving the largest singular values of submatrices of the unitary matrix connecting both bases. The first set of bounds gives better results for unitary matrices close to the Fourier matrix, while the second one provides a significant improvement in the opposite sectors. Some results derived admit generalization to arbitrary mixed states, so that corresponding bounds are increased by the von Neumann entropy of the measured state. The majorization approach is finally extended to the case of several measurements.

Functional brain abnormalities in major depressive disorder using the Hilbert-Huang transform.

PubMed

Yu, Haibin; Li, Feng; Wu, Tong; Li, Rui; Yao, Li; Wang, Chuanyue; Wu, Xia

2018-02-09

Major depressive disorder is a common disease worldwide, which is characterized by significant and persistent depression. Non-invasive accessory diagnosis of depression can be performed by resting-state functional magnetic resonance imaging (rs-fMRI). However, the fMRI signal may not satisfy linearity and stationarity. The Hilbert-Huang transform (HHT) is an adaptive time-frequency localization analysis method suitable for nonlinear and non-stationary signals. The objective of this study was to apply the HHT to rs-fMRI to find the abnormal brain areas of patients with depression. A total of 35 patients with depression and 37 healthy controls were subjected to rs-fMRI. The HHT was performed to extract the Hilbert-weighted mean frequency of the rs-fMRI signals, and multivariate receiver operating characteristic analysis was applied to find the abnormal brain regions with high sensitivity and specificity. We observed differences in Hilbert-weighted mean frequency between the patients and healthy controls mainly in the right hippocampus, right parahippocampal gyrus, left amygdala, and left and right caudate nucleus. Subsequently, the above-mentioned regions were included in the results obtained from the compared region homogeneity and the fractional amplitude of low frequency fluctuation method. We found brain regions with differences in the Hilbert-weighted mean frequency, and examined their sensitivity and specificity, which suggested a potential neuroimaging biomarker to distinguish between patients with depression and healthy controls. We further clarified the pathophysiological abnormality of these regions for the population with major depressive disorder.

Evolution inclusions governed by the difference of two subdifferentials in reflexive Banach spaces

NASA Astrophysics Data System (ADS)

Akagi, Goro; Ôtani, Mitsuharu

The existence of strong solutions of Cauchy problem for the following evolution equation du(t)/dt+∂ϕ1(u(t))-∂ϕ2(u(t))∋f(t) is considered in a real reflexive Banach space V, where ∂ϕ1 and ∂ϕ2 are subdifferential operators from V into its dual V*. The study for this type of problems has been done by several authors in the Hilbert space setting. The scope of our study is extended to the V- V* setting. The main tool employed here is a certain approximation argument in a Hilbert space and for this purpose we need to assume that there exists a Hilbert space H such that V⊂H≡H*⊂V* with densely defined continuous injections. The applicability of our abstract framework will be exemplified in discussing the existence of solutions for the nonlinear heat equation: ut(x,t)-Δpu(x,t)-|u|u(x,t)=f(x,t), x∈Ω, t>0, u|=0, where Ω is a bounded domain in RN. In particular, the existence of local (in time) weak solution is shown under the subcritical growth condition q

Exact dimension estimation of interacting qubit systems assisted by a single quantum probe

NASA Astrophysics Data System (ADS)

Sone, Akira; Cappellaro, Paola

2017-12-01

Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine, e.g., the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics, and observables. Here we propose a more practical strategy that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the system dimension can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved.

Quantum Entanglement in Random Physical States

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Santra, Siddhartha; Zanardi, Paolo

2012-07-01

Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate—among other things—the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many-body system are not physically accessible. We define physical ensembles of states acting on random factorized states by a circuit of length k of random and independent unitaries with local support. We study the typicality of entanglement by means of the purity of the reduced state. We find that for a time k=O(1), the typical purity obeys the area law. Thus, the upper bounds for area law are actually saturated, on average, with a variance that goes to zero for large systems. Similarly, we prove that by means of local evolution a subsystem of linear dimensions L is typically entangled with a volume law when the time scales with the size of the subsystem. Moreover, we show that for large values of k the reduced state becomes very close to the completely mixed state.

Topologies on quantum topoi induced by quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Kunji

2013-07-15

In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantummore » topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.« less

Note on a Family of Monotone Quantum Relative Entropies

NASA Astrophysics Data System (ADS)

Deuchert, Andreas; Hainzl, Christian; Seiringer, Robert

2015-10-01

Given a convex function and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691-705, 2014) the relative entropy defined by . Among other things, they prove that the so-defined quantity is monotone if and only if is operator monotone. The monotonicity is then used to properly define for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections with strongly, the limit is shown to exist and to be independent of the sequence of projections . The question whether this sequence converges to its "obvious" limit, namely , has been left open. We answer this question in principle affirmatively and show that . If the operators A and B are regular enough, that is ( A - B), and are trace-class, the identity holds.

Elementary operators on self-adjoint operators

NASA Astrophysics Data System (ADS)

Molnar, Lajos; Semrl, Peter

2007-03-01

Let H be a Hilbert space and let and be standard *-operator algebras on H. Denote by and the set of all self-adjoint operators in and , respectively. Assume that and are surjective maps such that M(AM*(B)A)=M(A)BM(A) and M*(BM(A)B)=M*(B)AM*(B) for every pair , . Then there exist an invertible bounded linear or conjugate-linear operator and a constant c[set membership, variant]{-1,1} such that M(A)=cTAT*, , and M*(B)=cT*BT, .

Generation of dark hollow beams by using a fractional radial Hilbert transform system

NASA Astrophysics Data System (ADS)

Xie, Qiansen; Zhao, Daomu

2007-07-01

The radial Hilbert transform has been extend to the fractional field, which could be called the fractional radial Hilbert transform (FRHT). Using edge-enhancement characteristics of this transform, we convert a Gaussian light beam into a variety of dark hollow beams (DHBs). Based on the fact that a hard-edged aperture can be expanded approximately as a finite sum of complex Gaussian functions, the analytical expression of a Gaussian beam passing through a FRHT system has been derived. As a numerical example, the properties of the DHBs with different fractional orders are illustrated graphically. The calculation results obtained by use of the analytical method and the integral method are also compared.

Computer implemented empirical mode decomposition method, apparatus and article of manufacture

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

1999-01-01

A computer implemented physical signal analysis method is invented. This method includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum.

Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.

PubMed

Huang, Yongxiang; Biferale, Luca; Calzavarini, Enrico; Sun, Chao; Toschi, Federico

2013-04-01

The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].

Towards a second law for Lovelock theories

NASA Astrophysics Data System (ADS)

Bhattacharyya, Sayantani; Haehl, Felix M.; Kundu, Nilay; Loganayagam, R.; Rangamani, Mukund

2017-03-01

In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking's area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge construction does not provide. We propose such an entropy function for the family of Lovelock theories, treating the higher derivative terms as perturbations to the Einstein-Hilbert theory. Working around a dynamical black hole solution, and making no assumptions about the amplitude of departure from equilibrium, we construct a candidate entropy functional valid to all orders in the low energy effective field theory. This entropy functional satisfies a second law, modulo a certain subtle boundary term, which deserves further investigation in non-spherically symmetric situations.

Thermodynamic limit of random partitions and dispersionless Toda hierarchy

NASA Astrophysics Data System (ADS)

Takasaki, Kanehisa; Nakatsu, Toshio

2012-01-01

We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physical observables correspond to external potentials in the statistical model. The partition function is reformulated in terms of the density function of Maya diagrams. The thermodynamic limit is governed by a limit shape of Young diagrams associated with dominant terms in the partition function. The limit shape is characterized by a variational problem, which is further converted to a scalar-valued Riemann-Hilbert problem. This Riemann-Hilbert problem is solved with the aid of a complex curve, which may be thought of as the Seiberg-Witten curve of the deformed U(1) gauge theory. This solution of the Riemann-Hilbert problem is identified with a special solution of the dispersionless Toda hierarchy that satisfies a pair of generalized string equations. The generalized string equations for the 5D gauge theory are shown to be related to hidden symmetries of the statistical model. The prepotential and the Seiberg-Witten differential are also considered.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Müller-Hermes, Alexander, E-mail: muellerh@ma.tum.de; Wolf, Michael M., E-mail: m.wolf@tum.de; Reeb, David, E-mail: reeb.qit@gmail.com

We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transposemore » bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task.« less

Hilbert and Blaschke phases in the temporal coherence function of stationary broadband light.

PubMed

Fernández-Pousa, Carlos R; Maestre, Haroldo; Torregrosa, Adrián J; Capmany, Juan

2008-10-27

We show that the minimal phase of the temporal coherence function gamma (tau) of stationary light having a partially-coherent symmetric spectral peak can be computed as a relative logarithmic Hilbert transform of its amplitude with respect to its asymptotic behavior. The procedure is applied to experimental data from amplified spontaneous emission broadband sources in the 1.55 microm band with subpicosecond coherence times, providing examples of degrees of coherence with both minimal and non-minimal phase. In the latter case, the Blaschke phase is retrieved and the position of the Blaschke zeros determined.

A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertola, Marco, E-mail: Marco.Bertola@concordia.ca; Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec H3C 3J7; SISSA/ISAS, via Bonomea 265, Trieste

2015-06-15

Two-phase solutions of focusing NLS equation are classically constructed out of an appropriate Riemann surface of genus two and expressed in terms of the corresponding theta-function. We show here that in a certain limiting regime, such solutions reduce to some elementary ones called “Solitons on unstable condensate.” This degeneration turns out to be conveniently studied by means of basic tools from the theory of Riemann-Hilbert problems. In particular, no acquaintance with Riemann surfaces and theta-function is required for such analysis.

Improved specimen reconstruction by Hilbert phase contrast tomography.

PubMed

Barton, Bastian; Joos, Friederike; Schröder, Rasmus R

2008-11-01

The low signal-to-noise ratio (SNR) in images of unstained specimens recorded with conventional defocus phase contrast makes it difficult to interpret 3D volumes obtained by electron tomography (ET). The high defocus applied for conventional tilt series generates some phase contrast but leads to an incomplete transfer of object information. For tomography of biological weak-phase objects, optimal image contrast and subsequently an optimized SNR are essential for the reconstruction of details such as macromolecular assemblies at molecular resolution. The problem of low contrast can be partially solved by applying a Hilbert phase plate positioned in the back focal plane (BFP) of the objective lens while recording images in Gaussian focus. Images recorded with the Hilbert phase plate provide optimized positive phase contrast at low spatial frequencies, and the contrast transfer in principle extends to the information limit of the microscope. The antisymmetric Hilbert phase contrast (HPC) can be numerically converted into isotropic contrast, which is equivalent to the contrast obtained by a Zernike phase plate. Thus, in-focus HPC provides optimal structure factor information without limiting effects of the transfer function. In this article, we present the first electron tomograms of biological specimens reconstructed from Hilbert phase plate image series. We outline the technical implementation of the phase plate and demonstrate that the technique is routinely applicable for tomography. A comparison between conventional defocus tomograms and in-focus HPC volumes shows an enhanced SNR and an improved specimen visibility for in-focus Hilbert tomography.

Structured functional additive regression in reproducing kernel Hilbert spaces.

PubMed

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2014-06-01

Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.

Inverse Problems and Imaging (Pitman Research Notes in Mathematics Series Number 245)

DTIC Science & Technology

1991-01-01

Multiparamcter spectral theory in Hilbert space functional differential cquations B D Sleeman F Kappel and W Schappacher 24 Mathematical modelling...techniques 49 Sequence spaces R Aris W 11 Ruckle 25 Singular points of smooth mappings 50 Recent contributions to nonlinear C G Gibson partial...of convergence in the central limit T Husain theorem 86 Hamilton-Jacobi equations in Hilbert spaces Peter Hall V Barbu and G Da Prato 63 Solution of

Homogenization via Sequential Projection to Nested Subspaces Spanned by Orthogonal Scaling and Wavelet Orthonormal Families of Functions

DTIC Science & Technology

2008-07-01

operators in Hilbert spaces. The homogenization procedure through successive multi- resolution projections is presented, followed by a numerical example of...is intended to be essentially self-contained. The mathematical ( Greenberg 1978; Gilbert 2006) and signal processing (Strang and Nguyen 1995...literature listed in the references. The ideas behind multi-resolution analysis unfold from the theory of linear operators in Hilbert spaces (Davis 1975

Spherical harmonics and rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Celeghini, E.; Gadella, M.; del Olmo, M. A.

2018-05-01

This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3, 2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of rigged Hilbert spaces. We prove the continuity of relevant operators and the operators in the algebras spanned by them using appropriate topologies on our spaces. Finally, we discuss the properties of the functionals that form the continuous basis.

Experimental validation of a structural damage detection method based on marginal Hilbert spectrum

NASA Astrophysics Data System (ADS)

Banerji, Srishti; Roy, Timir B.; Sabamehr, Ardalan; Bagchi, Ashutosh

2017-04-01

Structural Health Monitoring (SHM) using dynamic characteristics of structures is crucial for early damage detection. Damage detection can be performed by capturing and assessing structural responses. Instrumented structures are monitored by analyzing the responses recorded by deployed sensors in the form of signals. Signal processing is an important tool for the processing of the collected data to diagnose anomalies in structural behavior. The vibration signature of the structure varies with damage. In order to attain effective damage detection, preservation of non-linear and non-stationary features of real structural responses is important. Decomposition of the signals into Intrinsic Mode Functions (IMF) by Empirical Mode Decomposition (EMD) and application of Hilbert-Huang Transform (HHT) addresses the time-varying instantaneous properties of the structural response. The energy distribution among different vibration modes of the intact and damaged structure depicted by Marginal Hilbert Spectrum (MHS) detects location and severity of the damage. The present work investigates damage detection analytically and experimentally by employing MHS. The testing of this methodology for different damage scenarios of a frame structure resulted in its accurate damage identification. The sensitivity of Hilbert Spectral Analysis (HSA) is assessed with varying frequencies and damage locations by means of calculating Damage Indices (DI) from the Hilbert spectrum curves of the undamaged and damaged structures.

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2004-01-01

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2002-01-01

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Computer implemented empirical mode decomposition method apparatus, and article of manufacture utilizing curvature extrema

NASA Technical Reports Server (NTRS)

Shen, Zheng (Inventor); Huang, Norden Eh (Inventor)

2003-01-01

A computer implemented physical signal analysis method is includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals based on local extrema and curvature extrema. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum.

Structured functional additive regression in reproducing kernel Hilbert spaces

PubMed Central

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2013-01-01

Summary Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application. PMID:25013362

A New Method for Nonlinear and Nonstationary Time Series Analysis and Its Application to the Earthquake and Building Response Records

NASA Technical Reports Server (NTRS)

Huang, Norden E.

1999-01-01

A new method for analyzing nonlinear and nonstationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum, Example of application of this method to earthquake and building response will be given. The results indicate those low frequency components, totally missed by the Fourier analysis, are clearly identified by the new method. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.

On Replacing "Quantum Thinking" with Counterfactual Reasoning

NASA Astrophysics Data System (ADS)

Narens, Louis

The probability theory used in quantum mechanics is currently being employed by psychologists to model the impact of context on decision. Its event space consists of closed subspaces of a Hilbert space, and its probability function sometimes violate the law of the finite additivity of probabilities. Results from the quantum mechanics literature indicate that such a "Hilbert space probability theory" cannot be extended in a useful way to standard, finitely additive, probability theory by the addition of new events with specific probabilities. This chapter presents a new kind of probability theory that shares many fundamental algebraic characteristics with Hilbert space probability theory but does extend to standard probability theory by adjoining new events with specific probabilities. The new probability theory arises from considerations about how psychological experiments are related through counterfactual reasoning.

Frequency hopping signal detection based on wavelet decomposition and Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Zheng, Yang; Chen, Xihao; Zhu, Rui

2017-07-01

Frequency hopping (FH) signal is widely adopted by military communications as a kind of low probability interception signal. Therefore, it is very important to research the FH signal detection algorithm. The existing detection algorithm of FH signals based on the time-frequency analysis cannot satisfy the time and frequency resolution requirement at the same time due to the influence of window function. In order to solve this problem, an algorithm based on wavelet decomposition and Hilbert-Huang transform (HHT) was proposed. The proposed algorithm removes the noise of the received signals by wavelet decomposition and detects the FH signals by Hilbert-Huang transform. Simulation results show the proposed algorithm takes into account both the time resolution and the frequency resolution. Correspondingly, the accuracy of FH signals detection can be improved.

A Riemann-Hilbert Approach to Complex Sharma-Tasso-Olver Equation on Half Line*

NASA Astrophysics Data System (ADS)

Zhang, Ning; Xia, Tie-Cheng; Hu, Bei-Bei

2017-11-01

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma-Tasso-Olver (cSTO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann-Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions \\{a(λ ),b(λ )\\} and \\{A(λ ),B(λ )\\} , which depending on initial data {u}0(x)=u(x,0) and boundary data {g}0(y)=u(0,y), {g}1(y)={u}x(0,y), {g}2(y)={u}{xx}(0,y). These spectral functions are not independent, they satisfy a global relation.

Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians.

PubMed

Vidmar, Lev; Rigol, Marcos

2017-12-01

In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the average entanglement entropy is known to be nearly maximal, with a deviation that is, at most, a constant. Here we prove that, in a system that is away from half filling and divided in two equal halves, an upper bound for the average entanglement entropy of random pure states with a fixed particle number and normally distributed real coefficients exhibits a deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system size.

Separability and Entanglement in the Hilbert Space Reference Frames Related Through the Generic Unitary Transform for Four Level System

NASA Astrophysics Data System (ADS)

Man'ko, V. I.; Markovich, L. A.

2018-02-01

Quantum correlations in the state of four-level atom are investigated by using generic unitary transforms of the classical (diagonal) density matrix. Partial cases of pure state, X-state, Werner state are studied in details. The geometrical meaning of unitary Hilbert reference-frame rotations generating entanglement in the initially separable state is discussed. Characteristics of the entanglement in terms of concurrence, entropy and negativity are obtained as functions of the unitary matrix rotating the reference frame.

New gravitational solutions via a Riemann-Hilbert approach

NASA Astrophysics Data System (ADS)

Cardoso, G. L.; Serra, J. C.

2018-03-01

We consider the Riemann-Hilbert factorization approach to solving the field equations of dimensionally reduced gravity theories. First we prove that functions belonging to a certain class possess a canonical factorization due to properties of the underlying spectral curve. Then we use this result, together with appropriate matricial decompositions, to study the canonical factorization of non-meromorphic monodromy matrices that describe deformations of seed monodromy matrices associated with known solutions. This results in new solutions, with unusual features, to the field equations.

The Hilbert-Huang Transform-Based Denoising Method for the TEM Response of a PRBS Source Signal

NASA Astrophysics Data System (ADS)

Hai, Li; Guo-qiang, Xue; Pan, Zhao; Hua-sen, Zhong; Khan, Muhammad Younis

2016-08-01

The denoising process is critical in processing transient electromagnetic (TEM) sounding data. For the full waveform pseudo-random binary sequences (PRBS) response, an inadequate noise estimation may result in an erroneous interpretation. We consider the Hilbert-Huang transform (HHT) and its application to suppress the noise in the PRBS response. The focus is on the thresholding scheme to suppress the noise and the analysis of the signal based on its Hilbert time-frequency representation. The method first decomposes the signal into the intrinsic mode function, and then, inspired by the thresholding scheme in wavelet analysis; an adaptive and interval thresholding is conducted to set to zero all the components in intrinsic mode function which are lower than a threshold related to the noise level. The algorithm is based on the characteristic of the PRBS response. The HHT-based denoising scheme is tested on the synthetic and field data with the different noise levels. The result shows that the proposed method has a good capability in denoising and detail preservation.

A New Scheme for the Design of Hilbert Transform Pairs of Biorthogonal Wavelet Bases

NASA Astrophysics Data System (ADS)

Shi, Hongli; Luo, Shuqian

2010-12-01

In designing the Hilbert transform pairs of biorthogonal wavelet bases, it has been shown that the requirements of the equal-magnitude responses and the half-sample phase offset on the lowpass filters are the necessary and sufficient condition. In this paper, the relationship between the phase offset and the vanishing moment difference of biorthogonal scaling filters is derived, which implies a simple way to choose the vanishing moments so that the phase response requirement can be satisfied structurally. The magnitude response requirement is approximately achieved by a constrained optimization procedure, where the objective function and constraints are all expressed in terms of the auxiliary filters of scaling filters rather than the scaling filters directly. Generally, the calculation burden in the design implementation will be less than that of the current schemes. The integral of magnitude response difference between the primal and dual scaling filters has been chosen as the objective function, which expresses the magnitude response requirements in the whole frequency range. Two design examples illustrate that the biorthogonal wavelet bases designed by the proposed scheme are very close to Hilbert transform pairs.

Connes distance function on fuzzy sphere and the connection between geometry and statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devi, Yendrembam Chaoba, E-mail: chaoba@bose.res.in; Chakraborty, Biswajit, E-mail: biswajit@bose.res.in; Prajapat, Shivraj, E-mail: shraprajapat@gmail.com

An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the su(2) algebra. This has been computed for both the discrete and the Perelemov’s SU(2) coherent state. Here also, we get a connection between geometry and statistics which ismore » shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by n ∈ ℤ/2.« less

Semiclassical propagation: Hilbert space vs. Wigner representation

NASA Astrophysics Data System (ADS)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.

Applications of Hilbert Spectral Analysis for Speech and Sound Signals

NASA Technical Reports Server (NTRS)

Huang, Norden E.

2003-01-01

A new method for analyzing nonlinear and nonstationary data has been developed, and the natural applications are to speech and sound signals. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time, which give sharp identifications of imbedded structures. This method invention can be used to process all acoustic signals. Specifically, it can process the speech signals for Speech synthesis, Speaker identification and verification, Speech recognition, and Sound signal enhancement and filtering. Additionally, as the acoustical signals from machinery are essentially the way the machines are talking to us. Therefore, the acoustical signals, from the machines, either from sound through air or vibration on the machines, can tell us the operating conditions of the machines. Thus, we can use the acoustic signal to diagnosis the problems of machines.

Small violations of Bell inequalities for multipartite pure random states

NASA Astrophysics Data System (ADS)

Drumond, Raphael C.; Duarte, Cristhiano; Oliveira, Roberto I.

2018-05-01

For any finite number of parts, measurements, and outcomes in a Bell scenario, we estimate the probability of random N-qudit pure states to substantially violate any Bell inequality with uniformly bounded coefficients. We prove that under some conditions on the local dimension, the probability to find any significant amount of violation goes to zero exponentially fast as the number of parts goes to infinity. In addition, we also prove that if the number of parts is at least 3, this probability also goes to zero as the local Hilbert space dimension goes to infinity.

Mutually unbiased bases and semi-definite programming

NASA Astrophysics Data System (ADS)

Brierley, Stephen; Weigert, Stefan

2010-11-01

A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and on Gröbner bases. A third algorithmic approach is presented: the non-existence of more than three mutually unbiased bases in composite dimensions can be decided by a global optimization method known as semidefinite programming. The method is used to confirm that the spectral matrix cannot be part of a complete set of seven mutually unbiased bases in dimension six.

Binary Inspiral in Quadratic Gravity

NASA Astrophysics Data System (ADS)

Yagi, Kent

2015-01-01

Quadratic gravity is a general class of quantum-gravity-inspired theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to a scalar field. In this article, we focus on the scalar Gauss- Bonnet (sGB) theory and consider the black hole binary inspiral in this theory. By applying the post-Newtonian (PN) formalism, we found that there is a scalar dipole radiation which leads to -1PN correction in the energy flux relative to gravitational radiation in general relativity. From the orbital decay rate of a low-mass X-ray binary A0600-20, we obtain the bound that is six orders of magnitude stronger than the current solar system bound. Furthermore, we show that the excess in the orbital decay rate of XTE J1118+480 can be explained by the scalar radiation in sGB theory.

Joint estimation of phase and phase diffusion for quantum metrology.

PubMed

Vidrighin, Mihai D; Donati, Gaia; Genoni, Marco G; Jin, Xian-Min; Kolthammer, W Steven; Kim, M S; Datta, Animesh; Barbieri, Marco; Walmsley, Ian A

2014-04-14

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here we investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states--split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental set-up for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements.

Entanglement negativity bounds for fermionic Gaussian states

NASA Astrophysics Data System (ADS)

Eisert, Jens; Eisler, Viktor; Zimborás, Zoltán

2018-04-01

The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for noninteracting bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, in this work, we introduce efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semidefinite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators. We discuss examples in quantum many-body theory and hint at applications in the study of topological properties at finite temperature.

Feature Extraction and Classification of EHG between Pregnancy and Labour Group Using Hilbert-Huang Transform and Extreme Learning Machine.

PubMed

Chen, Lili; Hao, Yaru

2017-01-01

Preterm birth (PTB) is the leading cause of perinatal mortality and long-term morbidity, which results in significant health and economic problems. The early detection of PTB has great significance for its prevention. The electrohysterogram (EHG) related to uterine contraction is a noninvasive, real-time, and automatic novel technology which can be used to detect, diagnose, or predict PTB. This paper presents a method for feature extraction and classification of EHG between pregnancy and labour group, based on Hilbert-Huang transform (HHT) and extreme learning machine (ELM). For each sample, each channel was decomposed into a set of intrinsic mode functions (IMFs) using empirical mode decomposition (EMD). Then, the Hilbert transform was applied to IMF to obtain analytic function. The maximum amplitude of analytic function was extracted as feature. The identification model was constructed based on ELM. Experimental results reveal that the best classification performance of the proposed method can reach an accuracy of 88.00%, a sensitivity of 91.30%, and a specificity of 85.19%. The area under receiver operating characteristic (ROC) curve is 0.88. Finally, experimental results indicate that the method developed in this work could be effective in the classification of EHG between pregnancy and labour group.

Quantum catastrophes: a case study

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2012-11-01

The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e. made Hermitian via an ad hoc choice of the inner product in the physical Hilbert space of quantum bound states (i.e. via an ad hoc construction of the operator Θ called the metric). The name quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e. to the scenario in which we leave the domain D along such a path that at the boundary of D, an N-plet of bound-state energies degenerates and, subsequently, complexifies. At any fixed N ⩾ 2, this process is simulated via an N × N benchmark effective matrix Hamiltonian H. It is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.

Power Spectral Density and Hilbert Transform

DTIC Science & Technology

2016-12-01

Fourier transform, Hilbert transform, digital filter , SDR 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER...terms. A very good approximation to the ideal Hilbert transform is a low-pass finite impulse response (FIR) filter . In Fig. 7, we show a real signal...220), converted to an analytic signal using a 255-tap Hilbert transform low-pass filter . For an ideal Hilbert

Faults Diagnostics of Railway Axle Bearings Based on IMF’s Confidence Index Algorithm for Ensemble EMD

PubMed Central

Yi, Cai; Lin, Jianhui; Zhang, Weihua; Ding, Jianming

2015-01-01

As train loads and travel speeds have increased over time, railway axle bearings have become critical elements which require more efficient non-destructive inspection and fault diagnostics methods. This paper presents a novel and adaptive procedure based on ensemble empirical mode decomposition (EEMD) and Hilbert marginal spectrum for multi-fault diagnostics of axle bearings. EEMD overcomes the limitations that often hypothesize about data and computational efforts that restrict the application of signal processing techniques. The outputs of this adaptive approach are the intrinsic mode functions that are treated with the Hilbert transform in order to obtain the Hilbert instantaneous frequency spectrum and marginal spectrum. Anyhow, not all the IMFs obtained by the decomposition should be considered into Hilbert marginal spectrum. The IMFs’ confidence index arithmetic proposed in this paper is fully autonomous, overcoming the major limit of selection by user with experience, and allows the development of on-line tools. The effectiveness of the improvement is proven by the successful diagnosis of an axle bearing with a single fault or multiple composite faults, e.g., outer ring fault, cage fault and pin roller fault. PMID:25970256

Hilbert-Huang transform analysis of dynamic and earthquake motion recordings

USGS Publications Warehouse

Zhang, R.R.; Ma, S.; Safak, E.; Hartzell, S.

2003-01-01

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition (EMD) and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function (IMF) components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low- and high-frequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.

Numerical optimization in Hilbert space using inexact function and gradient evaluations

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

Interference in the classical probabilistic model and its representation in complex Hilbert space

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei Yu.

2005-10-01

The notion of a context (complex of physical conditions, that is to say: specification of the measurement setup) is basic in this paper.We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present already in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: “first context and only then probability”. We construct the representation of the general contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function (in particular, Schrödinger's dynamics) can be considered as Hilbert space projections of a realistic dynamics in a “prespace”. The basic condition for representing of the prespace-dynamics is the law of statistical conservation of energy-conservation of probabilities. In general the Hilbert space projection of the “prespace” dynamics can be nonlinear and even irreversible (but it is always unitary). Methods developed in this paper can be applied not only to quantum mechanics, but also to classical statistical mechanics. The main quantum-like structures (e.g., interference of probabilities) might be found in some models of classical statistical mechanics. Quantum-like probabilistic behavior can be demonstrated by biological systems. In particular, it was recently found in some psychological experiments.

Cosmic transit and anisotropic models in f(R,T) gravity

NASA Astrophysics Data System (ADS)

Sahu, S. K.; Tripathy, S. K.; Sahoo, P. K.; Nath, A.

2017-06-01

Accelerating cosmological models are constructed in a modified gravity theory dubbed as $f(R,T)$ gravity at the backdrop of an anisotropic Bianchi type-III universe. $f(R,T)$ is a function of the Ricci scalar $R$ and the trace $T$ of the energy-momentum tensor and it replaces the Ricci scalar in the Einstein-Hilbert action of General Relativity. The models are constructed for two different ways of modification of the Einstein-Hilbert action. Exact solutions of the field equations are obtained by a novel method of integration. We have explored the behaviour of the cosmic transit from an decelerated phase of expansion to an accelerated phase to get the dynamical features of the universe. Within the formalism of the present work, it is found that, the modification of the Einstein-Hilbert action does not affect the scale factor. However the dynamics of the effective dark energy equation of state is significantly affected.

Computer implemented empirical mode decomposition method, apparatus, and article of manufacture for two-dimensional signals

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2001-01-01

A computer implemented method of processing two-dimensional physical signals includes five basic components and the associated presentation techniques of the results. The first component decomposes the two-dimensional signal into one-dimensional profiles. The second component is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF's) from each profile based on local extrema and/or curvature extrema. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the profiles. In the third component, the IMF's of each profile are then subjected to a Hilbert Transform. The fourth component collates the Hilbert transformed IMF's of the profiles to form a two-dimensional Hilbert Spectrum. A fifth component manipulates the IMF's by, for example, filtering the two-dimensional signal by reconstructing the two-dimensional signal from selected IMF(s).

Liquid identification by Hilbert spectroscopy

NASA Astrophysics Data System (ADS)

Lyatti, M.; Divin, Y.; Poppe, U.; Urban, K.

2009-11-01

Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- Tc Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.

On infinite-dimensional state spaces

NASA Astrophysics Data System (ADS)

Fritz, Tobias

2013-05-01

It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.

Computing Instantaneous Frequency by normalizing Hilbert Transform

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2005-01-01

This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.

Computing Instantaneous Frequency by normalizing Hilbert Transform

DOEpatents

Huang, Norden E.

2005-05-31

This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.

Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method

NASA Astrophysics Data System (ADS)

Schnack, J.; Wendland, O.

2010-12-01

The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 109. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s = 1/2. We show how genuine quantum features such as the magnetization plateau behave as a function of temperature.

Spinors in Hilbert Space

NASA Astrophysics Data System (ADS)

Plymen, Roger; Robinson, Paul

1995-01-01

Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.

Invariance of Topological Indices Under Hilbert Space Truncation

DOE PAGES

Huang, Zhoushen; Zhu, Wei; Arovas, Daniel P.; ...

2018-01-05

Here, we show that the topological index of a wave function, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, Z 2 topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possiblemore » application, we propose a partial quantum tomography scheme from which the topological index of a generic multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.« less

Invariance of Topological Indices Under Hilbert Space Truncation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Zhoushen; Zhu, Wei; Arovas, Daniel P.

Here, we show that the topological index of a wave function, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, Z 2 topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possiblemore » application, we propose a partial quantum tomography scheme from which the topological index of a generic multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.« less

Side-channel-free quantum key distribution.

PubMed

Braunstein, Samuel L; Pirandola, Stefano

2012-03-30

Quantum key distribution (QKD) offers the promise of absolutely secure communications. However, proofs of absolute security often assume perfect implementation from theory to experiment. Thus, existing systems may be prone to insidious side-channel attacks that rely on flaws in experimental implementation. Here we replace all real channels with virtual channels in a QKD protocol, making the relevant detectors and settings inside private spaces inaccessible while simultaneously acting as a Hilbert space filter to eliminate side-channel attacks. By using a quantum memory we find that we are able to bound the secret-key rate below by the entanglement-distillation rate computed over the distributed states.

Effects of stochastic noise on dynamical decoupling procedures

NASA Astrophysics Data System (ADS)

Bernád, J. Z.; Frydrych, H.

2014-06-01

Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap between fidelity improvements achieved in practice compared to theoretical predictions. We propose a model for imperfect dynamical decoupling based on a stochastic Ito differential equation which could explain the observed gap. We discuss the impact of our model on the time evolution of various quantum systems in finite- and infinite-dimensional Hilbert spaces. Analytical results are given for the limit of continuous control, whereas we present numerical simulations and upper bounds for the case of finite control.

State-transfer simulation in integrated waveguide circuits

NASA Astrophysics Data System (ADS)

Latmiral, L.; Di Franco, C.; Mennea, P. L.; Kim, M. S.

2015-08-01

Spin-chain models have been widely studied in terms of quantum information processes, for instance for the faithful transmission of quantum states. Here, we investigate the limitations of mapping this process to an equivalent one through a bosonic chain. In particular, we keep in mind experimental implementations, which the progress in integrated waveguide circuits could make possible in the very near future. We consider the feasibility of exploiting the higher dimensionality of the Hilbert space of the chain elements for the transmission of a larger amount of information, and the effects of unwanted excitations during the process. Finally, we exploit the information-flux method to provide bounds to the transfer fidelity.

A kernel adaptive algorithm for quaternion-valued inputs.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2015-10-01

The use of quaternion data can provide benefit in applications like robotics and image recognition, and particularly for performing transforms in 3-D space. Here, we describe a kernel adaptive algorithm for quaternions. A least mean square (LMS)-based method was used, resulting in the derivation of the quaternion kernel LMS (Quat-KLMS) algorithm. Deriving this algorithm required describing the idea of a quaternion reproducing kernel Hilbert space (RKHS), as well as kernel functions suitable with quaternions. A modified HR calculus for Hilbert spaces was used to find the gradient of cost functions defined on a quaternion RKHS. In addition, the use of widely linear (or augmented) filtering is proposed to improve performance. The benefit of the Quat-KLMS and widely linear forms in learning nonlinear transformations of quaternion data are illustrated with simulations.

Iterative Region-of-Interest Reconstruction from Limited Data Using Prior Information

NASA Astrophysics Data System (ADS)

Vogelgesang, Jonas; Schorr, Christian

2017-12-01

In practice, computed tomography and computed laminography applications suffer from incomplete data. In particular, when inspecting large objects with extremely different diameters in longitudinal and transversal directions or when high resolution reconstructions are desired, the physical conditions of the scanning system lead to restricted data and truncated projections, also known as the interior or region-of-interest (ROI) problem. To recover the searched-for density function of the inspected object, we derive a semi-discrete model of the ROI problem that inherently allows the incorporation of geometrical prior information in an abstract Hilbert space setting for bounded linear operators. Assuming that the attenuation inside the object is approximately constant, as for fibre reinforced plastics parts or homogeneous objects where one is interested in locating defects like cracks or porosities, we apply the semi-discrete Landweber-Kaczmarz method to recover the inner structure of the object inside the ROI from the measured data resulting in a semi-discrete iteration method. Finally, numerical experiments for three-dimensional tomographic applications with both an inherent restricted source and ROI problem are provided to verify the proposed method for the ROI reconstruction.

Distinguishability of generic quantum states

NASA Astrophysics Data System (ADS)

Puchała, Zbigniew; Pawela, Łukasz; Życzkowski, Karol

2016-06-01

Properties of random mixed states of dimension N distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large N , due to the concentration of measure, the trace distance between two random states tends to a fixed number D ˜=1 /4 +1 /π , which yields the Helstrom bound on their distinguishability. To arrive at this result, we apply free random calculus and derive the symmetrized Marchenko-Pastur distribution, which is shown to describe numerical data for the model of coupled quantum kicked tops. Asymptotic value for the root fidelity between two random states, √{F }=3/4 , can serve as a universal reference value for further theoretical and experimental studies. Analogous results for quantum relative entropy and Chernoff quantity provide other bounds on the distinguishablity of both states in a multiple measurement setup due to the quantum Sanov theorem. We study also mean entropy of coherence of random pure and mixed states and entanglement of a generic mixed state of a bipartite system.

Pure state `really' informationally complete with rank-1 POVM

NASA Astrophysics Data System (ADS)

Wang, Yu; Shang, Yun

2018-03-01

What is the minimal number of elements in a rank-1 positive operator-valued measure (POVM) which can uniquely determine any pure state in d-dimensional Hilbert space H_d? The known result is that the number is no less than 3d-2. We show that this lower bound is not tight except for d=2 or 4. Then we give an upper bound 4d-3. For d=2, many rank-1 POVMs with four elements can determine any pure states in H_2. For d=3, we show eight is the minimal number by construction. For d=4, the minimal number is in the set of {10,11,12,13}. We show that if this number is greater than 10, an unsettled open problem can be solved that three orthonormal bases cannot distinguish all pure states in H_4. For any dimension d, we construct d+2k-2 adaptive rank-1 positive operators for the reconstruction of any unknown pure state in H_d, where 1≤ k ≤ d.

Combinatorial quantisation of the Euclidean torus universe

NASA Astrophysics Data System (ADS)

Meusburger, C.; Noui, K.

2010-12-01

We quantise the Euclidean torus universe via a combinatorial quantisation formalism based on its formulation as a Chern-Simons gauge theory and on the representation theory of the Drinfel'd double DSU(2). The resulting quantum algebra of observables is given by two commuting copies of the Heisenberg algebra, and the associated Hilbert space can be identified with the space of square integrable functions on the torus. We show that this Hilbert space carries a unitary representation of the modular group and discuss the role of modular invariance in the theory. We derive the classical limit of the theory and relate the quantum observables to the geometry of the torus universe.

A Functional Central Limit Theorem for the Becker-Döring Model

NASA Astrophysics Data System (ADS)

Sun, Wen

2018-04-01

We investigate the fluctuations of the stochastic Becker-Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. It is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation (SDE) in a Hilbert space. We also prove that, at equilibrium, the solution of this SDE is a Gaussian process. The proofs are based on a specific representation of the evolution equations, the introduction of a convenient Hilbert space and several technical estimates to control the fluctuations, especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process.

