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.

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.

How weak values emerge in joint measurements on cloned quantum systems.

PubMed

Hofmann, Holger F

2012-07-13

A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but nonpositive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems, resulting in perfect correlations for all observables. The joint probabilities for noncommuting measurements on separate clones then correspond to the real parts of the complex joint probabilities observed in weak measurements on a single system, where the measurements on the two clones replace the corresponding sequence of weak measurement and postselection. The imaginary parts of weak measurement statics can be obtained by replacing the cloning process with a partial swap operation. A controlled-swap operation combines both processes, making the complete weak measurement statistics accessible as a well-defined contribution to the joint probabilities of fully resolved projective measurements on the two output systems.

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.

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.

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

Excluding joint probabilities from quantum theory

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Danageozian, Arshag

2018-03-01

Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.

A note on the regularity of solutions of infinite dimensional Riccati equations

NASA Technical Reports Server (NTRS)

Burns, John A.; King, Belinda B.

1994-01-01

This note is concerned with the regularity of solutions of algebraic Riccati equations arising from infinite dimensional LQR and LQG control problems. We show that distributed parameter systems described by certain parabolic partial differential equations often have a special structure that smoothes solutions of the corresponding Riccati equation. This analysis is motivated by the need to find specific representations for Riccati operators that can be used in the development of computational schemes for problems where the input and output operators are not Hilbert-Schmidt. This situation occurs in many boundary control problems and in certain distributed control problems associated with optimal sensor/actuator placement.

Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints

NASA Astrophysics Data System (ADS)

Burić, Nikola

2010-12-01

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent, i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory.

Spectral density of mixtures of random density matrices for qubits

NASA Astrophysics Data System (ADS)

Zhang, Lin; Wang, Jiamei; Chen, Zhihua

2018-06-01

We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral densities to calculate the average entropy of mixtures of random density matrices, and show that the average entropy of the arithmetic-mean-state of n qubit density matrices randomly chosen from the Hilbert-Schmidt ensemble is never decreasing with the number n. We also get the exact value of the average squared fidelity. Some conjectures and open problems related to von Neumann entropy are also proposed.

The Stokes-Einstein relation at moderate Schmidt number.

PubMed

Balboa Usabiaga, Florencio; Xie, Xiaoyi; Delgado-Buscalioni, Rafael; Donev, Aleksandar

2013-12-07

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

Fe3O4@MOF core-shell magnetic microspheres as excellent catalysts for the Claisen-Schmidt condensation reaction

NASA Astrophysics Data System (ADS)

Ke, Fei; Qiu, Ling-Guang; Zhu, Junfa

2014-01-01

Separation and recycling of catalysts after catalytic reactions are critically required to reduce the cost of catalysts as well as to avoid the generation of waste in industrial applications. In this work, we present a facile fabrication and characterization of a novel type of MOF-based porous catalyst, namely, Fe3O4@MIL-100(Fe) core-shell magnetic microspheres. It has been shown that these catalysts not only exhibit high catalytic activities for the Claisen-Schmidt condensation reactions under environmentally friendly conditions, but remarkably, they can be easily separated and recycled without significant loss of catalytic efficiency after being used for many times. Therefore, compared to other reported catalysts used in the Claisen-Schmidt condensation reactions, these catalysts are green, cheap and more suitable for large scale industrial applications.Separation and recycling of catalysts after catalytic reactions are critically required to reduce the cost of catalysts as well as to avoid the generation of waste in industrial applications. In this work, we present a facile fabrication and characterization of a novel type of MOF-based porous catalyst, namely, Fe3O4@MIL-100(Fe) core-shell magnetic microspheres. It has been shown that these catalysts not only exhibit high catalytic activities for the Claisen-Schmidt condensation reactions under environmentally friendly conditions, but remarkably, they can be easily separated and recycled without significant loss of catalytic efficiency after being used for many times. Therefore, compared to other reported catalysts used in the Claisen-Schmidt condensation reactions, these catalysts are green, cheap and more suitable for large scale industrial applications. Electronic supplementary information (ESI) available: SEM and TEM images, and GC-MS spectra for chalcones. See DOI: 10.1039/c3nr05051c

Manipulation of a two-photon state in a χ(2)-modulated nonlinear waveguide array

NASA Astrophysics Data System (ADS)

Yang, Y.; Xu, P.; Lu, L. L.; Zhu, S. N.

2014-10-01

We propose to engineer the quantum state in a high-dimensional Hilbert space by taking advantage of a χ(2)-modulated nonlinear waveguide array. By varying the pump condition and the waveguide array length, the momentum correlation between the signal and idler photons can be manipulated, exhibiting bunching, antibunching, and the evolution between these two states, which are characterized by the Schmidt number. We find the Schmidt number is dependent on a structure parameter, namely the ratio of the array length and the number of channels pumped. By designing the linear profile waveguide array, the degree of spatial entanglement shows a periodic relationship with the slope of linear profile, during which a high degree of position-bunching state is suggested. The two-photon self-focusing effect is disclosed when the χ(2) modulation in the waveguide array contains a parabolic profile, which can be designed for efficient coupling between a waveguide array and fibers. These results shed light on a feasible way to achieve desirable quantum state on a single waveguide chip by a compact engineering of χ(2) and also suggest a degree of freedom for quantum walk and other related applications.

Limitations of shallow nets approximation.

PubMed

Lin, Shao-Bo

2017-10-01

In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

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.

Tsirelson's bound and supersymmetric entangled states

PubMed Central

Borsten, L.; Brádler, K.; Duff, M. J.

2014-01-01

A superqubit, belonging to a (2|1)-dimensional super-Hilbert space, constitutes the minimal supersymmetric extension of the conventional qubit. In order to see whether superqubits are more non-local than ordinary qubits, we construct a class of two-superqubit entangled states as a non-local resource in the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the result depends on how we extract real probabilities and we examine three choices of map: (1) DeWitt (2) Trigonometric and (3) Modified Rogers. In cases (1) and (2), the winning probability reaches the Tsirelson bound pwin=cos2π/8≃0.8536 of standard quantum mechanics. Case (3) crosses Tsirelson's bound with pwin≃0.9265. Although all states used in the game involve probabilities lying between 0 and 1, case (3) permits other changes of basis inducing negative transition probabilities. PMID:25294964

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.

Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type

NASA Astrophysics Data System (ADS)

Scarpa, Luca

2017-08-01

We prove well-posedness for doubly nonlinear parabolic stochastic partial differential equations of the form dXt - div γ (∇Xt) dt + β (Xt) dt ∋ B (t ,Xt) dWt, where γ and β are the two nonlinearities, assumed to be multivalued maximal monotone operators everywhere defined on Rd and R respectively, and W is a cylindrical Wiener process. Using variational techniques, suitable uniform estimates (both pathwise and in expectation) and some compactness results, well-posedness is proved under the classical Leray-Lions conditions on γ and with no restrictive smoothness or growth assumptions on β. The operator B is assumed to be Hilbert-Schmidt and to satisfy some classical Lipschitz conditions in the second variable.

Subnormalized states and trace-nonincreasing maps

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

Cappellini, Valerio; Sommers, Hans-Juergen; Zyczkowski, Karol

2007-05-15

We investigate the set of completely positive, trace-nonincreasing linear maps acting on the set M{sub N} of mixed quantum states of size N. Extremal point of this set of maps are characterized and its volume with respect to the Hilbert-Schmidt (HS) (Euclidean) measure is computed explicitly for an arbitrary N. The spectra of partially reduced rescaled dynamical matrices associated with trace-nonincreasing completely positive maps belong to the N cube inscribed in the set of subnormalized states of size N. As a by-product we derive the measure in M{sub N} induced by partial trace of mixed quantum states distributed uniformly withmore » respect to the HS measure in M{sub N{sup 2}}.« less

Quantum teleportation via quantum channels with non-maximal Schmidt rank

NASA Astrophysics Data System (ADS)

Solís-Prosser, M. A.; Jiménez, O.; Neves, L.; Delgado, A.

2013-03-01

We study the problem of teleporting unknown pure states of a single qudit via a pure quantum channel with non-maximal Schmidt rank. We relate this process to the discrimination of linearly dependent symmetric states with the help of the maximum-confidence discrimination strategy. We show that with a certain probability, it is possible to teleport with a fidelity larger than the fidelity optimal deterministic teleportation.

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.

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.

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.

Entanglement spectrum of random-singlet quantum critical points

NASA Astrophysics Data System (ADS)

Fagotti, Maurizio; Calabrese, Pasquale; Moore, Joel E.

2011-01-01

The entanglement spectrum (i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix) contains more information than the conventional entanglement entropy and has been studied recently in several many-particle systems. We compute the disorder-averaged entanglement spectrum in the form of the disorder-averaged moments TrρAα̲ of the reduced density matrix ρA for a contiguous block of many spins at the random-singlet quantum critical point in one dimension. The result compares well in the scaling limit with numerical studies on the random XX model and is also expected to describe the (interacting) random Heisenberg model. Our numerical studies on the XX case reveal that the dependence of the entanglement entropy and spectrum on the geometry of the Hilbert space partition is quite different than for conformally invariant critical points.

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.

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1987-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains 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 controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1988-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains 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 controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

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.

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.

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

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.

The finite scaling for S = 1 XXZ chains with uniaxial single-ion-type anisotropy

NASA Astrophysics Data System (ADS)

Wang, Honglei; Xiong, Xingliang

2014-03-01

The scaling behavior of criticality for spin-1 XXZ chains with uniaxial single-ion-type anisotropy is investigated by employing the infinite matrix product state representation with the infinite time evolving block decimation method. At criticality, the accuracy of the ground state of a system is limited by the truncation dimension χ of the local Hilbert space. We present four evidences for the scaling of the entanglement entropy, the largest eigenvalue of the Schmidt decomposition, the correlation length, and the connection between the actual correlation length ξ and the energy. The result shows that the finite scalings are governed by the central charge of the critical system. Also, it demonstrates that the infinite time evolving block decimation algorithm by the infinite matrix product state representation can be a quite accurate method to simulate the critical properties at criticality.

Modeling Scramjet Flows with Variable Turbulent Prandtl and Schmidt Numbers

NASA Technical Reports Server (NTRS)

Xiao, X.; Hassan, H. A.; Baurle, R. A.

2006-01-01

A complete turbulence model, where the turbulent Prandtl and Schmidt numbers are calculated as part of the solution and where averages involving chemical source terms are modeled, is presented. The ability of avoiding the use of assumed or evolution Probability Distribution Functions (PDF's) results in a highly efficient algorithm for reacting flows. The predictions of the model are compared with two sets of experiments involving supersonic mixing and one involving supersonic combustion. The results demonstrate the need for consideration of turbulence/chemistry interactions in supersonic combustion. In general, good agreement with experiment is indicated.

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.

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

GENERAL A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

NASA Astrophysics Data System (ADS)

Gerd, Niestegge

2010-12-01

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lüders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

A Generalized Quantum Theory

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2014-09-01

In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical model of the Lueders-von Neumann measurement process). It is shown how positive groups, automorphism groups, Lie algebras and statistical operators emerge from one major postulate - the non-existence of third-order interference (third-order interference and its impossibility in quantum mechanics were discovered by R. Sorkin in 1994). This again underlines the power of the combination of the conditional probability calculus with the postulate that there is no third-order interference. In two earlier papers, its impact on contextuality and nonlocality had already been revealed.

Suppression of turbulent energy cascade due to phase separation in homogenous binary mixture fluid

NASA Astrophysics Data System (ADS)

Takagi, Youhei; Okamoto, Sachiya

2015-11-01

When a multi-component fluid mixture becomes themophysically unstable state by quenching from well-melting condition, phase separation due to spinodal decomposition occurs, and a self-organized structure is formed. During phase separation, free energy is consumed for the structure formation. In our previous report, the phase separation in homogenous turbulence was numerically simulated and the coarsening process of phase separation was discussed. In this study, we extended our numerical model to a high Schmidt number fluid corresponding to actual polymer solution. The governing equations were continuity, Navier-Stokes, and Chan-Hiliard equations as same as our previous report. The flow filed was an isotropic homogenous turbulence, and the dimensionless parameters in the Chan-Hilliard equation were estimated based on the thermophysical condition of binary mixture. From the numerical results, it was found that turbulent energy cascade was drastically suppressed in the inertial subrange by phase separation for the high Schmidt number flow. By using the identification of turbulent and phase separation structure, we discussed the relation between total energy balance and the structures formation processes. This study is financially supported by the Grand-in-Aid for Young Scientists (B) (No. T26820045) from the Ministry of Education, Cul-ture, Sports, Science and Technology of Japan.