Analysis of turbine-grid interaction of grid-connected wind turbine using HHT

NASA Astrophysics Data System (ADS)

Chen, A.; Wu, W.; Miao, J.; Xie, D.

2018-05-01

This paper processes the output power of the grid-connected wind turbine with the denoising and extracting method based on Hilbert Huang transform (HHT) to discuss the turbine-grid interaction. At first, the detailed Empirical Mode Decomposition (EMD) and the Hilbert Transform (HT) are introduced. Then, on the premise of decomposing the output power of the grid-connected wind turbine into a series of Intrinsic Mode Functions (IMFs), energy ratio and power volatility are calculated to detect the unessential components. Meanwhile, combined with vibration function of turbine-grid interaction, data fitting of instantaneous amplitude and phase of each IMF is implemented to extract characteristic parameters of different interactions. Finally, utilizing measured data of actual parallel-operated wind turbines in China, this work accurately obtains the characteristic parameters of turbine-grid interaction of grid-connected wind turbine.

On infinite-dimensional state spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fritz, Tobias

It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context frommore » which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V{sup -1}U{sup 2}V=U{sup 3}, then finite-dimensionality entails the relation UV{sup -1}UV=V{sup -1}UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V{sup -1}U{sup 2}V=U{sup 3} holds only up to {epsilon} and then yields a lower bound on the dimension.« less

Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous-variable systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adesso, Gerardo; CNR-INFM Coherentia , Naples; Grup d'Informacio Quantica, Universitat Autonoma de Barcelona, E-08193 Bellaterra

2007-08-15

Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e., simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N{>=}4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding is of importance for the quantification, understanding, and potential exploitation of shared quantummore » correlations in continuous variable systems. We discuss how promiscuity gradually arises when considering simple families of discrete variable states, with increasing Hilbert space dimension towards the continuous variable limit. Such models are somehow analogous to Gaussian states with asymptotically diverging, but finite, squeezing. In this respect, we find that non-Gaussian states (which in general are more entangled than Gaussian states) exhibit also the interesting feature that their entanglement is more shareable: in the non-Gaussian multipartite arena, unlimited promiscuity can be already achieved among three entangled parties, while this is impossible for Gaussian, even infinitely squeezed states.« less

Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings.

PubMed

Ashrafi, Reza; Azaña, José

2012-07-01

A novel, all-optical design for implementing terahertz (THz) bandwidth real-time Hilbert transformers is proposed and numerically demonstrated. An all-optical Hilbert transformer can be implemented using a uniform-period long-period grating (LPG) with a properly designed amplitude-only grating apodization profile, incorporating a single π-phase shift in the middle of the grating length. The designed LPG-based Hilbert transformers can be practically implemented using either fiber-optic or integrated-waveguide technologies. As a generalization, photonic fractional Hilbert transformers are also designed based on the same optical platform. In this general case, the resulting LPGs have multiple π-phase shifts along the grating length. Our numerical simulations confirm that all-optical Hilbert transformers capable of processing arbitrary optical signals with bandwidths well in the THz range can be implemented using feasible fiber/waveguide LPG designs.

Hilbert's sixth problem and the failure of the Boltzmann to Euler limit

NASA Astrophysics Data System (ADS)

Slemrod, Marshall

2018-04-01

This paper addresses the main issue of Hilbert's sixth problem, namely the rigorous passage of solutions to the mesoscopic Boltzmann equation to macroscopic solutions of the Euler equations of compressible gas dynamics. The results of the paper are that (i) in general Hilbert's program will fail because of the appearance of van der Waals-Korteweg capillarity terms in a macroscopic description of motion of a gas, and (ii) the van der Waals-Korteweg theory itself might satisfy Hilbert's quest for a map from the `atomistic view' to the laws of motion of continua. This article is part of the theme issue `Hilbert's sixth problem'.

Chiral Bosonization of Superconformal Ghosts

NASA Technical Reports Server (NTRS)

Shi, Deheng; Shen, Yang; Liu, Jinling; Xiong, Yongjian

1996-01-01

We explain the difference of the Hilbert space of the superconformal ghosts (beta,gamma) system from that of its bosonized fields phi and chi. We calculate the chiral correlation functions of phi, chi fields by inserting appropriate projectors.

Faithful test of nonlocal realism with entangled coherent states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Chang-Woo; Jeong, Hyunseok; Paternostro, Mauro

2011-02-15

We investigate the violation of Leggett's inequality for nonlocal realism using entangled coherent states and various types of local measurements. We prove mathematically the relation between the violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when tested by the same resources. For Leggett inequalities, we generalize the nonlocal realistic bound to systems in Hilbert spaces larger than bidimensional ones and introduce an optimization technique that allows one to achieve larger degrees of violation by adjusting the local measurement settings. Our work describes the steps that should be performed to produce a self-consistent generalization of Leggett's original argumentsmore » to continuous-variable states.« less

Generalization Performance of Regularized Ranking With Multiscale Kernels.

PubMed

Zhou, Yicong; Chen, Hong; Lan, Rushi; Pan, Zhibin

2016-05-01

The regularized kernel method for the ranking problem has attracted increasing attentions in machine learning. The previous regularized ranking algorithms are usually based on reproducing kernel Hilbert spaces with a single kernel. In this paper, we go beyond this framework by investigating the generalization performance of the regularized ranking with multiscale kernels. A novel ranking algorithm with multiscale kernels is proposed and its representer theorem is proved. We establish the upper bound of the generalization error in terms of the complexity of hypothesis spaces. It shows that the multiscale ranking algorithm can achieve satisfactory learning rates under mild conditions. Experiments demonstrate the effectiveness of the proposed method for drug discovery and recommendation tasks.

Phenomenology of small violations of Fermi and Bose statistics

NASA Astrophysics Data System (ADS)

Greenberg, O. W.; Mohapatra, Rabindra N.

1989-04-01

In a recent paper, we proposed a ``paronic'' field-theory framework for possible small deviations from the Pauli exclusion principle. This theory cannot be represented in a positive-metric (Hilbert) space. Nonetheless, the issue of possible small violations of the exclusion principle can be addressed in the framework of quantum mechanics, without being connected with a local quantum field theory. In this paper, we discuss the phenomenology of small violations of both Fermi and Bose statistics. We consider the implications of such violations in atomic, nuclear, particle, and condensed-matter physics and in astrophysics and cosmology. We also discuss experiments that can detect small violations of Fermi and Bose statistics or place stringent bounds on their validity.

The U(1)-Kepler Problems

NASA Astrophysics Data System (ADS)

Meng, Guowu

2010-12-01

Let n ⩾ 2 be a positive integer. To each irreducible representation σ of U(1), a U(1)-Kepler problem in dimension (2n - 1) is constructed and analyzed. This system is superintegrable and when n = 2 it is equivalent to a MICZ-Kepler problem. The dynamical symmetry group of this system is widetildeU(n, n), and the Hilbert space of bound states {{H}}(σ ) is the unitary highest weight representation of widetildeU(n, n) with the minimal positive Gelfand-Kirillov dimension. Furthermore, it is shown that the correspondence between σ ^* (the dual of σ) and {H}(σ ) is the theta-correspondence for dual pair (U(1), U(n,n))subseteq Sp_{4n}({R}).

Norms of certain Jordan elementary operators

NASA Astrophysics Data System (ADS)

Zhang, Xiaoli; Ji, Guoxing

2008-10-01

Let be a complex Hilbert space and let denote the algebra of all bounded linear operators on . For , the Jordan elementary operator UA,B is defined by UA,B(X)=AXB+BXA, . In this short note, we discuss the norm of UA,B. We show that if and ||UA,B||=||A||||B||, then either AB* or B*A is 0. We give some examples of Jordan elementary operators UA,B such that ||UA,B||=||A||||B|| but AB*[not equal to]0 and B*A[not equal to]0, which answer negatively a question posed by M. Boumazgour in [M. Boumazgour, Norm inequalities for sums of two basic elementary operators, J. Math. Anal. Appl. 342 (2008) 386-393].

Quantum probability and Hilbert's sixth problem

NASA Astrophysics Data System (ADS)

Accardi, Luigi

2018-04-01

With the birth of quantum mechanics, the two disciplines that Hilbert proposed to axiomatize, probability and mechanics, became entangled and a new probabilistic model arose in addition to the classical one. Thus, to meet Hilbert's challenge, an axiomatization should account deductively for the basic features of all three disciplines. This goal was achieved within the framework of quantum probability. The present paper surveys the quantum probabilistic axiomatization. This article is part of the themed issue `Hilbert's sixth problem'.

Arbitrary-order Hilbert Spectral Analysis and Intermittency in Solar Wind Density Fluctuations

NASA Astrophysics Data System (ADS)

Carbone, Francesco; Sorriso-Valvo, Luca; Alberti, Tommaso; Lepreti, Fabio; Chen, Christopher H. K.; Němeček, Zdenek; Šafránková, Jana

2018-05-01

The properties of inertial- and kinetic-range solar wind turbulence have been investigated with the arbitrary-order Hilbert spectral analysis method, applied to high-resolution density measurements. Due to the small sample size and to the presence of strong nonstationary behavior and large-scale structures, the classical analysis in terms of structure functions may prove to be unsuccessful in detecting the power-law behavior in the inertial range, and may underestimate the scaling exponents. However, the Hilbert spectral method provides an optimal estimation of the scaling exponents, which have been found to be close to those for velocity fluctuations in fully developed hydrodynamic turbulence. At smaller scales, below the proton gyroscale, the system loses its intermittent multiscaling properties and converges to a monofractal process. The resulting scaling exponents, obtained at small scales, are in good agreement with those of classical fractional Brownian motion, indicating a long-term memory in the process, and the absence of correlations around the spectral-break scale. These results provide important constraints on models of kinetic-range turbulence in the solar wind.

Hilbert-Schmidt quantum coherence in multi-qudit systems

NASA Astrophysics Data System (ADS)

Maziero, Jonas

2017-11-01

Using Bloch's parametrization for qudits ( d-level quantum systems), we write the Hilbert-Schmidt distance (HSD) between two generic n-qudit states as an Euclidean distance between two vectors of observables mean values in R^{Π_{s=1}nds2-1}, where ds is the dimension for qudit s. Then, applying the generalized Gell-Mann's matrices to generate SU(ds), we use that result to obtain the Hilbert-Schmidt quantum coherence (HSC) of n-qudit systems. As examples, we consider in detail one-qubit, one-qutrit, two-qubit, and two copies of one-qubit states. In this last case, the possibility for controlling local and non-local coherences by tuning local populations is studied, and the contrasting behaviors of HSC, l1-norm coherence, and relative entropy of coherence in this regard are noticed. We also investigate the decoherent dynamics of these coherence functions under the action of qutrit dephasing and dissipation channels. At last, we analyze the non-monotonicity of HSD under tensor products and report the first instance of a consequence (for coherence quantification) of this kind of property of a quantum distance measure.

Single image super-resolution via an iterative reproducing kernel Hilbert space method.

PubMed

Deng, Liang-Jian; Guo, Weihong; Huang, Ting-Zhu

2016-11-01

Image super-resolution, a process to enhance image resolution, has important applications in satellite imaging, high definition television, medical imaging, etc. Many existing approaches use multiple low-resolution images to recover one high-resolution image. In this paper, we present an iterative scheme to solve single image super-resolution problems. It recovers a high quality high-resolution image from solely one low-resolution image without using a training data set. We solve the problem from image intensity function estimation perspective and assume the image contains smooth and edge components. We model the smooth components of an image using a thin-plate reproducing kernel Hilbert space (RKHS) and the edges using approximated Heaviside functions. The proposed method is applied to image patches, aiming to reduce computation and storage. Visual and quantitative comparisons with some competitive approaches show the effectiveness of the proposed method.

ADHM and the 4d quantum Hall effect

NASA Astrophysics Data System (ADS)

Barns-Graham, Alec; Dorey, Nick; Lohitsiri, Nakarin; Tong, David; Turner, Carl

2018-04-01

Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.

Construction of CASCI-type wave functions for very large active spaces.

PubMed

Boguslawski, Katharina; Marti, Konrad H; Reiher, Markus

2011-06-14

We present a procedure to construct a configuration-interaction expansion containing arbitrary excitations from an underlying full-configuration-interaction-type wave function defined for a very large active space. Our procedure is based on the density-matrix renormalization group (DMRG) algorithm that provides the necessary information in terms of the eigenstates of the reduced density matrices to calculate the coefficient of any basis state in the many-particle Hilbert space. Since the dimension of the Hilbert space scales binomially with the size of the active space, a sophisticated Monte Carlo sampling routine is employed. This sampling algorithm can also construct such configuration-interaction-type wave functions from any other type of tensor network states. The configuration-interaction information obtained serves several purposes. It yields a qualitatively correct description of the molecule's electronic structure, it allows us to analyze DMRG wave functions converged for the same molecular system but with different parameter sets (e.g., different numbers of active-system (block) states), and it can be considered a balanced reference for the application of a subsequent standard multi-reference configuration-interaction method.

Ice cream and orbifold Riemann-Roch

NASA Astrophysics Data System (ADS)

Buckley, Anita; Reid, Miles; Zhou, Shengtian

2013-06-01

We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of {K3} surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.

Geometry of entanglement witnesses and local detection of entanglement

NASA Astrophysics Data System (ADS)

Pittenger, Arthur O.; Rubin, Morton H.

2003-01-01

Let H[N]=H[d1]⊗⋯⊗H[dn] be a tensor product of Hilbert spaces and let τ0 be the closest separable state in the Hilbert-Schmidt norm to an entangled state ρ0. Let τ˜0 denote the closest separable state to ρ0 along the line segment from I/N to ρ0 where I is the identity matrix. Following A. O. Pittenger and M. H. Rubin [Linear Algebr. Appl. 346, 75 (2002)] a witness W0 detecting the entanglement of ρ0 can be constructed in terms of I, τ0, and τ˜0. If representations of τ0 and τ˜0 as convex combinations of separable projections are known, then the entanglement of ρ0 can be detected by local measurements. Gühne et al. [Phys. Rev. A 66, 062305 (2002)] obtain the minimum number of measurement settings required for a class of two-qubit states. We use our geometric approach to generalize their result to the corresponding two-qudit case when d is prime and obtain the minimum number of measurement settings. In those particular bipartite cases, τ0=τ˜0. We illustrate our general approach with a two-parameter family of three-qubit bound entangled states for which τ0≠τ˜0 and we show that our approach works for n qubits. We elaborated earlier [A. O. Pittenger, Linear Algebr. App. 359, 235 (2003)] on the role of a “far face” of the separable states relative to a bound entangled state ρ0 constructed from an orthogonal unextendible product base. In this paper the geometric approach leads to an entanglement witness expressible in terms of a constant times I and a separable density μ0 on the far face from ρ0. Up to a normalization this coincides with the witness obtained by Gühne et al. for the particular example analyzed there.

Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

NASA Astrophysics Data System (ADS)

Lempert, László; Szőke, Róbert

2014-04-01

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H s of Hilbert spaces, and the question arises if the spaces H s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787-902, 1991) and Hitchin (Commun. Math. Phys. 131:347-380, 1990) suggest viewing H s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle along a non-proper map . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Szőke (Bull. Lond. Math. Soc. 44:367-374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.

Aspects of neutrino oscillation in alternative gravity theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakraborty, Sumanta, E-mail: sumantac.physics@gmail.com

2015-10-01

Neutrino spin and flavour oscillation in curved spacetime have been studied for the most general static spherically symmetric configuration. Having exploited the spherical symmetry we have confined ourselves to the equatorial plane in order to determine the spin and flavour oscillation frequency in this general set-up. Using the symmetry properties we have derived spin oscillation frequency for neutrino moving along a geodesic or in a circular orbit. Starting from the expression of neutrino spin oscillation frequency we have shown that even in this general context, in high energy limit the spin oscillation frequency for neutrino moving along circular orbit vanishes.more » We have verified previous results along this line by transforming to Schwarzschild coordinates under appropriate limit. This finally lends itself to the probability of neutrino helicity flip which turns out to be non-zero. While for neutrino flavour oscillation we have derived general results for oscillation phase, which subsequently have been applied to three different gravity theories. One, of them appears as low-energy approximation to string theory, where we have an additional field, namely, dilaton field coupled to Maxwell field tensor. This yields a realization of Reissner-Nordström solution in string theory at low-energy. Next one corresponds to generalization of Schwarzschild solution by introduction of quadratic curvature terms of all possible form to the Einstein-Hilbert action. Finally, we have also discussed regular black hole solutions. In all these cases the flavour oscillation probabilities can be determined for solar neutrinos and thus can be used to put bounds on the parameters of these gravity theories. While for spin oscillation probability, we have considered two cases, Gauss-Bonnet term added to the Einstein-Hilbert action and the f(R) gravity theory. In both these cases we could impose bounds on the parameters which are consistent with previous considerations. In a nutshell, in this work we have presented both spin and flavour oscillation frequency of neutrino in most general static spherically symmetric spacetime, encompassing a vast class of solutions, which when applied to three such instances in alternative theories for flavour oscillation and two alternative theories for spin oscillation put bounds on the parameters of these theories. Implications are also discussed.« less

On the Hilbert-Huang Transform Theoretical Developments

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Patrick, David; Hestnes, Phyllis

2005-01-01

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.

On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Petrick, David; Hestness, Phyllis

2006-01-01

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,

Differentiable representations of finite dimensional Lie groups in rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Wickramasekara, Sujeewa

The inceptive motivation for introducing rigged Hilbert spaces (RHS) in quantum physics in the mid 1960's was to provide the already well established Dirac formalism with a proper mathematical context. It has since become clear, however, that this mathematical framework is lissome enough to accommodate a class of solutions to the dynamical equations of quantum physics that includes some which are not possible in the normative Hilbert space theory. Among the additional solutions, in particular, are those which describe aspects of scattering and decay phenomena that have eluded the orthodox quantum physics. In this light, the RHS formulation seems to provide a mathematical rubric under which various phenomenological observations and calculational techniques, commonly known in the study of resonance scattering and decay as ``effective theories'' (e.g., the Wigner- Weisskopf method), receive a unified theoretical foundation. These observations lead to the inference that a theory founded upon the RHS mathematics may prove to be of better utility and value in understanding quantum physical phenomena. This dissertation primarily aims to contribute to the general formalism of the RHS theory of quantum mechanics by undertaking a study of differentiable representations of finite dimensional Lie groups. In particular, it is shown that a finite dimensional operator Lie algebra G in a rigged Hilbert space can be always integrated, provided one parameter integrability holds true for the elements of any basis for G . This result differs from and extends the well known integration theorem of E. Nelson and the subsequent works of others on unitary representations in that it does not require any assumptions on the existence of analytic vectors. Also presented here is a construction of a particular rigged Hilbert space of Hardy class functions that appears useful in formulating a relativistic version of the RHS theory of resonances and decay. As a contexture for the construction, a synopsis of the new relativistic theory is presented.

Theoretical foundations of the chronometric cosmology.

PubMed

Segal, I E

1976-03-01

The derivation of the redshift (z)-distance (r) relation in the chronometric theory of the Cosmos is amplified. The basic physical quantities are represented by precisely defined self-adjoint operators in global Hilbert spaces. Computations yielding explicit bounds for the deviation of the theoretical prediction from the relation z = tan(2)(r/2R) (where R denotes the radius of the universe), earlier derived employing less formal procedures, are carried out for: (a) a cut-off plane wave in two dimensions; (b) a scalar spherical wave in four dimensions; (c) the same as (b) with appropriate incorporation of the photon spin. Both this deviation and the (quantum) dispersion in redshift are shown to be unobservably small. A parallel classical treatment is possible and leads to similar results.

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

Communication: Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

NASA Astrophysics Data System (ADS)

Vanfleteren, Diederik; Van Neck, Dimitri; Bultinck, Patrick; Ayers, Paul W.; Waroquier, Michel

2010-12-01

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.

Hilbert's 'Foundations of Physics': Gravitation and electromagnetism within the axiomatic method

NASA Astrophysics Data System (ADS)

Brading, K. A.; Ryckman, T. A.

2008-01-01

In November and December 1915, Hilbert presented two communications to the Göttingen Academy of Sciences under the common title 'The Foundations of Physics'. Versions of each eventually appeared in the Nachrichten of the Academy. Hilbert's first communication has received significant reconsideration in recent years, following the discovery of printer's proofs of this paper, dated 6 December 1915. The focus has been primarily on the 'priority dispute' over the Einstein field equations. Our contention, in contrast, is that the discovery of the December proofs makes it possible to see the thematic linkage between the material that Hilbert cut from the published version of the first communication and the content of the second, as published in 1917. The latter has been largely either disregarded or misinterpreted, and our aim is to show that (a) Hilbert's two communications should be regarded as part of a wider research program within the overarching framework of 'the axiomatic method' (as Hilbert expressly stated was the case), and (b) the second communication is a fine and coherent piece of work within this framework, whose principal aim is to address an apparent tension between general invariance and causality (in the precise sense of Cauchy determination), pinpointed in Theorem I of the first communication. This is not the same problem as that found in Einstein's 'hole argument'-something that, we argue, never confused Hilbert.

An Alternative to the Gauge Theoretic Setting

NASA Astrophysics Data System (ADS)

Schroer, Bert

2011-10-01

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner's representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on the intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation. The new stringlike approach to gauge theory also revives the idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric description of the Higgs spontaneous symmetry breaking and its accompanying tale about "God's particle" and its mass generation for all the other particles.

Hilbert-Huang Transform: A Spectral Analysis Tool Applied to Sunspot Number and Total Solar Irradiance Variations, as well as Near-Surface Atmospheric Variables

NASA Astrophysics Data System (ADS)

Barnhart, B. L.; Eichinger, W. E.; Prueger, J. H.

2010-12-01

Hilbert-Huang transform (HHT) is a relatively new data analysis tool which is used to analyze nonstationary and nonlinear time series data. It consists of an algorithm, called empirical mode decomposition (EMD), which extracts the cyclic components embedded within time series data, as well as Hilbert spectral analysis (HSA) which displays the time and frequency dependent energy contributions from each component in the form of a spectrogram. The method can be considered a generalized form of Fourier analysis which can describe the intrinsic cycles of data with basis functions whose amplitudes and phases may vary with time. The HHT will be introduced and compared to current spectral analysis tools such as Fourier analysis, short-time Fourier analysis, wavelet analysis and Wigner-Ville distributions. A number of applications are also presented which demonstrate the strengths and limitations of the tool, including analyzing sunspot number variability and total solar irradiance proxies as well as global averaged temperature and carbon dioxide concentration. Also, near-surface atmospheric quantities such as temperature and wind velocity are analyzed to demonstrate the nonstationarity of the atmosphere.

The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains

NASA Astrophysics Data System (ADS)

Chandran, A.; Schulz, Marc D.; Burnell, F. J.

2016-12-01

Many phases of matter, including superconductors, fractional quantum Hall fluids, and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this paper, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free nonintegrable model. We also find that certain nonlocal observables obey ETH.

Schwinger-Keldysh superspace in quantum mechanics

NASA Astrophysics Data System (ADS)

Geracie, Michael; Haehl, Felix M.; Loganayagam, R.; Narayan, Prithvi; Ramirez, David M.; Rangamani, Mukund

2018-05-01

We examine, in a quantum mechanical setting, the Hilbert space representation of the Becchi, Rouet, Stora, and Tyutin (BRST) symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals in coarse-grained systems with dissipation, or in open quantum systems. Operationally, this entails uplifting the standard Schwinger-Keldysh two-copy formalism into superspace by appending BRST ghost degrees of freedom. These statements were previously argued at the level of the correlation functions. We provide herein a complementary perspective by working out the Hilbert space structure explicitly. Our analysis clarifies two crucial issues not evident in earlier works: first, certain background ghost insertions necessary to reproduce the correct Schwinger-Keldysh correlators arise naturally, and, second, the Schwinger-Keldysh difference operators are systematically dressed by the ghost bilinears, which turn out to be necessary to give rise to a consistent operator algebra. We also elaborate on the structure of the final state (which is BRST closed) and the future boundary condition of the ghost fields.

Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Wu, Jianping; Geng, Xianguo

2017-12-01

The inverse scattering transform of the coupled modified Korteweg-de Vries equation is studied by the Riemann-Hilbert approach. In the direct scattering process, the spectral analysis of the Lax pair is performed, from which a Riemann-Hilbert problem is established for the equation. In the inverse scattering process, by solving Riemann-Hilbert problems corresponding to the reflectionless cases, three types of multi-soliton solutions are obtained. The multi-soliton classification is based on the zero structures of the Riemann-Hilbert problem. In addition, some figures are given to illustrate the soliton characteristics of the coupled modified Korteweg-de Vries equation.

A novel analysis method for near infrared spectroscopy based on Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Zhou, Zhenyu; Yang, Hongyu; Liu, Yun; Ruan, Zongcai; Luo, Qingming; Gong, Hui; Lu, Zuhong

2007-05-01

Near Infrared Imager (NIRI) has been widely used to access the brain functional activity non-invasively. We use a portable, multi-channel and continuous-wave NIR topography instrument to measure the concentration changes of each hemoglobin species and map cerebral cortex functional activation. By extracting some essential features from the BOLD signals, optical tomography is able to be a new way of neuropsychological studies. Fourier spectral analysis provides a common framework for examining the distribution of global energy in the frequency domain. However, this method assumes that the signal should be stationary, which limits its application in non-stationary system. The hemoglobin species concentration changes are of such kind. In this work we develop a new signal processing method using Hilbert-Huang transform to perform spectral analysis of the functional NIRI signals. Compared with wavelet based multi-resolution analysis (MRA), we demonstrated the extraction of task related signal for observation of activation in the prefrontal cortex (PFC) in vision stimulation experiment. This method provides a new analysis tool for functional NIRI signals. Our experimental results show that the proposed approach provides the unique method for reconstructing target signal without losing original information and enables us to understand the episode of functional NIRI more precisely.

Signal Processing for Determining Water Height in Steam Pipes with Dynamic Surface Conditions

NASA Technical Reports Server (NTRS)

Lih, Shyh-Shiuh; Lee, Hyeong Jae; Bar-Cohen, Yoseph

2015-01-01

An enhanced signal processing method based on the filtered Hilbert envelope of the auto-correlation function of the wave signal has been developed to monitor the height of condensed water through the steel wall of steam pipes with dynamic surface conditions. The developed signal processing algorithm can also be used to estimate the thickness of the pipe to determine the cut-off frequency for the low pass filter frequency of the Hilbert Envelope. Testing and analysis results by using the developed technique for dynamic surface conditions are presented. A multiple array of transducers setup and methodology are proposed for both the pulse-echo and pitch-catch signals to monitor the fluctuation of the water height due to disturbance, water flow, and other anomaly conditions.

A time-frequency analysis method to obtain stable estimates of magnetotelluric response function based on Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Cai, Jianhua

2017-05-01

The time-frequency analysis method represents signal as a function of time and frequency, and it is considered a powerful tool for handling arbitrary non-stationary time series by using instantaneous frequency and instantaneous amplitude. It also provides a possible alternative to the analysis of the non-stationary magnetotelluric (MT) signal. Based on the Hilbert-Huang transform (HHT), a time-frequency analysis method is proposed to obtain stable estimates of the magnetotelluric response function. In contrast to conventional methods, the response function estimation is performed in the time-frequency domain using instantaneous spectra rather than in the frequency domain, which allows for imaging the response parameter content as a function of time and frequency. The theory of the method is presented and the mathematical model and calculation procedure, which are used to estimate response function based on HHT time-frequency spectrum, are discussed. To evaluate the results, response function estimates are compared with estimates from a standard MT data processing method based on the Fourier transform. All results show that apparent resistivities and phases, which are calculated from the HHT time-frequency method, are generally more stable and reliable than those determined from the simple Fourier analysis. The proposed method overcomes the drawbacks of the traditional Fourier methods, and the resulting parameter minimises the estimation bias caused by the non-stationary characteristics of the MT data.

Hybrid Techniques for Quantum Circuit Simulation

DTIC Science & Technology

2014-02-01

Detailed theorems and proofs describing these results are included in our published manuscript [10]. Embedding of stabilizer geometry in the Hilbert ...space. We also describe how the discrete embedding of stabilizer geometry in Hilbert space complicates several natural geometric tasks. As described...the Hilbert space in which they are embedded, and that they are arranged in a fairly uniform pattern. These factors suggest that, if one seeks a

The generalization ability of online SVM classification based on Markov sampling.

PubMed

Xu, Jie; Yan Tang, Yuan; Zou, Bin; Xu, Zongben; Li, Luoqing; Lu, Yang

2015-03-01

In this paper, we consider online support vector machine (SVM) classification learning algorithms with uniformly ergodic Markov chain (u.e.M.c.) samples. We establish the bound on the misclassification error of an online SVM classification algorithm with u.e.M.c. samples based on reproducing kernel Hilbert spaces and obtain a satisfactory convergence rate. We also introduce a novel online SVM classification algorithm based on Markov sampling, and present the numerical studies on the learning ability of online SVM classification based on Markov sampling for benchmark repository. The numerical studies show that the learning performance of the online SVM classification algorithm based on Markov sampling is better than that of classical online SVM classification based on random sampling as the size of training samples is larger.

On τ-Compactness of Products of τ-Measurable Operators

NASA Astrophysics Data System (ADS)

Bikchentaev, Airat M.

2017-12-01

Let M be a von Neumann algebra of operators on a Hilbert space H, τ be a faithful normal semifinite trace on M. We obtain some new inequalities for rearrangements of τ-measurable operators products. We also establish some sufficient τ-compactness conditions for products of selfadjoint τ-measurable operators. Next we obtain a τ-compactness criterion for product of a nonnegative τ-measurable operator with an arbitrary τ-measurable operator. We construct an example that shows importance of nonnegativity for one of the factors. The similar results are obtained also for elementary operators from M. We apply our results to symmetric spaces on (M, τ ). The results are new even for the *-algebra B(H) of all linear bounded operators on H endowed with the canonical trace τ = tr.

H-SLAM: Rao-Blackwellized Particle Filter SLAM Using Hilbert Maps.

PubMed

Vallicrosa, Guillem; Ridao, Pere

2018-05-01

Occupancy Grid maps provide a probabilistic representation of space which is important for a variety of robotic applications like path planning and autonomous manipulation. In this paper, a SLAM (Simultaneous Localization and Mapping) framework capable of obtaining this representation online is presented. The H-SLAM (Hilbert Maps SLAM) is based on Hilbert Map representation and uses a Particle Filter to represent the robot state. Hilbert Maps offer a continuous probabilistic representation with a small memory footprint. We present a series of experimental results carried both in simulation and with real AUVs (Autonomous Underwater Vehicles). These results demonstrate that our approach is able to represent the environment more consistently while capable of running online.

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Hilbert's axiomatic method and Carnap's general axiomatics.

PubMed

Stöltzner, Michael

2015-10-01

This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's axiomatic method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' 'material' talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics. Copyright © 2015 Elsevier Ltd. All rights reserved.

The place of probability in Hilbert's axiomatization of physics, ca. 1900-1928

NASA Astrophysics Data System (ADS)

Verburgt, Lukas M.

2016-02-01

Although it has become a common place to refer to the 'sixth problem' of Hilbert's (1900) Paris lecture as the starting point for modern axiomatized probability theory, his own views on probability have received comparatively little explicit attention. The central aim of this paper is to provide a detailed account of this topic in light of the central observation that the development of Hilbert's project of the axiomatization of physics went hand-in-hand with a redefinition of the status of probability theory and the meaning of probability. Where Hilbert first regarded the theory as a mathematizable physical discipline and later approached it as a 'vague' mathematical application in physics, he eventually understood probability, first, as a feature of human thought and, then, as an implicitly defined concept without a fixed physical interpretation. It thus becomes possible to suggest that Hilbert came to question, from the early 1920s on, the very possibility of achieving the goal of the axiomatization of probability as described in the 'sixth problem' of 1900.

A combined approach for weak fault signature extraction of rolling element bearing using Hilbert envelop and zero frequency resonator

NASA Astrophysics Data System (ADS)

Kumar, Keshav; Shukla, Sumitra; Singh, Sachin Kumar

2018-04-01

Periodic impulses arise due to localised defects in rolling element bearing. At the early stage of defects, the weak impulses are immersed in strong machinery vibration. This paper proposes a combined approach based upon Hilbert envelop and zero frequency resonator for the detection of the weak periodic impulses. In the first step, the strength of impulses is increased by taking normalised Hilbert envelop of the signal. It also helps in better localization of these impulses on time axis. In the second step, Hilbert envelope of the signal is passed through the zero frequency resonator for the exact localization of the periodic impulses. Spectrum of the resonator output gives peak at the fault frequency. Simulated noisy signal with periodic impulses is used to explain the working of the algorithm. The proposed technique is verified with experimental data also. A comparison of the proposed method with Hilbert-Haung transform (HHT) based method is presented to establish the effectiveness of the proposed method.

On the Hilbert-Huang Transform Data Processing System Development

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Flatley, Thomas P.; Huang, Norden E.; Cornwell, Evette; Smith, Darell

2003-01-01

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Loubenets, Elena R.

We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and context-invariant, reproducing all the von Neumann joint probabilities via non-negative values of real-valued measures and all the quantum product expectations—via the qHV (classical-like) average of the product of the corresponding random variables. In a context-invariant model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence ofmore » this model negates the general opinion that, in terms of random variables, the Hilbert space description of all the joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of a statistically noncontextual qHV model, in particular, implies that every N-partite quantum state admits a local quasi hidden variable model introduced in Loubenets [J. Math. Phys. 53, 022201 (2012)]. The new results of the present paper point also to the generality of the quasi-classical probability model proposed in Loubenets [J. Phys. A: Math. Theor. 45, 185306 (2012)].« less

On Quantile Regression in Reproducing Kernel Hilbert Spaces with Data Sparsity Constraint

PubMed Central

Zhang, Chong; Liu, Yufeng; Wu, Yichao

2015-01-01

For spline regressions, it is well known that the choice of knots is crucial for the performance of the estimator. As a general learning framework covering the smoothing splines, learning in a Reproducing Kernel Hilbert Space (RKHS) has a similar issue. However, the selection of training data points for kernel functions in the RKHS representation has not been carefully studied in the literature. In this paper we study quantile regression as an example of learning in a RKHS. In this case, the regular squared norm penalty does not perform training data selection. We propose a data sparsity constraint that imposes thresholding on the kernel function coefficients to achieve a sparse kernel function representation. We demonstrate that the proposed data sparsity method can have competitive prediction performance for certain situations, and have comparable performance in other cases compared to that of the traditional squared norm penalty. Therefore, the data sparsity method can serve as a competitive alternative to the squared norm penalty method. Some theoretical properties of our proposed method using the data sparsity constraint are obtained. Both simulated and real data sets are used to demonstrate the usefulness of our data sparsity constraint. PMID:27134575

Elliptic complexes over C∗-algebras of compact operators

NASA Astrophysics Data System (ADS)

Krýsl, Svatopluk

2016-03-01

For a C∗-algebra A of compact operators and a compact manifold M, we prove that the Hodge theory holds for A-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective A-Hilbert bundles over M. For these C∗-algebras and manifolds, we get a topological isomorphism between the cohomology groups of an A-elliptic complex and the space of harmonic elements of the complex. Consequently, the cohomology groups appear to be finitely generated projective C∗-Hilbert modules and especially, Banach spaces. We also prove that in the category of Hilbert A-modules and continuous adjointable Hilbert A-module homomorphisms, the property of a complex of being self-adjoint parametrix possessing characterizes the complexes of Hodge type.

On orthogonal expansions of the space of vector functions which are square-summable over a given domain and the vector analysis operators

NASA Technical Reports Server (NTRS)

Bykhovskiy, E. B.; Smirnov, N. V.

1983-01-01

The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined.

Functional Renormalization Group Flows on Friedman-Lemaître-Robertson-Walker backgrounds

NASA Astrophysics Data System (ADS)

Platania, Alessia; Saueressig, Frank

2018-06-01

We revisit the construction of the gravitational functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation emphasizing its connection to the covariant formulation. The results obtained from projecting the renormalization group flow onto the Einstein-Hilbert action are reviewed in detail and we provide a novel example illustrating how the formalism may be connected to the causal dynamical triangulations approach to quantum gravity.

A Riemann-Hilbert formulation for the finite temperature Hubbard model

NASA Astrophysics Data System (ADS)

Cavaglià, Andrea; Cornagliotto, Martina; Mattelliano, Massimo; Tateo, Roberto

2015-06-01

Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.

Bath-induced correlations in an infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Nizama, Marco; Cáceres, Manuel O.

2017-09-01

Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

Quantum decimation in Hilbert space: Coarse graining without structure

NASA Astrophysics Data System (ADS)

Singh, Ashmeet; Carroll, Sean M.

2018-03-01

We present a technique to coarse grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred set of operators (local or otherwise) in an associated algebra. Rather, we use the data corresponding to a given set of states, either specified independently or constructed from a single state evolving in time. Our technique is based on principle component analysis (PCA), and the resulting coarse-grained quantum states live in a lower-dimensional Hilbert space whose basis is defined using the underlying (isometric embedding) transformation of the set of fine-grained states we wish to coarse grain. Physically, the transformation can be interpreted to be an "entanglement coarse-graining" scheme that retains most of the global, useful entanglement structure of each state, while needing fewer degrees of freedom for its reconstruction. This scheme could be useful for efficiently describing collections of states whose number is much smaller than the dimension of Hilbert space, or a single state evolving over time.

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics.

PubMed

Corry, Leo

2018-04-28

The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics

NASA Astrophysics Data System (ADS)

Corry, Leo

2018-04-01

The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932. This article is part of the theme issue `Hilbert's sixth problem'.

Basis adaptation in homogeneous chaos spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tipireddy, Ramakrishna; Ghanem, Roger

2014-02-01

We present a new meth for the characterization of subspaces associated with low-dimensional quantities of interet (QoI). The probability density function of these QoI is found to be concentrated around one-dimensional subspaces for which we develop projection operators. Our approach builds on the properties of Gaussian Hilbert spaces and associated tensor product spaces.

Deterministic alternatives to the full configuration interaction quantum Monte Carlo method for strongly correlated systems

NASA Astrophysics Data System (ADS)

Tubman, Norm; Whaley, Birgitta

The development of exponential scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, allows exact diagonalization through stochastically sampling of determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, together with a stochastic projected wave function, which are used to explore the important parts of Hilbert space. However, a stochastic representation of the wave function is not required to search Hilbert space efficiently and new deterministic approaches have recently been shown to efficiently find the important parts of determinant space. We shall discuss the technique of Adaptive Sampling Configuration Interaction (ASCI) and the related heat-bath Configuration Interaction approach for ground state and excited state simulations. We will present several applications for strongly correlated Hamiltonians. This work was supported through the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences.

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagarello, F., E-mail: fabio.bagarello@unipa.it

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we willmore » find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.« less

Singular value decomposition for the truncated Hilbert transform

NASA Astrophysics Data System (ADS)

Katsevich, A.

2010-11-01

Starting from a breakthrough result by Gelfand and Graev, inversion of the Hilbert transform became a very important tool for image reconstruction in tomography. In particular, their result is useful when the tomographic data are truncated and one deals with an interior problem. As was established recently, the interior problem admits a stable and unique solution when some a priori information about the object being scanned is available. The most common approach to solving the interior problem is based on converting it to the Hilbert transform and performing analytic continuation. Depending on what type of tomographic data are available, one gets different Hilbert inversion problems. In this paper, we consider two such problems and establish singular value decomposition for the operators involved. We also propose algorithms for performing analytic continuation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vostokov, S V

A new method for calculating an explicit form of the Hilbert pairing is proposed. It is used to calculate the Hilbert pairing in a classical local field and in a complete higher-dimensional field. Bibliography: 25 titles.

The spectral function of a singular differential operator of order 2m

NASA Astrophysics Data System (ADS)

Kozko, Artem I.; Pechentsov, Alexander S.

2010-12-01

We study the spectral function of a self-adjoint semibounded below differential operator on a Hilbert space L_2 \\lbrack 0,\\infty) and obtain the formulae for the spectral function of the operator (-1)^{m}y^{(2m)}(x) with general boundary conditions at the zero. In particular, for the boundary conditions y(0)=y'(0)=\\dots=y^{(m-1)}(0)=0 we find the explicit form of the spectral function \\Theta_{mB'}(x,x,\\lambda) on the diagonal x=y for \\lambda \\ge 0.

On the physical Hilbert space of loop quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noui, Karim; Perez, Alejandro; Vandersloot, Kevin

2005-02-15

In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable, consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology.

Experimental Issues in Coherent Quantum-State Manipulation of Trapped Atomic Ions

DTIC Science & Technology

1998-05-01

in Hilbert space and almost always precludes the exis- tence of “large” Schrödinger-cat-like states except on extremely short time scales. A...Hamiltonian Hideal operate on the Hilbert space formed by the ↓l and ↑l states of the L qubits. In practice, for the case of trapped ions, the...auxiliary state (Sec. 3.3). If decoherence mechanisms cause other states to be populated, the Hilbert space must be expanded. Although more streamlined

An Efficient Multiparty Quantum Secret Sharing Protocol Based on Bell States in the High Dimension Hilbert Space

NASA Astrophysics Data System (ADS)

Gao, Gan; Wang, Li-Ping

2010-11-01

We propose a quantum secret sharing protocol, in which Bell states in the high dimension Hilbert space are employed. The biggest advantage of our protocol is the high source capacity. Compared with the previous secret sharing protocol, ours has the higher controlling efficiency. In addition, as decoy states in the high dimension Hilbert space are used, we needn’t destroy quantum entanglement for achieving the goal to check the channel security.

The Laplace method for probability measures in Banach spaces

NASA Astrophysics Data System (ADS)

Piterbarg, V. I.; Fatalov, V. R.

1995-12-01

Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Hölder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces L_k^p and l^2. Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the l_k^p-norm of a Gaussian finite-dimensional vector with dependent coordinates, p > 1 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type \\chi^2 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of l^2-valued Gaussian processes 8.5. Exact asymptotics of large deviations for the l^2-valued Ornstein-Uhlenbeck process Bibliography

Modern Electromagnetic Scattering

DTIC Science & Technology

2013-08-10

Kramers– Kronig relations and is therefore a complex-valued function of angular frequency. The same is true for permeability. Thus, in general, we have...Kramers– Kronig relations, then (ω) and µ(ω) are analytic functions in the upper-half ω-plane. Furthermore, it can be shown that (ω) and µ(ω) are never...Kramers– Kronig (KK) relations (the Hilbert transform pair) in the Fourier-domain, namely, 6For our purposes, it is more convenient to work with (3.3

A characterization of positive linear maps and criteria of entanglement for quantum states

NASA Astrophysics Data System (ADS)

Hou, Jinchuan

2010-09-01

Let H and K be (finite- or infinite-dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from {\\mathcal B}(H) into {\\mathcal B}(K) is given, which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras. This characterization is then applied to give a representation of quantum channels (operations) between infinite-dimensional systems. A necessary and sufficient criterion of separability is given which shows that a state ρ on HotimesK is separable if and only if (ΦotimesI)ρ >= 0 for all positive finite-rank elementary operators Φ. Examples of NCP and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the PPT criterion and the realignment criterion.

Projective flatness in the quantisation of bosons and fermions

NASA Astrophysics Data System (ADS)

Wu, Siye

2015-07-01

We compare the quantisation of linear systems of bosons and fermions. We recall the appearance of projectively flat connection and results on parallel transport in the quantisation of bosons. We then discuss pre-quantisation and quantisation of fermions using the calculus of fermionic variables. We define a natural connection on the bundle of Hilbert spaces and show that it is projectively flat. This identifies, up to a phase, equivalent spinor representations constructed by various polarisations. We introduce the concept of metaplectic correction for fermions and show that the bundle of corrected Hilbert spaces is naturally flat. We then show that the parallel transport in the bundle of Hilbert spaces along a geodesic is a rescaled projection provided that the geodesic lies within the complement of a cut locus. Finally, we study the bundle of Hilbert spaces when there is a symmetry.

Effective Numerical Methods for Solving Elliptical Problems in Strengthened Sobolev Spaces

NASA Technical Reports Server (NTRS)

D'yakonov, Eugene G.

1996-01-01

Fourth-order elliptic boundary value problems in the plane can be reduced to operator equations in Hilbert spaces G that are certain subspaces of the Sobolev space W(sub 2)(exp 2)(Omega) is identical with G(sup (2)). Appearance of asymptotically optimal algorithms for Stokes type problems made it natural to focus on an approach that considers rot w is identical with (D(sub 2)w - D(sub 1)w) is identical with vector of u as a new unknown vector-function, which automatically satisfies the condition div vector of u = 0. In this work, we show that this approach can also be developed for an important class of problems from the theory of plates and shells with stiffeners. The main mathematical problem was to show that the well-known inf-sup condition (normal solvability of the divergence operator) holds for special Hilbert spaces. This result is also essential for certain hydrodynamics problems.

Coherence-generating power of quantum dephasing processes

NASA Astrophysics Data System (ADS)

Styliaris, Georgios; Campos Venuti, Lorenzo; Zanardi, Paolo

2018-03-01

We provide a quantification of the capability of various quantum dephasing processes to generate coherence out of incoherent states. The measures defined, admitting computable expressions for any finite Hilbert-space dimension, are based on probabilistic averages and arise naturally from the viewpoint of coherence as a resource. We investigate how the capability of a dephasing process (e.g., a nonselective orthogonal measurement) to generate coherence depends on the relevant bases of the Hilbert space over which coherence is quantified and the dephasing process occurs, respectively. We extend our analysis to include those Lindblad time evolutions which, in the infinite-time limit, dephase the system under consideration and calculate their coherence-generating power as a function of time. We further identify specific families of such time evolutions that, although dephasing, have optimal (over all quantum processes) coherence-generating power for some intermediate time. Finally, we investigate the coherence-generating capability of random dephasing channels.

Magnetic states at short distances

NASA Astrophysics Data System (ADS)

Crater, Horace W.; Wong, Cheuk-Yin

2012-06-01

The magnetic interactions between a fermion and an antifermion of opposite electric or color charges in the S0-+1 and P0++3 states with J=0 are very attractive and singular near the origin and may allow the formation of new bound and resonance states at short distances. In the two-body Dirac equations formulated in constraint dynamics, the short-distance attraction for these states for point particles leads to a quasipotential that behaves near the origin as -α2/r2, where α is the coupling constant. Representing this quasipotential at short distances as λ(λ+1)/r2 with λ=(-1+1-4α2)/2, both S0-+1 and P0++3 states admit two types of eigenstates with drastically different behaviors for the radial wave function u=rψ. One type of states, with u growing as rλ+1 at small r, will be called usual states. The other type of states with u growing as r-λ will be called peculiar states. Both of the usual and peculiar eigenstates have admissible behaviors at short distances. Remarkably, the solutions for both sets of S01 states can be written out analytically. The usual bound S01 states possess attributes the same as those one usually encounters in QED and QCD, with bound QED state energies explicitly agreeing with the standard perturbative results through order α4. In contrast, the peculiar bound S01 states, yet to be observed, not only have different behaviors at the origin, but also distinctly different bound state properties (and scattering phase shifts). For the peculiar S01 ground state of fermion-antifermion pair with fermion rest mass m, the root-mean-square radius is approximately 1/m, binding energy is approximately (2-2)m, and rest mass approximately 2m. On the other hand, the (n+1)S01 peculiar state with principal quantum number (n+1) is nearly degenerate in energy and approximately equal in size with the nS01 usual states. For the P03 states, the usual solutions lead to the standard bound state energies and no resonance, but resonances have been found for the peculiar states whose energies depend on the description of the internal structure of the charges, the mass of the constituent, and the coupling constant. The existence of both usual and peculiar eigenstates in the same system leads to the non-self-adjoint property of the mass operator and two nonorthogonal complete sets. As both sets of states are physically admissible, the mass operator can be made self-adjoint with a single complete set of admissible states by introducing a new peculiarity quantum number and an enlarged Hilbert space that contains both the usual and peculiar states in different peculiarity sectors. Whether or not these newly-uncovered quantum-mechanically acceptable peculiar S01 bound states and P03 resonances for point fermion-antifermion systems correspond to physical states remains to be further investigated.

International Roughness Index (IRI) measurement using Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Zhang, Wenjin; Wang, Ming L.

2018-03-01

International Roughness Index (IRI) is an important metric to measure condition of roadways. This index is usually used to justify the maintenance priority and scheduling for roadways. Various inspection methods and algorithms are used to assess this index through the use of road profiles. This study proposes to calculate IRI values using Hilbert-Huang Transform (HHT) algorithm. In particular, road profile data is provided using surface radar attached to a vehicle driving at highway speed. Hilbert-Huang transform (HHT) is used in this study because of its superior properties for nonstationary and nonlinear data. Empirical mode decomposition (EMD) processes the raw data into a set of intrinsic mode functions (IMFs), representing various dominating frequencies. These various frequencies represent noises from the body of the vehicle, sensor location, and the excitation induced by nature frequency of the vehicle, etc. IRI calculation can be achieved by eliminating noises that are not associated with the road profile including vehicle inertia effect. The resulting IRI values are compared favorably to the field IRI values, where the filtered IMFs captures the most characteristics of road profile while eliminating noises from the vehicle and the vehicle inertia effect. Therefore, HHT is an effect method for road profile analysis and for IRI measurement. Furthermore, the application of HHT method has the potential to eliminate the use of accelerometers attached to the vehicle as part of the displacement measurement used to offset the inertia effect.

Quantum Computation of Fluid Dynamics

DTIC Science & Technology

1998-02-16

state of the quantum computer’s "memory". With N qubits, the quantum state IT) resides in an exponentially large Hilbert space with 2 N dimensions. A new...size of the Hilbert space in which the entanglement occurs. And to make matters worse, even if a quantum computer was constructed with a large number of...number of qubits "* 2 N is the size of the full Hilbert space "* 2 B is the size of the on-site submanifold, denoted 71 "* B is the size of the

On Hilbert-Huang Transform Based Synthesis of a Signal Contaminated by Radio Frequency Interference or Fringes

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Shiri, Ron S.; Vootukuru, Meg; Coletti, Alessandro

2015-01-01

Norden E. Huang et al. had proposed and published the Hilbert-Huang Transform (HHT) concept correspondently in 1996, 1998. The HHT is a novel method for adaptive spectral analysis of non-linear and non-stationary signals. The HHT comprises two components: - the Huang Empirical Mode Decomposition (EMD), resulting in an adaptive data-derived basis of Intrinsic Mode functions (IMFs), and the Hilbert Spectral Analysis (HSA1) based on the Hilbert Transform for 1-dimension (1D) applied to the EMD IMF's outcome. Although paper describes the HHT concept in great depth, it does not contain all needed methodology to implement the HHT computer code. In 2004, Semion Kizhner and Karin Blank implemented the reference digital HHT real-time data processing system for 1D (HHT-DPS Version 1.4). The case for 2-Dimension (2D) (HHT2) proved to be difficult due to the computational complexity of EMD for 2D (EMD2) and absence of a suitable Hilbert Transform for 2D spectral analysis (HSA2). The real-time EMD2 and HSA2 comprise the real-time HHT2. Kizhner completed the real-time EMD2 and the HSA2 reference digital implementations respectively in 2013 & 2014. Still, the HHT2 outcome synthesis remains an active research area. This paper presents the initial concepts and preliminary results of HHT2-based synthesis and its application to processing of signals contaminated by Radio-Frequency Interference (RFI), as well as optical systems' fringe detection and mitigation at design stage. The Soil Moisture Active Passive (SMAP mission (SMAP) carries a radiometer instrument that measures Earth soil moisture at L1 frequency (1.4 GHz polarimetric - H, V, 3rd and 4th Stokes parameters). There is abundant RFI at L1 and because soil moisture is a strategic parameter, it is important to be able to recover the RFI-contaminated measurement samples (15% of telemetry). State-of-the-art only allows RFI detection and removes RFI-contaminated measurements. The HHT-based analysis and synthesis facilitates recovery of measurements contaminated by all kinds of RFI, including jamming [7-8]. The fringes are inherent in optical systems and multi-layer complex contour expensive coatings are employed to remove the unwanted fringes. HHT2-based analysis allows test image decomposition to analyze and detect fringes, and HHT2-based synthesis of useful image.

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Support vector machine based decision for mechanical fault condition monitoring in induction motor using an advanced Hilbert-Park transform.

PubMed

Ben Salem, Samira; Bacha, Khmais; Chaari, Abdelkader

2012-09-01

In this work we suggest an original fault signature based on an improved combination of Hilbert and Park transforms. Starting from this combination we can create two fault signatures: Hilbert modulus current space vector (HMCSV) and Hilbert phase current space vector (HPCSV). These two fault signatures are subsequently analysed using the classical fast Fourier transform (FFT). The effects of mechanical faults on the HMCSV and HPCSV spectrums are described, and the related frequencies are determined. The magnitudes of spectral components, relative to the studied faults (air-gap eccentricity and outer raceway ball bearing defect), are extracted in order to develop the input vector necessary for learning and testing the support vector machine with an aim of classifying automatically the various states of the induction motor. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

A Probabilistic Framework for the Validation and Certification of Computer Simulations

NASA Technical Reports Server (NTRS)

Ghanem, Roger; Knio, Omar

2000-01-01

The paper presents a methodology for quantifying, propagating, and managing the uncertainty in the data required to initialize computer simulations of complex phenomena. The purpose of the methodology is to permit the quantitative assessment of a certification level to be associated with the predictions from the simulations, as well as the design of a data acquisition strategy to achieve a target level of certification. The value of a methodology that can address the above issues is obvious, specially in light of the trend in the availability of computational resources, as well as the trend in sensor technology. These two trends make it possible to probe physical phenomena both with physical sensors, as well as with complex models, at previously inconceivable levels. With these new abilities arises the need to develop the knowledge to integrate the information from sensors and computer simulations. This is achieved in the present work by tracing both activities back to a level of abstraction that highlights their commonalities, thus allowing them to be manipulated in a mathematically consistent fashion. In particular, the mathematical theory underlying computer simulations has long been associated with partial differential equations and functional analysis concepts such as Hilbert spares and orthogonal projections. By relying on a probabilistic framework for the modeling of data, a Hilbert space framework emerges that permits the modeling of coefficients in the governing equations as random variables, or equivalently, as elements in a Hilbert space. This permits the development of an approximation theory for probabilistic problems that parallels that of deterministic approximation theory. According to this formalism, the solution of the problem is identified by its projection on a basis in the Hilbert space of random variables, as opposed to more traditional techniques where the solution is approximated by its first or second-order statistics. The present representation, in addition to capturing significantly more information than the traditional approach, facilitates the linkage between different interacting stochastic systems as is typically observed in real-life situations.

[EMD Time-Frequency Analysis of Raman Spectrum and NIR].

PubMed

Zhao, Xiao-yu; Fang, Yi-ming; Tan, Feng; Tong, Liang; Zhai, Zhe

2016-02-01

This paper analyzes the Raman spectrum and Near Infrared Spectrum (NIR) with time-frequency method. The empirical mode decomposition spectrum becomes intrinsic mode functions, which the proportion calculation reveals the Raman spectral energy is uniform distributed in each component, while the NIR's low order intrinsic mode functions only undertakes fewer primary spectroscopic effective information. Both the real spectrum and numerical experiments show that the empirical mode decomposition (EMD) regard Raman spectrum as the amplitude-modulated signal, which possessed with high frequency adsorption property; and EMD regards NIR as the frequency-modulated signal, which could be preferably realized high frequency narrow-band demodulation during first-order intrinsic mode functions. The first-order intrinsic mode functions Hilbert transform reveals that during the period of empirical mode decomposes Raman spectrum, modal aliasing happened. Through further analysis of corn leaf's NIR in time-frequency domain, after EMD, the first and second orders components of low energy are cut off, and reconstruct spectral signal by using the remaining intrinsic mode functions, the root-mean-square error is 1.001 1, and the correlation coefficient is 0.981 3, both of these two indexes indicated higher accuracy in re-construction; the decomposition trend term indicates the absorbency is ascending along with the decreasing to wave length in the near-infrared light wave band; and the Hilbert transform of characteristic modal component displays, 657 cm⁻¹ is the specific frequency by the corn leaf stress spectrum, which could be regarded as characteristic frequency for identification.

The use of transmission line modelling to test the effectiveness of I-kaz as autonomous selection of intrinsic mode function

NASA Astrophysics Data System (ADS)

Yusop, Hanafi M.; Ghazali, M. F.; Yusof, M. F. M.; PiRemli, M. A.; Karollah, B.; Rusman

2017-10-01

Pressure transient signal occurred due to sudden changes in fluid propagation filled in pipelines system, which is caused by rapid pressure and flow fluctuation in a system, such as closing and opening valve rapidly. The application of Hilbert-Huang Transform (HHT) as the method to analyse the pressure transient signal utilised in this research. However, this method has the difficulty in selecting the suitable IMF for the further post-processing, which is Hilbert Transform (HT). This paper proposed the implementation of Integrated Kurtosis-based Algorithm for z-filter Technique (I-kaz) to kurtosis ratio (I-kaz-Kurtosis) for that allows automatic selection of intrinsic mode function (IMF) that’s should be used. This work demonstrated the synthetic pressure transient signal generates using transmission line modelling (TLM) in order to test the effectiveness of I-kaz as the autonomous selection of intrinsic mode function (IMF). A straight fluid network was designed using TLM fixing with higher resistance at some point act as a leak and connecting to the pipe feature (junction, pipefitting or blockage). The analysis results using I-kaz-kurtosis ratio revealed that the method can be utilised as an automatic selection of intrinsic mode function (IMF) although the noise level ratio of the signal is lower. I-kaz-kurtosis ratio is recommended and advised to be implemented as automatic selection of intrinsic mode function (IMF) through HHT analysis.

Infrared length scale and extrapolations for the no-core shell model

DOE PAGES

Wendt, K. A.; Forssén, C.; Papenbrock, T.; ...

2015-06-03

In this paper, we precisely determine the infrared (IR) length scale of the no-core shell model (NCSM). In the NCSM, the A-body Hilbert space is truncated by the total energy, and the IR length can be determined by equating the intrinsic kinetic energy of A nucleons in the NCSM space to that of A nucleons in a 3(A-1)-dimensional hyper-radial well with a Dirichlet boundary condition for the hyper radius. We demonstrate that this procedure indeed yields a very precise IR length by performing large-scale NCSM calculations for 6Li. We apply our result and perform accurate IR extrapolations for bound statesmore » of 4He, 6He, 6Li, and 7Li. Finally, we also attempt to extrapolate NCSM results for 10B and 16O with bare interactions from chiral effective field theory over tens of MeV.« less

Online Distributed Learning Over Networks in RKH Spaces Using Random Fourier Features

NASA Astrophysics Data System (ADS)

Bouboulis, Pantelis; Chouvardas, Symeon; Theodoridis, Sergios

2018-04-01

We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number of parameters as time iterations evolve. Besides complexity, this leads to an increased need of communication resources, in a distributed setting. In contrast, the proposed method approximates the solution as a fixed-size vector (of larger dimension than the input space) using Random Fourier Features. This paves the way to use standard linear combine-then-adapt techniques. To the best of our knowledge, this is the first time that a complete protocol for distributed online learning in RKHS is presented. Conditions for asymptotic convergence and boundness of the networkwise regret are also provided. The simulated tests illustrate the performance of the proposed scheme.

A double commutant theorem for Murray–von Neumann algebras

PubMed Central

Liu, Zhe

2012-01-01

Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165

A Hilbert Space Representation of Generalized Observables and Measurement Processes in the ESR Model

NASA Astrophysics Data System (ADS)

Sozzo, Sandro; Garola, Claudio

2010-12-01

The extended semantic realism ( ESR) model recently worked out by one of the authors embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here a Hilbert space representation of the generalized observables introduced by the ESR model that satisfy a simple physical condition, propose a generalization of the projection postulate, and suggest a possible mathematical description of the measurement process in terms of evolution of the compound system made up of the measured system and the measuring apparatus.

Adaptive learning in complex reproducing kernel Hilbert spaces employing Wirtinger's subgradients.

PubMed

Bouboulis, Pantelis; Slavakis, Konstantinos; Theodoridis, Sergios

2012-03-01

This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources.

Vertical integration from the large Hilbert space

NASA Astrophysics Data System (ADS)

Erler, Theodore; Konopka, Sebastian

2017-12-01

We develop an alternative description of the procedure of vertical integration based on the observation that amplitudes can be written in BRST exact form in the large Hilbert space. We relate this approach to the description of vertical integration given by Sen and Witten.

Master Lovas-Andai and equivalent formulas verifying the 8/33 two-qubit Hilbert-Schmidt separability probability and companion rational-valued conjectures

NASA Astrophysics Data System (ADS)

Slater, Paul B.

2018-04-01

We begin by investigating relationships between two forms of Hilbert-Schmidt two-rebit and two-qubit "separability functions"—those recently advanced by Lovas and Andai (J Phys A Math Theor 50(29):295303, 2017), and those earlier presented by Slater (J Phys A 40(47):14279, 2007). In the Lovas-Andai framework, the independent variable ɛ \\in [0,1] is the ratio σ (V) of the singular values of the 2 × 2 matrix V=D_2^{1/2} D_1^{-1/2} formed from the two 2 × 2 diagonal blocks (D_1, D_2) of a 4 × 4 density matrix D= ||ρ _{ij}||. In the Slater setting, the independent variable μ is the diagonal-entry ratio √{ρ _{11} ρ _ {44}/ρ _ {22 ρ _ {33}}}—with, of central importance, μ =ɛ or μ =1/ɛ when both D_1 and D_2 are themselves diagonal. Lovas and Andai established that their two-rebit "separability function" \\tilde{χ }_1 (ɛ ) (≈ ɛ ) yields the previously conjectured Hilbert-Schmidt separability probability of 29/64. We are able, in the Slater framework (using cylindrical algebraic decompositions [CAD] to enforce positivity constraints), to reproduce this result. Further, we newly find its two-qubit, two-quater[nionic]-bit and "two-octo[nionic]-bit" counterparts, \\tilde{χ _2}(ɛ ) =1/3 ɛ ^2 ( 4-ɛ ^2) , \\tilde{χ _4}(ɛ ) =1/35 ɛ ^4 ( 15 ɛ ^4-64 ɛ ^2+84) and \\tilde{χ _8} (ɛ )= 1/1287ɛ ^8 ( 1155 ɛ ^8-7680 ɛ ^6+20160 ɛ ^4-25088 ɛ ^2+12740) . These immediately lead to predictions of Hilbert-Schmidt separability/PPT-probabilities of 8/33, 26/323 and 44482/4091349, in full agreement with those of the "concise formula" (Slater in J Phys A 46:445302, 2013), and, additionally, of a "specialized induced measure" formula. Then, we find a Lovas-Andai "master formula," \\tilde{χ _d}(ɛ )= ɛ ^d Γ (d+1)^3 _3\\tilde{F}_2( -{d/2,d/2,d;d/2+1,3 d/2+1;ɛ ^2) }/{Γ ( d/2+1) ^2}, encompassing both even and odd values of d. Remarkably, we are able to obtain the \\tilde{χ _d}(ɛ ) formulas, d=1,2,4, applicable to full (9-, 15-, 27-) dimensional sets of density matrices, by analyzing (6-, 9, 15-) dimensional sets, with not only diagonal D_1 and D_2, but also an additional pair of nullified entries. Nullification of a further pair still leads to X-matrices, for which a distinctly different, simple Dyson-index phenomenon is noted. C. Koutschan, then, using his HolonomicFunctions program, develops an order-4 recurrence satisfied by the predictions of the several formulas, establishing their equivalence. A two-qubit separability probability of 1-256/27 π ^2 is obtained based on the operator monotone function √{x}, with the use of \\tilde{χ _2}(ɛ ).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Znojil, Miloslav

For many quantum models an apparent non-Hermiticity of observables just corresponds to their hidden Hermiticity in another, physical Hilbert space. For these models we show that the existence of observables which are manifestly time-dependent may require the use of a manifestly time-dependent representation of the physical Hilbert space of states.

Computational algebraic geometry of epidemic models

NASA Astrophysics Data System (ADS)

Rodríguez Vega, Martín.

2014-06-01

Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

Applications of rigged Hilbert spaces in quantum mechanics and signal processing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Celeghini, E., E-mail: celeghini@fi.infn.it; Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, Paseo Belén 7, 47011 Valladolid; Gadella, M., E-mail: manuelgadella1@gmail.com

Simultaneous use of discrete and continuous bases in quantum systems is not possible in the context of Hilbert spaces, but only in the more general structure of rigged Hilbert spaces (RHS). In addition, the relevant operators in RHS (but not in Hilbert space) are a realization of elements of a Lie enveloping algebra and support representations of semigroups. We explicitly construct here basis dependent RHS of the line and half-line and relate them to the universal enveloping algebras of the Weyl-Heisenberg algebra and su(1, 1), respectively. The complete sub-structure of both RHS and of the operators acting on them ismore » obtained from their algebraic structures or from the related fractional Fourier transforms. This allows us to describe both quantum and signal processing states and their dynamics. Two relevant improvements are introduced: (i) new kinds of filters related to restrictions to subspaces and/or the elimination of high frequency fluctuations and (ii) an operatorial structure that, starting from fix objects, describes their time evolution.« less

Single and two-shot quantitative phase imaging using Hilbert-Huang Transform based fringe pattern analysis

NASA Astrophysics Data System (ADS)

Trusiak, Maciej; Micó, Vicente; Patorski, Krzysztof; García-Monreal, Javier; Sluzewski, Lukasz; Ferreira, Carlos

2016-08-01

In this contribution we propose two Hilbert-Huang Transform based algorithms for fast and accurate single-shot and two-shot quantitative phase imaging applicable in both on-axis and off-axis configurations. In the first scheme a single fringe pattern containing information about biological phase-sample under study is adaptively pre-filtered using empirical mode decomposition based approach. Further it is phase demodulated by the Hilbert Spiral Transform aided by the Principal Component Analysis for the local fringe orientation estimation. Orientation calculation enables closed fringes efficient analysis and can be avoided using arbitrary phase-shifted two-shot Gram-Schmidt Orthonormalization scheme aided by Hilbert-Huang Transform pre-filtering. This two-shot approach is a trade-off between single-frame and temporal phase shifting demodulation. Robustness of the proposed techniques is corroborated using experimental digital holographic microscopy studies of polystyrene micro-beads and red blood cells. Both algorithms compare favorably with the temporal phase shifting scheme which is used as a reference method.

Monopole operators and Hilbert series of Coulomb branches of 3 d = 4 gauge theories

NASA Astrophysics Data System (ADS)

Cremonesi, Stefano; Hanany, Amihay; Zaffaroni, Alberto

2014-01-01

This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.

The Application of Hilbert-Huang Transforms to Meteorological Datasets

NASA Technical Reports Server (NTRS)

Duffy, Dean G.

2003-01-01

Recently a new spectral technique as been developed for the analysis of aperiodic and nonlinear signals - the Hilbert-Huang transform. This paper shows how these transforms can be used to discover synoptic and climatic features: For sea level data, the transforms capture the oceanic tides as well as large, aperiodic river outflows. In the case of solar radiation, we observe variations in the diurnal and seasonal cycles. Finally, from barographic data, the Hilbert-Huang transform reveals the passage of extratropical cyclones, fronts, and troughs. Thus, this technique can flag significant weather events such its a flood or the passage of a squall line.

Optical Hilbert transform using fiber Bragg gratings

NASA Astrophysics Data System (ADS)

Ge, Jing; Wang, Chinhua; Zhu, Xiaojun

2010-11-01

In this paper, we demonstrate that a simple and practical phase-shifted fiber Bragg grating (PSFBG) operated in reflection can provide the required spectral response for implementing an all-optical Hilbert transformer (HT), including both integer and fractional orders. The PSFBG consists of two concatenated identical uniform FBGs with a phase shift between them. It can be proved that the phase shift of the FBG and the apodizing profile of the refractive index modulation determine the order of the transform. The device shows a good accuracy in calculating the Hilbert transform of the complex field of an arbitrary input optical waveforms when compared with the theoretical results.

Hilbert's Hotel in polarization singularities.

PubMed

Wang, Yangyundou; Gbur, Greg

2017-12-15

We demonstrate theoretically how the creation of polarization singularities by the evolution of a fractional nonuniform polarization optical element involves the peculiar mathematics of countably infinite sets in the form of "Hilbert's Hotel." Two distinct topological processes can be observed, depending on the structure of the fractional optical element.

FAST TRACK COMMUNICATION: General approach to \\mathfrak {SU}(n) quasi-distribution functions

NASA Astrophysics Data System (ADS)

Klimov, Andrei B.; de Guise, Hubert

2010-10-01

We propose an operational form for the kernel of a mapping between an operator acting in a Hilbert space of a quantum system with an \\mathfrak {SU}(n) symmetry group and its symbol in the corresponding classical phase space. For symmetric irreps of \\mathfrak {SU}(n) , this mapping is bijective. We briefly discuss complications that will occur in the general case.

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R. K.

1985-01-01

Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

Acquisition of High Field Nuclear Magnetic Resonance Spectrometers for Research in Molecular Structure, Function and Dynamics

DTIC Science & Technology

2012-09-01

2005) Fibrinogen and fibrin. Adv Protein Chem 70, 247-299 2. Ariens, R. A., Lai, T. S., Weisel, J. W., Greenberg , C. S., and Grant, P. J. (2002) Role...matrix for the z-component of angular momentum # general case of spin j, Hilbert space has 2j+1 dimensions Iz j=5/2; Iz=diag([j:-1:-j

Entanglement entropy in (3 + 1)-d free U(1) gauge theory

NASA Astrophysics Data System (ADS)

Soni, Ronak M.; Trivedi, Sandip P.

2017-02-01

We consider the entanglement entropy for a free U(1) theory in 3+1 dimensions in the extended Hilbert space definition. By taking the continuum limit carefully we obtain a replica trick path integral which calculates this entanglement entropy. The path integral is gauge invariant, with a gauge fixing delta function accompanied by a Faddeev -Popov determinant. For a spherical region it follows that the result for the logarithmic term in the entanglement, which is universal, is given by the a anomaly coefficient. We also consider the extractable part of the entanglement, which corresponds to the number of Bell pairs which can be obtained from entanglement distillation or dilution. For a spherical region we show that the coefficient of the logarithmic term for the extractable part is different from the extended Hilbert space result. We argue that the two results will differ in general, and this difference is accounted for by a massless scalar living on the boundary of the region of interest.

Hardware-efficient Bell state preparation using Quantum Zeno Dynamics in superconducting circuits

NASA Astrophysics Data System (ADS)

Flurin, Emmanuel; Blok, Machiel; Hacohen-Gourgy, Shay; Martin, Leigh S.; Livingston, William P.; Dove, Allison; Siddiqi, Irfan

By preforming a continuous joint measurement on a two qubit system, we restrict the qubit evolution to a chosen subspace of the total Hilbert space. This extension of the quantum Zeno effect, called Quantum Zeno Dynamics, has already been explored in various physical systems such as superconducting cavities, single rydberg atoms, atomic ensembles and Bose Einstein condensates. In this experiment, two superconducting qubits are strongly dispersively coupled to a high-Q cavity (χ >> κ) allowing for the doubly excited state | 11 〉 to be selectively monitored. The Quantum Zeno Dynamics in the complementary subspace enables us to coherently prepare a Bell state. As opposed to dissipation engineering schemes, we emphasize that our protocol is deterministic, does not rely direct coupling between qubits and functions only using single qubit controls and cavity readout. Such Quantum Zeno Dynamics can be generalized to larger Hilbert space enabling deterministic generation of many-body entangled states, and thus realizes a decoherence-free subspace allowing alternative noise-protection schemes.

Evolution of wave function in a dissipative system

NASA Technical Reports Server (NTRS)

Yu, Li-Hua; Sun, Chang-Pu

1994-01-01

For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner line width theory follows easily.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suchanecki, Z.; Antoniou, I.; Tasaki, S.

We consider the problem of rigging for the Koopman operators of the Renyi and the baker maps. We show that the rigged Hilbert space for the Renyi maps has some of the properties of a strict inductive limit and give a detailed description of the rigged Hilbert space for the baker maps. {copyright} {ital 1996 American Institute of Physics.}

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Directionality fields generated by a local Hilbert transform

NASA Astrophysics Data System (ADS)

Ahmed, W. W.; Herrero, R.; Botey, M.; Hayran, Z.; Kurt, H.; Staliunas, K.

2018-03-01

We propose an approach based on a local Hilbert transform to design non-Hermitian potentials generating arbitrary vector fields of directionality, p ⃗(r ⃗) , with desired shapes and topologies. We derive a local Hilbert transform to systematically build such potentials by modifying background potentials (being either regular or random, extended or localized). We explore particular directionality fields, for instance in the form of a focus to create sinks for probe fields (which could help to increase absorption at the sink), or to generate vortices in the probe fields. Physically, the proposed directionality fields provide a flexible mechanism for dynamical shaping and precise control over probe fields leading to novel effects in wave dynamics.

OSA Proceedings of the International Topical Meeting on Photonic Switching, Held in Salt Lake City, Utah on 6 - 8 March, 1992. Volume 8

DTIC Science & Technology

1992-05-22

Frobenius Theory : Why Hilberts Metric ?," Mathematics of Operations Research 7 (1982) pp.198-210. 11. H. S. M. Cnxeter, Regular Complex Poly- topes...can be made to perform logic functions by pre-setting the device to a given state. We can, in theory , achieve arbitrary logical functionality by using...then extrapolating on the basis of this theory , is about 2000 two diffracted spots appear in the focal plane of the channels. output lenslet array

The Modeling and Control of Acoustic/Structure Interaction Problems via Piezoceramic Actuators: 2-D Numerical Examples

DTIC Science & Technology

1992-04-01

the voltage applied to the it" patch, K ’ is a parameter which depends on the geometry and piezoceramic...in the state space II L 2(fQ) x L2 (F0 ). Here L2(Q) is the quotient space of L2 over the constant functions. The use of the quotient space results...form of the problem, we also define the Hilbert space V = fti(Q) x H(F 0 ) where h!(Q) is the quotient space of Il’ over the constant functions

The Riemann-Hilbert approach to the Helmholtz equation in a quarter-plane: Neumann, Robin and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Its, Alexander; Its, Elizabeth

2018-04-01

We revisit the Helmholtz equation in a quarter-plane in the framework of the Riemann-Hilbert approach to linear boundary value problems suggested in late 1990s by A. Fokas. We show the role of the Sommerfeld radiation condition in Fokas' scheme.

Group-theoretical approach to the construction of bases in 2{sup n}-dimensional Hilbert space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, A.; Romero, J. L.; Klimov, A. B., E-mail: klimov@cencar.udg.mx

2011-06-15

We propose a systematic procedure to construct all the possible bases with definite factorization structure in 2{sup n}-dimensional Hilbert space and discuss an algorithm for the determination of basis separability. The results are applied for classification of bases for an n-qubit system.

Observables and density matrices embedded in dual Hilbert spaces

NASA Astrophysics Data System (ADS)

Prosen, T.; Martignon, L.; Seligman, T. H.

2015-06-01

The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured that we deal with Hilbert spaces although the mathematical background was not entirely clear, particularly, when dealing with bosonic operators. This in turn caused some doubts about the correct way to combine bosonic and fermionic operators or, in other words, regular and Grassmann variables. In this paper we present a formal answer to the problems on a simple and very general basis. We illustrate the resulting construction by revisiting the Bargmann transform and finding the known connection between {{L}}2({{R}}) and the Bargmann-Hilbert space. We pursue this line of thinking one step further and discuss the representations of complex extensions of linear canonical transformations as isometries between dual Hilbert spaces. We then use the formalism to give an explicit formulation for Fock spaces involving both fermions and bosons thus solving the problem at the origin of our considerations.

Basis-neutral Hilbert-space analyzers

PubMed Central

Martin, Lane; Mardani, Davood; Kondakci, H. Esat; Larson, Walker D.; Shabahang, Soroush; Jahromi, Ali K.; Malhotra, Tanya; Vamivakas, A. Nick; Atia, George K.; Abouraddy, Ayman F.

2017-01-01

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes – a critical task for spatial-mode multiplexing and quantum communication – basis-specific principles are invoked that are altogether distinct from that of ‘delay’. Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis – exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a ‘delay’ obtains modal weights in the associated Hilbert space. By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization-interferometer, we have constructed a ‘Hilbert-space analyzer’ capable of projecting optical beams onto any modal basis. PMID:28344331

Remarks on the "Non-canonicity Puzzle": Lagrangian Symmetries of the Einstein-Hilbert Action

NASA Astrophysics Data System (ADS)

Kiriushcheva, N.; Komorowski, P. G.; Kuzmin, S. V.

2012-07-01

Given the non-canonical relationship between variables used in the Hamiltonian formulations of the Einstein-Hilbert action (due to Pirani, Schild, Skinner (PSS) and Dirac) and the Arnowitt-Deser-Misner (ADM) action, and the consequent difference in the gauge transformations generated by the first-class constraints of these two formulations, the assumption that the Lagrangians from which they were derived are equivalent leads to an apparent contradiction that has been called "the non-canonicity puzzle". In this work we shall investigate the group properties of two symmetries derived for the Einstein-Hilbert action: diffeomorphism, which follows from the PSS and Dirac formulations, and the one that arises from the ADM formulation. We demonstrate that unlike the diffeomorphism transformations, the ADM transformations (as well as others, which can be constructed for the Einstein-Hilbert Lagrangian using Noether's identities) do not form a group. This makes diffeomorphism transformations unique (the term "canonical" symmetry might be suggested). If the two Lagrangians are to be called equivalent, canonical symmetry must be preserved. The interplay between general covariance and the canonicity of the variables used is discussed.