Husimi coordinates of multipartite separable states

NASA Astrophysics Data System (ADS)

Parfionov, Georges; Zapatrin, Romàn R.

2010-12-01

A parametrization of multipartite separable states in a finite-dimensional Hilbert space is suggested. It is proved to be a diffeomorphism between the set of zero-trace operators and the interior of the set of separable density operators. The result is applicable to any tensor product decomposition of the state space. An analytical criterion for separability of density operators is established in terms of the boundedness of a sequence of operators.

Statistical hydrodynamics and related problems in spaces of probability measures

NASA Astrophysics Data System (ADS)

Dostoglou, Stamatios

2017-11-01

A rigorous theory of statistical solutions of the Navier-Stokes equations, suitable for exploring Kolmogorov's ideas, has been developed by M.I. Vishik and A.V. Fursikov, culminating in their monograph "Mathematical problems of Statistical Hydromechanics." We review some progress made in recent years following this approach, with emphasis on problems concerning the correlation of velocities and corresponding questions in the space of probability measures on Hilbert spaces.

From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems.

PubMed

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia

2018-04-28

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper , we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E ; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. 'explore or not?'; 'open new well or not?'; 'contaminated by water or not?'; 'double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism).This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems

NASA Astrophysics Data System (ADS)

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia

2018-04-01

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper, we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E. The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. `explore or not?'; `open new well or not?'; `contaminated by water or not?'; `double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism). This article is part of the theme issue `Hilbert's sixth problem'.

Response monitoring using quantitative ultrasound methods and supervised dictionary learning in locally advanced breast cancer

NASA Astrophysics Data System (ADS)

Gangeh, Mehrdad J.; Fung, Brandon; Tadayyon, Hadi; Tran, William T.; Czarnota, Gregory J.

2016-03-01

A non-invasive computer-aided-theragnosis (CAT) system was developed for the early assessment of responses to neoadjuvant chemotherapy in patients with locally advanced breast cancer. The CAT system was based on quantitative ultrasound spectroscopy methods comprising several modules including feature extraction, a metric to measure the dissimilarity between "pre-" and "mid-treatment" scans, and a supervised learning algorithm for the classification of patients to responders/non-responders. One major requirement for the successful design of a high-performance CAT system is to accurately measure the changes in parametric maps before treatment onset and during the course of treatment. To this end, a unified framework based on Hilbert-Schmidt independence criterion (HSIC) was used for the design of feature extraction from parametric maps and the dissimilarity measure between the "pre-" and "mid-treatment" scans. For the feature extraction, HSIC was used to design a supervised dictionary learning (SDL) method by maximizing the dependency between the scans taken from "pre-" and "mid-treatment" with "dummy labels" given to the scans. For the dissimilarity measure, an HSIC-based metric was employed to effectively measure the changes in parametric maps as an indication of treatment effectiveness. The HSIC-based feature extraction and dissimilarity measure used a kernel function to nonlinearly transform input vectors into a higher dimensional feature space and computed the population means in the new space, where enhanced group separability was ideally obtained. The results of the classification using the developed CAT system indicated an improvement of performance compared to a CAT system with basic features using histogram of intensity.

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.

Nonlinear association criterion, nonlinear Granger causality and related issues with applications to neuroimage studies.

PubMed

Tao, Chenyang; Feng, Jianfeng

2016-03-15

Quantifying associations in neuroscience (and many other scientific disciplines) is often challenged by high-dimensionality, nonlinearity and noisy observations. Many classic methods have either poor power or poor scalability on data sets of the same or different scales such as genetical, physiological and image data. Based on the framework of reproducing kernel Hilbert spaces we proposed a new nonlinear association criteria (NAC) with an efficient numerical algorithm and p-value approximation scheme. We also presented mathematical justification that links the proposed method to related methods such as kernel generalized variance, kernel canonical correlation analysis and Hilbert-Schmidt independence criteria. NAC allows the detection of association between arbitrary input domain as long as a characteristic kernel is defined. A MATLAB package was provided to facilitate applications. Extensive simulation examples and four real world neuroscience examples including functional MRI causality, Calcium imaging and imaging genetic studies on autism [Brain, 138(5):13821393 (2015)] and alcohol addiction [PNAS, 112(30):E4085-E4093 (2015)] are used to benchmark NAC. It demonstrates the superior performance over the existing procedures we tested and also yields biologically significant results for the real world examples. NAC beats its linear counterparts when nonlinearity is presented in the data. It also shows more robustness against different experimental setups compared with its nonlinear counterparts. In this work we presented a new and robust statistical approach NAC for measuring associations. It could serve as an interesting alternative to the existing methods for datasets where nonlinearity and other confounding factors are present. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

Quantum correlations of helicity entangled states in non-inertial frames beyond single mode approximation

NASA Astrophysics Data System (ADS)

Harsij, Zeynab; Mirza, Behrouz

2014-12-01

A helicity entangled tripartite state is considered in which the degree of entanglement is preserved in non-inertial frames. It is shown that Quantum Entanglement remains observer independent. As another measure of quantum correlation, Quantum Discord has been investigated. It is explicitly shown that acceleration has no effect on the degree of quantum correlation for the bipartite and tripartite helicity entangled states. Geometric Quantum Discord as a Hilbert-Schmidt distance is computed for helicity entangled states. It is shown that living in non-inertial frames does not make any influence on this distance, either. In addition, the analysis has been extended beyond single mode approximation to show that acceleration does not have any impact on the quantum features in the limit beyond the single mode. As an interesting result, while the density matrix depends on the right and left Unruh modes, the Negativity as a measure of Quantum Entanglement remains constant. Also, Quantum Discord does not change beyond single mode approximation.

Nonadiabatic effect on the quantum heat flux control.

PubMed

Uchiyama, Chikako

2014-05-01

We provide a general formula of quantum transfer that includes the nonadiabatic effect under periodic environmental modulation by using full counting statistics in Hilbert-Schmidt space. Applying the formula to an anharmonic junction model that interacts with two bosonic environments within the Markovian approximation, we find that the quantum transfer is divided into the adiabatic (dynamical and geometrical phases) and nonadiabatic contributions. This extension shows the dependence of quantum transfer on the initial condition of the anharmonic junction just before the modulation, as well as the characteristic environmental parameters such as interaction strength and cut-off frequency of spectral density. We show that the nonadiabatic contribution represents the reminiscent effect of past modulation including the transition from the initial condition of the anharmonic junction to a steady state determined by the very beginning of the modulation. This enables us to tune the frequency range of modulation, whereby we can obtain the quantum flux corresponding to the geometrical phase by setting the initial condition of the anharmonic junction.

Universality of Schmidt decomposition and particle identity

NASA Astrophysics Data System (ADS)

Sciara, Stefania; Lo Franco, Rosario; Compagno, Giuseppe

2017-03-01

Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, its formulation for identical particles remains controversial, jeopardizing its application to analyze general many-body quantum systems. Here we prove, using a newly developed approach, a universal Schmidt decomposition which allows faithful quantification of the physical entanglement due to the identity of particles. We find that it is affected by single-particle measurement localization and state overlap. We study paradigmatic two-particle systems where identical qubits and qutrits are located in the same place or in separated places. For the case of two qutrits in the same place, we show that their entanglement behavior, whose physical interpretation is given, differs from that obtained before by different methods. Our results are generalizable to multiparticle systems and open the way for further developments in quantum information processing exploiting particle identity as a resource.

Universality of Schmidt decomposition and particle identity

PubMed Central

Sciara, Stefania; Lo Franco, Rosario; Compagno, Giuseppe

2017-01-01

Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, its formulation for identical particles remains controversial, jeopardizing its application to analyze general many-body quantum systems. Here we prove, using a newly developed approach, a universal Schmidt decomposition which allows faithful quantification of the physical entanglement due to the identity of particles. We find that it is affected by single-particle measurement localization and state overlap. We study paradigmatic two-particle systems where identical qubits and qutrits are located in the same place or in separated places. For the case of two qutrits in the same place, we show that their entanglement behavior, whose physical interpretation is given, differs from that obtained before by different methods. Our results are generalizable to multiparticle systems and open the way for further developments in quantum information processing exploiting particle identity as a resource. PMID:28333163

Universality of Schmidt decomposition and particle identity.

PubMed

Sciara, Stefania; Lo Franco, Rosario; Compagno, Giuseppe

2017-03-23

Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, its formulation for identical particles remains controversial, jeopardizing its application to analyze general many-body quantum systems. Here we prove, using a newly developed approach, a universal Schmidt decomposition which allows faithful quantification of the physical entanglement due to the identity of particles. We find that it is affected by single-particle measurement localization and state overlap. We study paradigmatic two-particle systems where identical qubits and qutrits are located in the same place or in separated places. For the case of two qutrits in the same place, we show that their entanglement behavior, whose physical interpretation is given, differs from that obtained before by different methods. Our results are generalizable to multiparticle systems and open the way for further developments in quantum information processing exploiting particle identity as a resource.

Projective filtering of the fundamental eigenmode from spatially multimode radiation

NASA Astrophysics Data System (ADS)

Pérez, A. M.; Sharapova, P. R.; Straupe, S. S.; Miatto, F. M.; Tikhonova, O. V.; Leuchs, G.; Chekhova, M. V.

2015-11-01

Lossless filtering of a single coherent (Schmidt) mode from spatially multimode radiation is a problem crucial for optics in general and for quantum optics in particular. It becomes especially important in the case of nonclassical light that is fragile to optical losses. An example is bright squeezed vacuum generated via high-gain parametric down conversion or four-wave mixing. Its highly multiphoton and multimode structure offers a huge increase in the information capacity provided that each mode can be addressed separately. However, the nonclassical signature of bright squeezed vacuum, photon-number correlations, are highly susceptible to losses. Here we demonstrate lossless filtering of a single spatial Schmidt mode by projecting the spatial spectrum of bright squeezed vacuum on the eigenmode of a single-mode fiber. Moreover, we show that the first Schmidt mode can be captured by simply maximizing the fiber-coupled intensity. Importantly, the projection operation does not affect the targeted mode and leaves it usable for further applications.

Renormalization group approach to symmetry protected topological phases

NASA Astrophysics Data System (ADS)

van Nieuwenburg, Evert P. L.; Schnyder, Andreas P.; Chen, Wei

2018-04-01

A defining feature of a symmetry protected topological phase (SPT) in one dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

Alternative probability theories for cognitive psychology.

PubMed

Narens, Louis

2014-01-01

Various proposals for generalizing event spaces for probability functions have been put forth in the mathematical, scientific, and philosophic literatures. In cognitive psychology such generalizations are used for explaining puzzling results in decision theory and for modeling the influence of context effects. This commentary discusses proposals for generalizing probability theory to event spaces that are not necessarily boolean algebras. Two prominent examples are quantum probability theory, which is based on the set of closed subspaces of a Hilbert space, and topological probability theory, which is based on the set of open sets of a topology. Both have been applied to a variety of cognitive situations. This commentary focuses on how event space properties can influence probability concepts and impact cognitive modeling. Copyright © 2013 Cognitive Science Society, Inc.

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.

A short walk in quantum probability

NASA Astrophysics Data System (ADS)

Hudson, Robin

2018-04-01

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas. This article is part of the themed issue `Hilbert's sixth problem'.

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.

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.

Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm

NASA Astrophysics Data System (ADS)

Pusev, R. S.

2010-10-01

We obtain results on small deviations of Bogoliubov’s Gaussian measure occurring in the theory of the statistical equilibrium of quantum systems. For some random processes related to Bogoliubov processes, we find the exact asymptotic probability of their small deviations with respect to a Hilbert norm.

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

Digital Hilbert transformation for separation measurement of thicknesses and refractive indices of layered objects by use of a wavelength-scanning heterodyne interference confocal microscope.

PubMed

Watanabe, Yuuki; Yamaguchi, Ichirou

2002-08-01

A wavelength-scanning heterodyne interference confocal microscope quickly accomplishes the simultaneous measurement of the thickness and the refractive index of a sample by detection of the amplitude and the phase of the interference signal during a sample scan. However, the measurement range of the optical path difference (OPD) that is obtained from the phase changes is limited by the time response of the phase-locked loop circuit in the FM demodulator. To overcome this limitation and to improve the accuracy of the separation measurement, we propose an OPD detection using digital signal processing with a Hilbert transform. The measurement range is extended approximately five times, and the resolution of the OPD is improved to 5.5 from 9 microm without the electrical noise of the FM demodulator circuit. By applying this method for simultaneous measurement of thickness and the refractive index, we can measure samples 20-30-microm thick with refractive indices between 1 and 1.5.

Digital Hilbert transformation for separation measurement of thicknesses and refractive indices of layered objects by use of a wavelength-scanning heterodyne interference confocal microscope

NASA Astrophysics Data System (ADS)

Watanabe, Yuuki; Yamaguchi, Ichirou

2002-08-01

A wavelength-scanning heterodyne interference confocal microscope quickly accomplishes the simultaneous measurement of the thickness and the refractive index of a sample by detection of the amplitude and the phase of the interference signal during a sample scan. However, the measurement range of the optical path difference (OPD) that is obtained from the phase changes is limited by the time response of the phase-locked loop circuit in the FM demodulator. To overcome this limitation and to improve the accuracy of the separation measurement, we propose an OPD detection using digital signal processing with a Hilbert transform. The measurement range is extended approximately five times, and the resolution of the OPD is improved to 5.5 from 9 mum without the electrical noise of the FM demodulator circuit. By applying this method for simultaneous measurement of thickness and the refractive index, we can measure samples 20-30-mum thick with refractive indices between 1 and 1.5.

Flow-induced separation in wall turbulence.

PubMed

Nguyen, Quoc; Srinivasan, Chiranth; Papavassiliou, Dimitrios V

2015-03-01

One of the defining characteristics of turbulence is its ability to promote mixing. We present here a case where the opposite happens-simulation results indicate that particles can separate near the wall of a turbulent channel flow, when they have sufficiently different Schmidt numbers without use of any other means. The physical mechanism of the separation is understood when the interplay between convection and diffusion, as expressed by their characteristic time scales, is considered, leading to the determination of the necessary conditions for a successful separation between particles. Practical applications of these results can be found when very small particles need to be separated or removed from a fluid.

Universe creation from the third-quantized vacuum

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

McGuigan, M.

1989-04-15

Third quantization leads to a Hilbert space containing a third-quantized vacuum in which no universes are present as well as multiuniverse states. We consider the possibility of universe creation for the special case where the universe emerges in a no-particle state. The probability of such a creation is computed from both the path-integral and operator formalisms.

Universe creation from the third-quantized vacuum

NASA Astrophysics Data System (ADS)

McGuigan, Michael

1989-04-01

Third quantization leads to a Hilbert space containing a third-quantized vacuum in which no universes are present as well as multiuniverse states. We consider the possibility of universe creation for the special case where the universe emerges in a no-particle state. The probability of such a creation is computed from both the path-integral and operator formalisms.

Determination of fundamental asteroseismic parameters using the Hilbert transform

NASA Astrophysics Data System (ADS)

Kiefer, René; Schad, Ariane; Herzberg, Wiebke; Roth, Markus

2015-06-01

Context. Solar-like oscillations exhibit a regular pattern of frequencies. This pattern is dominated by the small and large frequency separations between modes. The accurate determination of these parameters is of great interest, because they give information about e.g. the evolutionary state and the mass of a star. Aims: We want to develop a robust method to determine the large and small frequency separations for time series with low signal-to-noise ratio. For this purpose, we analyse a time series of the Sun from the GOLF instrument aboard SOHO and a time series of the star KIC 5184732 from the NASA Kepler satellite by employing a combination of Fourier and Hilbert transform. Methods: We use the analytic signal of filtered stellar oscillation time series to compute the signal envelope. Spectral analysis of the signal envelope then reveals frequency differences of dominant modes in the periodogram of the stellar time series. Results: With the described method the large frequency separation Δν can be extracted from the envelope spectrum even for data of poor signal-to-noise ratio. A modification of the method allows for an overview of the regularities in the periodogram of the time series.

Dynamics of the quantum search and quench-induced first-order phase transitions.

PubMed

Coulamy, Ivan B; Saguia, Andreia; Sarandy, Marcelo S

2017-02-01

We investigate the excitation dynamics at a first-order quantum phase transition (QPT). More specifically, we consider the quench-induced QPT in the quantum search algorithm, which aims at finding out a marked element in an unstructured list. We begin by deriving the exact dynamics of the model, which is shown to obey a Riccati differential equation. Then, we discuss the probabilities of success by adopting either global or local adiabaticity strategies. Moreover, we determine the disturbance of the quantum criticality as a function of the system size. In particular, we show that the critical point exponentially converges to its thermodynamic limit even in a fast evolution regime, which is characterized by both entanglement QPT estimators and the Schmidt gap. The excitation pattern is manifested in terms of quantum domain walls separated by kinks. The kink density is then shown to follow an exponential scaling as a function of the evolution speed, which can be interpreted as a Kibble-Zurek mechanism for first-order QPTs.

Quantum Teleportation and Grover's Algorithm Without the Wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2017-02-01

In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.

A short walk in quantum probability.

PubMed

Hudson, Robin

2018-04-28

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas.This article is part of the themed issue 'Hilbert's sixth problem'. © 2018 The Author(s).

A discussion on the origin of quantum probabilities

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

Holik, Federico, E-mail: olentiev2@gmail.com; Departamento de Matemática - Ciclo Básico Común, Universidad de Buenos Aires - Pabellón III, Ciudad Universitaria, Buenos Aires; Sáenz, Manuel

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case). -- Highlights: •Several recent works use a derivation similar to that of R.T. Cox to obtain quantum probabilities. •We apply Cox’s method to the lattice of subspaces of the Hilbert space. •We obtain a derivationmore » of quantum probabilities which includes mixed states. •The method presented in this work is susceptible to generalization. •It includes quantum mechanics and classical mechanics as particular cases.« less

Dynamical Correspondence in a Generalized Quantum Theory

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2015-05-01

In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and JBW-algebras). One particularly important distinguishing property was identified by Alfsen and Shultz and is the existence of a dynamical correspondence. It reproduces the dual role of the selfadjoint operators as observables and generators of dynamical groups in quantum mechanics. In the paper, this concept is extended to another class of nonassociative algebras, arising from recent studies of the quantum logics with a conditional probability calculus and particularly of those that rule out third-order interference. The conditional probability calculus is a mathematical model of the Lüders-von Neumann quantum measurement process, and third-order interference is a property of the conditional probabilities which was discovered by Sorkin (Mod Phys Lett A 9:3119-3127, 1994) and which is ruled out by quantum mechanics. It is shown then that the postulates that a dynamical correspondence exists and that the square of any algebra element is positive still characterize, in the class considered, those algebras that emerge from the selfadjoint parts of C*-algebras equipped with the Jordan product. Within this class, the two postulates thus result in ordinary quantum mechanics using the complex Hilbert space or, vice versa, a genuine generalization of quantum theory must omit at least one of them.

Bernhard Schmidt and the Schmidt Telescope for Mapping the Sky

NASA Astrophysics Data System (ADS)

Wolfschmidt, G.

Bernhard Voldemar Schmidt (1879--1935) was born in Estonia. He ran an optical workshop in Mittweida, Saxonia, between 1901 and 1927. Astronomers appreciated the quality of his telescopes. Starting in 1925, working freelance in Hamburg Observatory, he developed a short focal length optical system with a large field of view. He succeeded in inventing the ``Schmidt Telescope'' in 1930, which allows the imaging a large field of the sky without any distortions. Shortly after Schmidt's death, the director of the observatory published details on the invention and production of the Schmidt Telescope. After World War II, Schmidt telescopes have been widely used. The first large Schmidt telescope was built in 1948, the ``Big Schmidt'' (126 cm), Mount Palomar, USA. Schmidt telescopes are also important tools for cosmology. The result of the Palomar Observatory Sky Surveys (1949--1958, 1985--1999) is a data base of about 20 million galaxies and over 100 million stars, supplemented in 1971 by the ESO Schmidt for the southern sky. Also high resolution spectrometers can be fitted to the Schmidt telescope. The 80 cm Schmidt telescope of Hamburg Observatory, planned since 1936, finished 1955, is on Calar Alto, Spain, since 1975. Combined with two objective prisms, it was used for a Quasar survey project.

Phase operator problem and macroscopic extension of quantum mechanics

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

Ozawa, M.

1997-06-01

To find the Hermitian phase operator of a single-mode electromagnetic field in quantum mechanics, the Schr{umlt o}dinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is a Naimark extension of the optimal probability operator-valued measure for the phase parameter found by Helstrom. Eventually, the two promising approaches to themore » statistics of the phase in quantum mechanics are synthesized by means of the Hermitian phase operator in the macroscopic extension of the Schr{umlt o}dinger representation. {copyright} 1997 Academic Press, Inc.« less

Theory of the Decoherence Effect in Finite and Infinite Open Quantum Systems Using the Algebraic Approach

NASA Astrophysics Data System (ADS)

Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert

Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.

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 .

Quantum key distribution without the wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key distribution allows a much more general and abstract access than commonly thought. The results include some generalizations of the Hilbert space version of quantum key distribution, but are based upon a general nonclassical extension of conditional probability. A special state-independent conditional probability is identified as origin of the superior security of quantum key distribution; this is a purely algebraic property of the quantum logic and represents the transition probability between the outcomes of two consecutive quantum measurements.

A quantum probability explanation for violations of ‘rational’ decision theory

PubMed Central

Pothos, Emmanuel M.; Busemeyer, Jerome R.

2009-01-01

Two experimental tasks in psychology, the two-stage gambling game and the Prisoner's Dilemma game, show that people violate the sure thing principle of decision theory. These paradoxical findings have resisted explanation by classical decision theory for over a decade. A quantum probability model, based on a Hilbert space representation and Schrödinger's equation, provides a simple and elegant explanation for this behaviour. The quantum model is compared with an equivalent Markov model and it is shown that the latter is unable to account for violations of the sure thing principle. Accordingly, it is argued that quantum probability provides a better framework for modelling human decision-making. PMID:19324743

Schmidt-number witnesses and bound entanglement

NASA Astrophysics Data System (ADS)

Sanpera, Anna; Bruß, Dagmar; Lewenstein, Maciej

2001-05-01

The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by studying Schmidt-number witnesses that detect it. We present a canonical form of such witnesses and provide constructive methods for their optimization. Finally, we present strong evidence that all bound entangled states with positive partial transpose in C3⊗C3 have Schmidt number 2.

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.

Process, System, Causality, and Quantum Mechanics: A Psychoanalysis of Animal Faith

NASA Astrophysics Data System (ADS)

Etter, Tom; Noyes, H. Pierre

We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y, define a link between x and y to be the condition x=y on J. Define the {\\it state} D of a link x=y as the joint probability distribution matrix on x and y without the link. The two core laws of quantum mechanics are the Born probability rule, and the unitary dynamical law whose best known form is the Schrodinger's equation. Von Neumann formulated these two laws in the language of Hilbert space as prob(P) = trace(PD) and D'T = TD respectively, where P is a projection, D and D' are (von Neumann) density matrices, and T is a unitary transformation. We'll see that if we regard link states as density matrices, the algebraic forms of these two core laws occur as completely general theorems about links. When we extend probability theory by allowing cases to count negatively, we find that the Hilbert space framework of quantum mechanics proper emerges from the assumption that all D's are symmetrical in rows and columns. On the other hand, Markovian systems emerge when we assume that one of every linked variable pair has a uniform probability distribution. By representing quantum and Markovian structure in this way, we see clearly both how they differ, and also how they can coexist in natural harmony with each other, as they must in quantum measurement, which we'll examine in some detail. Looking beyond quantum mechanics, we see how both structures have their special places in a much larger continuum of formal systems that we have yet to look for in nature.