On the BV formalism of open superstring field theory in the large Hilbert space

NASA Astrophysics Data System (ADS)

Matsunaga, Hiroaki; Nomura, Mitsuru

2018-05-01

We construct several BV master actions for open superstring field theory in the large Hilbert space. First, we show that a naive use of the conventional BV approach breaks down at the third order of the antifield number expansion, although it enables us to define a simple "string antibracket" taking the Darboux form as spacetime antibrackets. This fact implies that in the large Hilbert space, "string fields-antifields" should be reassembled to obtain master actions in a simple manner. We determine the assembly of the string anti-fields on the basis of Berkovits' constrained BV approach, and give solutions to the master equation defined by Dirac antibrackets on the constrained string field-antifield space. It is expected that partial gauge-fixing enables us to relate superstring field theories based on the large and small Hilbert spaces directly: reassembling string fields-antifields is rather natural from this point of view. Finally, inspired by these results, we revisit the conventional BV approach and construct a BV master action based on the minimal set of string fields-antifields.

Backward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz source

NASA Astrophysics Data System (ADS)

Nho Hào, Dinh; Van Duc, Nguyen; Van Thang, Nguyen

2018-05-01

Let H be a Hilbert space with the inner product and the norm , a positive self-adjoint unbounded time-dependent operator on H and . We establish stability estimates of Hölder type and propose a regularization method with error estimates of Hölder type for the ill-posed backward semi-linear parabolic equation with the source function f satisfying a local Lipschitz condition.

Projective loop quantum gravity. I. State space

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2016-12-01

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolów, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.

Computation and visualization of geometric partial differential equations

NASA Astrophysics Data System (ADS)

Tiee, Christopher L.

The chief goal of this work is to explore a modern framework for the study and approximation of partial differential equations, recast common partial differential equations into this framework, and prove theorems about such equations and their approximations. A central motivation is to recognize and respect the essential geometric nature of such problems, and take it into consideration when approximating. The hope is that this process will lead to the discovery of more refined algorithms and processes and apply them to new problems. In the first part, we introduce our quantities of interest and reformulate traditional boundary value problems in the modern framework. We see how Hilbert complexes capture and abstract the most important properties of such boundary value problems, leading to generalizations of important classical results such as the Hodge decomposition theorem. They also provide the proper setting for numerical approximations. We also provide an abstract framework for evolution problems in these spaces: Bochner spaces. We next turn to approximation. We build layers of abstraction, progressing from functions, to differential forms, and finally, to Hilbert complexes. We explore finite element exterior calculus (FEEC), which allows us to approximate solutions involving differential forms, and analyze the approximation error. In the second part, we prove our central results. We first prove an extension of current error estimates for the elliptic problem in Hilbert complexes. This extension handles solutions with nonzero harmonic part. Next, we consider evolution problems in Hilbert complexes and prove abstract error estimates. We apply these estimates to the problem for Riemannian hypersurfaces in R. {n+1},generalizing current results for open subsets of R. {n}. Finally, we applysome of the concepts to a nonlinear problem, the Ricci flow on surfaces, and use tools from nonlinear analysis to help develop and analyze the equations. In the appendices, we detail some additional motivation and a source for further examples: canonical geometries that are realized as steady-state solutions to parabolic equations similar to that of Ricci flow. An eventual goal is to compute such solutions using the methods of the previous chapters.

Unveiling signatures of interdecadal climate changes by Hilbert analysis

NASA Astrophysics Data System (ADS)

Zappalà, Dario; Barreiro, Marcelo; Masoller, Cristina

2017-04-01

A recent study demonstrated that, in a class of networks of oscillators, the optimal network reconstruction from dynamics is obtained when the similarity analysis is performed not on the original dynamical time series, but on transformed series obtained by Hilbert transform. [1] That motivated us to use Hilbert transform to study another kind of (in a broad sense) "oscillating" series, such as the series of temperature. Actually, we found that Hilbert analysis of SAT (Surface Air Temperature) time series uncovers meaningful information about climate and is therefore a promising tool for the study of other climatological variables. [2] In this work we analysed a large dataset of SAT series, performing Hilbert transform and further analysis with the goal of finding signs of climate change during the analysed period. We used the publicly available ERA-Interim dataset, containing reanalysis data. [3] In particular, we worked on daily SAT time series, from year 1979 to 2015, in 16380 points arranged over a regular grid on the Earth surface. From each SAT time series we calculate the anomaly series and also, by using the Hilbert transform, we calculate the instantaneous amplitude and instantaneous frequency series. Our first approach is to calculate the relative variation: the difference between the average value on the last 10 years and the average value on the first 10 years, divided by the average value over all the analysed period. We did this calculations on our transformed series: frequency and amplitude, both with average values and standard deviation values. Furthermore, to have a comparison with an already known analysis methods, we did these same calculations on the anomaly series. We plotted these results as maps, where the colour of each site indicates the value of its relative variation. Finally, to gain insight in the interpretation of our results over real SAT data, we generated synthetic sinusoidal series with various levels of additive noise. By applying Hilbert analysis to the synthetic data, we uncovered a clear trend between mean amplitude and mean frequency: as the noise level grows, the amplitude increases while the frequency decreases. Research funded in part by AGAUR (Generalitat de Catalunya), EU LINC project (Grant No. 289447) and Spanish MINECO (FIS2015-66503-C3-2-P).

Coherence in quantum estimation

NASA Astrophysics Data System (ADS)

Giorda, Paolo; Allegra, Michele

2018-01-01

The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it establishes the ultimate bounds of the achievable precision. We show a relation between the statistical distance between infinitesimally close quantum states and the second order variation of the coherence of the optimal measurement basis with respect to the state of the probe. In quantum phase estimation protocols, this leads to propose coherence as the relevant resource that one has to engineer and control to optimize the estimation precision. Furthermore, the main object of the theory i.e. the symmetric logarithmic derivative, in many cases allows one to identify a proper factorization of the whole Hilbert space in two subsystems. The factorization allows one to discuss the role of coherence versus correlations in estimation protocols; to show how certain estimation processes can be completely or effectively described within a single-qubit subsystem; and to derive lower bounds for the scaling of the estimation precision with the number of probes used. We illustrate how the framework works for both noiseless and noisy estimation procedures, in particular those based on multi-qubit GHZ-states. Finally we succinctly analyze estimation protocols based on zero-temperature critical behavior. We identify the coherence that is at the heart of their efficiency, and we show how it exhibits the non-analyticities and scaling behavior proper of a large class of quantum phase transitions.

Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability

NASA Technical Reports Server (NTRS)

Haddad, Wassim M.; Bernstein, Dennis S.

1991-01-01

Lyapunov function proofs of sufficient conditions for asymptotic stability are given for feedback interconnections of bounded real and positive real transfer functions. Two cases are considered: (1) a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and (2) two strictly proper bounded real (resp., positive real) transfer functions. A similar treatment is given for the circle and Popov theorems. Application of these results to robust stability with time-varying bounded real, positive real, and sector-bounded uncertainty is discussed.

An algorithm for the split-feasibility problems with application to the split-equality problem.

PubMed

Chuang, Chih-Sheng; Chen, Chi-Ming

2017-01-01

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

MURI: Optimal Quantum Dynamic Discrimination of Chemical and Biological Agents

DTIC Science & Technology

2008-06-12

multiparameter) Hilbert space for enhanced detection and classification: an application of receiver operating curve statistics to laser-based mass...Adaptive reshaping of objects in (multiparameter) Hilbert space for enhanced detection and classification: an application of receiver operating curve...Doctoral Associate Muhannad Zamari, Graduate Student Ilya Greenberg , Computer Consultant Getahun Menkir, Graduate Student Lalinda Palliyaguru, Graduate

Hidden simplicity of the gravity action

DOE PAGES

Cheung, Clifford; Remmen, Grant N.

2017-09-01

We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons and a single auxiliary field. The corresponding equations of motion are the Einstein field equations rewritten as two coupled first-order differential equations. Since all Feynman diagrams are cubic, we are able to derive new off-shell recursion relations for tree-level graviton scattering amplitudes. With a judicious choice of gauge fixing, we then construct an especially compact form for the Einstein-Hilbert action in which all graviton interactions are simplymore » proportional to the graviton kinetic term. Our results apply to graviton perturbations about an arbitrary curved background spacetime.« less

Hidden simplicity of the gravity action

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheung, Clifford; Remmen, Grant N.

We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons and a single auxiliary field. The corresponding equations of motion are the Einstein field equations rewritten as two coupled first-order differential equations. Since all Feynman diagrams are cubic, we are able to derive new off-shell recursion relations for tree-level graviton scattering amplitudes. With a judicious choice of gauge fixing, we then construct an especially compact form for the Einstein-Hilbert action in which all graviton interactions are simplymore » proportional to the graviton kinetic term. Our results apply to graviton perturbations about an arbitrary curved background spacetime.« less

Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C.

1992-11-01

The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schrödinger equation as an example, we show that all types of solutions of the linear problems, as well as spectral data known in the literature, are given as specific values of this unique function — the resolvent function. A new form of the inverse problem is formulated.

Adaptive multiregression in reproducing kernel Hilbert spaces: the multiaccess MIMO channel case.

PubMed

Slavakis, Konstantinos; Bouboulis, Pantelis; Theodoridis, Sergios

2012-02-01

This paper introduces a wide framework for online, i.e., time-adaptive, supervised multiregression tasks. The problem is formulated in a general infinite-dimensional reproducing kernel Hilbert space (RKHS). In this context, a fairly large number of nonlinear multiregression models fall as special cases, including the linear case. Any convex, continuous, and not necessarily differentiable function can be used as a loss function in order to quantify the disagreement between the output of the system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. To this end, we demonstrate a way to calculate the subgradients of robust loss functions, suitable for the multiregression task. As it is by now well documented, when dealing with online schemes in RKHS, the memory keeps increasing with each iteration step. To attack this problem, a simple sparsification strategy is utilized, which leads to an algorithmic scheme of linear complexity with respect to the number of unknown parameters. A convergence analysis of the technique, based on arguments of convex analysis, is also provided. To demonstrate the capacity of the proposed method, the multiregressor is applied to the multiaccess multiple-input multiple-output channel equalization task for a setting with poor resources and nonavailable channel information. Numerical results verify the potential of the method, when its performance is compared with those of the state-of-the-art linear techniques, which, in contrast, use space-time coding, more antenna elements, as well as full channel information.

Non-algebraic integrability of the Chew-Low reversible dynamical system of the Cremona type and the relation with the 7th Hilbert problem (non-resonant case)

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

A smooth reversible dynamical system (SRDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions (the Chew-Low equations for p- wave πN- scattering) are considered. This SRDS is splitted into 1- and 2-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous 3-point functional equation. Non-algebraic integrability of SRDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a non-resonant fixed point. The proof is based on the classical Feldman-Baker theorem on linear forms of logarithms of algebraic numbers, which, in turn, relies upon solving the 7th Hilbert problem by A.I. Gel'fond and T. Schneider and new powerful methods of A. Baker in the theory of transcendental numbers. The general theorem, following from the Feldman-Baker theorem, on applicability of the Siegel theorem to the set of the eigenvalues λ ɛ Cn of a mapping at a non-resonant fixed point which belong to the algebraic number field A is formulated and proved. The main results are presented in Theorems 1-3, 5, 7, 8 and Remarks 3, 7.

An assessment of envelope-based demodulation in case of proximity of carrier and modulation frequencies

NASA Astrophysics Data System (ADS)

Shahriar, Md Rifat; Borghesani, Pietro; Randall, R. B.; Tan, Andy C. C.

2017-11-01

Demodulation is a necessary step in the field of diagnostics to reveal faults whose signatures appear as an amplitude and/or frequency modulation. The Hilbert transform has conventionally been used for the calculation of the analytic signal required in the demodulation process. However, the carrier and modulation frequencies must meet the conditions set by the Bedrosian identity for the Hilbert transform to be applicable for demodulation. This condition, basically requiring the carrier frequency to be sufficiently higher than the frequency of the modulation harmonics, is usually satisfied in many traditional diagnostic applications (e.g. vibration analysis of gear and bearing faults) due to the order-of-magnitude ratio between the carrier and modulation frequency. However, the diversification of the diagnostic approaches and applications shows cases (e.g. electrical signature analysis-based diagnostics) where the carrier frequency is in close proximity to the modulation frequency, thus challenging the applicability of the Bedrosian theorem. This work presents an analytic study to quantify the error introduced by the Hilbert transform-based demodulation when the Bedrosian identity is not satisfied and proposes a mitigation strategy to combat the error. An experimental study is also carried out to verify the analytical results. The outcome of the error analysis sets a confidence limit on the estimated modulation (both shape and magnitude) achieved through the Hilbert transform-based demodulation in case of violated Bedrosian theorem. However, the proposed mitigation strategy is found effective in combating the demodulation error aroused in this scenario, thus extending applicability of the Hilbert transform-based demodulation.

Dynamic characterization of a damaged beam using empirical mode decomposition and Hilbert spectrum method

NASA Astrophysics Data System (ADS)

Chang, Chih-Chen; Poon, Chun-Wing

2004-07-01

Recently, the empirical mode decomposition (EMD) in combination with the Hilbert spectrum method has been proposed to identify the dynamic characteristics of linear structures. In this study, this EMD and Hilbert spectrum method is used to analyze the dynamic characteristics of a damaged reinforced concrete (RC) beam in the laboratory. The RC beam is 4m long with a cross section of 200mm X 250mm. The beam is sequentially subjected to a concentrated load of different magnitudes at the mid-span to produce different degrees of damage. An impact load is applied around the mid-span to excite the beam. Responses of the beam are recorded by four accelerometers. Results indicate that the EMD and Hilbert spectrum method can reveal the variation of the dynamic characteristics in the time domain. These results are also compared with those obtained using the Fourier analysis. In general, it is found that the two sets of results correlate quite well in terms of mode counts and frequency values. Some differences, however, can be seen in the damping values, which perhaps can be attributed to the linear assumption of the Fourier transform.

A combinatorial filtering method for magnetotelluric time-series based on Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Cai, Jianhua

2014-11-01

Magnetotelluric (MT) time-series are often contaminated with noise from natural or man-made processes. A substantial improvement is possible when the time-series are presented as clean as possible for further processing. A combinatorial method is described for filtering of MT time-series based on the Hilbert-Huang transform that requires a minimum of human intervention and leaves good data sections unchanged. Good data sections are preserved because after empirical mode decomposition the data are analysed through hierarchies, morphological filtering, adaptive threshold and multi-point smoothing, allowing separation of noise from signals. The combinatorial method can be carried out without any assumption about the data distribution. Simulated data and the real measured MT time-series from three different regions, with noise caused by baseline drift, high frequency noise and power-line contribution, are processed to demonstrate the application of the proposed method. Results highlight the ability of the combinatorial method to pick out useful signals, and the noise is suppressed greatly so that their deleterious influence is eliminated for the MT transfer function estimation.

Non-Destructive Detection of Wire Rope Discontinuities from Residual Magnetic Field Images Using the Hilbert-Huang Transform and Compressed Sensing

PubMed Central

Zhang, Juwei; Tan, Xiaojiang; Zheng, Pengbo

2017-01-01

Electromagnetic methods are commonly employed to detect wire rope discontinuities. However, determining the residual strength of wire rope based on the quantitative recognition of discontinuities remains problematic. We have designed a prototype device based on the residual magnetic field (RMF) of ferromagnetic materials, which overcomes the disadvantages associated with in-service inspections, such as large volume, inconvenient operation, low precision, and poor portability by providing a relatively small and lightweight device with improved detection precision. A novel filtering system consisting of the Hilbert-Huang transform and compressed sensing wavelet filtering is presented. Digital image processing was applied to achieve the localization and segmentation of defect RMF images. The statistical texture and invariant moment characteristics of the defect images were extracted as the input of a radial basis function neural network. Experimental results show that the RMF device can detect defects in various types of wire rope and prolong the service life of test equipment by reducing the friction between the detection device and the wire rope by accommodating a high lift-off distance. PMID:28300790

Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry

NASA Astrophysics Data System (ADS)

Moretti, Valter; Oppio, Marco

As earlier conjectured by several authors and much later established by Solèr (relying on partial results by Piron, Maeda-Maeda and other authors), from the lattice theory point of view, Quantum Mechanics may be formulated in real, complex or quaternionic Hilbert spaces only. Stückelberg provided some physical, but not mathematically rigorous, reasons for ruling out the real Hilbert space formulation, assuming that any formulation should encompass a statement of Heisenberg principle. Focusing on this issue from another — in our opinion, deeper — viewpoint, we argue that there is a general fundamental reason why elementary quantum systems are not described in real Hilbert spaces. It is their basic symmetry group. In the first part of the paper, we consider an elementary relativistic system within Wigner’s approach defined as a locally-faithful irreducible strongly-continuous unitary representation of the Poincaré group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincaré invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation itself. This complex structure leads to a physically equivalent reformulation of the theory in a complex Hilbert space. Within this complex formulation, differently from what happens in the real one, all selfadjoint operators represent observables in accordance with Solèr’s thesis, and the standard quantum version of Noether theorem may be formulated. In the second part of this work, we focus on the physical hypotheses adopted to define a quantum elementary relativistic system relaxing them on the one hand, and making our model physically more general on the other hand. We use a physically more accurate notion of irreducibility regarding the algebra of observables only, we describe the symmetries in terms of automorphisms of the restricted lattice of elementary propositions of the quantum system and we adopt a notion of continuity referred to the states viewed as probability measures on the elementary propositions. Also in this case, the final result proves that there exists a unique (up to sign) Poincaré invariant complex structure making the theory complex and completely fitting into Solèr’s picture. This complex structure reveals a nice interplay of Poincaré symmetry and the classification of the commutant of irreducible real von Neumann algebras.

Photonic Hilbert transformers based on laterally apodized integrated waveguide Bragg gratings on a SOI wafer.

PubMed

Bazargani, Hamed Pishvai; Burla, Maurizio; Chrostowski, Lukas; Azaña, José

2016-11-01

We experimentally demonstrate high-performance integer and fractional-order photonic Hilbert transformers based on laterally apodized Bragg gratings in a silicon-on-insulator technology platform. The sub-millimeter-long gratings have been fabricated using single-etch electron beam lithography, and the resulting HT devices offer operation bandwidths approaching the THz range, with time-bandwidth products between 10 and 20.

Heterotic reduction of Courant algebroid connections and Einstein-Hilbert actions

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Vysoký, Jan

2016-08-01

We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein-Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Optimum constrained image restoration filters

NASA Technical Reports Server (NTRS)

Riemer, T. E.; Mcgillem, C. D.

1974-01-01

The filter was developed in Hilbert space by minimizing the radius of gyration of the overall or composite system point-spread function subject to constraints on the radius of gyration of the restoration filter point-spread function, the total noise power in the restored image, and the shape of the composite system frequency spectrum. An iterative technique is introduced which alters the shape of the optimum composite system point-spread function, producing a suboptimal restoration filter which suppresses undesirable secondary oscillations. Finally this technique is applied to multispectral scanner data obtained from the Earth Resources Technology Satellite to provide resolution enhancement. An experimental approach to the problems involving estimation of the effective scanner aperture and matching the ERTS data to available restoration functions is presented.

Multivariate approximation methods and applications to geophysics and geodesy

NASA Technical Reports Server (NTRS)

Munteanu, M. J.

1979-01-01

The first report in a series is presented which is intended to be written by the author with the purpose of treating a class of approximation methods of functions in one and several variables and ways of applying them to geophysics and geodesy. The first report is divided in three parts and is devoted to the presentation of the mathematical theory and formulas. Various optimal ways of representing functions in one and several variables and the associated error when information is had about the function such as satellite data of different kinds are discussed. The framework chosen is Hilbert spaces. Experiments were performed on satellite altimeter data and on satellite to satellite tracking data.

The eigenfrequency spectrum of linear magnetohydrodynamic perturbations in stationary equilibria: A variational principle

NASA Astrophysics Data System (ADS)

Andries, Jesse

2010-11-01

The frequencies of the normal modes of oscillation of linear magnetohydrodynamic perturbations of a stationary equilibrium are related to the stationary points of a quadratic functional over the Hilbert space of Lagrangian displacement vectors, which is subject to a constraint. In the absence of a background flow (or of a uniform flow), the relation reduces to the well-known Rayleigh-Ritz variational principle. In contrast to the existing variational principles for perturbations of stationary equilibria, the present treatment does neither impose additional symmetry restrictions on the equilibrium, nor does it involve the generalization to bilinear functionals instead of quadratic forms. This allows a more natural interpretation of the quadratic forms as energy functionals.

Large dynamic range optical vector analyzer based on optical single-sideband modulation and Hilbert transform

NASA Astrophysics Data System (ADS)

Xue, Min; Pan, Shilong; Zhao, Yongjiu

2016-07-01

A large dynamic range optical vector analyzer (OVA) based on optical single-sideband modulation is proposed and demonstrated. By dividing the optical signal after optical device under test into two paths, reversing the phase of one swept sideband using a Hilbert transformer in one path, and detecting the two signals from the two paths with a balanced photodetector, the measurement errors induced by the residual -1st-order sideband and the high-order sidebands can be eliminated and the dynamic range of the measurement is increased. In a proof-of-concept experiment, the stimulated Brillouin scattering and a fiber Bragg grating are measured by OVAs with and without the Hilbert transform and balanced photodetection. Results show that about 40-dB improvement in the measurement dynamic range is realized by the proposed OVA.

An "unreasonable effectiveness" of Hilbert transform for the transition phase behavior in an Aharonov-Bohm two-path interferometer

NASA Astrophysics Data System (ADS)

Englman, R.

2016-08-01

The recent phase shift data of Takada et al. (Phys. Rev. Lett. 113 (2014) 126601) for a two level system are reconstructed from their current intensity curves by the method of Hilbert transform, for which the underlying Physics is the principle of causality. An introductory algebraic model illustrates pedagogically the working of the method and leads to newly derived relationships involving phenomenological parameters, in particular for the sign of the phase slope between the resonance peaks. While the parametrization of the experimental current intensity data in terms of a few model parameters shows only a qualitative agreement for the phase shift, due to the strong impact of small, detailed variations in the experimental intensity curve on the phase behavior, the numerical Hilbert transform yields a satisfactory reproduction of the phase.

An Image Encryption Algorithm Utilizing Julia Sets and Hilbert Curves

PubMed Central

Sun, Yuanyuan; Chen, Lina; Xu, Rudan; Kong, Ruiqing

2014-01-01

Image encryption is an important and effective technique to protect image security. In this paper, a novel image encryption algorithm combining Julia sets and Hilbert curves is proposed. The algorithm utilizes Julia sets’ parameters to generate a random sequence as the initial keys and gets the final encryption keys by scrambling the initial keys through the Hilbert curve. The final cipher image is obtained by modulo arithmetic and diffuse operation. In this method, it needs only a few parameters for the key generation, which greatly reduces the storage space. Moreover, because of the Julia sets’ properties, such as infiniteness and chaotic characteristics, the keys have high sensitivity even to a tiny perturbation. The experimental results indicate that the algorithm has large key space, good statistical property, high sensitivity for the keys, and effective resistance to the chosen-plaintext attack. PMID:24404181

Semiconductor laser self-mixing micro-vibration measuring technology based on Hilbert transform

NASA Astrophysics Data System (ADS)

Tao, Yufeng; Wang, Ming; Xia, Wei

2016-06-01

A signal-processing synthesizing Wavelet transform and Hilbert transform is employed to measurement of uniform or non-uniform vibrations in self-mixing interferometer on semiconductor laser diode with quantum well. Background noise and fringe inclination are solved by decomposing effect, fringe counting is adopted to automatic determine decomposing level, a couple of exact quadrature signals are produced by Hilbert transform to extract vibration. The tempting potential of real-time measuring micro vibration with high accuracy and wide dynamic response bandwidth using proposed method is proven by both simulation and experiment. Advantages and error sources are presented as well. Main features of proposed semiconductor laser self-mixing interferometer are constant current supply, high resolution, simplest optical path and much higher tolerance to feedback level than existing self-mixing interferometers, which is competitive for non-contact vibration measurement.

Application of Huang-Hilbert Transforms to Geophysical Datasets

NASA Technical Reports Server (NTRS)

Duffy, Dean G.

2003-01-01

The Huang-Hilbert transform is a promising new method for analyzing nonstationary and nonlinear datasets. In this talk I will apply this technique to several important geophysical datasets. To understand the strengths and weaknesses of this method, multi- year, hourly datasets of the sea level heights and solar radiation will be analyzed. Then we will apply this transform to the analysis of gravity waves observed in a mesoscale observational net.

Efficient Asymptotic Preserving Deterministic methods for the Boltzmann Equation

DTIC Science & Technology

2011-04-01

history tracing back to Hilbert , Chapmann and Enskog (Cercignani, 1988) at the beginning of the last century. The mathematical difficulties related to the...accurate determin- istic computations of the stationary solutions, which may be treated by schemes aimed to capture the stationary state ( Greenberg and...Stokes model, can be considered using the Chapmann-Enskog and the Hilbert expansions. We refer to Levermore (1996) for a mathematical setting of the

The Einstein-Hilbert gravitation with minimum length

NASA Astrophysics Data System (ADS)

Louzada, H. L. C.

2018-05-01

We study the Einstein-Hilbert gravitation with the deformed Heisenberg algebra leading to the minimum length, with the intention to find and estimate the corrections in this theory, clarifying whether or not it is possible to obtain, by means of the minimum length, a theory, in D=4, which is causal, unitary and provides a massive graviton. Therefore, we will calculate and analyze the dispersion relationships of the considered theory.

Concepts and Bounded Rationality: An Application of Niestegge's Approach to Conditional Quantum Probabilities

NASA Astrophysics Data System (ADS)

Blutner, Reinhard

2009-03-01

Recently, Gerd Niestegge developed a new approach to quantum mechanics via conditional probabilities developing the well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization. I will apply his powerful and rigorous approach to the treatment of concepts using a geometrical model of meaning. In this model, instances are treated as vectors of a Hilbert space H. In the present approach there are at least two possibilities to form categories. The first possibility sees categories as a mixture of its instances (described by a density matrix). In the simplest case we get the classical probability theory including the Bayesian formula. The second possibility sees categories formed by a distinctive prototype which is the superposition of the (weighted) instances. The construction of prototypes can be seen as transferring a mixed quantum state into a pure quantum state freezing the probabilistic characteristics of the superposed instances into the structure of the formed prototype. Closely related to the idea of forming concepts by prototypes is the existence of interference effects. Such inference effects are typically found in macroscopic quantum systems and I will discuss them in connection with several puzzles of bounded rationality. The present approach nicely generalizes earlier proposals made by authors such as Diederik Aerts, Andrei Khrennikov, Ricardo Franco, and Jerome Busemeyer. Concluding, I will suggest that an active dialogue between cognitive approaches to logic and semantics and the modern approach of quantum information science is mandatory.

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity Field Modelling

DTIC Science & Technology

1984-04-01

5.15) where a is a positive constant and 11 IIH the Hilbert space norm associated with the chosen covariance function K. The constant a is arbitrary...Density Anomalies 14 5. Unknown Densities - Geophysical Inversion 16 6. Density Modelling Using Rectangular Prisms 24 6.1 Space Domain 24 6.2 Frequency...theory: to calculate the gravity potential and its derivatives in space due to 6 • given density distributions. When the prime interest is in "external

Analyzing nonstationary financial time series via hilbert-huang transform (HHT)

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2008-01-01

An apparatus, computer program product and method of analyzing non-stationary time varying phenomena. A representation of a non-stationary time varying phenomenon is recursively sifted using Empirical Mode Decomposition (EMD) to extract intrinsic mode functions (IMFs). The representation is filtered to extract intrinsic trends by combining a number of IMFs. The intrinsic trend is inherent in the data and identifies an IMF indicating the variability of the phenomena. The trend also may be used to detrend the data.

Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Gandt, Francois

2006-06-19

In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that 'axiomatics', following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?.

An Investigation of the Overlap Among Disinhibited Eating Behaviors in Children and Adolescents

DTIC Science & Technology

2013-09-01

findings suggest that emotional eating may be linked with aberrant eating patterns--excess overall energy intake and consumption of high- fat foods-that...overweight and have greater body fat mass than youth who reported no loss of control eating episodes (Ackard, Neumark-Sztainer, Story, & Perry, 2003; Field...reporting loss of control eating consumed more overall energy (Hilbert & Czaja, 2009; Hilbert, et al., 2010), especially from fat and carbohydrate

Experimental Test of Nonclassicality for a Single Particle

DTIC Science & Technology

2008-08-01

photon Greenberger -Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000). 15. G. Brida, M. Genovese, C. Novero, and E. Predazzi, “New experimental...33, 34]) and its ability to show that some quantum states in a two dimensional Hilbert space cannot be classical. We note that because this is a...dimensional Hilbert space and a physical implementation of that test. Appendix A necessary requirement for a convincingly realizing the Alicki-Van Ryn’s

Using the Hilbert uniqueness method in a reconstruction algorithm for electrical impedance tomography.

PubMed

Dai, W W; Marsili, P M; Martinez, E; Morucci, J P

1994-05-01

This paper presents a new version of the layer stripping algorithm in the sense that it works essentially by repeatedly stripping away the outermost layer of the medium after having determined the conductivity value in this layer. In order to stabilize the ill posed boundary value problem related to each layer, we base our algorithm on the Hilbert uniqueness method (HUM) and implement it with the boundary element method (BEM).

Quantum Hilbert Hotel.

PubMed

Potoček, Václav; Miatto, Filippo M; Mirhosseini, Mohammad; Magaña-Loaiza, Omar S; Liapis, Andreas C; Oi, Daniel K L; Boyd, Robert W; Jeffers, John

2015-10-16

In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity." In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.

Spectral Automorphisms in Quantum Logics

NASA Astrophysics Data System (ADS)

Ivanov, Alexandru; Caragheorgheopol, Dan

2010-12-01

In quantum mechanics, the Hilbert space formalism might be physically justified in terms of some axioms based on the orthomodular lattice (OML) mathematical structure (Piron in Foundations of Quantum Physics, Benjamin, Reading, 1976). We intend to investigate the extent to which some fundamental physical facts can be described in the more general framework of OMLs, without the support of Hilbert space-specific tools. We consider the study of lattice automorphisms properties as a “substitute” for Hilbert space techniques in investigating the spectral properties of observables. This is why we introduce the notion of spectral automorphism of an OML. Properties of spectral automorphisms and of their spectra are studied. We prove that the presence of nontrivial spectral automorphisms allow us to distinguish between classical and nonclassical theories. We also prove, for finite dimensional OMLs, that for every spectral automorphism there is a basis of invariant atoms. This is an analogue of the spectral theorem for unitary operators having purely point spectrum.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

NASA Astrophysics Data System (ADS)

Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.

2008-11-01

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Independence and totalness of subspaces in phase space methods

NASA Astrophysics Data System (ADS)

Vourdas, A.

2018-04-01

The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota's formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.

Diurnal characteristics of turbulent intermittency in the Taklimakan Desert

NASA Astrophysics Data System (ADS)

Wei, Wei; Wang, Minzhong; Zhang, Hongsheng; He, Qing; Ali, Mamtimin; Wang, Yinjun

2017-12-01

A case study is performed to investigate the behavior of turbulent intermittency in the Taklimakan Desert using an intuitive, direct, and adaptive method, the arbitrary-order Hilbert spectral analysis (arbitrary-order HSA). Decomposed modes from the vertical wind speed series confirm the dyadic filter-bank essence of the empirical mode decomposition processes. Due to the larger eddies in the CBL, higher energy modes occur during the day. The second-order Hilbert spectra L2 (ω ) delineate the spectral gap separating fine-scale turbulence from large-scale motions. Both the values of kurtosis and the Hilbert-based scaling exponent ξ ( q ) reveal that the turbulence intermittency at night is much stronger than that during the day, and the stronger intermittency is associated with more stable stratification under clear-sky conditions. This study fills the gap in the characteristics of turbulence intermittency in the Taklimakan Desert area using a relatively new method.

Relaxation in control systems of subdifferential type

NASA Astrophysics Data System (ADS)

Tolstonogov, A. A.

2006-02-01

In a separable Hilbert space we consider a control system with evolution operators that are subdifferentials of a proper convex lower semicontinuous function depending on time. The constraint on the control is given by a multivalued function with non-convex values that is lower semicontinuous with respect to the variable states. Along with the original system we consider the system in which the constraint on the control is the upper semicontinuous convex-valued regularization of the original constraint. We study relations between the solution sets of these systems. As an application we consider a control variational inequality. We give an example of a control system of parabolic type with an obstacle.

Research on Bounded Rationality of Fuzzy Choice Functions

PubMed Central

Wu, Xinlin; Zhao, Yong

2014-01-01

The rationality of a fuzzy choice function is a hot research topic in the study of fuzzy choice functions. In this paper, two common fuzzy sets are studied and analyzed in the framework of the Banerjee choice function. The complete rationality and bounded rationality of fuzzy choice functions are defined based on the two fuzzy sets. An assumption is presented to study the fuzzy choice function, and especially the fuzzy choice function with bounded rationality is studied combined with some rationality conditions. Results show that the fuzzy choice function with bounded rationality also satisfies some important rationality conditions, but not vice versa. The research gives supplements to the investigation in the framework of the Banerjee choice function. PMID:24782677

Research on bounded rationality of fuzzy choice functions.

PubMed

Wu, Xinlin; Zhao, Yong

2014-01-01

The rationality of a fuzzy choice function is a hot research topic in the study of fuzzy choice functions. In this paper, two common fuzzy sets are studied and analyzed in the framework of the Banerjee choice function. The complete rationality and bounded rationality of fuzzy choice functions are defined based on the two fuzzy sets. An assumption is presented to study the fuzzy choice function, and especially the fuzzy choice function with bounded rationality is studied combined with some rationality conditions. Results show that the fuzzy choice function with bounded rationality also satisfies some important rationality conditions, but not vice versa. The research gives supplements to the investigation in the framework of the Banerjee choice function.

Deep Learning Methods for Underwater Target Feature Extraction and Recognition

PubMed Central

Peng, Yuan; Qiu, Mengran; Shi, Jianfei; Liu, Liangliang

2018-01-01

The classification and recognition technology of underwater acoustic signal were always an important research content in the field of underwater acoustic signal processing. Currently, wavelet transform, Hilbert-Huang transform, and Mel frequency cepstral coefficients are used as a method of underwater acoustic signal feature extraction. In this paper, a method for feature extraction and identification of underwater noise data based on CNN and ELM is proposed. An automatic feature extraction method of underwater acoustic signals is proposed using depth convolution network. An underwater target recognition classifier is based on extreme learning machine. Although convolution neural networks can execute both feature extraction and classification, their function mainly relies on a full connection layer, which is trained by gradient descent-based; the generalization ability is limited and suboptimal, so an extreme learning machine (ELM) was used in classification stage. Firstly, CNN learns deep and robust features, followed by the removing of the fully connected layers. Then ELM fed with the CNN features is used as the classifier to conduct an excellent classification. Experiments on the actual data set of civil ships obtained 93.04% recognition rate; compared to the traditional Mel frequency cepstral coefficients and Hilbert-Huang feature, recognition rate greatly improved. PMID:29780407

Simulating the Generalized Gibbs Ensemble (GGE): A Hilbert space Monte Carlo approach

NASA Astrophysics Data System (ADS)

Alba, Vincenzo

By combining classical Monte Carlo and Bethe ansatz techniques we devise a numerical method to construct the Truncated Generalized Gibbs Ensemble (TGGE) for the spin-1/2 isotropic Heisenberg (XXX) chain. The key idea is to sample the Hilbert space of the model with the appropriate GGE probability measure. The method can be extended to other integrable systems, such as the Lieb-Liniger model. We benchmark the approach focusing on GGE expectation values of several local observables. As finite-size effects decay exponentially with system size, moderately large chains are sufficient to extract thermodynamic quantities. The Monte Carlo results are in agreement with both the Thermodynamic Bethe Ansatz (TBA) and the Quantum Transfer Matrix approach (QTM). Remarkably, it is possible to extract in a simple way the steady-state Bethe-Gaudin-Takahashi (BGT) roots distributions, which encode complete information about the GGE expectation values in the thermodynamic limit. Finally, it is straightforward to simulate extensions of the GGE, in which, besides the local integral of motion (local charges), one includes arbitrary functions of the BGT roots. As an example, we include in the GGE the first non-trivial quasi-local integral of motion.

Dissipation and entropy production in open quantum systems

NASA Astrophysics Data System (ADS)

Majima, H.; Suzuki, A.

2010-11-01

A microscopic description of an open system is generally expressed by the Hamiltonian of the form: Htot = Hsys + Henviron + Hsys-environ. We developed a microscopic theory of entropy and derived a general formula, so-called "entropy-Hamiltonian relation" (EHR), that connects the entropy of the system to the interaction Hamiltonian represented by Hsys-environ for a nonequilibrium open quantum system. To derive the EHR formula, we mapped the open quantum system to the representation space of the Liouville-space formulation or thermo field dynamics (TFD), and thus worked on the representation space Script L := Script H otimes , where Script H denotes the ordinary Hilbert space while the tilde Hilbert space conjugates to Script H. We show that the natural transformation (mapping) of nonequilibrium open quantum systems is accomplished within the theoretical structure of TFD. By using the obtained EHR formula, we also derived the equation of motion for the distribution function of the system. We demonstrated that by knowing the microscopic description of the interaction, namely, the specific form of Hsys-environ on the representation space Script L, the EHR formulas enable us to evaluate the entropy of the system and to gain some information about entropy for nonequilibrium open quantum systems.

Application of Hilbert-Huang Transform for Improved Defect Detection in Terahertz NDE of Shuttle Tiles

NASA Technical Reports Server (NTRS)

Anastasi, Robert F.; Madaras, Eric I.

2005-01-01

Terahertz NDE is being examined as a method to inspect the adhesive bond-line of Space Shuttle tiles for defects. Terahertz signals are generated and detected, using optical excitation of biased semiconductors with femtosecond laser pulses. Shuttle tile samples were manufactured with defects that included repair regions unbond regions, and other conditions that occur in Shuttle structures. These samples were inspected with a commercial terahertz NDE system that scanned a tile and generated a data set of RF signals. The signals were post processed to generate C-scan type images that are typically seen in ultrasonic NDE. To improve defect visualization the Hilbert-Huang Transform, a transform that decomposes a signal into oscillating components called intrinsic mode functions, was applied to test signals identified as being in and out of the defect regions and then on a complete data set. As expected with this transform, the results showed that the decomposed low-order modes correspond to signal noise while the high-order modes correspond to low frequency oscillations in the signal and mid-order modes correspond to local signal oscillations. The local oscillations compare well with various reflection interfaces and the defect locations in the original signal.