Mixing in High Schmidt Number Turbulent Jets

DTIC Science & Technology

1991-01-01

the higher Sc jet is less well mixed. The difference is less pronounced at higher Re. Flame length estimates imply either an increase in entrainment...72 8.0 Estimation of flame lengths ....................................... 74 8.1 Estim ation m...A.4) Lf flame length N number of trials (Eq. 3.1) p exponent in fits of the variance behavior with Re p probability of a binomial event (Eq. 3.1) p

Winning Attitude & Dedication to Physical Therapy Keep Sam Schmidt on Track

ERIC Educational Resources Information Center

Bosley, Nikki Prevenslik

2006-01-01

This article relates how Sam Schmidt returned to living a productive life after an accident left him with spinal cord injury. Schmidt was a former Indy Racing League driver who founded Sam Schmidt Motorsports after his accident in 2000. Schmidt's car hit the wall as he exited turn two during a practice session at Walt Disney World Speedway in…

Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces

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

Vourdas, A.

2014-08-15

The orthocomplemented modular lattice of subspaces L[H(d)], of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)]). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H{sub 1},H{sub 2}), which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H{sub 1}),P(H{sub 2}), to the subspacesmore » H{sub 1}, H{sub 2}. As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities.« less

Transition probability spaces in loop quantum gravity

NASA Astrophysics Data System (ADS)

Guo, Xiao-Kan

2018-03-01

We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is exemplified by first checking such structures in covariant quantum mechanics and then identifying the transition probability spaces in spin foam models via a simplified version of general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the discrete analog of the Hilbert space of the canonical theory and the relevant quantum logical structures. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize in spin foam models two proposals by Crane about the mathematical structures of quantum gravity, namely, the quantum topos and causal sites. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.

Student Observations of Double Star Delta Orionis (STFA 14 AC)

NASA Astrophysics Data System (ADS)

Estrada, Reed; Aguilera, Sophia; Bowden, Sam; Gillette, Travis; Givens, Jalynn; Reder, Gabriel; Rhoades, Breauna; Sharpe, Scott; Shattles, Jenna; Cha, Brendon; Do, Vicky; Ewing, Malachi; Kiamco, Alex Junior; Nelms, Brenda; Peña, Emilie; Maricarmen, Richard; Thielen, Austin

2018-01-01

A group of eight eighth graders and eight high schoolers studied the double star STFA 14 AC. They used the procedure from Argyle's book to get the separation and position angle for the double star. The students used a Celestron C8 Schmidt-Cassegrain telescope with a Baader Planetarium microguide eyepiece with similar markings to a Celestron Eyepiece. The students determined the separation to be 56 arcseconds and the position angle to be 4.19°. They compared their results to the Washington Double Star Catalog and found that they had a 2.88 arcseconds difference in separation and a 2.19° in position angle.

Fast separation of two trapped ions (Open Access, Publisher’s Version)

DTIC Science & Technology

2015-09-17

of quantum states and separation of ions in a dual rf ion trapQuantum Inf. Comput . 2 257 [10] KaufmannH, Ruster T, SchmiegelowCT, Schmidt-Kaler F...Ruschhaupt et al. Shortcuts to adiabaticity for an ion in a rotating radially-tight trap M Palmero, Shuo Wang, D Guéry-Odelin et al. Optimal shortcuts for...Kiely, J P L McGuinness, J G Muga et al. Quantum simulations with cold trapped ions Michael Johanning, Andrés F Varón and Christof Wunderlich Quantum

High-Speed Quantum Key Distribution Using Photonic Integrated Circuits

DTIC Science & Technology

2013-01-01

protocol [14] that uses energy-time entanglement of pairs of photons. We are employing the QPIC architecture to implement a novel high-dimensional disper...continuous Hilbert spaces using measures of the covariance matrix. Although we focus the discussion on a scheme employing entangled photon pairs...is the probability that parameter estimation fails [20]. The parameter ε̄ accounts for the accuracy of estimating the smooth min- entropy , which

A multithreaded and GPU-optimized compact finite difference algorithm for turbulent mixing at high Schmidt number using petascale computing

NASA Astrophysics Data System (ADS)

Clay, M. P.; Yeung, P. K.; Buaria, D.; Gotoh, T.

2017-11-01

Turbulent mixing at high Schmidt number is a multiscale problem which places demanding requirements on direct numerical simulations to resolve fluctuations down the to Batchelor scale. We use a dual-grid, dual-scheme and dual-communicator approach where velocity and scalar fields are computed by separate groups of parallel processes, the latter using a combined compact finite difference (CCD) scheme on finer grid with a static 3-D domain decomposition free of the communication overhead of memory transposes. A high degree of scalability is achieved for a 81923 scalar field at Schmidt number 512 in turbulence with a modest inertial range, by overlapping communication with computation whenever possible. On the Cray XE6 partition of Blue Waters, use of a dedicated thread for communication combined with OpenMP locks and nested parallelism reduces CCD timings by 34% compared to an MPI baseline. The code has been further optimized for the 27-petaflops Cray XK7 machine Titan using GPUs as accelerators with the latest OpenMP 4.5 directives, giving 2.7X speedup compared to CPU-only execution at the largest problem size. Supported by NSF Grant ACI-1036170, the NCSA Blue Waters Project with subaward via UIUC, and a DOE INCITE allocation at ORNL.

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

Self-entanglement and the dissociation of homonuclear diatomic molecules

DOE PAGES

Gonis, A.; Zhang, X. -G.; Nicholson, D. M.; ...

2014-01-14

The concept of self-entanglement is introduced to describe a mixed state or ensemble density as a pure state in an augmented Hilbert space formed by the products of the individual states forming a mixed state (or ensemble). We use this representation of mixed states to show that upon dissociation a neutral homonuclear diatomic molecule will separate into two neutral atoms.

A Primer on Vibrational Ball Bearing Feature Generation for Prognostics and Diagnostics Algorithms

DTIC Science & Technology

2015-03-01

Atlas -Marks (Cone-Shaped Kernel) ........................................................36 8.7.7 Hilbert-Huang Transform...bearing surface and eventually progress to the surface where the material will separate. Also known as pitting, spalling, or flaking. • Wear ...normal degradation caused by dirt and foreign particles causing abrasion of the contact surfaces over time resulting in alterations in the raceway and

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

Entanglement transitions induced by large deviations

NASA Astrophysics Data System (ADS)

Bhosale, Udaysinh T.

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B , is computed analytically using a Coulomb gas method. It is shown that this probability, for large N , goes as exp[-β N2Φ (ζ ) ] , where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ (ζ ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A , using the properties of the density matrix's partial transpose ρ12Γ. The density of states of ρ12Γ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ . Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Entanglement transitions induced by large deviations.

PubMed

Bhosale, Udaysinh T

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B, is computed analytically using a Coulomb gas method. It is shown that this probability, for large N, goes as exp[-βN^{2}Φ(ζ)], where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ(ζ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A, using the properties of the density matrix's partial transpose ρ_{12}^{Γ}. The density of states of ρ_{12}^{Γ} is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ. Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Stego on FPGA: An IWT Approach

PubMed Central

Ramalingam, Balakrishnan

2014-01-01

A reconfigurable hardware architecture for the implementation of integer wavelet transform (IWT) based adaptive random image steganography algorithm is proposed. The Haar-IWT was used to separate the subbands namely, LL, LH, HL, and HH, from 8 × 8 pixel blocks and the encrypted secret data is hidden in the LH, HL, and HH blocks using Moore and Hilbert space filling curve (SFC) scan patterns. Either Moore or Hilbert SFC was chosen for hiding the encrypted data in LH, HL, and HH coefficients, whichever produces the lowest mean square error (MSE) and the highest peak signal-to-noise ratio (PSNR). The fixated random walk's verdict of all blocks is registered which is nothing but the furtive key. Our system took 1.6 µs for embedding the data in coefficient blocks and consumed 34% of the logic elements, 22% of the dedicated logic register, and 2% of the embedded multiplier on Cyclone II field programmable gate array (FPGA). PMID:24723794

Geometric descriptions of entangled states by auxiliary varieties

NASA Astrophysics Data System (ADS)

Holweck, Frédéric; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-01

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 × 2 × (n + 1), for n ⩾ 1, quantum systems and a new description with the 2 × 3 × 3 quantum system. Our results complete the approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

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.

Tool Wear Feature Extraction Based on Hilbert Marginal Spectrum

NASA Astrophysics Data System (ADS)

Guan, Shan; Song, Weijie; Pang, Hongyang

2017-09-01

In the metal cutting process, the signal contains a wealth of tool wear state information. A tool wear signal’s analysis and feature extraction method based on Hilbert marginal spectrum is proposed. Firstly, the tool wear signal was decomposed by empirical mode decomposition algorithm and the intrinsic mode functions including the main information were screened out by the correlation coefficient and the variance contribution rate. Secondly, Hilbert transform was performed on the main intrinsic mode functions. Hilbert time-frequency spectrum and Hilbert marginal spectrum were obtained by Hilbert transform. Finally, Amplitude domain indexes were extracted on the basis of the Hilbert marginal spectrum and they structured recognition feature vector of tool wear state. The research results show that the extracted features can effectively characterize the different wear state of the tool, which provides a basis for monitoring tool wear condition.

Schmidt Telescope

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

A type of telescope, invented by the Estonian optician Bernhard Schmidt (1879-1935), that is used to photograph large areas of the sky. Because, in its original design, it was useable only for photography, the instrument is also known as the Schmidt camera. The Schmidt uses a concave spherical mirror as its light collector and corrects for the optical defect, known as spherical aberration, that i...

Evaluation of the Schmidt-STRATOS spreader.

DOT National Transportation Integrated Search

2005-07-01

In the fall of 2004, the Maine Department of Transportation (MAINEDOT) entered into an arrangement : with Schmidt International of St.Blasien, Germany to evaluate Schmidts STRATOS material spreader. : The MAINEDOT agreed to evaluate the equipment ...

About the nonclassicality of states defined by nonpositivity of the P-quasiprobability

NASA Astrophysics Data System (ADS)

Wünsche, Alfred

2004-02-01

The definition of nonclassical states in quantum optics by the nonpositivity of their Glauber-Sudarshan quasiprobability P(\\alpha,\\alpha^*)\\leftrightarrow P(q,p) is investigated and it is shown that it hides some serious problems. It leads to a subdivision of squeezed thermal states into classical and nonclassical states which is difficult to interpret physically by some qualitatively different behaviour of the states. Nonclassical states are found in arbitrarily small neighbourhoods of every classical state that is illustrated by a very artificial modified thermal state. The observability of the criterion in comparison to that for nonclassicality of states determined by the nearest Hilbert-Schmidt distance to a class of reference states is discussed. The behaviour of the nonclassicality of states in models of phase-insensitive processes of damping and amplification is investigated and it is found that every nonclassical state eventually makes a transition to a classical state. However, this is not specific for the negativities or singularities of the Glauber-Sudarshan quasiprobability and is found in similar form for other quasiprobabilities, for example, for the Wigner quasiprobability. We discuss in quite general form some defects of the Glauber-Sudarshan quasiprobability if compared with classical distribution functions over the phase space, in particular the failure of an earlier advertised superposition formula.