FAST TRACK COMMUNICATION: SUSY transformations with complex factorization constants: application to spectral singularities

NASA Astrophysics Data System (ADS)

Samsonov, Boris F.

2010-10-01

Supersymmetric (SUSY) transformation operators with complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. The obtained results are applied to Hamiltonians possessing spectral singularities which are non-Hermitian SUSY partners of self-adjoint operators. A new regularization procedure for the resolution of the identity operator in terms of a continuous biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed. It is also argued that if the binorm of continuous spectrum eigenfunctions is interpreted in the same way as the norm of similar functions in the usual Hermitian case, then one can state that the function corresponding to a spectral singularity has zero binorm.

Modeling and Control of Large Flexible Structures.

DTIC Science & Technology

1984-07-31

59 4.5 Spectral factorization using the Hilbert transform 62 4.6 Gain computations 64 4.7 Software development and control system performance 66 Part...in the Hilbert space - L2(S) with the natural inner product, ,>. In many cases A O has a discrete spectrum with associated 2 eigenfunctions which...Davis and Barry 1977) ( Greenberg , MacCamy Nisel and 1968). The natural boundary~.; ’? , : conditions for (17) are in terms of s(zt) at s-O and 1

Multirate Integration Properties of Waveform Relaxation with Applications to Circuit Simulation and Parallel Computation

DTIC Science & Technology

1985-11-18

Greenberg and K. Sakallah at Digital Equipment Corporation, and C-F. Chen, L Nagel, and P. ,. Subrahmanyam at AT&T Bell Laboratories, both for providing...Circuit Theory McGraw-Hill, 1969. [37] R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics...McGraw-Hill, N.Y., 1965. Page 161 [44) R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

1994-01-01

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics

NASA Astrophysics Data System (ADS)

Rowe, David E.

One of the most famous episodes in the early history of general relativity involves the ``race'' in November 1915 between Albert Einstein and David Hilbert to uncover the ``correct'' form for the ten gravitational field equations. In light of recent archival findings, however, this story now has become a topic of renewed interest and controversy among historians of physics and mathematics. Drawing on recent studies and newly found sources, the present essay takes up this familiar tale from a new perspective, one that has seldom received due attention in the standard literature, namely, the mathematical issues at the heart of Einstein's theory. Told from this angle, the leading actors are Einstein's collaborator Marcel Grossmann, his critic Tullio Levi-Civita, his competitor David Hilbert, and several other mathematicians, many of them connected with Hilbert's Göttingen colleagues such as Hermann Weyl, Felix Klein, and Emmy Noether. As Einstein was the first to admit, Göttingen was far more important than Berlin as an active center for research in general relativity. Any account which, like this one, tries to understand both the actions and motives of the leading players must confront the problem of interpreting the rather sparse documentary evidence available. The interpretation offered herein, whatever its merits, aims first and foremost to show how mathematical issues deeply permeated the early history of general relativity.

Career Development and Personal Functioning Differences between Work-Bound and Non-Work Bound Students

ERIC Educational Resources Information Center

Creed, Peter A.; Patton, Wendy; Hood, Michelle

2010-01-01

We surveyed 506 Australian high school students on career development (exploration, planning, job-knowledge, decision-making, indecision), personal functioning (well-being, self-esteem, life satisfaction, school satisfaction) and control variables (parent education, school achievement), and tested differences among work-bound, college-bound and…

Bounds for the Eventual Positivity of Difference Functions of Partitions

NASA Astrophysics Data System (ADS)

Woodford, Roger

2007-01-01

In this paper we specialize work done by Bateman and Erdos concerning difference functions of partition functions. In particular, we are concerned with partitions into fixed powers of the primes. We show that any difference function of these partition functions is eventually increasing, and derive explicit bounds for when it will attain strictly positive values. From these bounds an asymptotic result is derived.

Pipe leak diagnostic using high frequency piezoelectric pressure sensor and automatic selection of intrinsic mode function

NASA Astrophysics Data System (ADS)

Yusop, Hanafi M.; Ghazali, M. F.; Yusof, M. F. M.; Remli, M. A. Pi; Kamarulzaman, M. H.

2017-10-01

In a recent study, the analysis of pressure transient signals could be seen as an accurate and low-cost method for leak and feature detection in water distribution systems. Transient phenomena occurs due to sudden changes in the fluid’s propagation in pipelines system caused by rapid pressure and flow fluctuation due to events such as closing and opening valves rapidly or through pump failure. In this paper, the feasibility of the Hilbert-Huang transform (HHT) method/technique in analysing the pressure transient signals in presented and discussed. HHT is a way to decompose a signal into intrinsic mode functions (IMF). However, the advantage of HHT is its difficulty in selecting the suitable IMF for the next data postprocessing method which is Hilbert Transform (HT). This paper reveals that utilizing the application of an integrated kurtosis-based algorithm for a z-filter technique (I-Kaz) to kurtosis ratio (I-Kaz-Kurtosis) allows/contributes to/leads to automatic selection of the IMF that should be used. This technique is demonstrated on a 57.90-meter medium high-density polyethylene (MDPE) pipe installed with a single artificial leak. The analysis results using the I-Kaz-kurtosis ratio revealed/confirmed that the method can be used as an automatic selection of the IMF although the noise level ratio of the signal is low. Therefore, the I-Kaz-kurtosis ratio method is recommended as a means to implement an automatic selection technique of the IMF for HHT analysis.

Interior tomography from differential phase contrast data via Hilbert transform based on spline functions

NASA Astrophysics Data System (ADS)

Yang, Qingsong; Cong, Wenxiang; Wang, Ge

2016-10-01

X-ray phase contrast imaging is an important mode due to its sensitivity to subtle features of soft biological tissues. Grating-based differential phase contrast (DPC) imaging is one of the most promising phase imaging techniques because it works with a normal x-ray tube of a large focal spot at a high flux rate. However, a main obstacle before this paradigm shift is the fabrication of large-area gratings of a small period and a high aspect ratio. Imaging large objects with a size-limited grating results in data truncation which is a new type of the interior problem. While the interior problem was solved for conventional x-ray CT through analytic extension, compressed sensing and iterative reconstruction, the difficulty for interior reconstruction from DPC data lies in that the implementation of the system matrix requires the differential operation on the detector array, which is often inaccurate and unstable in the case of noisy data. Here, we propose an iterative method based on spline functions. The differential data are first back-projected to the image space. Then, a system matrix is calculated whose components are the Hilbert transforms of the spline bases. The system matrix takes the whole image as an input and outputs the back-projected interior data. Prior information normally assumed for compressed sensing is enforced to iteratively solve this inverse problem. Our results demonstrate that the proposed algorithm can successfully reconstruct an interior region of interest (ROI) from the differential phase data through the ROI.

Coarse graining of entanglement classes in 2 ×m ×n systems

NASA Astrophysics Data System (ADS)

Hebenstreit, M.; Gachechiladze, M.; Gühne, O.; Kraus, B.

2018-03-01

We consider three-partite pure states in the Hilbert space C2⊗Cm⊗Cn and investigate to which states a given state can be locally transformed with a nonvanishing probability. Whenever the initial and final states are elements of the same Hilbert space, the problem can be solved via the characterization of the entanglement classes which are determined via stochastic local operations and classical communication (SLOCC). In the particular case considered here, the matrix pencil theory can be utilized to address this point. In general, there are infinitely many SLOCC classes. However, when considering transformations from higher to lower dimensional Hilbert spaces, an additional hierarchy among the classes can be found. This hierarchy of SLOCC classes coarse grains SLOCC classes which can be reached from a common resource state of higher dimension. We first show that a generic set of states in C2⊗Cm⊗Cn for n =m is the union of infinitely many SLOCC classes, which can be parameterized by m -3 parameters. However, for n ≠m there exists a single SLOCC class which is generic. Using this result, we then show that there is a full-measure set of states in C2⊗Cm⊗Cn such that any state within this set can be transformed locally to a full measure set of states in any lower dimensional Hilbert space. We also investigate resource states, which can be transformed to any state (not excluding any zero-measure set) in the smaller dimensional Hilbert space. We explicitly derive a state in C2⊗Cm⊗C2 m -2 which is the optimal common resource of all states in C2⊗Cm⊗Cm . We also show that for any n <2 m it is impossible to reach all states in C2⊗Cm⊗Cn ˜ whenever n ˜>m .

Improving 3d Spatial Queries Search: Newfangled Technique of Space Filling Curves in 3d City Modeling

NASA Astrophysics Data System (ADS)

Uznir, U.; Anton, F.; Suhaibah, A.; Rahman, A. A.; Mioc, D.

2013-09-01

The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc.. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using web standards. However, these 3D city models consume much more storage compared to two dimensional (2D) spatial data. They involve extra geometrical and topological information together with semantic data. Without a proper spatial data clustering method and its corresponding spatial data access method, retrieving portions of and especially searching these 3D city models, will not be done optimally. Even though current developments are based on an open data model allotted by the Open Geospatial Consortium (OGC) called CityGML, its XML-based structure makes it challenging to cluster the 3D urban objects. In this research, we propose an opponent data constellation technique of space-filling curves (3D Hilbert curves) for 3D city model data representation. Unlike previous methods, that try to project 3D or n-dimensional data down to 2D or 3D using Principal Component Analysis (PCA) or Hilbert mappings, in this research, we extend the Hilbert space-filling curve to one higher dimension for 3D city model data implementations. The query performance was tested using a CityGML dataset of 1,000 building blocks and the results are presented in this paper. The advantages of implementing space-filling curves in 3D city modeling will improve data retrieval time by means of optimized 3D adjacency, nearest neighbor information and 3D indexing. The Hilbert mapping, which maps a subinterval of the [0, 1] interval to the corresponding portion of the d-dimensional Hilbert's curve, preserves the Lebesgue measure and is Lipschitz continuous. Depending on the applications, several alternatives are possible in order to cluster spatial data together in the third dimension compared to its clustering in 2D.

Transfer Function Bounds for Partial-unit-memory Convolutional Codes Based on Reduced State Diagram

NASA Technical Reports Server (NTRS)

Lee, P. J.

1984-01-01

The performance of a coding system consisting of a convolutional encoder and a Viterbi decoder is analytically found by the well-known transfer function bounding technique. For the partial-unit-memory byte-oriented convolutional encoder with m sub 0 binary memory cells and (k sub 0 m sub 0) inputs, a state diagram of 2(K) (sub 0) was for the transfer function bound. A reduced state diagram of (2 (m sub 0) +1) is used for easy evaluation of transfer function bounds for partial-unit-memory codes.

A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints.

PubMed

Liang, X B; Wang, J

2000-01-01

This paper presents a continuous-time recurrent neural-network model for nonlinear optimization with any continuously differentiable objective function and bound constraints. Quadratic optimization with bound constraints is a special problem which can be solved by the recurrent neural network. The proposed recurrent neural network has the following characteristics. 1) It is regular in the sense that any optimum of the objective function with bound constraints is also an equilibrium point of the neural network. If the objective function to be minimized is convex, then the recurrent neural network is complete in the sense that the set of optima of the function with bound constraints coincides with the set of equilibria of the neural network. 2) The recurrent neural network is primal and quasiconvergent in the sense that its trajectory cannot escape from the feasible region and will converge to the set of equilibria of the neural network for any initial point in the feasible bound region. 3) The recurrent neural network has an attractivity property in the sense that its trajectory will eventually converge to the feasible region for any initial states even at outside of the bounded feasible region. 4) For minimizing any strictly convex quadratic objective function subject to bound constraints, the recurrent neural network is globally exponentially stable for almost any positive network parameters. Simulation results are given to demonstrate the convergence and performance of the proposed recurrent neural network for nonlinear optimization with bound constraints.

The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry

2015-01-01

We present an inverse scattering transform (IST) approach for the (differentiated) Ostrovsky-Vakhnenko equation This equation can also be viewed as the short wave model for the Degasperis-Procesi (sDP) equation. Our IST approach is based on an associated Riemann-Hilbert problem, which allows us to give a representation for the classical (smooth) solution, to get the principal term of its long time asymptotics, and also to describe loop soliton solutions. Dedicated to Johannes Sjöstrand with gratitude and admiration.

Transactions of the Army Conference on Applied Mathematics and Computing (2nd) Held at Washington, DC on 22-25 May 1984

DTIC Science & Technology

1985-02-01

0 Here Q denotes the midplane of the plate ?assumed to be a Lipschitzian) with a smooth boundary ", and H (Q) and H (Q) are the Hilbert spaces of...using a reproducing kernel Hilbert space approach, Weinert [8,9] et al, developed a structural correspondence between spline interpolation and linear...597 A Mesh Moving Technique for Time Dependent Partial Differential Equations in Two Space Dimensions David C. Arney and Joseph

Global Bifurcation of Periodic Solutions with Symmetry,

DTIC Science & Technology

1987-07-01

C4-family of sectorial operators on a real Hilbert (2.32.a) space X, with dense domain D(A(A)) which is independent of A E E, and with compact...Vanl, theorem 2.5.91. If .F and E’ are both Hilbert spaces with orthogonal action of r, we may drop the assumption that 1 is compact. Just take...some meandering. Let us define a limit for any sequence Si of subsets of some metric space . Following Whyburn [Why], we define lir sup Si {z: z

Weak Solution Classes for Parabolic Integro-Differential Equations

DTIC Science & Technology

1982-09-01

different existence argument for solutions of (I). It is partly based on a method that was used in (2) and (6] to treat a Hilbert - space version of (I) and...xx Differential Equations 35 (1980), 200-231. 121 V. Barbut Integro-Oifferential Squatton. in Hilbert Spaces. Ann. St. Univ. *Al. 1. Cuaxa 19 (1973... Greenberg : O,% the Existence, Uniqueness, and stability of the Equation 00 Xtt - 3(XX)X) AX *x . J Math. Anal. Appl. 25 (1969), S75-591. (131 7

Effect of Hilbert space truncation on Anderson localization

NASA Astrophysics Data System (ADS)

Krishna, Akshay; Bhatt, R. N.

2018-05-01

The 1D Anderson model possesses a completely localized spectrum of eigenstates for all values of the disorder. We consider the effect of projecting the Hamiltonian to a truncated Hilbert space, destroying time-reversal symmetry. We analyze the ensuing eigenstates using different measures such as inverse participation ratio and sample-averaged moments of the position operator. In addition, we examine amplitude fluctuations in detail to detect the possibility of multifractal behavior (characteristic of mobility edges) that may arise as a result of the truncation procedure.

Hilbert-Schmidt Measure of Pairwise Quantum Discord for Three-Qubit X States

NASA Astrophysics Data System (ADS)

Daoud, M.; Laamara, R. Ahl; Seddik, S.

2015-10-01

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit X states. They include three-qubit states of W, GHZ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems.

En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Becker, D., E-mail: BeckerD@thep.physik.uni-mainz.ded; Reuter, M., E-mail: reuter@thep.physik.uni-mainz.de

2014-11-15

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Averagemore » Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the non-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed ‘single-metric truncations’ which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type. - Highlights: • The Asymptotic Safety scenario in quantum gravity is explored. • A bi-metric generalization of the Einstein–Hilbert truncation is investigated. • We find that Background Independence can coexist with Asymptotic Safety. • RG trajectories restoring (background-quantum) split-symmetry are constructed. • The degree of validity of single-metric truncations is critically assessed.« less

Variational bounds on the temperature distribution

NASA Astrophysics Data System (ADS)

Kalikstein, Kalman; Spruch, Larry; Baider, Alberto

1984-02-01

Upper and lower stationary or variational bounds are obtained for functions which satisfy parabolic linear differential equations. (The error in the bound, that is, the difference between the bound on the function and the function itself, is of second order in the error in the input function, and the error is of known sign.) The method is applicable to a range of functions associated with equalization processes, including heat conduction, mass diffusion, electric conduction, fluid friction, the slowing down of neutrons, and certain limiting forms of the random walk problem, under conditions which are not unduly restrictive: in heat conduction, for example, we do not allow the thermal coefficients or the boundary conditions to depend upon the temperature, but the thermal coefficients can be functions of space and time and the geometry is unrestricted. The variational bounds follow from a maximum principle obeyed by the solutions of these equations.

Full-field optical coherence tomography image restoration based on Hilbert transformation

NASA Astrophysics Data System (ADS)

Na, Jihoon; Choi, Woo June; Choi, Eun Seo; Ryu, Seon Young; Lee, Byeong Ha

2007-02-01

We propose the envelope detection method that is based on Hilbert transform for image restoration in full-filed optical coherence tomography (FF-OCT). The FF-OCT system presenting a high-axial resolution of 0.9 μm was implemented with a Kohler illuminator based on Linnik interferometer configuration. A 250 W customized quartz tungsten halogen lamp was used as a broadband light source and a CCD camera was used as a 2-dimentional detector array. The proposed image restoration method for FF-OCT requires only single phase-shifting. By using both the original and the phase-shifted images, we could remove the offset and the background signals from the interference fringe images. The desired coherent envelope image was obtained by applying Hilbert transform. With the proposed image restoration method, we demonstrate en-face imaging performance of the implemented FF-OCT system by presenting a tilted mirror surface, an integrated circuit chip, and a piece of onion epithelium.

Exact Fan-Beam Reconstruction With Arbitrary Object Translations and Truncated Projections

NASA Astrophysics Data System (ADS)

Hoskovec, Jan; Clackdoyle, Rolf; Desbat, Laurent; Rit, Simon

2016-06-01

This article proposes a new method for reconstructing two-dimensional (2D) computed tomography (CT) images from truncated and motion contaminated sinograms. The type of motion considered here is a sequence of rigid translations which are assumed to be known. The algorithm first identifies the sufficiency of angular coverage in each 2D point of the CT image to calculate the Hilbert transform from the local “virtual” trajectory which accounts for the motion and the truncation. By taking advantage of data redundancy in the full circular scan, our method expands the reconstructible region beyond the one obtained with chord-based methods. The proposed direct reconstruction algorithm is based on the Differentiated Back-Projection with Hilbert filtering (DBP-H). The motion is taken into account during backprojection which is the first step of our direct reconstruction, before taking the derivatives and inverting the finite Hilbert transform. The algorithm has been tested in a proof-of-concept study on Shepp-Logan phantom simulations with several motion cases and detector sizes.

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

NASA Astrophysics Data System (ADS)

Cao, ChunJun; Carroll, Sean M.

2018-04-01

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

Janus configurations with SL(2, ℤ)-duality twists, strings on mapping tori and a tridiagonal determinant formula

NASA Astrophysics Data System (ADS)

Ganor, Ori J.; Moore, Nathan P.; Sun, Hao-Yu; Torres-Chicon, Nesty R.

2014-07-01

We develop an equivalence between two Hilbert spaces: (i) the space of states of U(1) n Chern-Simons theory with a certain class of tridiagonal matrices of coupling constants (with corners) on T 2; and (ii) the space of ground states of strings on an associated mapping torus with T 2 fiber. The equivalence is deduced by studying the space of ground states of SL(2, ℤ)-twisted circle compactifications of U(1) gauge theory, connected with a Janus configuration, and further compactified on T 2. The equality of dimensions of the two Hilbert spaces (i) and (ii) is equivalent to a known identity on determinants of tridiagonal matrices with corners. The equivalence of operator algebras acting on the two Hilbert spaces follows from a relation between the Smith normal form of the Chern-Simons coupling constant matrix and the isometry group of the mapping torus, as well as the torsion part of its first homology group.

Renormalization group scale-setting from the action—a road to modified gravity theories

NASA Astrophysics Data System (ADS)

Domazet, Silvije; Štefančić, Hrvoje

2012-12-01

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor.

Reconstruction of Sensory Stimuli Encoded with Integrate-and-Fire Neurons with Random Thresholds

PubMed Central

Lazar, Aurel A.; Pnevmatikakis, Eftychios A.

2013-01-01

We present a general approach to the reconstruction of sensory stimuli encoded with leaky integrate-and-fire neurons with random thresholds. The stimuli are modeled as elements of a Reproducing Kernel Hilbert Space. The reconstruction is based on finding a stimulus that minimizes a regularized quadratic optimality criterion. We discuss in detail the reconstruction of sensory stimuli modeled as absolutely continuous functions as well as stimuli with absolutely continuous first-order derivatives. Reconstruction results are presented for stimuli encoded with single as well as a population of neurons. Examples are given that demonstrate the performance of the reconstruction algorithms as a function of threshold variability. PMID:24077610

Statistical Interior Tomography

PubMed Central

Xu, Qiong; Wang, Ge; Sieren, Jered; Hoffman, Eric A.

2011-01-01

This paper presents a statistical interior tomography (SIT) approach making use of compressed sensing (CS) theory. With the projection data modeled by the Poisson distribution, an objective function with a total variation (TV) regularization term is formulated in the maximization of a posteriori (MAP) framework to solve the interior problem. An alternating minimization method is used to optimize the objective function with an initial image from the direct inversion of the truncated Hilbert transform. The proposed SIT approach is extensively evaluated with both numerical and real datasets. The results demonstrate that SIT is robust with respect to data noise and down-sampling, and has better resolution and less bias than its deterministic counterpart in the case of low count data. PMID:21233044

Multidimensional optical spectroscopy of a single molecule in a current-carrying state

NASA Astrophysics Data System (ADS)

Rahav, S.; Mukamel, S.

2010-12-01

The nonlinear optical signals from an open system consisting of a molecule connected to metallic leads, in response to a sequence of impulsive pulses, are calculated using a superoperator formalism. Two detection schemes are considered: coherent stimulated emission and incoherent fluorescence. The two provide similar but not identical information. The necessary superoperator correlation functions are evaluated either by converting them to ordinary (Hilbert space) operators which are then expanded in many-body states, or by using Wick's theorem for superoperators to factorize them into nonequilibrium two point Green's functions. As an example we discuss a stimulated Raman process that shows resonances involving two different charge states of the molecule in the same signal.

A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra

NASA Astrophysics Data System (ADS)

Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia

2017-10-01

A generalized Hermitian (GH-) algebra is a generalization of the partially ordered Jordan algebra of all Hermitian operators on a Hilbert space. We introduce the notion of a gh-tribe, which is a commutative GH-algebra of functions on a nonempty set X with pointwise partial order and operations, and we prove that every commutative GH-algebra is the image of a gh-tribe under a surjective GH-morphism. Using this result, we prove that each element a of a GH-algebra A corresponds to a real observable ξa on the σ-orthomodular lattice of projections in A and that ξa determines the spectral resolution of a. Also, if f is a continuous function defined on the spectrum of a, we formulate a definition of f (a), thus obtaining a continuous functional calculus for A.

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

NASA Astrophysics Data System (ADS)

Campos, P.; Martins, M. G. R.; Fernandes, M. C. B.; Vianna, J. D. M.

2018-03-01

Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo-Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.

Optimally cloned binary coherent states

NASA Astrophysics Data System (ADS)

Müller, C. R.; Leuchs, G.; Marquardt, Ch.; Andersen, U. L.

2017-10-01

Binary coherent state alphabets can be represented in a two-dimensional Hilbert space. We capitalize this formal connection between the otherwise distinct domains of qubits and continuous variable states to map binary phase-shift keyed coherent states onto the Bloch sphere and to derive their quantum-optimal clones. We analyze the Wigner function and the cumulants of the clones, and we conclude that optimal cloning of binary coherent states requires a nonlinearity above second order. We propose several practical and near-optimal cloning schemes and compare their cloning fidelity to the optimal cloner.

Geometrical Method for the Calculation of Spherical Harmonics up to an Arbitrary Degree and Order

NASA Astrophysics Data System (ADS)

Svehla, D.

2009-12-01

We introduce a novel method for the computation and rotation of spherical harmonics, Legendre polynomials and associated Legendre functions without making use of recursive relations. This novel geometrical approach allows calculation of spherical harmonics without any numerical instability up to an arbitrary degree and order, i.e. up to a degree and order 1e6 and beyond. It is shown, that spherical harmonics can be treated as vectors in Hilbert hyperspace leading to the unitary hermitian rotation matrices with geometric properties.

A system of nonlinear set valued variational inclusions.

PubMed

Tang, Yong-Kun; Chang, Shih-Sen; Salahuddin, Salahuddin

2014-01-01

In this paper, we studied the existence theorems and techniques for finding the solutions of a system of nonlinear set valued variational inclusions in Hilbert spaces. To overcome the difficulties, due to the presence of a proper convex lower semicontinuous function ϕ and a mapping g which appeared in the considered problems, we have used the resolvent operator technique to suggest an iterative algorithm to compute approximate solutions of the system of nonlinear set valued variational inclusions. The convergence of the iterative sequences generated by algorithm is also proved. 49J40; 47H06.

Vibration of middle ear with shape memory prosthesis - Experimental and numerical study

NASA Astrophysics Data System (ADS)

Rafal, Rusinek; Szymanski, Marcin; Lajmert, Pawel

2018-01-01

The paper presents experimental investigations of ossicular chain vibrations using a Laser Doppler Vibrometer (LDV) for the intact middle ear and a reconstructed one by means of the new designed shape memory prosthesis. Vibrations of the round window are measured with the Laser Doppler vibrometer and studied classically by the transfer function analysis. Moreover, the recurrence plot technique and the Hilbert vibration decomposition method are used to extend the classical analysis. The new methods show additional vibrations components and provide more information about middle ear behaviour.

Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits

NASA Astrophysics Data System (ADS)

Lewin, Mathieu; Nam, Phan Thành; Rougerie, Nicolas

2018-04-01

We prove that Gibbs measures based on 1D defocusing nonlinear Schrödinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the corresponding grand-canonical ensemble for many bosons. The limit measure is supported on Sobolev spaces of negative regularity, and the corresponding density matrices are not trace-class. The general proof strategy is that of a previous paper of ours, but we have to complement it with Hilbert-Schmidt estimates on reduced density matrices.

Global existence of weak solutions to dissipative transport equations with nonlocal velocity

NASA Astrophysics Data System (ADS)

Bae, Hantaek; Granero-Belinchón, Rafael; Lazar, Omar

2018-04-01

We consider 1D dissipative transport equations with nonlocal velocity field: where is a nonlocal operator given by a Fourier multiplier. We especially consider two types of nonlocal operators: (1) , the Hilbert transform, (2) . In this paper, we show several global existence of weak solutions depending on the range of γ, δ and α. When , we take initial data having finite energy, while we take initial data in weighted function spaces (in the real variables or in the Fourier variables), which have infinite energy, when .

Symmetric factorization of the conformation tensor in viscoelastic fluid models

NASA Astrophysics Data System (ADS)

Thomases, Becca; Balci, Nusret; Renardy, Michael; Doering, Charles

2010-11-01

The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.

Generalized Pauli constraints in reduced density matrix functional theory.

PubMed

Theophilou, Iris; Lathiotakis, Nektarios N; Marques, Miguel A L; Helbig, Nicole

2015-04-21

Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman's ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.

The Ablowitz–Ladik system on a finite set of integers

NASA Astrophysics Data System (ADS)

Xia, Baoqiang

2018-07-01

We show how to solve initial-boundary value problems for integrable nonlinear differential–difference equations on a finite set of integers. The method we employ is the discrete analogue of the unified transform (Fokas method). The implementation of this method to the Ablowitz–Ladik system yields the solution in terms of the unique solution of a matrix Riemann–Hilbert problem, which has a jump matrix with explicit -dependence involving certain functions referred to as spectral functions. Some of these functions are defined in terms of the initial value, while the remaining spectral functions are defined in terms of two sets of boundary values. These spectral functions are not independent but satisfy an algebraic relation called global relation. We analyze the global relation to characterize the unknown boundary values in terms of the given initial and boundary values. We also discuss the linearizable boundary conditions.

Independent functions and the geometry of Banach spaces

NASA Astrophysics Data System (ADS)

Astashkin, Sergey V.; Sukochev, Fedor A.

2010-12-01

The main objective of this survey is to present the `state of the art' of those parts of the theory of independent functions which are related to the geometry of function spaces. The `size' of a sum of independent functions is estimated in terms of classical moments and also in terms of general symmetric function norms. The exposition is centred on the Rosenthal inequalities and their various generalizations and sharp conditions under which the latter hold. The crucial tool here is the recently developed construction of the Kruglov operator. The survey also provides a number of applications to the geometry of Banach spaces. In particular, variants of the classical Khintchine-Maurey inequalities, isomorphisms between symmetric spaces on a finite interval and on the semi-axis, and a description of the class of symmetric spaces with any sequence of symmetrically and identically distributed independent random variables spanning a Hilbert subspace are considered. Bibliography: 87 titles.

Stochastic functional evolution equations with monotone nonlinearity: Existence and stability of the mild solutions

NASA Astrophysics Data System (ADS)

Jahanipur, Ruhollah

In this paper, we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone condition. We prove the existence, uniqueness and exponentially asymptotic stability of the mild solutions. Our approach is to apply a convenient version of Burkholder inequality for convolution integrals and an iteration method based on the existence and measurability results for the functional integral equations in Hilbert spaces. An Itô-type inequality is the main tool to study the uniqueness, p-th moment and almost sure sample path asymptotic stability of the mild solutions. We also give some examples to illustrate the applications of the theorems and meanwhile we compare the results obtained in this paper with some others appeared in the literature.

Exact deconstruction of the 6D (2,0) theory

NASA Astrophysics Data System (ADS)

Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodríguez-Gómez, D.

2017-06-01

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: in the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the "half-BPS" limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 × T 2. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

The Quantum Measurement Problem and Physical reality: A Computation Theoretic Perspective

NASA Astrophysics Data System (ADS)

Srikanth, R.

2006-11-01

Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not ruled out. On the other hand, empirical evidence suggests that NP-complete problems are intractable in the physical world. Likewise, computational problems known to be algorithmically uncomputable do not seem to be computable by any physical means. We suggest that this close correspondence between the efficiency and power of abstract algorithms on the one hand, and physical computers on the other, finds a natural explanation if the universe is assumed to be algorithmic; that is, that physical reality is the product of discrete sub-physical information processing equivalent to the actions of a probabilistic Turing machine. This assumption can be reconciled with the observed exponentiality of quantum systems at microscopic scales, and the consequent possibility of implementing Shor's quantum polynomial time algorithm at that scale, provided the degree of superposition is intrinsically, finitely upper-bounded. If this bound is associated with the quantum-classical divide (the Heisenberg cut), a natural resolution to the quantum measurement problem arises. From this viewpoint, macroscopic classicality is an evidence that the universe is in BPP, and both questions raised above receive affirmative answers. A recently proposed computational model of quantum measurement, which relates the Heisenberg cut to the discreteness of Hilbert space, is briefly discussed. A connection to quantum gravity is noted. Our results are compatible with the philosophy that mathematical truths are independent of the laws of physics.

Detecting level crossings without solving the Hamiltonian. I. Mathematical background

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhattacharya, M.; Raman, C.

2007-03-15

When the parameters of a physical system are varied, the eigenvalues of observables can undergo crossings and avoided crossings among themselves. It is relevant to be aware of such points since important physical processes often occur there. In a recent paper [M. Bhattacharya and C. Raman, Phys. Rev. Lett. 97, 140405 (2006)] we introduced a powerful algebraic solution to the problem of finding (avoided) crossings in atomic and molecular spectra. This was done via a mapping to the problem of locating the roots of a polynomial in the parameters of interest. In this article we describe our method in detail.more » Given a physical system that can be represented by a matrix, we show how to find a bound on the number of (avoided) crossings in its spectrum, the scaling of this bound with the size of the Hilbert space and the parametric dependencies of the Hamiltonian, the interval in which the (avoided) crossings all lie in parameter space, the number of crossings at any given parameter value, and the minimum separation between the (avoided) crossings. We also show how the crossings can reveal the symmetries of the physical system, how (avoided) crossings can always be found without solving for the eigenvalues, how they may sometimes be found even in case the Hamiltonian is not fully known, and how crossings may be visualized in a more direct way than displayed by the spectrum. In the accompanying paper [M. Bhattacharya and C. Raman, Phys. Rev. A 75, 033406 (2007)] we detail the application of these techniques to atoms and molecules.« less

Quantifying non-Gaussianity for quantum information

NASA Astrophysics Data System (ADS)

Genoni, Marco G.; Paris, Matteo G. A.

2010-11-01

We address the quantification of non-Gaussianity (nG) of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in detail the properties and the relationships of two recently proposed measures of nG based on the Hilbert-Schmidt distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behavior in most of the examples taken into account. However, we also show that they introduce a different relation of order; that is, they are not strictly monotone to each other. We exploit the nG measures for states in order to introduce a measure of nG for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in detail the role played by nG in entanglement-distillation protocols. Besides, we exploit the QRE-based nG measure to provide different insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information, and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nG to the quantum Fisher information. Finally, since evaluation of the QRE nG measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to nG for some classes of states and by considering the possibility of performing on the states only certain efficient or inefficient measurements.

Verifying the error bound of numerical computation implemented in computer systems

DOEpatents

Sawada, Jun

2013-03-12

A verification tool receives a finite precision definition for an approximation of an infinite precision numerical function implemented in a processor in the form of a polynomial of bounded functions. The verification tool receives a domain for verifying outputs of segments associated with the infinite precision numerical function. The verification tool splits the domain into at least two segments, wherein each segment is non-overlapping with any other segment and converts, for each segment, a polynomial of bounded functions for the segment to a simplified formula comprising a polynomial, an inequality, and a constant for a selected segment. The verification tool calculates upper bounds of the polynomial for the at least two segments, beginning with the selected segment and reports the segments that violate a bounding condition.

Universal bounds on current fluctuations.

PubMed

Pietzonka, Patrick; Barato, Andre C; Seifert, Udo

2016-05-01

For current fluctuations in nonequilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any individual current, e.g., the rate of substrate consumption in a chemical reaction or the electron current in an electronic device. The bounds vary with respect to their degree of universality and tightness. A universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production. A second, stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states. These two bounds are conjectures based on extensive numerics. An exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved. This bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium. An asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived. This bound allows for the prediction of the asymptotic growth of the generating function. Even though our results are restricted to networks with a finite number of states, we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle. Our bounds provide a general class of constraints for nonequilibrium systems.

Isomonodromy for the Degenerate Fifth Painlevé Equation

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo B.; van der Put, Marius; Top, Jaap

2017-05-01

This is a sequel to papers by the last two authors making the Riemann-Hilbert correspondence and isomonodromy explicit. For the degenerate fifth Painlevé equation, the moduli spaces for connections and for monodromy are explicitly computed. It is proven that the extended Riemann-Hilbert morphism is an isomorphism. As a consequence these equations have the Painlevé property and the Okamoto-Painlevé space is identified with a moduli space of connections. Using MAPLE computations, one obtains formulas for the degenerate fifth Painlevé equation, for the Bäcklund transformations.

Near-complete teleportation of a superposed coherent state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheong, Yong Wook; Kim, Hyunjae; Lee, Hai-Woong

2004-09-01

The four Bell-type entangled coherent states, {alpha}>-{alpha}>{+-}-{alpha}>{alpha}> and {alpha}>{alpha}>{+-}-{alpha}>-{alpha}>, can be discriminated with a high probability using only linear optical means, as long as {alpha} is not too small. Based on this observation, we propose a simple scheme to almost completely teleport a superposed coherent state. The nonunitary transformation that is required to complete the teleportation can be achieved by embedding the receiver's field state in a larger Hilbert space consisting of the field and a single atom and performing a unitary transformation on this Hilbert space00.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

NASA Astrophysics Data System (ADS)

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.

2018-06-01

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet.

PubMed

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E; Sols, Fernando; Carr, Lincoln D

2018-06-08

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Proceedings of the MIT Student Workshop on VLSI and Parallel Systems Held in Dedham, Massachusetts on 21 July 1992

DTIC Science & Technology

1992-07-01

don’t multiplez the host References wtres, then neither does E., ® El. By repeated application of Theorem 1, using a leveled [1] D. S. Greenberg and S. N...1900, David Hilbert proposed twenty-three problems covering all areas of mathematics that guided the field for decades. These problems served a driving...session was to propose several grand challenge problems, similar in spirit to those of Hilbert [W1: [A] problem should be difficult in order to entice us

Majorana fermions and orthogonal complex structures

NASA Astrophysics Data System (ADS)

Calderón-García, J. S.; Reyes-Lega, A. F.

2018-05-01

Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain “doubling” of the Hilbert space. In this work, we show that this redundancy in the Hilbert space can be completely lifted if the relevant orthogonal structure is taken into account. Such an approach allows for a treatment of Majorana fermions which is both physically and mathematically transparent. Furthermore, an explicit connection between orthogonal complex structures and the topological ℤ2-invariant is given.

Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory

NASA Astrophysics Data System (ADS)

Junge, M.; Palazuelos, C.; Pérez-García, D.; Villanueva, I.; Wolf, M. M.

2010-12-01

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order {Ω left(sqrt{n}/log^2n right)} when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative L p embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise.

Dynamical structure of pure Lovelock gravity

NASA Astrophysics Data System (ADS)

Dadhich, Naresh; Durka, Remigiusz; Merino, Nelson; Miskovic, Olivera

2016-03-01

We study the dynamical structure of pure Lovelock gravity in spacetime dimensions higher than four using the Hamiltonian formalism. The action consists of a cosmological constant and a single higher-order polynomial in the Riemann tensor. Similarly to the Einstein-Hilbert action, it possesses a unique constant curvature vacuum and charged black hole solutions. We analyze physical degrees of freedom and local symmetries in this theory. In contrast to the Einstein-Hilbert case, the number of degrees of freedom depends on the background and can vary from zero to the maximal value carried by the Lovelock theory.

A New View of Earthquake Ground Motion Data: The Hilbert Spectral Analysis

NASA Technical Reports Server (NTRS)

Huang, Norden; Busalacchi, Antonio J. (Technical Monitor)

2000-01-01

A brief description of the newly developed Empirical Mode Decomposition (ENID) and Hilbert Spectral Analysis (HSA) method will be given. The decomposition is adaptive and can be applied to both nonlinear and nonstationary data. Example of the method applied to a sample earthquake record will be given. The results indicate those low frequency components, totally missed by the Fourier analysis, are clearly identified by the new method. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.

Extended space expectation values of position related operators for hydrogen-like quantum system evolutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalay, Berfin; Demiralp, Metin

2014-10-06

The expectation value definitions over an extended space from the considered Hilbert space of the system under consideration is given in another paper of the second author in this symposium. There, in that paper, the conceptuality rather than specification is emphasized on. This work uses that conceptuality to investigate the time evolutions of the position related operators' expectation values not in its standard meaning but rather in a new version of the definition over not the original Hilbert space but in the space obtained by extensions via introducing the images of the given initial wave packet under the positive integermore » powers of the system Hamiltonian. These images may not be residing in the same space of the initial wave packet when certain singularities appear in the structure of the system Hamiltonian. This may break down the existence of the integrals in the definitions of the expectation values. The cure is the use of basis functions in the abovementioned extended space and the sandwiching of the target operator whose expectation value is under questioning by an appropriately chosen operator guaranteeing the existence of the relevant integrals. Work specifically focuses on the hydrogen-like quantum systems whose Hamiltonians contain a polar singularity at the origin.« less

Terahertz Josephson spectral analysis and its applications

NASA Astrophysics Data System (ADS)

Snezhko, A. V.; Gundareva, I. I.; Lyatti, M. V.; Volkov, O. Y.; Pavlovskiy, V. V.; Poppe, U.; Divin, Y. Y.

2017-04-01

Principles of Hilbert-transform spectral analysis (HTSA) are presented and advantages of the technique in the terahertz (THz) frequency range are discussed. THz HTSA requires Josephson junctions with high values of characteristic voltages I c R n and dynamics described by a simple resistively shunted junction (RSJ) model. To meet these requirements, [001]- and [100]-tilt YBa2Cu3O7-x bicrystal junctions with deviations from the RSJ model less than 1% have been developed. Demonstrators of Hilbert-transform spectrum analyzers with various cryogenic environments, including integration into Stirling coolers, are described. Spectrum analyzers have been characterized in the spectral range from 50 GHz to 3 THz. Inside a power dynamic range of five orders, an instrumental function of the analyzers has been found to have a Lorentz form around a single frequency of 1.48 THz with a spectral resolution as low as 0.9 GHz. Spectra of THz radiation from optically pumped gas lasers and semiconductor frequency multipliers have been studied with these spectrum analyzers and the regimes of these radiation sources were optimized for a single-frequency operation. Future applications of HTSA will be related with quick and precise spectral characterization of new radiation sources and identification of substances in the THz frequency range.

Links between quantum physics and thought.

PubMed

Robson, Barry

2009-01-01

Quantum mechanics (QM) provides a variety of ideas that can assist in developing Artificial Intelligence for healthcare, and opens the possibility of developing a unified system of Best Practice for inference that will embrace both QM and classical inference. Of particular interest is inference in the hyperbolic-complex plane, the counterpart of the normal i-complex plane of basic QM. There are two reasons. First, QM appears to rotate from i-complex Hilbert space to hyperbolic-complex descriptions when observations are made on wave functions as particles, yielding classical results, and classical laws of probability manipulation (e.g. the law of composition of probabilities) then hold, whereas in the i-complex plane they do not. Second, i-complex Hilbert space is not the whole story in physics. Hyperbolic complex planes arise in extension from the Dirac-Clifford calculus to particle physics, in relativistic correction thereby, and in regard to spinors and twisters. Generalization of these forms resemble grammatical constructions and promote the idea that probability-weighted algebraic elements can be used to hold dimensions of syntactic and semantic meaning. It is also starting to look as though when a solution is reached by an inference system in the hyperbolic-complex, the hyperbolic-imaginary values disappear, while conversely hyperbolic-imaginary values are associated with the un-queried state of a system and goal seeking behavior.

Progress towards an effective model for FeSe from high-accuracy first-principles quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Busemeyer, Brian; Wagner, Lucas K.

While the origin of superconductivity in the iron-based materials is still controversial, the proximity of the superconductivity to magnetic order is suggestive that magnetism may be important. Our previous work has suggested that first-principles Diffusion Monte Carlo (FN-DMC) can capture magnetic properties of iron-based superconductors that density functional theory (DFT) misses, but which are consistent with experiment. We report on the progress of efforts to find simple effective models consistent with the FN-DMC description of the low-lying Hilbert space of the iron-based superconductor, FeSe. We utilize a procedure outlined by Changlani et al.[1], which both produces parameter values and indications of whether the model is a good description of the first-principles Hamiltonian. Using this procedure, we evaluate several models of the magnetic part of the Hilbert space found in the literature, as well as the Hubbard model, and a spin-fermion model. We discuss which interaction parameters are important for this material, and how the material-specific properties give rise to these interactions. U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program under Award No. FG02-12ER46875, as well as the NSF Graduate Research Fellowship Program.

Algorithms and Results of Eye Tissues Differentiation Based on RF Ultrasound

PubMed Central

Jurkonis, R.; Janušauskas, A.; Marozas, V.; Jegelevičius, D.; Daukantas, S.; Patašius, M.; Paunksnis, A.; Lukoševičius, A.

2012-01-01

Algorithms and software were developed for analysis of B-scan ultrasonic signals acquired from commercial diagnostic ultrasound system. The algorithms process raw ultrasonic signals in backscattered spectrum domain, which is obtained using two time-frequency methods: short-time Fourier and Hilbert-Huang transformations. The signals from selected regions of eye tissues are characterized by parameters: B-scan envelope amplitude, approximated spectral slope, approximated spectral intercept, mean instantaneous frequency, mean instantaneous bandwidth, and parameters of Nakagami distribution characterizing Hilbert-Huang transformation output. The backscattered ultrasound signal parameters characterizing intraocular and orbit tissues were processed by decision tree data mining algorithm. The pilot trial proved that applied methods are able to correctly classify signals from corpus vitreum blood, extraocular muscle, and orbit tissues. In 26 cases of ocular tissues classification, one error occurred, when tissues were classified into classes of corpus vitreum blood, extraocular muscle, and orbit tissue. In this pilot classification parameters of spectral intercept and Nakagami parameter for instantaneous frequencies distribution of the 1st intrinsic mode function were found specific for corpus vitreum blood, orbit and extraocular muscle tissues. We conclude that ultrasound data should be further collected in clinical database to establish background for decision support system for ocular tissue noninvasive differentiation. PMID:22654643

DOE Office of Scientific and Technical Information (OSTI.GOV)

Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.

Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violatesmore » the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.« less

Estimation of two ordered mean residual lifetime functions.

PubMed

Ebrahimi, N

1993-06-01

In many statistical studies involving failure data, biometric mortality data, and actuarial data, mean residual lifetime (MRL) function is of prime importance. In this paper we introduce the problem of nonparametric estimation of a MRL function on an interval when this function is bounded from below by another such function (known or unknown) on that interval, and derive the corresponding two functional estimators. The first is to be used when there is a known bound, and the second when the bound is another MRL function to be estimated independently. Both estimators are obtained by truncating the empirical estimator discussed by Yang (1978, Annals of Statistics 6, 112-117). In the first case, it is truncated at a known bound; in the second, at a point somewhere between the two empirical estimates. Consistency of both estimators is proved, and a pointwise large-sample distribution theory of the first estimator is derived.

Quantifying phase synchronization using instances of Hilbert phase slips

NASA Astrophysics Data System (ADS)

Govindan, R. B.

2018-07-01

We propose to quantify phase synchronization between two signals, x(t) and y(t), by calculating variance in the Hilbert phase of y(t) at instances of phase slips exhibited by x(t). The proposed approach is tested on numerically simulated coupled chaotic Roessler systems and second order autoregressive processes. Furthermore we compare the performance of the proposed and original approaches using uterine electromyogram signals and show that both approaches yield consistent results A standard phase synchronization approach, which involves unwrapping the Hilbert phases (ϕ1(t) and ϕ2(t)) of the two signals and analyzing the variance in the | n ṡϕ1(t) - m ṡϕ2(t) | , mod 2 π, (n and m are integers), was used for comparison. The synchronization indexes obtained from the proposed approach and the standard approach agree reasonably well in all of the systems studied in this work. Our results indicate that the proposed approach, unlike the traditional approach, does not require the non-invertible transformations - unwrapping of the phases and calculation of mod 2 π and it can be used to reliably to quantify phase synchrony between two signals.

Aveiro method in reproducing kernel Hilbert spaces under complete dictionary

NASA Astrophysics Data System (ADS)

Mai, Weixiong; Qian, Tao

2017-12-01

Aveiro Method is a sparse representation method in reproducing kernel Hilbert spaces (RKHS) that gives orthogonal projections in linear combinations of reproducing kernels over uniqueness sets. It, however, suffers from determination of uniqueness sets in the underlying RKHS. In fact, in general spaces, uniqueness sets are not easy to be identified, let alone the convergence speed aspect with Aveiro Method. To avoid those difficulties we propose an anew Aveiro Method based on a dictionary and the matching pursuit idea. What we do, in fact, are more: The new Aveiro method will be in relation to the recently proposed, the so called Pre-Orthogonal Greedy Algorithm (P-OGA) involving completion of a given dictionary. The new method is called Aveiro Method Under Complete Dictionary (AMUCD). The complete dictionary consists of all directional derivatives of the underlying reproducing kernels. We show that, under the boundary vanishing condition, bring available for the classical Hardy and Paley-Wiener spaces, the complete dictionary enables an efficient expansion of any given element in the Hilbert space. The proposed method reveals new and advanced aspects in both the Aveiro Method and the greedy algorithm.

ψ-Epistemic Models are Exponentially Bad at Explaining the Distinguishability of Quantum States

NASA Astrophysics Data System (ADS)

Leifer, M. S.

2014-04-01

The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (state of knowledge) or an ontic state (state of reality)? In realist models of quantum theory, the epistemic view asserts that nonorthogonal quantum states correspond to overlapping probability measures over the true ontic states. This naturally accounts for a large number of otherwise puzzling quantum phenomena. For example, the indistinguishability of nonorthogonal states is explained by the fact that the ontic state sometimes lies in the overlap region, in which case there is nothing in reality that could distinguish the two states. For this to work, the amount of overlap of the probability measures should be comparable to the indistinguishability of the quantum states. In this Letter, I exhibit a family of states for which the ratio of these two quantities must be ≤2de-cd in Hilbert spaces of dimension d that are divisible by 4. This implies that, for large Hilbert space dimension, the epistemic explanation of indistinguishability becomes implausible at an exponential rate as the Hilbert space dimension increases.

Discretized energy minimization in a wave guide with point sources

NASA Technical Reports Server (NTRS)

Propst, G.

1994-01-01

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Regularization by Functions of Bounded Variation and Applications to Image Enhancement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Casas, E.; Kunisch, K.; Pola, C.

1999-09-15

Optimization problems regularized by bounded variation seminorms are analyzed. The optimality system is obtained and finite-dimensional approximations of bounded variation function spaces as well as of the optimization problems are studied. It is demonstrated that the choice of the vector norm in the definition of the bounded variation seminorm is of special importance for approximating subspaces consisting of piecewise constant functions. Algorithms based on a primal-dual framework that exploit the structure of these nondifferentiable optimization problems are proposed. Numerical examples are given for denoising of blocky images with very high noise.

Self-acceleration in scalar-bimetric theories

NASA Astrophysics Data System (ADS)

Brax, Philippe; Valageas, Patrick

2018-05-01

We describe scalar-bimetric theories where the dynamics of the Universe are governed by two separate metrics, each with an Einstein-Hilbert term. In this setting, the baryonic and dark matter components of the Universe couple to metrics which are constructed as functions of these two gravitational metrics. More precisely, the two metrics coupled to matter are obtained by a linear combination of their vierbeins, with scalar-dependent coefficients. The scalar field, contrary to dark-energy models, does not have a potential of which the role is to mimic a late-time cosmological constant. The late-time acceleration of the expansion of the Universe can be easily obtained at the background level in these models by appropriately choosing the coupling functions appearing in the decomposition of the vierbeins for the baryonic and dark matter metrics. We explicitly show how the concordance model can be retrieved with negligible scalar kinetic energy. This requires the scalar coupling functions to show variations of order unity during the accelerated expansion era. This leads in turn to deviations of order unity for the effective Newton constants and a fifth force that is of the same order as Newtonian gravity, with peculiar features. The baryonic and dark matter self-gravities are amplified although the gravitational force between baryons and dark matter is reduced and even becomes repulsive at low redshift. This slows down the growth of baryonic density perturbations on cosmological scales, while dark matter perturbations are enhanced. These scalar-bimetric theories have a perturbative cutoff scale of the order of 1 AU, which prevents a precise comparison with Solar System data. On the other hand, we can deduce strong requirements on putative UV completions by analyzing the stringent constraints in the Solar System. Hence, in our local environment, the upper bound on the time evolution of Newton's constant requires an efficient screening mechanism that both damps the fifth force on small scales and decouples the local value of Newton constant from its cosmological value. This cannot be achieved by a quasistatic chameleon mechanism and requires going beyond the quasistatic regime and probably using derivative screenings, such as Kmouflage or Vainshtein screening, on small scales.

Supersymmetric symplectic quantum mechanics

NASA Astrophysics Data System (ADS)

de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.

2018-02-01

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

Entanglement quantification by local unitary operations

NASA Astrophysics Data System (ADS)

Monras, A.; Adesso, G.; Giampaolo, S. M.; Gualdi, G.; Davies, G. B.; Illuminati, F.

2011-07-01

Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as “mirror entanglement.” They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the “stellar mirror entanglement” associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.76.042301 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.

Entanglement quantification by local unitary operations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Monras, A.; Giampaolo, S. M.; Gualdi, G.

2011-07-15

Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as ''mirror entanglement.'' They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different localmore » unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the ''stellar mirror entanglement'' associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.« less

Remote preparation of a qudit using maximally entangled states of qubits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu Changshui; Song Heshan; Wang Yahong

2006-02-15

Known quantum pure states of a qudit can be remotely prepared onto a group of particles of qubits exactly or probabilistically with the aid of two-level Einstein-Podolsky-Rosen states. We present a protocol for such kind of remote state preparation. We are mainly focused on the remote preparation of the ensembles of equatorial states and those of states in real Hilbert space. In particular, a kind of states of qudits in real Hilbert space have been shown to be remotely prepared in faith without the limitation of the input space dimension.

Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach

NASA Astrophysics Data System (ADS)

Tovbis, Alexander; El, Gennady A.

2016-10-01

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated N-phase nonlinear wave solutions to the focusing nonlinear Schrödinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated N-phase nonlinear wave in the process of evolution. Both approaches have their own merits and limitations. Understanding of the interrelations between them could prove beneficial for a broad range of problems involving the semiclassical fNLS.

Wavefront reconstruction from non-modulated pyramid wavefront sensor data using a singular value type expansion

NASA Astrophysics Data System (ADS)

Hutterer, Victoria; Ramlau, Ronny

2018-03-01

The new generation of extremely large telescopes includes adaptive optics systems to correct for atmospheric blurring. In this paper, we present a new method of wavefront reconstruction from non-modulated pyramid wavefront sensor data. The approach is based on a simplified sensor model represented as the finite Hilbert transform of the incoming phase. Due to the non-compactness of the finite Hilbert transform operator the classical theory for singular systems is not applicable. Nevertheless, we can express the Moore-Penrose inverse as a singular value type expansion with weighted Chebychev polynomials.

Transactions of the Conference of Army Mathematicians (28th) Held at Bethesda, Maryland on 28-30 June 1982.

DTIC Science & Technology

1983-02-01

real part is the Hilbert transform of its imaginary part. Thus we have o) d4’ . (5.1)+," _ Here r(o) and 6(o) denote respectively T(4’,0-) and 0(o,0...linear operators A in a Hilbert space H, eigenuv.aueA are critical values of the Raqt.igh quo 5ient (5.1) R(y) = (Ay,y)/(y,y), y # 0. An eigenvalue X...Das Gupta Ballistic Research Laboratory Jim Greenberg National Science Foundation Charles Giardina Fairleigh-Dickinson University Frank P. Kuhl U. S

Noisy bases in Hilbert space: A new class of thermal coherent states and their properties

NASA Technical Reports Server (NTRS)

Vourdas, A.; Bishop, R. F.

1995-01-01

Coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, are introduced as a 'random' (or 'thermal' or 'noisy') basis in Hilbert space. A resolution of the identity for these states is proved and used to generalize the usual coherent state formalism for the finite temperature case. The Bargmann representation of an operator is introduced and its relation to the P and Q representations is studied. Generalized P and Q representations for the finite temperature case are also considered and several interesting relations among them are derived.

Geometry of quantum dynamics in infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana

2018-04-01

We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.

a Comparison Study of Different Kernel Functions for Svm-Based Classification of Multi-Temporal Polarimetry SAR Data

NASA Astrophysics Data System (ADS)

Yekkehkhany, B.; Safari, A.; Homayouni, S.; Hasanlou, M.

2014-10-01

In this paper, a framework is developed based on Support Vector Machines (SVM) for crop classification using polarimetric features extracted from multi-temporal Synthetic Aperture Radar (SAR) imageries. The multi-temporal integration of data not only improves the overall retrieval accuracy but also provides more reliable estimates with respect to single-date data. Several kernel functions are employed and compared in this study for mapping the input space to higher Hilbert dimension space. These kernel functions include linear, polynomials and Radial Based Function (RBF). The method is applied to several UAVSAR L-band SAR images acquired over an agricultural area near Winnipeg, Manitoba, Canada. In this research, the temporal alpha features of H/A/α decomposition method are used in classification. The experimental tests show an SVM classifier with RBF kernel for three dates of data increases the Overall Accuracy (OA) to up to 3% in comparison to using linear kernel function, and up to 1% in comparison to a 3rd degree polynomial kernel function.

Typical entanglement

NASA Astrophysics Data System (ADS)

Deelan Cunden, Fabio; Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio

2013-05-01

Let a pure state | ψ> be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix ρ A of an N-dimensional subsystem. The bipartite entanglement properties of | ψ> are encoded in the spectrum of ρ A . By means of a saddle point method and using a "Coulomb gas" model for the eigenvalues, we obtain the typical spectrum of reduced density matrices. We consider the cases of an unbiased ensemble of pure states and of a fixed value of the purity. We finally obtain the eigenvalue distribution by using a statistical mechanics approach based on the introduction of a partition function.

Minimal Cohomological Model of a Scalar Field on a Riemannian Manifold

NASA Astrophysics Data System (ADS)

Arkhipov, V. V.

2018-04-01

Lagrangians of the field-theory model of a scalar field are considered as 4-forms on a Riemannian manifold. The model is constructed on the basis of the Hodge inner product, this latter being an analog of the scalar product of two functions. Including the basis fields in the action of the terms with tetrads makes it possible to reproduce the Klein-Gordon equation and the Maxwell equations, and also the Einstein-Hilbert action. We conjecture that the principle of construction of the Lagrangians as 4-forms can give a criterion restricting possible forms of the field-theory models.

From SL(5, ℝ) Yang-Mills theory to induced gravity

NASA Astrophysics Data System (ADS)

Assimos, T. S.; Pereira, A. D.; Santos, T. R. S.; Sobreiro, R. F.; Tomaz, A. A.; Otoya, V. J. Vasquez

From pure Yang-Mills action for the SL(5, ℝ) group in four Euclidean dimensions we obtain a gravity theory in the first order formalism. Besides the Einstein-Hilbert term, the effective gravity has a cosmological constant term, a curvature squared term, a torsion squared term and a matter sector. To obtain such geometrodynamical theory, asymptotic freedom and the Gribov parameter (soft BRST symmetry breaking) are crucial. Particularly, Newton and cosmological constant are related to these parameters and they also run as functions of the energy scale. One-loop computations are performed and the results are interpreted.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu; Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089; Ghanem, Roger G., E-mail: ghanem@usc.edu

2017-07-15

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Extremal values of the sojourn time

NASA Astrophysics Data System (ADS)

Astaburuaga, M. A.; Cortés, V. H.; Duclos, P.

2010-11-01

Consider a self-adjoint operator H on a separable Hilbert space \\ {H} with non-trivial absolutely continuous component. We study the general properties of the real-valued functional, \\tau _{H}(\\psi )=\\int _{{\\ R}}|(e^{-itH}\\psi,\\psi )|^2\\,dt, which in quantum mechanics represents the sojourn time (or life time) of an initial state \\psi \\in \\ {H}. We characterize the critical points of the sojourn time, τX, of the operator multiplication by x in L^2({\\ R}), and prove that it attains a global maximum in the unit sphere of the Sobolev space \\ {W}^{1,2}({\\ R}).

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

NASA Astrophysics Data System (ADS)

Tsilifis, Panagiotis; Ghanem, Roger G.

2017-07-01

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Final Report on Scientific Activities Pursuant to the Provisions of Grant AFOSR-79-0018 during the Period November 1, 1982 to October 31, 1983.

DTIC Science & Technology

1984-05-01

structure. (See, in particular, the extensive work [A] of de Branges in this connection.) The most familiar of these spaces is the so-called "Paley-Wiener...more to say about this in Section 3. Just as in the case of the Paley-Wiener space and the other, related, spa- ces described by de Branges , the spaces...3] De Branges , L.: "Hilbert Spaces of Entire Functions", Prentice Hall Publ. Co. , Englewood Cliffs, N.J., 1968. [4] Duffin, R. J., and A. C

A linear programming approach to characterizing norm bounded uncertainty from experimental data

NASA Technical Reports Server (NTRS)

Scheid, R. E.; Bayard, D. S.; Yam, Y.

1991-01-01

The linear programming spectral overbounding and factorization (LPSOF) algorithm, an algorithm for finding a minimum phase transfer function of specified order whose magnitude tightly overbounds a specified nonparametric function of frequency, is introduced. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation).

Detection and reconstruction of large scale flow structures in a river by means of empirical mode decomposition combined with Hilbert transform

NASA Astrophysics Data System (ADS)

Franca, Mário J.; Lemmin, Ulrich

2014-05-01

The occurrence of large scale flow structures (LSFS) coherently organized throughout the flow depth has been reported in field and laboratory experiments of flows over gravel beds, especially under low relative submergence conditions. In these, the instantaneous velocity is synchronized over the whole vertical profile oscillating at a low frequency above or below the time-averaged value. The detection of large scale coherently organized regions in the flow field is often difficult since it requires detailed simultaneous observations of the flow velocities at several levels. The present research avoids the detection problem by using an Acoustic Doppler Velocity Profiler (ADVP), which permits measuring three-dimensional velocities quasi-simultaneously over the full water column. Empirical mode decomposition (EMD) combined with the application of the Hilbert transform is then applied to the instantaneous velocity data to detect and isolate LSFS. The present research was carried out in a Swiss river with low relative submergence of 2.9, herein defined as h/D50, (where h is the mean flow depth and D50 the bed grain size diameter for which 50% of the grains have smaller diameters). 3D ADVP instantaneous velocity measurements were made on a 3x5 rectangular horizontal grid (x-y). Fifteen velocity profiles were equally spaced in the spanwise direction with a distance of 10 cm, and in the streamwise direction with a distance of 15 cm. The vertical resolution of the measurements is roughly 0.5 cm. A measuring grid covering a 3D control volume was defined. The instantaneous velocity profiles were measured for 3.5 min with a sampling frequency of 26 Hz. Oscillating LSFS are detected and isolated in the instantaneous velocity signal of the 15 measured profiles. Their 3D cycle geometry is reconstructed and investigated through phase averaging based on the identification of the instantaneous signal phase (related to the Hilbert transform) applied to the original raw signal. Results for all the profiles are consistent and indicate clearly the presence of LSFS throughout the flow depth with impact on the three components of the velocity profile and on the bed friction velocity. A high correlation of the movement is found throughout the flow depth, thus corroborating the hypothesis of large-scale coherent motion evolving over the whole water depth. These latter are characterized in terms of period, horizontal scale and geometry. The high spatial and temporal resolution of our ADVP was crucial for obtaining comprehensive results on coherent structures dynamics. EMD combined with the Hilbert transform have previously been successfully applied to geophysical flow studies. Here we show that this method can also be used for the analysis of river dynamics. In particular, we demonstrate that a clean, well-behaved intrinsic mode function can be obtained from a noisy velocity time series that allowed a precise determination of the vertical structure of the coherent structures. The phase unwrapping of the UMR and the identification of the phase related velocity components brings new insight into the flow dynamics Research supported by the Swiss National Science Foundation (2000-063818). KEY WORDS: large scale flow structures (LSFS); gravel-bed rivers; empirical mode decomposition; Hilbert transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slater, Paul B.

Paralleling our recent computationally intensive (quasi-Monte Carlo) work for the case N=4 (e-print quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (e-print quant-ph/0304041) for the (N{sup 2}-1)-dimensional volume and (N{sup 2}-2)-dimensional hyperarea of the (separable and nonseparable) NxN density matrices, based on the Bures (minimal monotone) metric--and also their analogous formulas (e-print quant-ph/0302197) for the (nonmonotone) flat Hilbert-Schmidt metric. With the same seven 10{sup 9} well-distributed ('low-discrepancy') sample points, we estimate the unknown volumes and hyperareas based on five additional (monotone) metrics of interest, including the Kubo-Mori and Wigner-Yanase.more » Further, we estimate all of these seven volume and seven hyperarea (unknown) quantities when restricted to the separable density matrices. The ratios of separable volumes (hyperareas) to separable plus nonseparable volumes (hyperareas) yield estimates of the separability probabilities of generically rank-6 (rank-5) density matrices. The (rank-6) separability probabilities obtained based on the 35-dimensional volumes appear to be--independently of the metric (each of the seven inducing Haar measure) employed--twice as large as those (rank-5 ones) based on the 34-dimensional hyperareas. (An additional estimate--33.9982--of the ratio of the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite clearly close to integral too.) The doubling relationship also appears to hold for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit simple exact formulas to our estimates of the Hilbert-Schmidt separable volumes and hyperareas in both the N=4 and N=6 cases.« less

A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

NASA Astrophysics Data System (ADS)

Deift, P.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Venakides, S.; Zhou, X.

2001-08-01

A few years ago the authors introduced a new approach to study asymptotic questions for orthogonal polynomials. In this paper we give an overview of our method and review the results which have been obtained in Deift et al. (Internat. Math. Res. Notices (1997) 759, Comm. Pure Appl. Math. 52 (1999) 1491, 1335), Deift (Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes, Vol. 3, New York University, 1999), Kriecherbauer and McLaughlin (Internat. Math. Res. Notices (1999) 299) and Baik et al. (J. Amer. Math. Soc. 12 (1999) 1119). We mainly consider orthogonal polynomials with respect to weights on the real line which are either (1) Freud-type weights d[alpha](x)=e-Q(x) dx (Q polynomial or Q(x)=x[beta], [beta]>0), or (2) varying weights d[alpha]n(x)=e-nV(x) dx (V analytic, limx-->[infinity] V(x)/logx=[infinity]). We obtain Plancherel-Rotach-type asymptotics in the entire complex plane as well as asymptotic formulae with error estimates for the leading coefficients, for the recurrence coefficients, and for the zeros of the orthogonal polynomials. Our proof starts from an observation of Fokas et al. (Comm. Math. Phys. 142 (1991) 313) that the orthogonal polynomials can be determined as solutions of certain matrix valued Riemann-Hilbert problems. We analyze the Riemann-Hilbert problems by a steepest descent type method introduced by Deift and Zhou (Ann. Math. 137 (1993) 295) and further developed in Deift and Zhou (Comm. Pure Appl. Math. 48 (1995) 277) and Deift et al. (Proc. Nat. Acad. Sci. USA 95 (1998) 450). A crucial step in our analysis is the use of the well-known equilibrium measure which describes the asymptotic distribution of the zeros of the orthogonal polynomials.

Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space.

PubMed

Stępień, Grzegorz

2018-03-17

The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems-interior and exterior orientation of sensors-to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins) and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data). The accuracy of the results in the laboratory test is on the level of 10 -6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author's 2017 Total Free Station (TFS) transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation-MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.

The open quantum Brownian motions

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2014-09-01

Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H_z : orbital (walker) Hilbert space, {C}^{{Z}} in the discrete, L^2({R}) in the continuum H_c : internal spin (or gyroscope) Hilbert space H_sys=H_z\\otimesH_c : system Hilbert space H_p : probe (or quantum coin) Hilbert space, H_p={C}^2 \\rho^tot_t : density matrix for the total system (walker + internal spin + quantum coins) \\bar \\rho_t : reduced density matrix on H_sys : \\bar\\rho_t=\\int dxdy\\, \\bar\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | \\hat \\rho_t : system density matrix in a quantum trajectory: \\hat\\rho_t=\\int dxdy\\, \\hat\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | . If diagonal and localized in position: \\hat \\rho_t=\\rho_t\\otimes| X_t \\rangle _z\\langle X_t | ρt: internal density matrix in a simple quantum trajectory Xt: walker position in a simple quantum trajectory Bt: normalized Brownian motion ξt, \\xi_t^\\dagger : quantum noises

Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs

PubMed Central

Novo, Leonardo; Chakraborty, Shantanav; Mohseni, Masoud; Neven, Hartmut; Omar, Yasser

2015-01-01

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically using the Lanczos algorithm, to obtain the reduced set of states that encompass the dynamics of the problem at hand without the specific knowledge of underlying symmetries. First, we apply this method to obtain new instances of graphs where the spatial quantum search algorithm is optimal: complete graphs with broken links and complete bipartite graphs, in particular, the star graph. These examples show that regularity and high-connectivity are not needed to achieve optimal spatial search. We also show that this method considerably simplifies the calculation of quantum transport efficiencies. Furthermore, we observe improved efficiencies by removing a few links from highly symmetric graphs. Finally, we show that this reduction method also allows us to obtain an upper bound for the fidelity of a single qubit transfer on an XY spin network. PMID:26330082

Approximate symmetries of Hamiltonians

NASA Astrophysics Data System (ADS)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

Axioms for quantum mechanics: relativistic causality, retrocausality, and the existence of a classical limit

NASA Astrophysics Data System (ADS)

Rohrlich, Daniel

Y. Aharonov and A. Shimony both conjectured that two axioms - relativistic causality (``no superluminal signalling'') and nonlocality - so nearly contradict each other that only quantum mechanics reconciles them. Can we indeed derive quantum mechanics, at least in part, from these two axioms? No: ``PR-box'' correlations show that quantum correlations are not the most nonlocal correlations consistent with relativistic causality. Here we replace ``nonlocality'' with ``retrocausality'' and supplement the axioms of relativistic causality and retrocausality with a natural and minimal third axiom: the existence of a classical limit, in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this limit, PR-box correlations violaterelativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound (a theorem of quantum mechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantum mechanics, it points to the Hilbert space structure that underlies quantum correlations. I thank the John Templeton Foundation (Project ID 43297) and the Israel Science Foundation (Grant No. 1190/13) for support.

Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2017-12-01

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

Quantum simulation of the integer factorization problem: Bell states in a Penning trap

NASA Astrophysics Data System (ADS)

Rosales, Jose Luis; Martin, Vicente

2018-03-01

The arithmetic problem of factoring an integer N can be translated into the physics of a quantum device, a result that supports Pólya's and Hilbert's conjecture to demonstrate Riemann's hypothesis. The energies of this system, being univocally related to the factors of N , are the eigenvalues of a bounded Hamiltonian. Here we solve the quantum conditions and show that the histogram of the discrete energies, provided by the spectrum of the system, should be interpreted in number theory as the relative probability for a prime to be a factor candidate of N . This is equivalent to a quantum sieve that is shown to require only o (ln√{N}) 3 energy measurements to solve the problem, recovering Shor's complexity result. Hence the outcome can be seen as a probability map that a pair of primes solve the given factorization problem. Furthermore, we show that a possible embodiment of this quantum simulator corresponds to two entangled particles in a Penning trap. The possibility to build the simulator experimentally is studied in detail. The results show that factoring numbers, many orders of magnitude larger than those computed with experimentally available quantum computers, is achievable using typical parameters in Penning traps.

Quantum gravity inde Sitter space and anti-de Sitter space

NASA Astrophysics Data System (ADS)

Lippert, Matthew S.

In this thesis, we consider two aspects of quantum gravity---the nature of holography in anti-de Sitter space and string theory models of de Sitter space. Searching for a holographic resolution of the black hole information paradox, we pursue the identity of precursors in the context of AdS/CFT. We consider precursors that encode bulk information causally disconnected from the boundary and whose measurement involves nonlocal bulk processes. Previous arguments that these precursors are large, undecorated Wilson loops are found to be flawed. We construct a toy model of holography which encapsulates the expected properties of precursors and compare it with previous such discussions. The information contained in precursors is argued to be encoded in the high-energy sector of the theory and not observable by low-energy measurements. These considerations lead us to propose a locality bound, which indicates where locality breaks down due to black hole or stringy effects. We apply the locality bound to Hawking's argument for information loss in black hole evaporation. We argue that independence of internal and external Hilbert spaces cannot be established without incorporating strong gravitational effects that undermine locality and invalidate the use of quantum field theory in a semiclassical background geometry. We then turn to the investigation of the landscape of string theory vacua, and investigate a recently constructed de Sitter compactification of IIB string theory, which was shown to be metastable in agreement with general arguments about de Sitter spacetimes in quantum gravity. We describe how discrete flux choices lead to a closely-spaced set of vacua and explore various decay channels. We find that in many situations NS5-brane meditated decays which exchange NSNS 3-form flux for D3-branes are comparatively extremely fast.

Operator bases, S-matrices, and their partition functions

NASA Astrophysics Data System (ADS)

Henning, Brian; Lu, Xiaochuan; Melia, Tom; Murayama, Hitoshi

2017-10-01

Relativistic quantum systems that admit scattering experiments are quantitatively described by effective field theories, where S-matrix kinematics and symmetry considerations are encoded in the operator spectrum of the EFT. In this paper we use the S-matrix to derive the structure of the EFT operator basis, providing complementary descriptions in (i) position space utilizing the conformal algebra and cohomology and (ii) momentum space via an algebraic formulation in terms of a ring of momenta with kinematics implemented as an ideal. These frameworks systematically handle redundancies associated with equations of motion (on-shell) and integration by parts (momentum conservation). We introduce a partition function, termed the Hilbert series, to enumerate the operator basis — correspondingly, the S-matrix — and derive a matrix integral expression to compute the Hilbert series. The expression is general, easily applied in any spacetime dimension, with arbitrary field content and (linearly realized) symmetries. In addition to counting, we discuss construction of the basis. Simple algorithms follow from the algebraic formulation in momentum space. We explicitly compute the basis for operators involving up to n = 5 scalar fields. This construction universally applies to fields with spin, since the operator basis for scalars encodes the momentum dependence of n-point amplitudes. We discuss in detail the operator basis for non-linearly realized symmetries. In the presence of massless particles, there is freedom to impose additional structure on the S- matrix in the form of soft limits. The most na¨ıve implementation for massless scalars leads to the operator basis for pions, which we confirm using the standard CCWZ formulation for non-linear realizations. Although primarily discussed in the language of EFT, some of our results — conceptual and quantitative — may be of broader use in studying conformal field theories as well as the AdS/CFT correspondence.

Computational Studies of Strongly Correlated Quantum Matter

NASA Astrophysics Data System (ADS)

Shi, Hao

The study of strongly correlated quantum many-body systems is an outstanding challenge. Highly accurate results are needed for the understanding of practical and fundamental problems in condensed-matter physics, high energy physics, material science, quantum chemistry and so on. Our familiar mean-field or perturbative methods tend to be ineffective. Numerical simulations provide a promising approach for studying such systems. The fundamental difficulty of numerical simulation is that the dimension of the Hilbert space needed to describe interacting systems increases exponentially with the system size. Quantum Monte Carlo (QMC) methods are one of the best approaches to tackle the problem of enormous Hilbert space. They have been highly successful for boson systems and unfrustrated spin models. For systems with fermions, the exchange symmetry in general causes the infamous sign problem, making the statistical noise in the computed results grow exponentially with the system size. This hinders our understanding of interesting physics such as high-temperature superconductivity, metal-insulator phase transition. In this thesis, we present a variety of new developments in the auxiliary-field quantum Monte Carlo (AFQMC) methods, including the incorporation of symmetry in both the trial wave function and the projector, developing the constraint release method, using the force-bias to drastically improve the efficiency in Metropolis framework, identifying and solving the infinite variance problem, and sampling Hartree-Fock-Bogoliubov wave function. With these developments, some of the most challenging many-electron problems are now under control. We obtain an exact numerical solution of two-dimensional strongly interacting Fermi atomic gas, determine the ground state properties of the 2D Fermi gas with Rashba spin-orbit coupling, provide benchmark results for the ground state of the two-dimensional Hubbard model, and establish that the Hubbard model has a stripe order in the underdoped region.

Assessment of vocal cord nodules: a case study in speech processing by using Hilbert-Huang Transform

NASA Astrophysics Data System (ADS)

Civera, M.; Filosi, C. M.; Pugno, N. M.; Silvestrini, M.; Surace, C.; Worden, K.

2017-05-01

Vocal cord nodules represent a pathological condition for which the growth of unnatural masses on vocal folds affects the patients. Among other effects, changes in the vocal cords’ overall mass and stiffness alter their vibratory behaviour, thus changing the vocal emission generated by them. This causes dysphonia, i.e. abnormalities in the patients’ voice, which can be analysed and inspected via audio signals. However, the evaluation of voice condition through speech processing is not a trivial task, as standard methods based on the Fourier Transform, fail to fit the non-stationary nature of vocal signals. In this study, four audio tracks, provided by a volunteer patient, whose vocal fold nodules have been surgically removed, were analysed using a relatively new technique: the Hilbert-Huang Transform (HHT) via Empirical Mode Decomposition (EMD); specifically, by using the CEEMDAN (Complete Ensemble EMD with Adaptive Noise) algorithm. This method has been applied here to speech signals, which were recorded before removal surgery and during convalescence, to investigate specific trends. Possibilities offered by the HHT are exposed, but also some limitations of decomposing the signals into so-called intrinsic mode functions (IMFs) are highlighted. The results of these preliminary studies are intended to be a basis for the development of new viable alternatives to the softwares currently used for the analysis and evaluation of pathological voice.

Full dyon excitation spectrum in extended Levin-Wen models

NASA Astrophysics Data System (ADS)

Hu, Yuting; Geer, Nathan; Wu, Yong-Shi

2018-05-01

In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two-dimensional topological phases, it is relatively easy to describe only single-fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper. We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex to describe the internal charge degrees of freedom at the vertex. Then, we study the full dyon spectrum of the extended LW models, including both quantum numbers and wave functions for dyonic quasiparticle excitations. The local operators associated with the dyonic excitations are shown to form the so-called tube algebra, whose representations (modules) form the quantum double (categoric center) of the input data (unitary fusion category). In physically relevant cases, the input data are from a finite or quantum group (with braiding R matrices), and we find that the elementary excitations (or dyon species), as well as any localized/isolated excited states, are characterized by three quantum numbers: charge, fluxon type, and twist. They provide a "complete basis" for many-body states in the enlarged Hilbert space. Concrete examples are presented and the relevance of our results to the electric-magnetic duality existing in the models is addressed.

Multiscale Characterization of PM2.5 in Southern Taiwan based on Noise-assisted Multivariate Empirical Mode Decomposition and Time-dependent Intrinsic Correlation

NASA Astrophysics Data System (ADS)

Hsiao, Y. R.; Tsai, C.