Connecting dissipation and noncommutativity: A Bateman system case study

NASA Astrophysics Data System (ADS)

Pal, Sayan Kumar; Nandi, Partha; Chakraborty, Biswajit

2018-06-01

We present an approach to the problem of quantization of the damped harmonic oscillator. To start with, we adopt the standard method of doubling the degrees of freedom of the system (Bateman form) and then, by introducing some new parameters, we get a generalized coupled set of equations from the Bateman form. Using the corresponding time-independent Lagrangian, quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) are analyzed by using both path integral and canonical quantization schemes within the framework of the Hilbert-Schmidt operator formulation. Our method is distinct from those existing in the literature and where the ambient space was taken to be commutative. Our quantization shows that we end up again with a Bateman system except that the damping factor undergoes renormalization. Strikingly, the corresponding expression shows that the renormalized damping factor can be nonzero even if "bare" one is zero to begin with. In other words, noncommutativity can act as a source of dissipation. Conversely, the noncommutative parameter θ , taken to be a free one now, can be fine tuned to get a vanishing renormalized damping factor. This indicates in some sense a "duality" between dissipation and noncommutativity. Our results match the existing results in the commutative limit.

Compressible turbulent mixing: Effects of Schmidt number.

PubMed

Ni, Qionglin

2015-05-01

We investigated by numerical simulations the effects of Schmidt number on passive scalar transport in forced compressible turbulence. The range of Schmidt number (Sc) was 1/25∼25. In the inertial-convective range the scalar spectrum seemed to obey the k(-5/3) power law. For Sc≫1, there appeared a k(-1) power law in the viscous-convective range, while for Sc≪1, a k(-17/3) power law was identified in the inertial-diffusive range. The scaling constant computed by the mixed third-order structure function of the velocity-scalar increment showed that it grew over Sc, and the effect of compressibility made it smaller than the 4/3 value from incompressible turbulence. At small amplitudes, the probability distribution function (PDF) of scalar fluctuations collapsed to the Gaussian distribution whereas, at large amplitudes, it decayed more quickly than Gaussian. At large scales, the PDF of scalar increment behaved similarly to that of scalar fluctuation. In contrast, at small scales it resembled the PDF of scalar gradient. Furthermore, the scalar dissipation occurring at large magnitudes was found to grow with Sc. Due to low molecular diffusivity, in the Sc≫1 flow the scalar field rolled up and got mixed sufficiently. However, in the Sc≪1 flow the scalar field lost the small-scale structures by high molecular diffusivity and retained only the large-scale, cloudlike structures. The spectral analysis found that the spectral densities of scalar advection and dissipation in both Sc≫1 and Sc≪1 flows probably followed the k(-5/3) scaling. This indicated that in compressible turbulence the processes of advection and dissipation except that of scalar-dilatation coupling might deferring to the Kolmogorov picture. It then showed that at high wave numbers, the magnitudes of spectral coherency in both Sc≫1 and Sc≪1 flows decayed faster than the theoretical prediction of k(-2/3) for incompressible flows. Finally, the comparison with incompressible results showed that the scalar in compressible turbulence with Sc=1 lacked a conspicuous bump structure in its spectrum, but was more intermittent in the dissipative range.

Controlling the spectrum of photons generated on a silicon nanophotonic chip

PubMed Central

Kumar, Ranjeet; Ong, Jun Rong; Savanier, Marc; Mookherjea, Shayan

2014-01-01

Directly modulated semiconductor lasers are widely used, compact light sources in optical communications. Semiconductors can also be used to generate nonclassical light; in fact, CMOS-compatible silicon chips can be used to generate pairs of single photons at room temperature. Unlike the classical laser, the photon-pair source requires control over a two-dimensional joint spectral intensity (JSI) and it is not possible to process the photons separately, as this could destroy the entanglement. Here we design a photon-pair source, consisting of planar lightwave components fabricated using CMOS-compatible lithography in silicon, which has the capability to vary the JSI. By controlling either the optical pump wavelength, or the temperature of the chip, we demonstrate the ability to select different JSIs, with a large variation in the Schmidt number. Such control can benefit high-dimensional communications where detector-timing constraints can be relaxed by realizing a large Schmidt number in a small frequency range. PMID:25410792

Reliability of the sliding scale for collecting affective responses to words.

PubMed

Imbault, C; Shore, D; Kuperman, V

2018-01-25

Warriner, Shore, Schmidt, Imbault, and Kuperman, Canadian Journal of Experimental Psychology, 71; 71-88 (2017) have recently proposed a slider task in which participants move a manikin on a computer screen toward or further away from a word, and the distance (in pixels) is a measure of the word's valence. Warriner, Shore, Schmidt, Imbault, and Kuperman, Canadian Journal of Experimental Psychology, 71; 71-88 (2017) showed this task to be more valid than the widely used rating task, but they did not examine the reliability of the new methodology. In this study we investigated multiple aspects of this task's reliability. In Experiment 1 (Exps. 1.1-1.6), we showed that the sliding scale has high split-half reliability (r = .868 to .931). In Experiment 2, we also showed that the slider task elicits consistent repeated responses both within a single session (Exp. 2: r = .804) and across two sessions separated by one week (Exp. 3: r = .754). Overall, the slider task, in addition to having high validity, is highly reliable.

Measurements in a separation bubble on an airfoil using laser velocimetry

NASA Technical Reports Server (NTRS)

Fitzgerald, Edward J.; Mueller, Thomas J.

1990-01-01

An experimental investigation was conducted to measure the reverse flow within the transitional separation bubble that forms on an airfoil at low Reynolds numbers. Measurements were used to determine the effect of the reverse flow on integrated boundary-layer parameters often used to model the bubble. Velocity profile data were obtained on an NACA 663-018 airfoil at angle of attack of 12 deg and a chord Reynolds number of 140,000 using laser Doppler and single-sensor hot-wire anemometry. A new correlation is proposed based on zero velocity position, since the Schmidt (1986) correlations fail in the turbulent portion of the bubble.

(UK) Schmidt - AAO style into the 1990s

NASA Astrophysics Data System (ADS)

Savage, A.

Recommendations on the use of the AAO UK Schmidt telescope during the next three years are presented. There are four important functions which must be maintained: (1) the science from the schmidt material must continue to be of the same high quality as that on which the Schmidt's reputation has been built; (2) the service to the Australian and British communities must continue despite the new trim (slim) appearance of the Schmidt staff and budget; (3) links with ROE, its plate library and photolabs which provide some of the survey atlases must be maintained; and (4) Australian and British usage of the UK's large measuring machines APM and COSMOS should be promoted.

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.

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.

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'.

Shock Compression Chemistry in Materials Synthesis and Processing

DTIC Science & Technology

1984-12-21

Moore at Los Alamos Scientific Laboratory [Schmidt, Moore, and Shaner, 1983; Schmidt, Moore, Schiferl , and Shaner, 1983]. More speculative, but also...Synthesis and Processing, March 28-29, Seattle, Washington. Schmidt, S. C., D. S. Moore, D. Schiferl , and J. W. Shaner. 1983. Backward stimulated Raman

Detection of broken rotor bar faults in induction motor at low load using neural network.

PubMed

Bessam, B; Menacer, A; Boumehraz, M; Cherif, H

2016-09-01

The knowledge of the broken rotor bars characteristic frequencies and amplitudes has a great importance for all related diagnostic methods. The monitoring of motor faults requires a high resolution spectrum to separate different frequency components. The Discrete Fourier Transform (DFT) has been widely used to achieve these requirements. However, at low slip this technique cannot give good results. As a solution for these problems, this paper proposes an efficient technique based on a neural network approach and Hilbert transform (HT) for broken rotor bar diagnosis in induction machines at low load. The Hilbert transform is used to extract the stator current envelope (SCE). Two features are selected from the (SCE) spectrum (the amplitude and frequency of the harmonic). These features will be used as input for neural network. The results obtained are astonishing and it is capable to detect the correct number of broken rotor bars under different load conditions. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Geometric descriptions of entangled states by auxiliary varieties

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

Holweck, Frederic; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-15

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 Multiplication-Sign 2 Multiplication-Sign (n+ 1), for n Greater-Than-Or-Slanted-Equal-To 1, quantum systems and a new description with the 2 Multiplication-Sign 3 Multiplication-Sign 3 quantum system. Our results complete themore » approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.« less

What is Quantum Mechanics? A Minimal Formulation

NASA Astrophysics Data System (ADS)

Friedberg, R.; Hohenberg, P. C.

2018-03-01

This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called "microscopic theory", applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen-Specker-Bell theorem and Gleason's theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.

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.

Description of a new genus, Galgoria gen. nov. (Hemiptera: Cicadidae: Cicadinae: Leptopsaltriini: Leptopsaltriina).

PubMed

Lee, Young June

2016-05-10

A new cicada genus, Galgoria gen. nov., is described with Tanna herzbergi Schmidt, 1932 (from southern China) as its type species, which is placed in the subtribe Leptopsaltriina Moulton, 1923 of the tribe Leptopsaltriini Moulton, 1923 in the subfamily Cicadinae Latreille, 1802 (Hemiptera: Cicadidae). Tanna herzbergi Schmidt, 1932 is transferred from Tanna Distant, 1905 to Galgoria gen. nov. to become Galgoria herzbergi (Schmidt, 1932) comb. nov. Tanna apicalis Chen, 1940 syn. nov. and Tanna pseudocalis Lei & Chou, 1997 syn. nov. are synonymized here with Galgoria herzbergi (Schmidt, 1932) comb. nov.

Entanglement witness criteria of strong- k-separability for multipartite quantum states

NASA Astrophysics Data System (ADS)

Yan, Siqing; Hou, Jinchuan

2018-07-01

Let H1, H2,\\ldots ,Hn be separable complex Hilbert spaces with \\dim Hi≥ 2 and n≥ 2. Assume that ρ is a state in H=H_1⊗ H_2⊗ \\cdots ⊗ H_n. ρ is called strong- k-separable (2≤ k≤ n) if ρ is separable for any k-partite division of H. In this paper, an entanglement witnesses criterion of strong- k-separability is obtained, which says that ρ is not strong- k-separable if and only if there exist a k-division space H_{m1}⊗ \\cdots ⊗ H_{mk} of H, a finite-rank linear elementary operator positive on product states Λ: B(H_{m2}⊗ \\cdots ⊗ H_{mk})→ B(H_{m1}) and a state ρ 0\\in S(H_{m1}⊗ H_{m1}), such that Tr(Wρ )<0, where W=(Id⊗ Λ ^{\\dagger })ρ 0 is an entanglement witness. In addition, several different methods of constructing entanglement witnesses for multipartite states are also given.

A little-known 3-lens Catadioptric Camera by Bernard Schmidt

NASA Astrophysics Data System (ADS)

Busch, Wolfgang; Ceragioli, Roger C.; Stephani, Walter

2013-07-01

The authors investigate a prototype 3-lens f/1 catadioptric camera, built in 1934 by the famous optician Bernhard Schmidt at the Hamburg-Bergedorf Observatory in Germany, where Schmidt worked before his death in 1935. The prototype is in the observatory's collection of Schmidt artifacts, but its nature was not understood before the authors' recent examination. It is an astronomical camera of a form known as 'Buchroeder-Houghton', consisting of a spherical mirror and a 3-element afocal corrector lens placed at the mirror's center of curvature. The design is named for R.A. Buchroeder and J.L. Houghton who independently published this and related forms of wide-field spherical-lens cameras after 1942. Schmidt died before he could publish his own design. The authors disassembled the prototype and measured its optical parameters. These they present together with a transmission test of the corrector lens. The authors also consider the theoretical performance of the design as built, the theory of Houghton cameras, Schmidt's possible path to his invention, and the place of the prototype in his scientific output.

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

Tripartite-to-Bipartite Entanglement Transformation by Stochastic Local Operations and Classical Communication and the Structure of Matrix Spaces

NASA Astrophysics Data System (ADS)

Li, Yinan; Qiao, Youming; Wang, Xin; Duan, Runyao

2018-03-01

We study the problem of transforming a tripartite pure state to a bipartite one using stochastic local operations and classical communication (SLOCC). It is known that the tripartite-to-bipartite SLOCC convertibility is characterized by the maximal Schmidt rank of the given tripartite state, i.e. the largest Schmidt rank over those bipartite states lying in the support of the reduced density operator. In this paper, we further study this problem and exhibit novel results in both multi-copy and asymptotic settings, utilizing powerful results from the structure of matrix spaces. In the multi-copy regime, we observe that the maximal Schmidt rank is strictly super-multiplicative, i.e. the maximal Schmidt rank of the tensor product of two tripartite pure states can be strictly larger than the product of their maximal Schmidt ranks. We then provide a full characterization of those tripartite states whose maximal Schmidt rank is strictly super-multiplicative when taking tensor product with itself. Notice that such tripartite states admit strict advantages in tripartite-to-bipartite SLOCC transformation when multiple copies are provided. In the asymptotic setting, we focus on determining the tripartite-to-bipartite SLOCC entanglement transformation rate. Computing this rate turns out to be equivalent to computing the asymptotic maximal Schmidt rank of the tripartite state, defined as the regularization of its maximal Schmidt rank. Despite the difficulty caused by the super-multiplicative property, we provide explicit formulas for evaluating the asymptotic maximal Schmidt ranks of two important families of tripartite pure states by resorting to certain results of the structure of matrix spaces, including the study of matrix semi-invariants. These formulas turn out to be powerful enough to give a sufficient and necessary condition to determine whether a given tripartite pure state can be transformed to the bipartite maximally entangled state under SLOCC, in the asymptotic setting. Applying the recent progress on the non-commutative rank problem, we can verify this condition in deterministic polynomial time.

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

A blueprint for demonstrating quantum supremacy with superconducting qubits

NASA Astrophysics Data System (ADS)

Neill, C.; Roushan, P.; Kechedzhi, K.; Boixo, S.; Isakov, S. V.; Smelyanskiy, V.; Megrant, A.; Chiaro, B.; Dunsworth, A.; Arya, K.; Barends, R.; Burkett, B.; Chen, Y.; Chen, Z.; Fowler, A.; Foxen, B.; Giustina, M.; Graff, R.; Jeffrey, E.; Huang, T.; Kelly, J.; Klimov, P.; Lucero, E.; Mutus, J.; Neeley, M.; Quintana, C.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Neven, H.; Martinis, J. M.

2018-04-01

A key step toward demonstrating a quantum system that can address difficult problems in physics and chemistry will be performing a computation beyond the capabilities of any classical computer, thus achieving so-called quantum supremacy. In this study, we used nine superconducting qubits to demonstrate a promising path toward quantum supremacy. By individually tuning the qubit parameters, we were able to generate thousands of distinct Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert space. As the number of qubits increases, the system continues to explore the exponentially growing number of states. Extending these results to a system of 50 qubits has the potential to address scientific questions that are beyond the capabilities of any classical computer.

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.

Future-Minded: Aaron Schmidt--Thomas Ford Memorial Library, IL

ERIC Educational Resources Information Center

Library Journal, 2005

2005-01-01

Like many young people, Aaron Schmidt loves electronic gadgets. But not for their own sake. He believes the future of libraries depends on how well we meet the needs of today's young adults, who are far more tech-fluent than most librarians. As reference librarian and all-around technology guru at Thomas Ford Memorial Library, Schmidt created the…

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

NASA Astrophysics Data System (ADS)

Prodhan, Suryoday; Ramasesha, S.

2018-05-01

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

Processing of Digital Plates1.2m of Baldone Observatory Schmidt Telescope

NASA Astrophysics Data System (ADS)

Eglitis, Ilgmars; Andruk, Vitaly

2017-04-01

The aim of this research is to evaluate accuracy of Plate Processing Method and to perform a detailed study of the Epson Expression 10000XL scanner, which was used to digitize plates from the database collection of the 1.2 m Schmidt Telescope installed in the Baldone Observatory. Special software developed in LINUX/MIDAS/ROMAFOT environment was used for processing the scans. Results of the digitized files with grey gradations of 8- and 16-bits were compared; an estimation of the accuracy of the developed method for rectangular coordinates determination and photometry was made. Errors in the instrumental system are ±0.026 pixels and ±0.024m for coordinates and stellar magnitudes respectively. To evaluate the repeatability of the scanner's astrometric and photometric errors, six consecutive scans of one plate were processed with a spatial separation of 1200 dpi. The following error estimations are obtained for stars brighter than U< 13.5m: σxy = ±0.021 to 0.027 pixels and σm = ±0.014m to 0.016m for rectangular coordinates and instrumental stellar magnitudes respectively.

A reduced-dimensional model for near-wall transport in cardiovascular flows

PubMed Central

Hansen, Kirk B.

2015-01-01

Near-wall mass transport plays an important role in many cardiovascular processes, including the initiation of atherosclerosis, endothelial cell vasoregulation, and thrombogenesis. These problems are characterized by large Péclet and Schmidt numbers as well as a wide range of spatial and temporal scales, all of which impose computational difficulties. In this work, we develop an analytical relationship between the flow field and near-wall mass transport for high-Schmidt-number flows. This allows for the development of a wall-shear-stress-driven transport equation that lies on a codimension-one vessel-wall surface, significantly reducing computational cost in solving the transport problem. Separate versions of this equation are developed for the reaction-rate-limited and transport-limited cases, and numerical results in an idealized abdominal aortic aneurysm are compared to those obtained by solving the full transport equations over the entire domain. The reaction-rate-limited model matches the expected results well. The transport-limited model is accurate in the developed flow regions, but overpredicts wall flux at entry regions and reattachment points in the flow. PMID:26298313

Scalar transport across the turbulent/non-turbulent interface in jets: Schmidt number effects

NASA Astrophysics Data System (ADS)

Silva, Tiago S.; B. da Silva, Carlos; Idmec Team

2016-11-01

The dynamics of a passive scalar field near a turbulent/non-turbulent interface (TNTI) is analysed through direct numerical simulations (DNS) of turbulent planar jets, with Reynolds numbers ranging from 142 <= Reλ <= 246 , and Schmidt numbers from 0 . 07 <= Sc <= 7 . The steepness of the scalar gradient, as observed from conditional profiles near the TNTI, increases with the Schmidt number. Conditional scalar gradient budgets show that for low and moderate Schmidt numbers a diffusive superlayer emerges at the TNTI, where the scalar gradient diffusion dominates, while the production is negligible. For low Schmidt numbers the growth of the turbulent front is commanded by the molecular diffusion, whereas the scalar gradient convection is negligible. The authors acknowledge the Laboratory for Advanced Computing at University of Coimbra for providing HPC, computing, consulting resources that have contributed to the research results reported within this paper. URL http://www.lca.uc.pt.

Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

NASA Astrophysics Data System (ADS)

Pato, Mauricio P.; Oshanin, Gleb

2013-03-01

We study the probability distribution function P(β)n(w) of the Schmidt-like random variable w = x21/(∑j = 1nx2j/n), where xj, (j = 1, 2, …, n), are unordered eigenvalues of a given n × n β-Gaussian random matrix, β being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual (randomly chosen) eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n → ∞ and for arbitrary β the distribution P(β)n(w) converges to the Marčenko-Pastur form, i.e. is defined as P_{n}^{( \\beta )}(w) \\sim \\sqrt{(4 - w)/w} for w ∈ [0, 4] and equals zero outside of the support, despite the fact that formally w is defined on the interval [0, n]. Furthermore, for Gaussian unitary ensembles (β = 2) we present exact explicit expressions for P(β = 2)n(w) which are valid for arbitrary n and analyse their behaviour.

Polyhedral sweeping processes with unbounded nonconvex-valued perturbation

NASA Astrophysics Data System (ADS)

Tolstonogov, A. A.

2017-12-01

A polyhedral sweeping process with a multivalued perturbation whose values are nonconvex unbounded sets is studied in a separable Hilbert space. Polyhedral sweeping processes do not satisfy the traditional assumptions used to prove existence theorems for convex sweeping processes. We consider the polyhedral sweeping process as an evolution inclusion with subdifferential operators depending on time. The widely used assumption of Lipschitz continuity for the multivalued perturbation term is replaced by a weaker notion of (ρ - H) Lipschitzness. The existence of solutions is proved for this sweeping process.

Topological and Orthomodular Modeling of Context in Behavioral Science

NASA Astrophysics Data System (ADS)

Narens, Louis

2017-02-01

Two non-boolean methods are discussed for modeling context in behavioral data and theory. The first is based on intuitionistic logic, which is similar to classical logic except that not every event has a complement. Its probability theory is also similar to classical probability theory except that the definition of probability function needs to be generalized to unions of events instead of applying only to unions of disjoint events. The generalization is needed, because intuitionistic event spaces may not contain enough disjoint events for the classical definition to be effective. The second method develops a version of quantum logic for its underlying probability theory. It differs from Hilbert space logic used in quantum mechanics as a foundation for quantum probability theory in variety of ways. John von Neumann and others have commented about the lack of a relative frequency approach and a rational foundation for this probability theory. This article argues that its version of quantum probability theory does not have such issues. The method based on intuitionistic logic is useful for modeling cognitive interpretations that vary with context, for example, the mood of the decision maker, the context produced by the influence of other items in a choice experiment, etc. The method based on this article's quantum logic is useful for modeling probabilities across contexts, for example, how probabilities of events from different experiments are related.

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,…

Proton--H/sub 2/ scattering on an ab initio CI potential energy surface. II. Combined vibrational--rotational excitation at 4. 67 and 6 eV

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

Schinke, R.

1980-04-01

Infinite-order-sudden calculations have been performed at 4.67 and 6 eV on the ab initio CI potential energy surface determined recently by Schinke, Dupuis, and Lester. The vibrational degree of freedom has been treated exactly by solving vibrationally coupled radial equations. The rotationally summed differential cross sections for vibrational excitation are in good agreement with the measurements of Schmidt, Hermann, and Linder. It is shown that the rotational excitation cross sections in the vibrational ground state near the rainbow angle are almost exclusively determined by the potential between 2.5a/sub 0/ and 5a/sub 0/ proton--H/sub 2/ separations. In this region only themore » V/sub 2/ term of an expansion into Legendre polynomials is nonvanishing and is a factor of approx.3 smaller for the new surface than for the Giese and Gentry analytic potential. These differences result in a dramatic decrease of the rotational excitation cross sections in the rainbow region so that the present theoretical transition probabilities are in much better agreement with the experiments than our previous sudden vib--rotor calculations utilizing Giese and Gentry's surface.« less

Convection due to an unstable density difference across a permeable membrane

NASA Astrophysics Data System (ADS)

Puthenveettil, Baburaj A.; Arakeri, Jaywant H.

We study natural convection driven by unstable concentration differences of sodium chloride (NaCl) across a horizontal permeable membrane at Rayleigh numbers (Ra) of 1010 to 1011 and Schmidt number (Sc)=600. A layer of brine lies over a layer of distilled water, separated by the membrane, in square-cross-section tanks. The membrane is permeable enough to allow a small flow across it at higher driving potentials. Based on the predominant mode of transport across the membrane, three regimes of convection, namely an advection regime, a diffusion regime and a combined regime, are identified. The near-membrane flow in all the regimes consists of sheet plumes formed from the unstable layers of fluid near the membrane. In the advection regime observed at higher concentration differences (Bb) show a common log-normal probability density function at all Ra. We propose a phenomenology which predicts /line{lambda}_b sqrt{Z_w Z_{V_i}}, where Zw and Z_{V_i} are, respectively, the near-wall length scales in Rayleighnard convection (RBC) and due to the advection velocity. In the combined regime, which occurs at intermediate values of C/2)4/3. At lower driving potentials, in the diffusion regime, the flux scaling is similar to that in turbulent RBC.

Schmidt's syndrome: a rare cause of puberty menorrhagia.

PubMed

Sharma, J B; Tiwari, S; Gulati, N; Sharma, S

1990-12-01

Schmidt's syndrome, also known as polyglandular deficiency syndrome, is the presence of Addison's disease and hypothyrodism in a single patient. It is usually associated with other autoimmune disorders like vitiligo, diabetes mellitus, myasthenia gravis. A rare case of an 18-year-old girl having Schmidt's syndrome and vitiligo who presented with puberty menorrhagia is reported. A brief review of the literature is also given.