2017-12-01

As the WHO Air Quality Guideline indicates, ambient air pollution exposes world populations under threat of fatal symptoms (e.g. heart disease, lung cancer, asthma etc.), raising concerns of air pollution sources and relative factors. This study presents a novel approach to investigating the multiscale variations of PM2.5 in southern Taiwan over the past decade, with four meteorological influencing factors (Temperature, relative humidity, precipitation and wind speed),based on Noise-assisted Multivariate Empirical Mode Decomposition(NAMEMD) algorithm, Hilbert Spectral Analysis(HSA) and Time-dependent Intrinsic Correlation(TDIC) method. NAMEMD algorithm is a fully data-driven approach designed for nonlinear and nonstationary multivariate signals, and is performed to decompose multivariate signals into a collection of channels of Intrinsic Mode Functions (IMFs). TDIC method is an EMD-based method using a set of sliding window sizes to quantify localized correlation coefficients for multiscale signals. With the alignment property and quasi-dyadic filter bank of NAMEMD algorithm, one is able to produce same number of IMFs for all variables and estimates the cross correlation in a more accurate way. The performance of spectral representation of NAMEMD-HSA method is compared with Complementary Empirical Mode Decomposition/ Hilbert Spectral Analysis (CEEMD-HSA) and Wavelet Analysis. The nature of NAMAMD-based TDICC analysis is then compared with CEEMD-based TDIC analysis and the traditional correlation analysis.

Enhanced method to reconstruct mode shapes of continuous scanning measurements using the Hilbert Huang transform and the modal analysis method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Jongsuh; Hussain, Syed Hassaan; Wang, Semyung, E-mail: smwang@gist.ac.kr

2014-09-15

Generally, it is time consuming to experimentally identify the operating deflection shape or mode shape of a structure. To overcome this problem, the Hilbert Huang transform (HHT) technique has been recently proposed. This technique is used to extract the mode shape from measurements that continuously measure the vibration of a region of interest within a structure using a non-contact laser sensor. In previous research regarding the HHT, two technical processes were needed to obtain the mode shape for each mode. The purpose of this study is to improve and complement our previous research, and for this purpose, a modal analysismore » approach is adapted without using the two technical processes to obtain an accurate un-damped impulse response of each mode for continuous scanning measurements. In addition, frequency response functions for each type of beam are derived, making it possible to make continuously scanned measurements along a straight profile. In this paper, the technical limitations and drawbacks of the damping compensation technique used in previous research are identified. In addition, the separation of resonant frequency (the Doppler effect) that occurs in continuous scanning measurements and the separation of damping phenomenon are also observed. The proposed method is quantitatively verified by comparing it with the results obtained from a conventional approach to estimate the mode shape with an impulse response.« less

The short pulse equation by a Riemann-Hilbert approach

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry; Zielinski, Lech

2017-07-01

We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation u_{xt}=u+{1/6}(u^3)_{xx} with zero boundary conditions (as |x|→ ∞). This approach is directly applied to a Lax pair for the SP equation. It allows us to give a parametric representation of the solution to the Cauchy problem. This representation is then used for studying the longtime behavior of the solution as well as for retrieving the soliton solutions. Finally, the analysis of the longtime behavior allows us to formulate, in spectral terms, a sufficient condition for the wave breaking.

Computation and projection of spiral wave trajectories during atrial fibrillation: a computational study.

PubMed

Pashaei, Ali; Bayer, Jason; Meillet, Valentin; Dubois, Rémi; Vigmond, Edward

2015-03-01

To show how atrial fibrillation rotor activity on the heart surface manifests as phase on the torso, fibrillation was induced on a geometrically accurate computer model of the human atria. The Hilbert transform, time embedding, and filament detection were compared. Electrical activity on the epicardium was used to compute potentials on different surfaces from the atria to the torso. The Hilbert transform produces erroneous phase when pacing for longer than the action potential duration. The number of phase singularities, frequency content, and the dominant frequency decreased with distance from the heart, except for the convex hull. Copyright © 2015 Elsevier Inc. All rights reserved.

Towards deconstruction of the Type D (2,0) theory

NASA Astrophysics Data System (ADS)

Bourget, Antoine; Pini, Alessandro; Rodriguez-Gomez, Diego

2017-12-01

We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional (2, 0) theory of type D k . This 4d theory is defined by a necklace quiver with alternating gauge nodes O(2 k) and Sp( k). We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of O versus SO gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d.

On the Hilbert-Huang Transform Theoretical Foundation

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Huang, Norden E.

2004-01-01

The Hilbert-Huang Transform [HHT] is a novel empirical method for spectrum analysis of non-linear and non-stationary signals. The HHT is a recent development and much remains to be done to establish the theoretical foundation of the HHT algorithms. This paper develops the theoretical foundation for the convergence of the HHT sifting algorithm and it proves that the finest spectrum scale will always be the first generated by the HHT Empirical Mode Decomposition (EMD) algorithm. The theoretical foundation for cutting an extrema data points set into two parts is also developed. This then allows parallel signal processing for the HHT computationally complex sifting algorithm and its optimization in hardware.

Decrement of uterine myometrial burst duration as a correlate to active labor: a Hilbert phase approach.

PubMed

Govindan, Rathinaswamy B; Vairavan, Srinivasan; Furdea, Adrian; Murphy, Pam; Preissl, Hubert; Eswaran, Hari

2010-01-01

We propose a novel approach based on Hilbert phase to identify the burst in the uterine myometrial activity. We apply this approach to 24 serial magnetomyographic signals recorded from four pregnant women using a 151 SQUID array system. The bursts identified with this approach are evaluated for duration and are correlated with the gestational age. In all four subjects, we find a decrease in the duration of burst as the subject approaches active labor. As was shown in animal studies, this result indicates a faster conduction time between the muscle cells which activate a larger number of muscle units in a synchronous manner.

A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

NASA Astrophysics Data System (ADS)

Its, A.; Sukhanov, V.

2016-05-01

The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.

Minimal sufficient positive-operator valued measure on a separable Hilbert space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuramochi, Yui, E-mail: kuramochi.yui.22c@st.kyoto-u.ac.jp

We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.

Local quantum measurement and no-signaling imply quantum correlations.

PubMed

Barnum, H; Beigi, S; Boixo, S; Elliott, M B; Wehner, S

2010-04-09

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.

Application of the Hilbert space average method on heat conduction models.

PubMed

Michel, Mathias; Gemmer, Jochen; Mahler, Günter

2006-01-01

We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy diffusion with respect to a coarse-grained description for almost all initial states. Close to the respective equilibrium, we investigate this behavior in terms of heat transport and derive the heat conduction coefficient. Thus, we are able to show that both heat (energy) diffusive behavior as well as Fourier's law follows from and is compatible with a reversible Schrödinger dynamics on the complete level of description.

Remarks on entanglement entropy in string theory

NASA Astrophysics Data System (ADS)

Balasubramanian, Vijay; Parrikar, Onkar

2018-03-01

Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations." We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.

A High-Resolution Demodulation Algorithm for FBG-FP Static-Strain Sensors Based on the Hilbert Transform and Cross Third-Order Cumulant

PubMed Central

Huang, Wenzhu; Zhen, Tengkun; Zhang, Wentao; Zhang, Fusheng; Li, Fang

2015-01-01

Static strain can be detected by measuring a cross-correlation of reflection spectra from two fiber Bragg gratings (FBGs). However, the static-strain measurement resolution is limited by the dominant Gaussian noise source when using this traditional method. This paper presents a novel static-strain demodulation algorithm for FBG-based Fabry-Perot interferometers (FBG-FPs). The Hilbert transform is proposed for changing the Gaussian distribution of the two FBG-FPs’ reflection spectra, and a cross third-order cumulant is used to use the results of the Hilbert transform and get a group of noise-vanished signals which can be used to accurately calculate the wavelength difference of the two FBG-FPs. The benefit by these processes is that Gaussian noise in the spectra can be suppressed completely in theory and a higher resolution can be reached. In order to verify the precision and flexibility of this algorithm, a detailed theory model and a simulation analysis are given, and an experiment is implemented. As a result, a static-strain resolution of 0.9 nε under laboratory environment condition is achieved, showing a higher resolution than the traditional cross-correlation method. PMID:25923938

A High-Resolution Demodulation Algorithm for FBG-FP Static-Strain Sensors Based on the Hilbert Transform and Cross Third-Order Cumulant.

PubMed

Huang, Wenzhu; Zhen, Tengkun; Zhang, Wentao; Zhang, Fusheng; Li, Fang

2015-04-27

Static strain can be detected by measuring a cross-correlation of reflection spectra from two fiber Bragg gratings (FBGs). However, the static-strain measurement resolution is limited by the dominant Gaussian noise source when using this traditional method. This paper presents a novel static-strain demodulation algorithm for FBG-based Fabry-Perot interferometers (FBG-FPs). The Hilbert transform is proposed for changing the Gaussian distribution of the two FBG-FPs' reflection spectra, and a cross third-order cumulant is used to use the results of the Hilbert transform and get a group of noise-vanished signals which can be used to accurately calculate the wavelength difference of the two FBG-FPs. The benefit by these processes is that Gaussian noise in the spectra can be suppressed completely in theory and a higher resolution can be reached. In order to verify the precision and flexibility of this algorithm, a detailed theory model and a simulation analysis are given, and an experiment is implemented. As a result, a static-strain resolution of 0.9 nε under laboratory environment condition is achieved, showing a higher resolution than the traditional cross-correlation method.

Continuously tunable photonic fractional Hilbert transformer using a high-contrast germanium-doped silica-on-silicon microring resonator.

PubMed

Shahoei, Hiva; Dumais, Patrick; Yao, Jianping

2014-05-01

We propose and experimentally demonstrate a continuously tunable fractional Hilbert transformer (FHT) based on a high-contrast germanium-doped silica-on-silicon (SOS) microring resonator (MRR). The propagation loss of a high-contrast germanium-doped SOS waveguide can be very small (0.02 dB/cm) while the lossless bend radius can be less than 1 mm. These characteristics lead to the fabrication of an MRR with a high Q-factor and a large free-spectral range (FSR), which is needed to implement a Hilbert transformer (HT). The SOS MRR is strongly polarization dependent. By changing the polarization direction of the input signal, the phase shift introduced at the center of the resonance spectrum is changed. The tunable phase shift at the resonance wavelength can be used to implement a tunable FHT. A germanium-doped SOS MRR with a high-index contrast of 3.8% is fabricated. The use of the fabricated MRR for the implementation of a tunable FHT with tunable orders at 1, 0.85, 0.95, 1.05, and 1.13 for a Gaussian pulse with the temporal full width at half-maximum of 80 ps is experimentally demonstrated.

Practical interior tomography with radial Hilbert filtering and a priori knowledge in a small round area.

PubMed

Tang, Shaojie; Yang, Yi; Tang, Xiangyang

2012-01-01

Interior tomography problem can be solved using the so-called differentiated backprojection-projection onto convex sets (DBP-POCS) method, which requires a priori knowledge within a small area interior to the region of interest (ROI) to be imaged. In theory, the small area wherein the a priori knowledge is required can be in any shape, but most of the existing implementations carry out the Hilbert filtering either horizontally or vertically, leading to a vertical or horizontal strip that may be across a large area in the object. In this work, we implement a practical DBP-POCS method with radial Hilbert filtering and thus the small area with the a priori knowledge can be roughly round (e.g., a sinus or ventricles among other anatomic cavities in human or animal body). We also conduct an experimental evaluation to verify the performance of this practical implementation. We specifically re-derive the reconstruction formula in the DBP-POCS fashion with radial Hilbert filtering to assure that only a small round area with the a priori knowledge be needed (namely radial DBP-POCS method henceforth). The performance of the practical DBP-POCS method with radial Hilbert filtering and a priori knowledge in a small round area is evaluated with projection data of the standard and modified Shepp-Logan phantoms simulated by computer, followed by a verification using real projection data acquired by a computed tomography (CT) scanner. The preliminary performance study shows that, if a priori knowledge in a small round area is available, the radial DBP-POCS method can solve the interior tomography problem in a more practical way at high accuracy. In comparison to the implementations of DBP-POCS method demanding the a priori knowledge in horizontal or vertical strip, the radial DBP-POCS method requires the a priori knowledge within a small round area only. Such a relaxed requirement on the availability of a priori knowledge can be readily met in practice, because a variety of small round areas (e.g., air-filled sinuses or fluid-filled ventricles among other anatomic cavities) exist in human or animal body. Therefore, the radial DBP-POCS method with a priori knowledge in a small round area is more feasible in clinical and preclinical practice.

Gravity dual for a model of perception

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Yu, E-mail: nakayama@berkeley.edu

2011-01-15

One of the salient features of human perception is its invariance under dilatation in addition to the Euclidean group, but its non-invariance under special conformal transformation. We investigate a holographic approach to the information processing in image discrimination with this feature. We claim that a strongly coupled analogue of the statistical model proposed by Bialek and Zee can be holographically realized in scale invariant but non-conformal Euclidean geometries. We identify the Bayesian probability distribution of our generalized Bialek-Zee model with the GKPW partition function of the dual gravitational system. We provide a concrete example of the geometric configuration based onmore » a vector condensation model coupled with the Euclidean Einstein-Hilbert action. From the proposed geometry, we study sample correlation functions to compute the Bayesian probability distribution.« less

Projected quasiparticle theory for molecular electronic structure

NASA Astrophysics Data System (ADS)

Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Samanta, Kousik; Ellis, Jason K.

2011-09-01

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

On the nonlocal predictions of quantum optics

NASA Technical Reports Server (NTRS)

Marshall, Trevor W.; Santos, Emilio; Vidiella-Barranco, Antonio

1994-01-01

We give a definition of locality in quantum optics based upon Bell's work, and show that locality has been violated in no experiment performed up to now. We argue that the interpretation of the Wigner function as a probability density gives a very attractive local realistic picture of quantum optics provided that this function is nonnegative. We conjecture that this is the case for all states which can be realized in the laboratory. In particular, we believe that the usual representation of 'single photon states' by a Fock state of the Hilbert space is not correct and that a more physical, although less simple mathematically, representation involves density matrices. We study in some detail the experiment showing anticorrelation after a beam splitter and prove that it naturally involves a positive Wigner function. Our (quantum) predictions for this experiment disagree with the ones reported in the literature.

Identification of varying time scales in sediment transport using the Hilbert-Huang Transform method

NASA Astrophysics Data System (ADS)

Kuai, Ken Z.; Tsai, Christina W.

2012-02-01

SummarySediment transport processes vary at a variety of time scales - from seconds, hours, days to months and years. Multiple time scales exist in the system of flow, sediment transport and bed elevation change processes. As such, identification and selection of appropriate time scales for flow and sediment processes can assist in formulating a system of flow and sediment governing equations representative of the dynamic interaction of flow and particles at the desired details. Recognizing the importance of different varying time scales in the fluvial processes of sediment transport, we introduce the Hilbert-Huang Transform method (HHT) to the field of sediment transport for the time scale analysis. The HHT uses the Empirical Mode Decomposition (EMD) method to decompose a time series into a collection of the Intrinsic Mode Functions (IMFs), and uses the Hilbert Spectral Analysis (HSA) to obtain instantaneous frequency data. The EMD extracts the variability of data with different time scales, and improves the analysis of data series. The HSA can display the succession of time varying time scales, which cannot be captured by the often-used Fast Fourier Transform (FFT) method. This study is one of the earlier attempts to introduce the state-of-the-art technique for the multiple time sales analysis of sediment transport processes. Three practical applications of the HHT method for data analysis of both suspended sediment and bedload transport time series are presented. The analysis results show the strong impact of flood waves on the variations of flow and sediment time scales at a large sampling time scale, as well as the impact of flow turbulence on those time scales at a smaller sampling time scale. Our analysis reveals that the existence of multiple time scales in sediment transport processes may be attributed to the fractal nature in sediment transport. It can be demonstrated by the HHT analysis that the bedload motion time scale is better represented by the ratio of the water depth to the settling velocity, h/ w. In the final part, HHT results are compared with an available time scale formula in literature.

Computing an upper bound on contact stress with surrogate duality

NASA Astrophysics Data System (ADS)

Xuan, Zhaocheng; Papadopoulos, Panayiotis

2016-07-01

We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum—since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness.

Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds

NASA Astrophysics Data System (ADS)

Liu, Yang

2017-11-01

We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of the modular derivation through two local curvature functions. Explicit expressions for those functions are obtained for all even dimensions (greater than two). In dimension four, the one variable function shows striking similarity to the analytic functions of the characteristic classes appeared in the Atiyah-Singer local index formula, namely, it is roughly a product of the j-function (which defines the A ˆ -class of a manifold) and an exponential function (which defines the Chern character of a bundle). By performing two different computations for the variation of the Einstein-Hilbert action, we obtain deep internal relations between two local curvature functions. Straightforward verification for those relations gives a strong conceptual confirmation for the whole computational machinery we have developed so far, especially the Mathematica code hidden behind the paper.

[An EMD based time-frequency distribution and its application in EEG analysis].

PubMed

Li, Xiaobing; Chu, Meng; Qiu, Tianshuang; Bao, Haiping

2007-10-01

Hilbert-Huang transform (HHT) is a new time-frequency analytic method to analyze the nonlinear and the non-stationary signals. The key step of this method is the empirical mode decomposition (EMD), with which any complicated signal can be decomposed into a finite and small number of intrinsic mode functions (IMF). In this paper, a new EMD based method for suppressing the cross-term of Wigner-Ville distribution (WVD) is developed and is applied to analyze the epileptic EEG signals. The simulation data and analysis results show that the new method suppresses the cross-term of the WVD effectively with an excellent resolution.

Functors of White Noise Associated to Characters of the Infinite Symmetric Group

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Guţă, Mădălin

The characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to Veršik and Kerov. The von Neumann algebra generated by the fields with f in an infinite dimensional real Hilbert space is infinite and the vacuum vector is not separating. For a family depending on an integer N< - 1 an ``exclusion principle'' is found allowing at most ``identical particles'' on the same state: The algebras are type factors. Functors of white noise are constructed and proved to be non-equivalent for different values of N.

Scale matters

NASA Astrophysics Data System (ADS)

Margolin, L. G.

2018-04-01

The applicability of Navier-Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman-Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics. This article is part of the theme issue `Hilbert's sixth problem'.

Sparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model.

PubMed

Alvermann, A; Fehske, H

2009-04-17

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral, and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behavior, and dissipative spin dynamics in the spin-boson model.

Seizure classification in EEG signals utilizing Hilbert-Huang transform

PubMed Central

2011-01-01

Background Classification method capable of recognizing abnormal activities of the brain functionality are either brain imaging or brain signal analysis. The abnormal activity of interest in this study is characterized by a disturbance caused by changes in neuronal electrochemical activity that results in abnormal synchronous discharges. The method aims at helping physicians discriminate between healthy and seizure electroencephalographic (EEG) signals. Method Discrimination in this work is achieved by analyzing EEG signals obtained from freely accessible databases. MATLAB has been used to implement and test the proposed classification algorithm. The analysis in question presents a classification of normal and ictal activities using a feature relied on Hilbert-Huang Transform. Through this method, information related to the intrinsic functions contained in the EEG signal has been extracted to track the local amplitude and the frequency of the signal. Based on this local information, weighted frequencies are calculated and a comparison between ictal and seizure-free determinant intrinsic functions is then performed. Methods of comparison used are the t-test and the Euclidean clustering. Results The t-test results in a P-value < 0.02 and the clustering leads to accurate (94%) and specific (96%) results. The proposed method is also contrasted against the Multivariate Empirical Mode Decomposition that reaches 80% accuracy. Comparison results strengthen the contribution of this paper not only from the accuracy point of view but also with respect to its fast response and ease to use. Conclusion An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper. The proposed system bears the potential of providing several credible benefits such as fast diagnosis, high accuracy, good sensitivity and specificity, time saving and user friendly. Furthermore, the classification of mode mixing can be achieved using the extracted instantaneous information of every IMF, but it would be most likely a hard task if only the average value is used. Extra benefits of this proposed system include low cost, and ease of interface. All of that indicate the usefulness of the tool and its use as an efficient diagnostic tool. PMID:21609459

Seizure classification in EEG signals utilizing Hilbert-Huang transform.

PubMed

Oweis, Rami J; Abdulhay, Enas W

2011-05-24

Classification method capable of recognizing abnormal activities of the brain functionality are either brain imaging or brain signal analysis. The abnormal activity of interest in this study is characterized by a disturbance caused by changes in neuronal electrochemical activity that results in abnormal synchronous discharges. The method aims at helping physicians discriminate between healthy and seizure electroencephalographic (EEG) signals. Discrimination in this work is achieved by analyzing EEG signals obtained from freely accessible databases. MATLAB has been used to implement and test the proposed classification algorithm. The analysis in question presents a classification of normal and ictal activities using a feature relied on Hilbert-Huang Transform. Through this method, information related to the intrinsic functions contained in the EEG signal has been extracted to track the local amplitude and the frequency of the signal. Based on this local information, weighted frequencies are calculated and a comparison between ictal and seizure-free determinant intrinsic functions is then performed. Methods of comparison used are the t-test and the Euclidean clustering. The t-test results in a P-value < 0.02 and the clustering leads to accurate (94%) and specific (96%) results. The proposed method is also contrasted against the Multivariate Empirical Mode Decomposition that reaches 80% accuracy. Comparison results strengthen the contribution of this paper not only from the accuracy point of view but also with respect to its fast response and ease to use. An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper. The proposed system bears the potential of providing several credible benefits such as fast diagnosis, high accuracy, good sensitivity and specificity, time saving and user friendly. Furthermore, the classification of mode mixing can be achieved using the extracted instantaneous information of every IMF, but it would be most likely a hard task if only the average value is used. Extra benefits of this proposed system include low cost, and ease of interface. All of that indicate the usefulness of the tool and its use as an efficient diagnostic tool.

Quantum supersymmetric Bianchi IX cosmology

NASA Astrophysics Data System (ADS)

Damour, Thibault; Spindel, Philippe

2014-11-01

We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D =4 simple supergravity for a S U (2 ) -homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a 64-component spinor of spin(8,4) depending on the three squashing parameters, which satisfies Dirac-like, and Klein-Gordon-like, wave equations describing the propagation of a "quantum spinning particle" reflecting off spin-dependent potential walls. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact subalgebra of the rank-3 hyperbolic Kac-Moody algebra A E3 . The (quartic-in-fermions) squared-mass term μ^ 2 entering the Klein-Gordon-like equation has several remarkable properties: (i) it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; (ii) it is a quadratic function of the fermion number NF; and (iii) it is negative in most of the Hilbert space. The latter property leads to a possible quantum avoidance of the singularity ("cosmological bounce"), and suggests imposing the boundary condition that the wave function of the Universe vanish when the volume of space tends to zero (a type of boundary condition which looks like a final-state condition when considering the big crunch inside a black hole). The space of solutions is a mixture of "discrete-spectrum states" (parametrized by a few constant parameters, and known in explicit form) and of continuous-spectrum states (parametrized by arbitrary functions entering some initial-value problem). The predominantly negative values of the squared-mass term lead to a "bottle effect" between small-volume universes and large-volume ones, and to a possible reduction of the continuous spectrum to a discrete spectrum of quantum states looking like excited versions of the Planckian-size universes described by the discrete states at fermionic levels NF=0 and 1.

The canonical quantization of chaotic maps on the torus

NASA Astrophysics Data System (ADS)

Rubin, Ron Shai

In this thesis, a quantization method for classical maps on the torus is presented. The quantum algebra of observables is defined as the quantization of measurable functions on the torus with generators exp (2/pi ix) and exp (2/pi ip). The Hilbert space we use remains the infinite-dimensional L2/ (/IR, dx). The dynamics is given by a unitary quantum propagator such that as /hbar /to 0, the classical dynamics is returned. We construct such a quantization for the Kronecker map, the cat map, the baker's map, the kick map, and the Harper map. For the cat map, we find the same for the propagator on the plane the same integral kernel conjectured in (HB) using semiclassical methods. We also define a quantum 'integral over phase space' as a trace over the quantum algebra. Using this definition, we proceed to define quantum ergodicity and mixing for maps on the torus. We prove that the quantum cat map and Kronecker map are both ergodic, but only the cat map is mixing, true to its classical origins. For Planck's constant satisfying the integrality condition h = 1/N, with N/in doubz+, we construct an explicit isomorphism between L2/ (/IR, dx) and the Hilbert space of sections of an N-dimensional vector bundle over a θ-torus T2 of boundary conditions. The basis functions are distributions in L2/ (/IR, dx), given by an infinite comb of Dirac δ-functions. In Bargmann space these distributions take on the form of Jacobi ϑ-functions. Transformations from position to momentum representation can be implemented via a finite N-dimensional discrete Fourier transform. With the θ-torus, we provide a connection between the finite-dimensional quantum maps given in the physics literature and the canonical quantization presented here and found in the language of pseudo-differential operators elsewhere in mathematics circles. Specifically, at a fixed point of the dynamics on the θ-torus, we return a finite-dimensional matrix propagator. We present this connection explicitly for several examples.

Structure Functions of Bound Neutrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sebastian Kuhn

2005-04-01

We describe an experiment measuring electron scattering on a neutron bound in deuterium with coincident detection of a fast, backward-going spectator proton. Our data map out the relative importance of the pure PWIA spectator mechanism and final state interactions in various kinematic regions, and give a first glimpse of the modification of the structure function of a bound neutron as a function of its off-shell mass. We also discuss a new experimental program to study the structure of a free neutron by extending the same technique to much lower spectator momenta.

Coexistence of bounded and unbounded motions in a bouncing ball model

NASA Astrophysics Data System (ADS)

Marò, Stefano

2013-05-01

We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function f. We apply the Aubry-Mather theory to the generating function in order to prove the existence of bounded motions with prescribed mean time between the bounces. As the existence of unbounded motions is known, it is possible to find a class of functions f that allow both bounded and unbounded motions.

The Laughlin liquid in an external potential

NASA Astrophysics Data System (ADS)

Rougerie, Nicolas; Yngvason, Jakob

2018-04-01

We study natural perturbations of the Laughlin state arising from the effects of trapping and disorder. These are N-particle wave functions that have the form of a product of Laughlin states and analytic functions of the N variables. We derive an upper bound to the ground state energy in a confining external potential, matching exactly a recently derived lower bound in the large N limit. Irrespective of the shape of the confining potential, this sharp upper bound can be achieved through a modification of the Laughlin function by suitably arranged quasi-holes.

Suppressing Ionic Terms with Number-Counting Jastrow Factors in Real Space

DOE PAGES

Goetz, Brett Van Der; Neuscamman, Eric

2017-04-06

Here, we demonstrate that four-body real-space Jastrow factors are, with the right type of Jastrow basis function, capable of performing successful wave function stenciling to remove unwanted ionic terms from an overabundant Fermionic reference without unduly modifying the remaining components. In addition to greatly improving size consistency (restoring it exactly in the case of a geminal power), real-space wave function stenciling is, unlike its Hilbert-space predecessors, immediately compatible with diffusion Monte Carlo, allowing it to be used in the pursuit of compact, strongly correlated trial functions with reliable nodal surfaces. Furthermore, we demonstrate the efficacy of this approach in themore » context of a double bond dissociation by using it to extract a qualitatively correct nodal surface despite being paired with a restricted Slater determinant, that, due to ionic term errors, produces a ground state with a qualitatively incorrect nodal surface when used in the absence of the Jastrow.« less

Suppressing Ionic Terms with Number-Counting Jastrow Factors in Real Space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goetz, Brett Van Der; Neuscamman, Eric

Here, we demonstrate that four-body real-space Jastrow factors are, with the right type of Jastrow basis function, capable of performing successful wave function stenciling to remove unwanted ionic terms from an overabundant Fermionic reference without unduly modifying the remaining components. In addition to greatly improving size consistency (restoring it exactly in the case of a geminal power), real-space wave function stenciling is, unlike its Hilbert-space predecessors, immediately compatible with diffusion Monte Carlo, allowing it to be used in the pursuit of compact, strongly correlated trial functions with reliable nodal surfaces. Furthermore, we demonstrate the efficacy of this approach in themore » context of a double bond dissociation by using it to extract a qualitatively correct nodal surface despite being paired with a restricted Slater determinant, that, due to ionic term errors, produces a ground state with a qualitatively incorrect nodal surface when used in the absence of the Jastrow.« less

Error bounds of adaptive dynamic programming algorithms for solving undiscounted optimal control problems.

PubMed

Liu, Derong; Li, Hongliang; Wang, Ding

2015-06-01

In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.

Optimal bounds and extremal trajectories for time averages in dynamical systems

NASA Astrophysics Data System (ADS)

Tobasco, Ian; Goluskin, David; Doering, Charles

2017-11-01

For systems governed by differential equations it is natural to seek extremal solution trajectories, maximizing or minimizing the long-time average of a given quantity of interest. A priori bounds on optima can be proved by constructing auxiliary functions satisfying certain point-wise inequalities, the verification of which does not require solving the underlying equations. We prove that for any bounded autonomous ODE, the problems of finding extremal trajectories on the one hand and optimal auxiliary functions on the other are strongly dual in the sense of convex duality. As a result, auxiliary functions provide arbitrarily sharp bounds on optimal time averages. Furthermore, nearly optimal auxiliary functions provide volumes in phase space where maximal and nearly maximal trajectories must lie. For polynomial systems, such functions can be constructed by semidefinite programming. We illustrate these ideas using the Lorenz system, producing explicit volumes in phase space where extremal trajectories are guaranteed to reside. Supported by NSF Award DMS-1515161, Van Loo Postdoctoral Fellowships, and the John Simon Guggenheim Foundation.

On the emergence of the structure of physics

NASA Astrophysics Data System (ADS)

Majid, S.

2018-04-01

We consider Hilbert's problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space-time as motivated by this non-standard philosophy, including a new toy model of gravity on a space-time consisting of four points forming a square. This article is part of the theme issue `Hilbert's sixth problem'.

THz-bandwidth photonic Hilbert transformers based on fiber Bragg gratings in transmission.

PubMed

Fernández-Ruiz, María R; Wang, Lixian; Carballar, Alejandro; Burla, Maurizio; Azaña, José; LaRochelle, Sophie

2015-01-01

THz-bandwidth photonic Hilbert transformers (PHTs) are implemented for the first time, to the best of our knowledge, based on fiber Bragg grating (FBG) technology. To increase the practical bandwidth limitation of FBGs (typically <200  GHz), a superstructure based on two superimposed linearly-chirped FBGs operating in transmission has been employed. The use of a transmission FBG involves first a conversion of the non-minimum phase response of the PHT into a minimum-phase response by adding an anticipated instantaneous component to the desired system temporal impulse response. Using this methodology, a 3-THz-bandwidth integer PHT and a fractional (order 0.81) PHT are designed, fabricated, and successfully characterized.

Multichannel photonic Hilbert transformers based on complex modulated integrated Bragg gratings.

PubMed

Cheng, Rui; Chrostowski, Lukas

2018-03-01

Multichannel photonic Hilbert transformers (MPHTs) are reported. The devices are based on single compact spiral integrated Bragg gratings on silicon with coupling coefficients precisely modulated by the phase of each grating period. MPHTs with up to nine wavelength channels and a single-channel bandwidth of up to ∼625  GHz are achieved. The potential of the devices for multichannel single-sideband signal generation is suggested. The work offers a new possibility of utilizing wavelength as an extra degree of freedom in designing radio-frequency photonic signal processors. Such multichannel processors are expected to possess improved capacities and a potential to greatly benefit current widespread wavelength division multiplexed systems.

Bell - Kochen - Specker theorem for any finite dimension ?

NASA Astrophysics Data System (ADS)

Cabello, Adán; García-Alcaine, Guillermo

1996-03-01

The Bell - Kochen - Specker theorem against non-contextual hidden variables can be proved by constructing a finite set of `totally non-colourable' directions, as Kochen and Specker did in a Hilbert space of dimension n = 3. We generalize Kochen and Specker's set to Hilbert spaces of any finite dimension 0305-4470/29/5/016/img2, in a three-step process that shows the relationship between different kinds of proofs (`continuum', `probabilistic', `state-specific' and `state-independent') of the Bell - Kochen - Specker theorem. At the same time, this construction of a totally non-colourable set of directions in any dimension explicitly solves the question raised by Zimba and Penrose about the existence of such a set for n = 5.

On the emergence of the structure of physics.

PubMed

Majid, S

2018-04-28

We consider Hilbert's problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space-time as motivated by this non-standard philosophy, including a new toy model of gravity on a space-time consisting of four points forming a square.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations

NASA Astrophysics Data System (ADS)

Anosov, Dmitry V.; Leksin, Vladimir P.

2011-02-01

This paper contains an account of A.A. Bolibrukh's results obtained in the new directions of research that arose in the analytic theory of differential equations as a consequence of his sensational counterexample to the Riemann-Hilbert problem. A survey of results of his students in developing topics first considered by Bolibrukh is also presented. The main focus is on the role of the reducibility/irreducibility of systems of linear differential equations and their monodromy representations. A brief synopsis of results on the multidimensional Riemann-Hilbert problem and on isomonodromic deformations of Fuchsian systems is presented, and the main methods in the modern analytic theory of differential equations are sketched. Bibliography: 69 titles.

Decrement of uterine myometrial burst duration as a correlate to active labor: A Hilbert phase approach

PubMed Central

Govindan, Rathinaswamy B.; Vairavan, Srinivasan; Furdea, Adrian; Murphy, Pam; Preissl, Hubert; Eswaran, Hari

2011-01-01

We propose a novel approach based on Hilbert phase to identify the burst in the uterine myometrial activity. We apply this approach to 24 serial magnetomyographic signals recorded from four pregnant women using a 151 SQUID array system. The bursts identified with this approach are evaluated for duration and are correlated with the gestational age. In all four subjects, we find a decrease in the duration of burst as the subject approaches active labor. As was shown in animal studies, this result indicates a faster conduction time between the muscle cells which activate a larger number of muscle units in a synchronous manner. PMID:21096231

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

NASA Astrophysics Data System (ADS)

Anderson, B. E.; Sosa-Martinez, H.; Riofrío, C. A.; Deutsch, Ivan H.; Jessen, Poul S.

2015-06-01

Unitary transformations are the most general input-output maps available in closed quantum systems. Good control protocols have been developed for qubits, but questions remain about the use of optimal control theory to design unitary maps in high-dimensional Hilbert spaces, and about the feasibility of their robust implementation in the laboratory. Here we design and implement unitary maps in a 16-dimensional Hilbert space associated with the 6 S1 /2 ground state of 133Cs, achieving fidelities >0.98 with built-in robustness to static and dynamic perturbations. Our work has relevance for quantum information processing and provides a template for similar advances on other physical platforms.

Uncertainty Relation on Generalized Skew Information with aMonotone Pair

NASA Astrophysics Data System (ADS)

Liu, Jun-Tong; Wang, Qing-Wen; Li, Lei

2017-08-01

In this paper, we first define a generalized ( f, g)-skew information |I_{ ρ }^{(f, g)} |(A) and two related quantity |J_{ ρ }^{(f, g)} |(A) and |U_{ ρ }^{(f, g)} |(A) for any non-Hermitian Hilbert-Schmidt operator A and a density operator ρ on a Hilbert space H and discuss some properties of them. And then, we obtain the following uncertainty relation in terms of |U_{ ρ }^{(f, g)} |(A): |U_{ ρ}^{(f, g)}|(A)|U_{ ρ}^{(f, g)}|(B)≥ β_{(f, g)}|Tr( f(ρ)g(ρ)[A, B]0)|2, which is a generalization of a known uncertainty relation in Ko and Yoo (J. Math. Anal. Appl. 383, 208-214, 11).

Comparing fixed and variable-width Gaussian networks.

PubMed

Kůrková, Věra; Kainen, Paul C

2014-09-01

The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is proven that if two Gaussian RBF networks have the same input-output functions, then they must have the same numbers of units with the same centers and widths. Further, it is shown that while sets of input-output functions of Gaussian kernel networks with two different widths are disjoint, each such set is large enough to be a universal approximator. Embedding of RKHSs induced by "flatter" Gaussians into RKHSs induced by "sharper" Gaussians is described and growth of the ratios of norms on these spaces with increasing input dimension is estimated. Finally, large sets of argminima of error functionals in sets of input-output functions of Gaussian RBFs are described. Copyright © 2014 Elsevier Ltd. All rights reserved.

Exact results for the finite time thermodynamic uncertainty relation

NASA Astrophysics Data System (ADS)

Manikandan, Sreekanth K.; Krishnamurthy, Supriya

2018-03-01

We obtain exact results for the recently discovered finite-time thermodynamic uncertainty relation, for the dissipated work W d , in a stochastically driven system with non-Gaussian work statistics, both in the steady state and transient regimes, by obtaining exact expressions for any moment of W d at arbitrary times. The uncertainty function (the Fano factor of W d ) is bounded from below by 2k_BT as expected, for all times τ, in both steady state and transient regimes. The lower bound is reached at τ=0 as well as when certain system parameters vanish (corresponding to an equilibrium state). Surprisingly, we find that the uncertainty function also reaches a constant value at large τ for all the cases we have looked at. For a system starting and remaining in steady state, the uncertainty function increases monotonically, as a function of τ as well as other system parameters, implying that the large τ value is also an upper bound. For the same system in the transient regime, however, we find that the uncertainty function can have a local minimum at an accessible time τm , for a range of parameter values. The large τ value for the uncertainty function is hence not a bound in this case. The non-monotonicity suggests, rather counter-intuitively, that there might be an optimal time for the working of microscopic machines, as well as an optimal configuration in the phase space of parameter values. Our solutions show that the ratios of higher moments of the dissipated work are also bounded from below by 2k_BT . For another model, also solvable by our methods, which never reaches a steady state, the uncertainty function, is in some cases, bounded from below by a value less than 2k_BT .

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Tobasco, Ian; Goluskin, David; Doering, Charles R.

2018-02-01

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.

Implementing and Bounding a Cascade Heuristic for Large-Scale Optimization

DTIC Science & Technology

2017-06-01

solving the monolith, we develop a method for producing lower bounds to the optimal objective function value. To do this, we solve a new integer...as developing and analyzing methods for producing lower bounds to the optimal objective function value of the seminal problem monolith, which this...length of the window decreases, the end effects of the model typically increase (Zerr, 2016). There are four primary methods for correcting end

Large deviation function for a driven underdamped particle in a periodic potential

NASA Astrophysics Data System (ADS)

Fischer, Lukas P.; Pietzonka, Patrick; Seifert, Udo

2018-02-01

Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one-dimensional periodic potential. Two different approaches to the large deviation function of the particle current are presented. First, we derive an explicit expression for the large deviation functional of the empirical phase space density, which replaces the level 2.5 functional used for overdamped dynamics. Using this approach, we obtain several bounds on the large deviation function of the particle current. We compare these to bounds for overdamped dynamics that have recently been derived, motivated by the thermodynamic uncertainty relation. Second, we provide a method to calculate the large deviation function via the cumulant generating function. We use this method to assess the tightness of the bounds in a numerical case study for a cosine potential.

New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities

NASA Technical Reports Server (NTRS)

Mceliece, R. J.; Rodemich, E. R.; Rumsey, H., Jr.; Welch, L. R.