A proposed physical analog for a quantum probability amplitude

NASA Astrophysics Data System (ADS)

Boyd, Jeffrey

What is the physical analog of a probability amplitude? All quantum mathematics, including quantum information, is built on amplitudes. Every other science uses probabilities; QM alone uses their square root. Why? This question has been asked for a century, but no one previously has proposed an answer. We will present cylindrical helices moving toward a particle source, which particles follow backwards. Consider Feynman's book QED. He speaks of amplitudes moving through space like the hand of a spinning clock. His hand is a complex vector. It traces a cylindrical helix in Cartesian space. The Theory of Elementary Waves changes direction so Feynman's clock faces move toward the particle source. Particles follow amplitudes (quantum waves) backwards. This contradicts wave particle duality. We will present empirical evidence that wave particle duality is wrong about the direction of particles versus waves. This involves a paradigm shift; which are always controversial. We believe that our model is the ONLY proposal ever made for the physical foundations of probability amplitudes. We will show that our ``probability amplitudes'' in physical nature form a Hilbert vector space with adjoints, an inner product and support both linear algebra and Dirac notation.

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.

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.

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.

Systematic dimensionality reduction for continuous-time quantum walks of interacting fermions

NASA Astrophysics Data System (ADS)

Izaac, J. A.; Wang, J. B.

2017-09-01

To extend the continuous-time quantum walk (CTQW) to simulate P distinguishable particles on a graph G composed of N vertices, the Hamiltonian of the system is expanded to act on an NP-dimensional Hilbert space, in effect, simulating the multiparticle CTQW on graph G via a single-particle CTQW propagating on the Cartesian graph product G□P. The properties of the Cartesian graph product have been well studied, and classical simulation of multiparticle CTQWs are common in the literature. However, the above approach is generally applied as is when simulating indistinguishable particles, with the particle statistics then applied to the propagated NP state vector to determine walker probabilities. We address the following question: How can we modify the underlying graph structure G□P in order to simulate multiple interacting fermionic CTQWs with a reduction in the size of the state space? In this paper, we present an algorithm for systematically removing "redundant" and forbidden quantum states from consideration, which provides a significant reduction in the effective dimension of the Hilbert space of the fermionic CTQW. As a result, as the number of interacting fermions in the system increases, the classical computational resources required no longer increases exponentially for fixed N .

Gram-Schmidt algorithms for covariance propagation

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1977-01-01

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Gram-Schmidt algorithms for covariance propagation

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1975-01-01

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Representation of the contextual statistical model by hyperbolic amplitudes

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

Khrennikov, Andrei

We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. Wemore » also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy.« less

Representation of the contextual statistical model by hyperbolic amplitudes

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2005-06-01

We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. We also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy.

Introducing the Qplex: a novel arena for quantum theory

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Fuchs, Christopher A.; Stacey, Blake C.; Zhu, Huangjun

2017-07-01

We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, "Unperformed experiments have no results." The tools of quantum information theory, and in particular the symmetric informationally complete (SIC) measurements, provide a concise expression of how exactly Peres's dictum holds true. That expression is a constraint on how the probability distributions for outcomes of different, hypothetical and mutually exclusive experiments ought to mesh together, a type of constraint not foreseen in classical thinking. Taking this as our foundational principle, we show how to reconstruct the formalism of quantum theory in finite-dimensional Hilbert spaces. The central variety of mathematical entity in our reconstruction is the qplex, a very particular type of subset of a probability simplex. Along the way, by closely studying the symmetry properties of qplexes, we derive a condition for the existence of a d-dimensional SIC.

Measurements and mathematical formalism of quantum mechanics

NASA Astrophysics Data System (ADS)

Slavnov, D. A.

2007-03-01

A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.

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.

A Comparison of the Glass Meta-Analytic Technique with the Hunter-Schmidt Meta-Analytic Technique on Three Studies from the Education Literature.

ERIC Educational Resources Information Center

Hough, Susan L.; Hall, Bruce W.

The meta-analytic techniques of G. V. Glass (1976) and J. E. Hunter and F. L. Schmidt (1977) were compared through their application to three meta-analytic studies from education literature. The following hypotheses were explored: (1) the overall mean effect size would be larger in a Hunter-Schmidt meta-analysis (HSMA) than in a Glass…

Development of Targeted Therapeutic Agents for Botulism

DTIC Science & Technology

2001-02-01

peptides previously prepared by Schmidt & Bostian (1997) [where changes were made to a C-terminal 17-mer (187-203) of SNAP-25], attention was focussed here...arrest of intoxication with inhibitors (being prepared 8 successfully by Dr. J. Schmidt at USAMRIID; Schmidt et al., 1998) whilst replenshing the toxic...purified on the immobilised immunogen. Urografin (Schering Healthcare, G.D.R.), digitonin (Novabiochem, U.K.), radio -immunoassay (RIA) kit for human growth

A novel lobster-eye imaging system based on Schmidt-type objective for X-ray-backscattering inspection

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

Xu, Jie; Wang, Xin, E-mail: wangx@tongji.edu.cn, E-mail: mubz@tongji.edu.cn; Zhan, Qi

This paper presents a novel lobster-eye imaging system for X-ray-backscattering inspection. The system was designed by modifying the Schmidt geometry into a treble-lens structure in order to reduce the resolution difference between the vertical and horizontal directions, as indicated by ray-tracing simulations. The lobster-eye X-ray imaging system is capable of operating over a wide range of photon energies up to 100 keV. In addition, the optics of the lobster-eye X-ray imaging system was tested to verify that they meet the requirements. X-ray-backscattering imaging experiments were performed in which T-shaped polymethyl-methacrylate objects were imaged by the lobster-eye X-ray imaging system basedmore » on both the double-lens and treble-lens Schmidt objectives. The results show similar resolution of the treble-lens Schmidt objective in both the vertical and horizontal directions. Moreover, imaging experiments were performed using a second treble-lens Schmidt objective with higher resolution. The results show that for a field of view of over 200 mm and with a 500 mm object distance, this lobster-eye X-ray imaging system based on a treble-lens Schmidt objective offers a spatial resolution of approximately 3 mm.« less

A novel lobster-eye imaging system based on Schmidt-type objective for X-ray-backscattering inspection

NASA Astrophysics Data System (ADS)

Xu, Jie; Wang, Xin; Zhan, Qi; Huang, Shengling; Chen, Yifan; Mu, Baozhong

2016-07-01

This paper presents a novel lobster-eye imaging system for X-ray-backscattering inspection. The system was designed by modifying the Schmidt geometry into a treble-lens structure in order to reduce the resolution difference between the vertical and horizontal directions, as indicated by ray-tracing simulations. The lobster-eye X-ray imaging system is capable of operating over a wide range of photon energies up to 100 keV. In addition, the optics of the lobster-eye X-ray imaging system was tested to verify that they meet the requirements. X-ray-backscattering imaging experiments were performed in which T-shaped polymethyl-methacrylate objects were imaged by the lobster-eye X-ray imaging system based on both the double-lens and treble-lens Schmidt objectives. The results show similar resolution of the treble-lens Schmidt objective in both the vertical and horizontal directions. Moreover, imaging experiments were performed using a second treble-lens Schmidt objective with higher resolution. The results show that for a field of view of over 200 mm and with a 500 mm object distance, this lobster-eye X-ray imaging system based on a treble-lens Schmidt objective offers a spatial resolution of approximately 3 mm.

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.

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.

Collaborative Oceanographic Research Opportunities with Schmidt Ocean Institute

NASA Astrophysics Data System (ADS)

Zykov, V.

2014-12-01

Schmidt Ocean Institute (http://www.schmidtocean.org/) was founded by Dr. Eric Schmidt and Wendy Schmidt in 2009 to support frontier oceanographic research and exploration to expand the understanding of the world's oceans through technological advancement, intelligent, data-rich observation and analysis, and open sharing of information. Schmidt Ocean Institute operates a state-of-the-art globally capable research vessel Falkor (http://www.schmidtocean.org/story/show/47). After two years of scientific operations in the Atlantic Ocean, Gulf of Mexico, Caribbean, Eastern and Central Pacific, R/V Falkor is now preparing to support research in the Western Pacific and Eastern Indian Oceans in 2015 and 2016. As part of the long term research program development for Schmidt Ocean Institute, we aim to identify initiatives and projects that demonstrate strong alignment with our strategic interests. We focus on scientific opportunities that highlight effective use of innovative technologies to better understand the oceans, such as, for example, research enabled with remotely operated and autonomous vehicles, acoustics, in-situ sensing, telepresence, etc. Our technology-first approach to ocean science gave rise to infrastructure development initiatives, such as the development of a new full ocean depth Hybrid Remotely Operated Vehicle, new 6000m scientific Autonomous Underwater Vehicle, live HD video streaming from the ship to YouTube, shipboard high performance supercomputing, etc. We also support projects focusing on oceanographic technology research and development onboard R/V Falkor. We provide our collaborators with access to all of R/V Falkor's facilities and instrumentation in exchange for a commitment to make the resulting scientific data openly available to the international oceanographic community. This presentation aims to expand awareness about the interests and capabilities of Schmidt Ocean Institute and R/V Falkor among our scientific audiences and further develop the network of our research collaborations. We would also like to inform interested scientists and technology developers about our program development and proposal selection processes and explain how they can participate in future collaborations with Schmidt Ocean Institute.

Acoustical Applications of the HHT Method

NASA Technical Reports Server (NTRS)

Huang, Norden E.

2003-01-01

A document discusses applications of a method based on the Huang-Hilbert transform (HHT). The method was described, without the HHT name, in Analyzing Time Series Using EMD and Hilbert Spectra (GSC-13817), NASA Tech Briefs, Vol. 24, No. 10 (October 2000), page 63. To recapitulate: The method is especially suitable for analyzing time-series data that represent nonstationary and nonlinear physical phenomena. 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.

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.

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.

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.

Deterministic and unambiguous dense coding

NASA Astrophysics Data System (ADS)

Wu, Shengjun; Cohen, Scott M.; Sun, Yuqing; Griffiths, Robert B.

2006-04-01

Optimal dense coding using a partially-entangled pure state of Schmidt rank Dmacr and a noiseless quantum channel of dimension D is studied both in the deterministic case where at most Ld messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probability τx ) Bob knows for sure that Alice sent message x , and when it fails (probability 1-τx ) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For Dmacr ⩽D a bound is obtained for Ld in terms of the largest Schmidt coefficient of the entangled state, and is compared with published results by Mozes [Phys. Rev. A71, 012311 (2005)]. For Dmacr >D it is shown that Ld is strictly less than D2 unless Dmacr is an integer multiple of D , in which case uniform (maximal) entanglement is not needed to achieve the optimal protocol. The unambiguous case is studied for Dmacr ⩽D , assuming τx>0 for a set of Dmacr D messages, and a bound is obtained for the average ⟨1/τ⟩ . A bound on the average ⟨τ⟩ requires an additional assumption of encoding by isometries (unitaries when Dmacr =D ) that are orthogonal for different messages. Both bounds are saturated when τx is a constant independent of x , by a protocol based on one-shot entanglement concentration. For Dmacr >D it is shown that (at least) D2 messages can be sent unambiguously. Whether unitary (isometric) encoding suffices for optimal protocols remains a major unanswered question, both for our work and for previous studies of dense coding using partially-entangled states, including noisy (mixed) states.

The Tactical Center of Gravity: How Useful is the Concept?