1977-01-01

An upper bound on the rate of a binary code as a function of minimum code distance (using a Hamming code metric) is arrived at from Delsarte-MacWilliams inequalities. The upper bound so found is asymptotically less than Levenshtein's bound, and a fortiori less than Elias' bound. Appendices review properties of Krawtchouk polynomials and Q-polynomials utilized in the rigorous proofs.

On the matrix Fourier filtering problem for a class of models of nonlinear optical systems with a feedback

NASA Astrophysics Data System (ADS)

Razgulin, A. V.; Sazonova, S. V.

2017-09-01

A novel statement of the Fourier filtering problem based on the use of matrix Fourier filters instead of conventional multiplier filters is considered. The basic properties of the matrix Fourier filtering for the filters in the Hilbert-Schmidt class are established. It is proved that the solutions with a finite energy to the periodic initial boundary value problem for the quasi-linear functional differential diffusion equation with the matrix Fourier filtering Lipschitz continuously depend on the filter. The problem of optimal matrix Fourier filtering is formulated, and its solvability for various classes of matrix Fourier filters is proved. It is proved that the objective functional is differentiable with respect to the matrix Fourier filter, and the convergence of a version of the gradient projection method is also proved.

The solution of the sixth Hilbert problem: the ultimate Galilean revolution

NASA Astrophysics Data System (ADS)

D'Ariano, Giacomo Mauro

2018-04-01

I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: `physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as `clock', `rigid rod', `force', `inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory. This article is part of the theme issue `Hilbert's sixth problem'.

Hilbert space structure in quantum gravity: an algebraic perspective

DOE PAGES

Giddings, Steven B.

2015-12-16

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of themore » Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.« less

The solution of the sixth Hilbert problem: the ultimate Galilean revolution.

PubMed

D'Ariano, Giacomo Mauro

2018-04-28

I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: 'physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as 'clock', 'rigid rod', 'force', 'inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

General n-dimensional quadrature transform and its application to interferogram demodulation.

PubMed

Servin, Manuel; Quiroga, Juan Antonio; Marroquin, Jose Luis

2003-05-01

Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.

Hilbert space structure in quantum gravity: an algebraic perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giddings, Steven B.

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of themore » Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.« less

Multivariate Lipschitz optimization: Survey and computational comparison

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, P.; Gourdin, E.; Jaumard, B.

1994-12-31

Many methods have been proposed to minimize a multivariate Lipschitz function on a box. They pertain the three approaches: (i) reduction to the univariate case by projection (Pijavskii) or by using a space-filling curve (Strongin); (ii) construction and refinement of a single upper bounding function (Pijavskii, Mladineo, Mayne and Polak, Jaumard Hermann and Ribault, Wood...); (iii) branch and bound with local upper bounding functions (Galperin, Pint{acute e}r, Meewella and Mayne, the present authors). A survey is made, stressing similarities of algorithms, expressed when possible within a unified framework. Moreover, an extensive computational comparison is reported on.

Diagnostics and Robust Estimation When Transforming the Regression Model and the Response.

DTIC Science & Technology

1986-10-01

Bounded-influence estimators place a bound on the influence function of each observation. Bounded-influence regression estimators have been proposed by...Hampel et al. (1986, chapter 4) for further details. First we note that the influence function of 9 satisfying (14) is IF -)8""’IF.(yi,.9) B -.(Y. ,9...where 1 1.1-1 Page 21 B - N-I N T B N IZ NVT O(Y0]1=1 1 1iY~). This definition of the influence function is conditional on x .. XN but coincides with

GTP- and GDP-Dependent Rab27a Effectors in Pancreatic Beta-Cells.

PubMed

Yamaoka, Mami; Ishizaki, Toshimasa; Kimura, Toshihide

2015-01-01

Small guanosine triphosphatases (GTPases) participate in a wide variety of cellular functions including proliferation, differentiation, adhesion, and intracellular transport. Conventionally, only the guanosine 5'-triphosphate (GTP)-bound small GTPase interacts with effector proteins, and the resulting downstream signals control specific cellular functions. Therefore, the GTP-bound form is regarded as active, and the focus has been on searching for proteins that bind the GTP form to look for their effectors. The Rab family small GTPase Rab27a is highly expressed in some secretory cells and is involved in the control of membrane traffic. The present study reviews recent progress in our understanding of the roles of Rab27a and its effectors in pancreatic beta-cells. In the basal state, GTP-bound Rab27a controls insulin secretion at pre-exocytic stages via its GTP-dependent effectors. We previously identified novel guanosine 5'-diphosphate (GDP)-bound Rab27-interacting proteins. Interestingly, GDP-bound Rab27a controls endocytosis of the secretory membrane via its interaction with these proteins. We also demonstrated that the insulin secretagogue glucose converts Rab27a from its GTP- to GDP-bound forms. Thus, GTP- and GDP-bound Rab27a regulate pre-exocytic and endocytic stages in membrane traffic, respectively. Since the physiological importance of GDP-bound GTPases has been largely overlooked, we consider that the investigation of GDP-dependent effectors for other GTPases is necessary for further understanding of cellular function.

Bounded-Influence Inference in Regression.

DTIC Science & Technology

1984-02-01

be viewed as generalization of the classical F-test. By means of the influence function their robustness properties are investigated and optimally...robust tests that maximize the asymptotic power within each class, under the side condition of a bounded influence function , are constructed. Finally, an

Can a quantum state over time resemble a quantum state at a single time?

NASA Astrophysics Data System (ADS)

Horsman, Dominic; Heunen, Chris; Pusey, Matthew F.; Barrett, Jonathan; Spekkens, Robert W.

2017-09-01

The standard formalism of quantum theory treats space and time in fundamentally different ways. In particular, a composite system at a given time is represented by a joint state, but the formalism does not prescribe a joint state for a composite of systems at different times. If there were a way of defining such a joint state, this would potentially permit a more even-handed treatment of space and time, and would strengthen the existing analogy between quantum states and classical probability distributions. Under the assumption that the joint state over time is an operator on the tensor product of single-time Hilbert spaces, we analyse various proposals for such a joint state, including one due to Leifer and Spekkens, one due to Fitzsimons, Jones and Vedral, and another based on discrete Wigner functions. Finding various problems with each, we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system: that it is a Hermitian operator on the tensor product of the single-time Hilbert spaces; that it represents probabilistic mixing appropriately; that it has the appropriate classical limit; that it has the appropriate single-time marginals; that composing over multiple time steps is associative. We show that no construction satisfies all these requirements. If Hermiticity is dropped, then there is an essentially unique construction that satisfies the remaining four criteria.

Exact calculation of the time convolutionless master equation generator: Application to the nonequilibrium resonant level model

NASA Astrophysics Data System (ADS)

Kidon, Lyran; Wilner, Eli Y.; Rabani, Eran

2015-12-01

The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima-Zwanzig-Mori time-convolution (TC) and the other on the Tokuyama-Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called "memory kernel" or "generator," going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green's function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.

Basilar-membrane responses to broadband noise modeled using linear filters with rational transfer functions.

PubMed

Recio-Spinoso, Alberto; Fan, Yun-Hui; Ruggero, Mario A

2011-05-01

Basilar-membrane responses to white Gaussian noise were recorded using laser velocimetry at basal sites of the chinchilla cochlea with characteristic frequencies near 10 kHz and first-order Wiener kernels were computed by cross correlation of the stimuli and the responses. The presence or absence of minimum-phase behavior was explored by fitting the kernels with discrete linear filters with rational transfer functions. Excellent fits to the kernels were obtained with filters with transfer functions including zeroes located outside the unit circle, implying nonminimum-phase behavior. These filters accurately predicted basilar-membrane responses to other noise stimuli presented at the same level as the stimulus for the kernel computation. Fits with all-pole and other minimum-phase discrete filters were inferior to fits with nonminimum-phase filters. Minimum-phase functions predicted from the amplitude functions of the Wiener kernels by Hilbert transforms were different from the measured phase curves. These results, which suggest that basilar-membrane responses do not have the minimum-phase property, challenge the validity of models of cochlear processing, which incorporate minimum-phase behavior. © 2011 IEEE

Public channel cryptography: chaos synchronization and Hilbert's tenth problem.

PubMed

Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang

2008-08-22

The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.

Cooling schemes for two-component fermions in layered optical lattices

NASA Astrophysics Data System (ADS)

Goto, Shimpei; Danshita, Ippei

2017-12-01

Recently, a cooling scheme for ultracold atoms in a bilayer optical lattice has been proposed (A. Kantian et al., arXiv:1609.03579). In their scheme, the energy offset between the two layers is increased dynamically such that the entropy of one layer is transferred to the other layer. Using the full-Hilbert-space approach, we compute cooling dynamics subjected to the scheme in order to show that their scheme fails to cool down two-component fermions. We develop an alternative cooling scheme for two-component fermions, in which the spin-exchange interaction of one layer is significantly reduced. Using both full-Hilbert-space and matrix-product-state approaches, we find that our scheme can decrease the temperature of the other layer by roughly half.

[Realization of Heart Sound Envelope Extraction Implemented on LabVIEW Based on Hilbert-Huang Transform].

PubMed

Tan, Zhixiang; Zhang, Yi; Zeng, Deping; Wang, Hua

2015-04-01

We proposed a research of a heart sound envelope extraction system in this paper. The system was implemented on LabVIEW based on the Hilbert-Huang transform (HHT). We firstly used the sound card to collect the heart sound, and then implemented the complete system program of signal acquisition, pretreatment and envelope extraction on LabVIEW based on the theory of HHT. Finally, we used a case to prove that the system could collect heart sound, preprocess and extract the envelope easily. The system was better to retain and show the characteristics of heart sound envelope, and its program and methods were important to other researches, such as those on the vibration and voice, etc.

Structural stability and chaotic solutions of perturbed Benjamin-Ono equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Birnir, B.; Morrison, P.J.

1986-11-01

A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is verymore » sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform.« less

Unimodular F ( R ) gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nojiri, S.; Odintsov, S.D.; Oikonomou, V.K., E-mail: nojiri@gravity.phys.nagoya-u.ac.jp, E-mail: odintsov@ieec.uab.es, E-mail: v.k.oikonomou1979@gmail.com

2016-05-01

We extend the formalism of the Einstein-Hilbert unimodular gravity in the context of modified F ( R ) gravity. After appropriately modifying the Friedmann-Robertson-Walker metric in a way that it becomes compatible to the unimodular condition of having a constant metric determinant, we derive the equations of motion of the unimodular F ( R ) gravity by using the metric formalism of modified gravity with Lagrange multiplier constraint. The resulting equations are studied in frames of reconstruction method, which enables us to realize various cosmological scenarios, which was impossible to realize in the standard Einstein-Hilbert unimodular gravity. Several unimodular Fmore » ( R ) inflationary scenarios are presented, and in some cases, concordance with Planck and BICEP2 observational data can be achieved.« less

Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians.

PubMed

Vidmar, Lev; Hackl, Lucas; Bianchi, Eugenio; Rigol, Marcos

2017-07-14

In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is S_{ave}≃lnD_{A}-(1/2)D_{A}^{2}/D for 1≪D_{A}≤sqrt[D], where D_{A} and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S⟩ of all eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models lnD_{A}-(lnD_{A})^{2}/lnD≤⟨S⟩≤lnD_{A}-[1/(2ln2)](lnD_{A})^{2}/lnD. Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S⟩

Finite energy quantization on a topology changing spacetime

NASA Astrophysics Data System (ADS)

Krasnikov, S.

2016-08-01

The "trousers" spacetime is a pair of flat two-dimensional cylinders ("legs") merging into a single one ("trunk"). In spite of its simplicity this spacetime has a few features (including, in particular, a naked singularity in the "crotch") each of which is presumably unphysical, but for none of which a mechanism is known able to prevent its occurrence. Therefore, it is interesting and important to study the behavior of the quantum fields in such a space. Anderson and DeWitt were the first to consider the free scalar field in the trousers spacetime. They argued that the crotch singularity produces an infinitely bright flash, which was interpreted as evidence that the topology of space is dynamically preserved. Similar divergencies were later discovered by Manogue, Copeland, and Dray who used a more exotic quantization scheme. Later yet the same result obtained within a somewhat different approach led Sorkin to the conclusion that the topological transition in question is suppressed in quantum gravity. In this paper I show that the Anderson-DeWitt divergence is an artifact of their choice of the Fock space. By choosing a different one-particle Hilbert space one gets a quantum state in which the components of the stress-energy tensor (SET) are bounded in the frame of a free-falling observer.

Topos quantum theory on quantization-induced sheaves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Kunji, E-mail: nakayama@law.ryukoku.ac.jp

2014-10-15

In this paper, we construct a sheaf-based topos quantum theory. It is well known that a topos quantum theory can be constructed on the topos of presheaves on the category of commutative von Neumann algebras of bounded operators on a Hilbert space. Also, it is already known that quantization naturally induces a Lawvere-Tierney topology on the presheaf topos. We show that a topos quantum theory akin to the presheaf-based one can be constructed on sheaves defined by the quantization-induced Lawvere-Tierney topology. That is, starting from the spectral sheaf as a state space of a given quantum system, we construct sheaf-basedmore » expressions of physical propositions and truth objects, and thereby give a method of truth-value assignment to the propositions. Furthermore, we clarify the relationship to the presheaf-based quantum theory. We give translation rules between the sheaf-based ingredients and the corresponding presheaf-based ones. The translation rules have “coarse-graining” effects on the spaces of the presheaf-based ingredients; a lot of different proposition presheaves, truth presheaves, and presheaf-based truth-values are translated to a proposition sheaf, a truth sheaf, and a sheaf-based truth-value, respectively. We examine the extent of the coarse-graining made by translation.« less

Asymmetry of wind waves studied in a laboratory tank

NASA Astrophysics Data System (ADS)

Ileykin, L. A.; Donelan, M. A.; Mellen, R. H.; McLaughlin, D. J.

1995-03-01

Asymmetry of wind waves was studied in laboratory tank tinder varied wind and fetch conditions using both bispectral analysis of wave records and third-order statistics of the surface elevation. It is found skewness S (the normalized third-order moment of surface elevation describing the horizontal asymmetry waves) varies only slightly with the inverse wave u*/Cm (where u* is the air friction velocity and Cm is phase speed of the dominant waves). At the same time asymmetry A, which is determined from the Hilbert transform of the wave record and characterizes the skewness of the rate of change of surface elevation, increase consistently in magnitude with the ratio u*/Cm. This suggests that nonlinear distortion of the wave profile determined by the degree of wind forcing and is a sensitive indicator of wind-wave interaction processes. It is shown that the asymmetric profile of waves can described within the frameworks of the nonlinear nonspectral concept (Plate, 1972; Lake and Yuen, 197 according to which the wind-wave field can be represented as a coherent bound-wave system consisting mainly of dominant component w. and its harmonics propagating with the same speed C. , as observed by Ramamonjiaris and Coantic (1976). The phase shift between o). harmonics is found and shown to increase with the asymmetry of the waves.

Asymmetry of wind waves studied in a laboratory tank

NASA Astrophysics Data System (ADS)

Leykin, I. A.; Donelan, M. A.; Mellen, R. H.; McLaughlin, D. J.

Asymmetry of wind waves was studied in laboratory tank tinder varied wind and fetch conditions using both bispectral analysis of wave records and third-order statistics of the surface elevation. It is found skewness S (the normalized third-order moment of surface elevation describing the horizontal asymmetry waves) varies only slightly with the inverse wave u*/Cm (where u* is the air friction velocity and Cm is phase speed of the dominant waves). At the same time asymmetry A, which is determined from the Hilbert transform of the wave record and characterizes the skewness of the rate of change of surface elevation, increase consistently in magnitude with the ratio u*/Cm. This suggests that nonlinear distortion of the wave profile determined by the degree of wind forcing and is a sensitive indicator of wind-wave interaction processes. It is shown that the asymmetric profile of waves can described within the frameworks of the nonlinear nonspectral concept (Plate, 1972; Lake and Yuen, 197 according to which the wind-wave field can be represented as a coherent bound-wave system consisting mainly of dominant component w. and its harmonics propagating with the same speed C. , as observed by Ramamonjiaris and Coantic (1976). The phase shift between o). harmonics is found and shown to increase with the asymmetry of the waves.

Locally-Based Kernal PLS Smoothing to Non-Parametric Regression Curve Fitting

NASA Technical Reports Server (NTRS)

Rosipal, Roman; Trejo, Leonard J.; Wheeler, Kevin; Korsmeyer, David (Technical Monitor)

2002-01-01

We present a novel smoothing approach to non-parametric regression curve fitting. This is based on kernel partial least squares (PLS) regression in reproducing kernel Hilbert space. It is our concern to apply the methodology for smoothing experimental data where some level of knowledge about the approximate shape, local inhomogeneities or points where the desired function changes its curvature is known a priori or can be derived based on the observed noisy data. We propose locally-based kernel PLS regression that extends the previous kernel PLS methodology by incorporating this knowledge. We compare our approach with existing smoothing splines, hybrid adaptive splines and wavelet shrinkage techniques on two generated data sets.

A Thin Lens Model for Charged-Particle RF Accelerating Gaps

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allen, Christopher K.

Presented is a thin-lens model for an RF accelerating gap that considers general axial fields without energy dependence or other a priori assumptions. Both the cosine and sine transit time factors (i.e., Fourier transforms) are required plus two additional functions; the Hilbert transforms the transit-time factors. The combination yields a complex-valued Hamiltonian rotating in the complex plane with synchronous phase. Using Hamiltonians the phase and energy gains are computed independently in the pre-gap and post-gap regions then aligned using the asymptotic values of wave number. Derivations of these results are outlined, examples are shown, and simulations with the model aremore » presented.« less

Study of the convergence behavior of the complex kernel least mean square algorithm.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.

PubMed

Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto

2014-07-11

Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Period Integrals, L--Functions, and Applications to Subconvexity Bound and Mass Equidistribution

NASA Astrophysics Data System (ADS)

Hu, Yueke

In this thesis we first study a period integral which gives the cuspidal part of a restricted Eisenstein series defined over a quadratic extension. This integral can be thought of as a complementary case to the well-known Rankin-Selberg integral and Triple product formula. We shall show the L-functions it represents and compute local integrals with ramifications. In the second part we will give explicit formula or bound for Triple product integral with very general ramifications. Such results can be applied to prove the subconvexity bound of triple product L--function and Mass equidistribution problems, greatly generalizing previous works.

Cytoskeleton and Cytoskeleton-Bound RNA Visualization in Frog and Insect Oocytes.

PubMed

Kloc, Malgorzata; Bilinski, Szczepan; Kubiak, Jacek Z

2016-01-01

The majority of oocyte functions involves and depends on the cytoskeletal elements, which include microtubules and actin and cytokeratin filaments. Various structures and molecules are temporarily or permanently bound to the cytoskeletal elements and their functions rely on cytoskeleton integrity and its timely assembly. Thus the accurate visualization of cytoskeleton is often crucial for studies and analyses of oocyte structure and functions. Here we describe several reliable methods for microtubule and/or microfilaments preservation and visualization in Xenopus oocyte extracts, and in situ in live and fixed insect and frog (Xenopus) oocytes. In addition, we describe visualization of cytoskeleton-bound RNAs using molecular beacons in live Xenopus oocytes.

FAST TRACK COMMUNICATION: Shear coordinate description of the quantized versal unfolding of a D4 singularity

NASA Astrophysics Data System (ADS)

Chekhov, Leonid; Mazzocco, Marta

2010-11-01

In this communication, by using Teichmüller theory of a sphere with four holes/orbifold points, we obtain a system of flat coordinates on the general affine cubic surface having a D4 singularity at the origin. We show that the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere coincides with the Etingof-Ginzburg Poisson bracket on the affine D4 cubic. We prove that this bracket is the image under the Riemann-Hilbert map of the Poisson-Lie bracket on \\oplus _{1}^3\\mathfrak {sl}^\\ast (2,{{\\bb C}}) . We realize the action of the mapping class group by the action of the braid group on the geodesic functions. This action coincides with the procedure of analytic continuation of solutions of the sixth Painlevé equation. Finally, we produce the explicit quantization of the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere and of the braid group action.

Latent cardiac dysfunction as assessed by echocardiography in bed-bound patients following cerebrovascular accidents: comparison with nutritional status.

PubMed

Masugata, Hisashi; Senda, Shoichi; Goda, Fuminori; Yoshihara, Yumiko; Yoshikawa, Kay; Fujita, Norihiro; Himoto, Takashi; Okuyama, Hiroyuki; Taoka, Teruhisa; Imai, Masanobu; Kohno, Masakazu

2007-07-01

The aim of this study was to elucidate the cardiac function in bed-bound patients following cerebrovascular accidents. In accord with the criteria for activities of daily living (ADL) of the Japanese Ministry of Health, Labour and Welfare, 51 age-matched poststroke patients without heart disease were classified into 3 groups: rank A (house-bound) (n = 16, age, 85 +/- 6 years), rank B (chair-bound) (n = 16, age, 84 +/- 8 years), and rank C (bed-bound) (n = 19, age, 85 +/- 9 years). Using echocardiography, the left ventricular (LV) diastolic function was assessed by the ratio of early filling (E) and atrial contraction (A) transmitral flow velocities (E/A) of LV inflow. LV systolic function was assessed by LV ejection fraction (LVEF), and the Tei index was also measured to assess both LV systolic and diastolic function. No difference was observed in the E/A and LVEF among the 3 groups. The Tei index was higher in rank C (0.56 +/- 0.17) than in rank A (0.39 +/- 0.06) and rank B (0.48 +/- 0.17), and a statistically significant difference was observed between rank A and rank C (P < 0.05). Serum albumin and blood hemoglobin were significantly lower in rank C (3.1 +/- 0.4 and 10.6 +/- 1.8 g/dL) than in rank A (4.1 +/- 0.3 and 12.4 +/- 1.2 g/dL) (P < 0.001 and P < 0.05, respectively). These results indicate that latent cardiac dysfunction and poor nutritional status may exist in bed-bound patients (rank C) following cerebrovascular accidents. The Tei index may be a useful index of cardiac dysfunction in bed-bound patients because it is independent of the cardiac loading condition.

Automatic moment segmentation and peak detection analysis of heart sound pattern via short-time modified Hilbert transform.

PubMed

Sun, Shuping; Jiang, Zhongwei; Wang, Haibin; Fang, Yu

2014-05-01

This paper proposes a novel automatic method for the moment segmentation and peak detection analysis of heart sound (HS) pattern, with special attention to the characteristics of the envelopes of HS and considering the properties of the Hilbert transform (HT). The moment segmentation and peak location are accomplished in two steps. First, by applying the Viola integral waveform method in the time domain, the envelope (E(T)) of the HS signal is obtained with an emphasis on the first heart sound (S1) and the second heart sound (S2). Then, based on the characteristics of the E(T) and the properties of the HT of the convex and concave functions, a novel method, the short-time modified Hilbert transform (STMHT), is proposed to automatically locate the moment segmentation and peak points for the HS by the zero crossing points of the STMHT. A fast algorithm for calculating the STMHT of E(T) can be expressed by multiplying the E(T) by an equivalent window (W(E)). According to the range of heart beats and based on the numerical experiments and the important parameters of the STMHT, a moving window width of N=1s is validated for locating the moment segmentation and peak points for HS. The proposed moment segmentation and peak location procedure method is validated by sounds from Michigan HS database and sounds from clinical heart diseases, such as a ventricular septal defect (VSD), an aortic septal defect (ASD), Tetralogy of Fallot (TOF), rheumatic heart disease (RHD), and so on. As a result, for the sounds where S2 can be separated from S1, the average accuracies achieved for the peak of S1 (AP₁), the peak of S2 (AP₂), the moment segmentation points from S1 to S2 (AT₁₂) and the cardiac cycle (ACC) are 98.53%, 98.31% and 98.36% and 97.37%, respectively. For the sounds where S1 cannot be separated from S2, the average accuracies achieved for the peak of S1 and S2 (AP₁₂) and the cardiac cycle ACC are 100% and 96.69%. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

A parallel variable metric optimization algorithm

NASA Technical Reports Server (NTRS)

Straeter, T. A.

1973-01-01

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Decision and function problems based on boson sampling

NASA Astrophysics Data System (ADS)

Nikolopoulos, Georgios M.; Brougham, Thomas

2016-07-01

Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and the possible usefulness of boson-sampling devices is mainly limited to the proof of quantum supremacy. The purpose of this work is to investigate whether boson sampling can be used as a resource of decision and function problems that are computationally hard, and may thus have cryptographic applications. After the definition of a rather general theoretical framework for the design of such problems, we discuss their solution by means of a brute-force numerical approach, as well as by means of nonboson samplers. Moreover, we estimate the sample sizes required for their solution by passive linear interferometers, and it is shown that they are independent of the size of the Hilbert space.

Superiorization with level control

NASA Astrophysics Data System (ADS)

Cegielski, Andrzej; Al-Musallam, Fadhel

2017-04-01

The convex feasibility problem is to find a common point of a finite family of closed convex subsets. In many applications one requires something more, namely finding a common point of closed convex subsets which minimizes a continuous convex function. The latter requirement leads to an application of the superiorization methodology which is actually settled between methods for convex feasibility problem and the convex constrained minimization. Inspired by the superiorization idea we introduce a method which sequentially applies a long-step algorithm for a sequence of convex feasibility problems; the method employs quasi-nonexpansive operators as well as subgradient projections with level control and does not require evaluation of the metric projection. We replace a perturbation of the iterations (applied in the superiorization methodology) by a perturbation of the current level in minimizing the objective function. We consider the method in the Euclidean space in order to guarantee the strong convergence, although the method is well defined in a Hilbert space.

Hilbert's 17th Problem and the Quantumness of States

NASA Astrophysics Data System (ADS)

Korbicz, J. K.; Cirac, J. I.; Wehr, Jan; Lewenstein, M.

2005-04-01

A state of a quantum system can be regarded as classical (quantum) with respect to measurements of a set of canonical observables if and only if there exists (does not exist) a well defined, positive phase-space distribution, the so called Glauber-Sudarshan P representation. We derive a family of classicality criteria that requires that the averages of positive functions calculated using P representation must be positive. For polynomial functions, these criteria are related to Hilbert’s 17th problem, and have physical meaning of generalized squeezing conditions; alternatively, they may be interpreted as nonclassicality witnesses. We show that every generic nonclassical state can be detected by a polynomial that is a sum-of-squares of other polynomials. We introduce a very natural hierarchy of states regarding their degree of quantumness, which we relate to the minimal degree of a sum-of-squares polynomial that detects them.

Axial 3D region of interest reconstruction using weighted cone beam BPF/DBPF algorithm cascaded with adequately oriented orthogonal butterfly filtering

NASA Astrophysics Data System (ADS)

Tang, Shaojie; Tang, Xiangyang

2016-03-01

Axial cone beam (CB) computed tomography (CT) reconstruction is still the most desirable in clinical applications. As the potential candidates with analytic form for the task, the back projection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical and axial reconstruction from CB and fan beam projection data, respectively. These two algorithms have been heuristically extended for axial CB reconstruction via adoption of virtual PI-line segments. Unfortunately, however, streak artifacts are induced along the Hilbert filtering direction, since these algorithms are no longer accurate on the virtual PI-line segments. We have proposed to cascade the extended BPF/DBPF algorithm with orthogonal butterfly filtering for image reconstruction (namely axial CB-BPP/DBPF cascaded with orthogonal butterfly filtering), in which the orientation-specific artifacts caused by post-BP Hilbert transform can be eliminated, at a possible expense of losing the BPF/DBPF's capability of dealing with projection data truncation. Our preliminary results have shown that this is not the case in practice. Hence, in this work, we carry out an algorithmic analysis and experimental study to investigate the performance of the axial CB-BPP/DBPF cascaded with adequately oriented orthogonal butterfly filtering for three-dimensional (3D) reconstruction in region of interest (ROI).

Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations

PubMed Central

2013-01-01

In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328

Graphene based tunable fractal Hilbert curve array broadband radar absorbing screen for radar cross section reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Xianjun, E-mail: xianjun.huang@manchester.ac.uk; College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073; Hu, Zhirun

2014-11-15

This paper proposes a new type of graphene based tunable radar absorbing screen. The absorbing screen consists of Hilbert curve metal strip array and chemical vapour deposition (CVD) graphene sheet. The graphene based screen is not only tunable when the chemical potential of the graphene changes, but also has broadband effective absorption. The absorption bandwidth is from 8.9GHz to 18.1GHz, ie., relative bandwidth of more than 68%, at chemical potential of 0eV, which is significantly wider than that if the graphene sheet had not been employed. As the chemical potential varies from 0 to 0.4eV, the central frequency of themore » screen can be tuned from 13.5GHz to 19.0GHz. In the proposed structure, Hilbert curve metal strip array was designed to provide multiple narrow band resonances, whereas the graphene sheet directly underneath the metal strip array provides tunability and averagely required surface resistance so to significantly extend the screen operation bandwidth by providing broadband impedance matching and absorption. In addition, the thickness of the screen has been optimized to achieve nearly the minimum thickness limitation for a nonmagnetic absorber. The working principle of this absorbing screen is studied in details, and performance under various incident angles is presented. This work extends applications of graphene into tunable microwave radar cross section (RCS) reduction applications.« less

Possible treatment of the ghost states in the Lee-Wick standard model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shalaby, Abouzeid M.; Physics Department, Faculty of Science, Qassim University

2009-07-15

In this work, we employ the techniques used to cure the indefinite norm problem in pseudo-Hermitian Hamiltonians to show that the ghost states in a higher derivative scalar field theory are not real ghosts. For the model under investigation, an imaginary auxiliary field is introduced to have an equivalent non-Hermitian two-field scalar theory. We were able to calculate exactly the positive definite metric operator {eta} for the quantum mechanical as well as the quantum field versions of the theory. While the equivalent Hamiltonian is non-Hermitian in a Hilbert space characterized by the Dirac sense inner product, it is, however, amore » Hermitian in a Hilbert space endowed with the inner product . The main feature of the latter Hilbert space is that the propagator has the correct sign (no Lee-Wick fields). Moreover, the calculated metric operator diagonalizes the Hamiltonian in the two fields (no mixing). We found that the Hermiticity of the calculated metric operator to lead to the constrain M>2m for the two Higgs masses, in agreement with other calculations in the literature. Besides, our mass formulas coincide with those obtained in other works (obtained by a very different regime but with the existence of ghost states), which means that our positive normed Hamiltonian form preserves the mass spectra.« less

Time-frequency analysis of neuronal populations with instantaneous resolution based on noise-assisted multivariate empirical mode decomposition.

PubMed

Alegre-Cortés, J; Soto-Sánchez, C; Pizá, Á G; Albarracín, A L; Farfán, F D; Felice, C J; Fernández, E

2016-07-15

Linear analysis has classically provided powerful tools for understanding the behavior of neural populations, but the neuron responses to real-world stimulation are nonlinear under some conditions, and many neuronal components demonstrate strong nonlinear behavior. In spite of this, temporal and frequency dynamics of neural populations to sensory stimulation have been usually analyzed with linear approaches. In this paper, we propose the use of Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD), a data-driven template-free algorithm, plus the Hilbert transform as a suitable tool for analyzing population oscillatory dynamics in a multi-dimensional space with instantaneous frequency (IF) resolution. The proposed approach was able to extract oscillatory information of neurophysiological data of deep vibrissal nerve and visual cortex multiunit recordings that were not evidenced using linear approaches with fixed bases such as the Fourier analysis. Texture discrimination analysis performance was increased when Noise-Assisted Multivariate Empirical Mode plus Hilbert transform was implemented, compared to linear techniques. Cortical oscillatory population activity was analyzed with precise time-frequency resolution. Similarly, NA-MEMD provided increased time-frequency resolution of cortical oscillatory population activity. Noise-Assisted Multivariate Empirical Mode Decomposition plus Hilbert transform is an improved method to analyze neuronal population oscillatory dynamics overcoming linear and stationary assumptions of classical methods. Copyright © 2016 Elsevier B.V. All rights reserved.

Interconnect patterns for printed organic thermoelectric devices with large fill factors

NASA Astrophysics Data System (ADS)

Gordiz, Kiarash; Menon, Akanksha K.; Yee, Shannon K.

2017-09-01

Organic materials can be printed into thermoelectric (TE) devices for low temperature energy harvesting applications. The output voltage of printed devices is often limited by (i) small temperature differences across the active materials attributed to small leg lengths and (ii) the lower Seebeck coefficient of organic materials compared to their inorganic counterparts. To increase the voltage, a large number of p- and n-type leg pairs is required for organic TEs; this, however, results in an increased interconnect resistance, which then limits the device output power. In this work, we discuss practical concepts to address this problem by positioning TE legs in a hexagonal closed-packed layout. This helps achieve higher fill factors (˜91%) than conventional inorganic devices (˜25%), which ultimately results in higher voltages and power densities due to lower interconnect resistances. In addition, wiring the legs following a Hilbert spacing-filling pattern allows for facile load matching to each application. This is made possible by leveraging the fractal nature of the Hilbert interconnect pattern, which results in identical sub-modules. Using the Hilbert design, sub-modules can better accommodate non-uniform temperature distributions because they naturally self-localize. These device design concepts open new avenues for roll-to-roll printing and custom TE module shapes, thereby enabling organic TE modules for self-powered sensors and wearable electronic applications.

Space Inside a Liquid Sphere Transforms into De Sitter Space by Hilbert Radius

NASA Astrophysics Data System (ADS)

Rabounski, Dmitri; Borissova, Larissa

2010-04-01

Consider space inside a sphere of incompressible liquid, and space surrounding a mass-point. Metrics of the spaces were deduced in 1916 by Karl Schwarzschild. 1) Our calculation shows that a liquid sphere can be in the state of gravitational collapse (g00 = 0) only if its mass and radius are close to those of the Universe (M = 8.7x10^55 g, a = 1.3x10^28 cm). However if the same mass is presented as a mass-point, the radius of collapse rg (Hilbert radius) is many orders lesser: g00 = 0 realizes in a mass-point's space by other conditions. 2) We considered a liquid sphere whose radius meets, formally, the Hilbert radius of a mass-point bearing the same mass: a = rg, however the liquid sphere is not a collapser (see above). We show that in this case the metric of the liquid sphere's internal space can be represented as de Sitter's space metric, wherein λ = 3/a^2 > 0: physical vacuum (due to the λ-term) is the same as the field of an ideal liquid where ρ0 < 0 and p = -ρ0 c^2 > 0 (the mirror world liquid). The gravitational redshift inside the sphere is produced by the non-Newtonian force of repulsion (which is due to the λ-term, λ = 3/a^2 > 0); it is also calculated.

Communication: An exact bound on the bridge function in integral equation theories.

PubMed

Kast, Stefan M; Tomazic, Daniel

2012-11-07

We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.

Operator bases, S-matrices, and their partition functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henning, Brian; Lu, Xiaochuan; Melia, Tom

Relativistic quantum systems that admit scattering experiments are quantitatively described by effective field theories, where S-matrix kinematics and symmetry considerations are encoded in the operator spectrum of the EFT. Here in this paper we use the S-matrix to derive the structure of the EFT operator basis, providing complementary descriptions in (i) position space utilizing the conformal algebra and cohomology and (ii) momentum space via an algebraic formulation in terms of a ring of momenta with kinematics implemented as an ideal. These frameworks systematically handle redundancies associated with equations of motion (on-shell) and integration by parts (momentum conservation). We introduce amore » partition function, termed the Hilbert series, to enumerate the operator basis — correspondingly, the S-matrix — and derive a matrix integral expression to compute the Hilbert series. The expression is general, easily applied in any spacetime dimension, with arbitrary field content and (linearly realized) symmetries. In addition to counting, we discuss construction of the basis. Simple algorithms follow from the algebraic formulation in momentum space. We explicitly compute the basis for operators involving up to n = 5 scalar fields. This construction universally applies to fields with spin, since the operator basis for scalars encodes the momentum dependence of n-point amplitudes. We discuss in detail the operator basis for non-linearly realized symmetries. In the presence of massless particles, there is freedom to impose additional structure on the S- matrix in the form of soft limits. The most naÏve implementation for massless scalars leads to the operator basis for pions, which we confirm using the standard CCWZ formulation for non-linear realizations. Finally, although primarily discussed in the language of EFT, some of our results — conceptual and quantitative — may be of broader use in studying conformal field theories as well as the AdS/CFT correspondence.« less

Operator bases, S-matrices, and their partition functions

DOE PAGES

Henning, Brian; Lu, Xiaochuan; Melia, Tom; ...

2017-10-27

Relativistic quantum systems that admit scattering experiments are quantitatively described by effective field theories, where S-matrix kinematics and symmetry considerations are encoded in the operator spectrum of the EFT. Here in this paper we use the S-matrix to derive the structure of the EFT operator basis, providing complementary descriptions in (i) position space utilizing the conformal algebra and cohomology and (ii) momentum space via an algebraic formulation in terms of a ring of momenta with kinematics implemented as an ideal. These frameworks systematically handle redundancies associated with equations of motion (on-shell) and integration by parts (momentum conservation). We introduce amore » partition function, termed the Hilbert series, to enumerate the operator basis — correspondingly, the S-matrix — and derive a matrix integral expression to compute the Hilbert series. The expression is general, easily applied in any spacetime dimension, with arbitrary field content and (linearly realized) symmetries. In addition to counting, we discuss construction of the basis. Simple algorithms follow from the algebraic formulation in momentum space. We explicitly compute the basis for operators involving up to n = 5 scalar fields. This construction universally applies to fields with spin, since the operator basis for scalars encodes the momentum dependence of n-point amplitudes. We discuss in detail the operator basis for non-linearly realized symmetries. In the presence of massless particles, there is freedom to impose additional structure on the S- matrix in the form of soft limits. The most naÏve implementation for massless scalars leads to the operator basis for pions, which we confirm using the standard CCWZ formulation for non-linear realizations. Finally, although primarily discussed in the language of EFT, some of our results — conceptual and quantitative — may be of broader use in studying conformal field theories as well as the AdS/CFT correspondence.« less

Optical soliton solutions, periodic wave solutions and complexitons of the cubic Schrödinger equation with a bounded potential

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2018-01-01

In this paper, we consider the cubic Schrödinger equation with a bounded potential, which describes the propagation properties of optical soliton solutions. By employing an ansatz method, we precisely derive the bright and dark soliton solutions of the equation. Moreover, we obtain three classes of analytic periodic wave solutions expressed in terms of the Jacobi's elliptic functions including cn ,sn and dn functions. Finally, by using a tanh function method, its complexitons solutions are derived in a very natural way. It is hoped that our results can enrich the nonlinear dynamical behaviors of the cubic Schrödinger equation with a bounded potential.

Adiabatic markovian dynamics.

PubMed

Oreshkov, Ognyan; Calsamiglia, John

2010-07-30

We propose a theory of adiabaticity in quantum markovian dynamics based on a decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As two applications of our theory, we propose a general framework for decoherence-assisted computation in noiseless codes and a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by nondissipative means.

Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

NASA Astrophysics Data System (ADS)

Pelinovsky, Dmitry E.; Sulem, Catherine

A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.