DTIC Science & Technology

1990-01-06

through the Huertgen Forest, across the Kall River, capture the town of Kommerscheidt, and then capture Schmidt. The regiment also was required to protect...south through the woods, cross country to the Kall River, to take Kommerscheidt. The 3rd Battalion was to follow the 1st Battalion and take Schmidt on...desperate struggle. The lead battalions were destroyed piecemeal by the Germans in Kommerscheidt and Schmidt and along the Kall Trail. Poor

Profile: Brian Schmidt

NASA Astrophysics Data System (ADS)

Bhathal, Ragbir

2012-02-01

Brian Schmidt was awarded the Nobel Prize for Physics in 2011 along with Saul Perlmutter and Adam Riess. He is a Fellow of the Australian Academy of Science and of the US National Academy of Sciences. Schmidt has made significant contributions in observational cosmology, supernovae, gamma-ray bursts and all-sky surveys. Ragbir Bhathal interviewed him in 2006 for the National Oral History Project on significant Australian Astronomers sponsored by the National Library of Australia. (Photos: Belinda Pratten)

Potential improvement of Schmidt-hammer exposure-age dating (SHD) of moraines in the Southern Alps, New Zealand, by application of the new electronic Schmidt-hammer (SilverSchmidt)

NASA Astrophysics Data System (ADS)

Winkler, Stefan; Corbett, David

2014-05-01

The Southern Alps of New Zealand are among the few key study sites for investigating Holocene glacier chronologies in the mid-latitudinal Southern Hemisphere. Their characteristic highly dynamic geomorphological process systems prove, however, to be a considerable challenge for all attempts to date and palaeoclimatologically interpret the existing Holocene moraines record. As a multi-proxy approach combining 10Be terrestrial cosmogenic nuclide dating (TCND) with Schmidt-hammer testing, the recently developed Schmidt-hammer exposure-age dating (SHD) has already shown its potential in this study area (cf. Winkler 2005, 2009, 2013). An electronic Schmidt-hammer (named SilverSchmidt) was introduced by the manufacturer of the original mechanical Schmidt-hammer (Proceq SA) a few years ago. It offers, in particular, facilities for much easier data processing and constitutes a major improvement and potential replacement for the mechanical Schmidt-hammer. However, its different approach to the measurement of surface hardness - based on Q-(velocity) values instead of R-(rebound) values - is a potential drawback. This difference effectively means that measurements from the two instruments are not easily interconvertible and, hence, that the instruments cannot be used interchangeably without previous comparative tests of both instruments under field conditions. Both instruments used in this comparative study were N-type models with identical impact energy of 2.207 Nm for the plunger. To compare both instruments and explore interconvertibility, parallel measurements were performed on a selected number of boulders (10 boulders per site with 5 impacts each, at least 2 sites per moraine) on moraines of homogeneous lithology but different established ages covering the entire Holocene and the Late Glacial. All moraines are located east of the Main Divide of the Southern Alps at Mueller Glacier, Tasman Glacier, and in the outer Tasman River Valley. All paired samples (n = 50) were collected so that the plunger impacts of both instruments were set close together on the rock surface (to avoid any influence of modifications to the surface by consecutive impacts on the same spot). In order to test their performance at the higher and lower end of surface hardness, similar paired sample tests were also made on the full-metal test anvil. The results of paired samples for all sites/moraines reveal that Q-/R-value pairs are closely clustered for young surfaces but more scattered for the older ones with a corresponding moderate R2 for a calculated linear trend. The greater variability of the older, weathered surfaces with greater scatter and hence higher standard deviations and broader confidence intervals has been recognised in numerous previous Schmidt-hammer studies and is elated to the effects of micro-scale lithological variability, which becomes a more pronounced influence with time exposed to subaerial weathering. But most important, Q-values and R-values are closely related and Q-values are systematically higher than R-values by c. 10 - 12 units over most of the operational range of both instruments. Linear conversion equations indicate a conversion factor in the order of + 11 units is applicable when converting R-values to Q-values. These estimates agree well with data obtained on the standard test anvil. Given the apparent interconvertibility of the two instruments, the SilverSchmidt is regarded as a potential replacement for the mechanical Schmidt hammer. This enables, moreover, continuity in study areas with existing R-value data archives. However, when comparing data sets of different age, adjustments must be made for any changes to the instrumental calibration value over time. References: Winkler, S. (2005): The 'Schmidt hammer' as a relative-age dating technique: potential and limitations of its application on Holocene moraines in Mt Cook National Park, Southern Alps, New Zealand. New Zealand Journal of Geology and Geophysics 48, 105 - 116. Winkler, S. (2009): First attempt to combine terrestrial cosmogenic nuclide (10Be) and Schmidt hammer relative-age dating: Strauchon Glacier, Southern Alps, New Zealand. Central European Journal of Geosciences 1, 274 - 290. Winkler, S. (2013): Investigation of late-Holocene moraines in the western Southern Alps, New Zealand, applying Schmidt-hammer exposure-age dating (SHD). The Holocene (online), doi: 10.1177/0959683613512169.

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

Testing the Dimension of Hilbert Spaces

NASA Astrophysics Data System (ADS)

Brunner, Nicolas; Pironio, Stefano; Acin, Antonio; Gisin, Nicolas; Méthot, André Allan; Scarani, Valerio

2008-05-01

Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describe such correlations? We introduce the concept of dimension witness to put lower bounds on d. This work represents a first step in a broader research program aiming to characterize Hilbert space dimension in various contexts related to fundamental questions and quantum information applications.

Kahn Bani Sa’ad Correctional Facility, Kahn Bani Sa’ad, Iraq

DTIC Science & Technology

2008-07-25

building (Building No. 07/03): 1. Ground floor columns were tested with a Schmidt hammer devise (measures the elastic properties or strength of...3. First floor columns – Schmidt hammer and ultrasonic tests were conducted on all the first floor columns. The test results showed the strength...Building Nos. 07/02 and 07/01): 1. Ground floor columns – Using a Schmidt hammer device, very few columns showed low strength. Further study and

Crater size estimates for large-body terrestrial impact

NASA Technical Reports Server (NTRS)

Schmidt, Robert M.; Housen, Kevin R.

1988-01-01

Calculating the effects of impacts leading to global catastrophes requires knowledge of the impact process at very large size scales. This information cannot be obtained directly but must be inferred from subscale physical simulations, numerical simulations, and scaling laws. Schmidt and Holsapple presented scaling laws based upon laboratory-scale impact experiments performed on a centrifuge (Schmidt, 1980 and Schmidt and Holsapple, 1980). These experiments were used to develop scaling laws which were among the first to include gravity dependence associated with increasing event size. At that time using the results of experiments in dry sand and in water to provide bounds on crater size, they recognized that more precise bounds on large-body impact crater formation could be obtained with additional centrifuge experiments conducted in other geological media. In that previous work, simple power-law formulae were developed to relate final crater diameter to impactor size and velocity. In addition, Schmidt (1980) and Holsapple and Schmidt (1982) recognized that the energy scaling exponent is not a universal constant but depends upon the target media. Recently, Holsapple and Schmidt (1987) includes results for non-porous materials and provides a basis for estimating crater formation kinematics and final crater size. A revised set of scaling relationships for all crater parameters of interest are presented. These include results for various target media and include the kinematics of formation. Particular attention is given to possible limits brought about by very large impactors.

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.

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.

Statistical Optics

NASA Astrophysics Data System (ADS)

Goodman, Joseph W.

2000-07-01

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research

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.

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.

Effects of roughness and permeability on solute transfer at the sediment water interface.

PubMed

Han, Xu; Fang, Hongwei; He, Guojian; Reible, Danny

2018-02-01

Understanding the mechanisms of solute transfer across the sediment-water interface plays a crucial role in water quality prediction and management. In this study, different arranged particles are used to form typical rough and permeable beds. Large Eddy Simulation (LES) is used to model the solute transfer from the overlying water to sediment beds. Three rough wall turbulence regimes, i.e., smooth, transitional and rough regime, are separately considered and the effects of bed roughness on solute transfer are quantitatively analyzed. Results show that the classic laws related to Schmidt numbers can well reflect the solute transfer under the smooth regime with small roughness Reynolds numbers. Under the transitional regime, the solute transfer coefficient (K L + ) is enhanced and the effect of Schmidt number is weakened by increasing roughness Reynolds number. Under the rough regime, the solute transfer is suppressed by the transition layer (Brinkman layer) and controlled by the bed permeability. Moreover, it is found that water depth, friction velocity and bed permeability can be used to estimate the solute transfer velocity (K L ) under the completely rough regime. Copyright © 2017 Elsevier Ltd. All rights reserved.

Himmelsfotografie MIT Schmidt-Teleskopen

NASA Astrophysics Data System (ADS)

Marx, Siegfried; Pfau, Werner

Auf dem Höhepunkt der Verbreitung und astronomischen Anwendung von Schmidt-Teleskopen legen S. Marx und W. Pfau einen reich illustrierten Bildband zu diesem Fernrohrtyp vor. Der thematische Bogen reicht von der Teleskoptechnik und ihrer Geschichte über das Leben von Berhard Schmidt bis zu den schönsten, hier in hervorragender Qualität wiedergegebenen Himmelsaufnahmen und ihrer wissenschaftlichen Interpretation. Praktische Hinweise zu eigener fotografischer Tätigkeit und ein Glossar machen das Buch nützlich für jeden Liebhaber der Himmelskunde.

The Politics of Modernizing Short-Range Nuclear Forces in West Germany

DTIC Science & Technology

1989-09-01

observers on both sides of the Atlantic would undoubtedly have shared the view of former West German chancellor Helmut Schmidt , who publicly termed the FOTL...Western observers were slow to note such trends in the SPD, in large part because of the dominant role Helmut Schmidt still played in setting official... Schmidt was faced with signifi- cant opposition from the outset and managed to keep his own party in line only by threatening to resign on several occasions

A blueprint for demonstrating quantum supremacy with superconducting qubits.

PubMed

Neill, C; Roushan, P; Kechedzhi, K; Boixo, S; Isakov, S V; Smelyanskiy, V; Megrant, A; Chiaro, B; Dunsworth, A; Arya, K; Barends, R; Burkett, B; Chen, Y; Chen, Z; Fowler, A; Foxen, B; Giustina, M; Graff, R; Jeffrey, E; Huang, T; Kelly, J; Klimov, P; Lucero, E; Mutus, J; Neeley, M; Quintana, C; Sank, D; Vainsencher, A; Wenner, J; White, T C; Neven, H; Martinis, J M

2018-04-13

A key step toward demonstrating a quantum system that can address difficult problems in physics and chemistry will be performing a computation beyond the capabilities of any classical computer, thus achieving so-called quantum supremacy. In this study, we used nine superconducting qubits to demonstrate a promising path toward quantum supremacy. By individually tuning the qubit parameters, we were able to generate thousands of distinct Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert space. As the number of qubits increases, the system continues to explore the exponentially growing number of states. Extending these results to a system of 50 qubits has the potential to address scientific questions that are beyond the capabilities of any classical computer. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Zeno subspace in quantum-walk dynamics

NASA Astrophysics Data System (ADS)

Chandrashekar, C. M.

2010-11-01

We investigate discrete-time quantum-walk evolution under the influence of periodic measurements in position subspace. The undisturbed survival probability of the particle at the position subspace P(0,t) is compared with the survival probability after frequent (n) measurements at interval τ=t/n, P(0,τ)n. We show that P(0,τ)n>P(0,t) leads to the quantum Zeno effect in position subspace when a parameter θ in the quantum coin operations and frequency of measurements is greater than the critical value, θ>θc and n>nc. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has the potential to play a significant role in quantum tasks such as preserving the quantum state of the particle at any particular position, and to understand the Zeno dynamics in a multidimensional system that is highly transient in nature.

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.

Exploration of Use of Copulas in Analysing the Relationship between Precipitation and Meteorological Drought in Beijing, China

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

Fan, Linlin; Wang, Hongrui; Wang, Cheng

Drought risk analysis is essential for regional water resource management. In this study, the probabilistic relationship between precipitation and meteorological drought in Beijing, China, was calculated under three different precipitation conditions (precipitation equal to, greater than, or less than a threshold) based on copulas. The Standardized Precipitation Evapotranspiration Index (SPEI) was calculated based on monthly total precipitation and monthly mean temperature data. The trends and variations in the SPEI were analysed using Hilbert-Huang Transform (HHT) and Mann-Kendall (MK) trend tests with a running approach. The results of the HHT and MK test indicated a significant decreasing trend in the SPEI.more » The copula-based conditional probability indicated that the probability of meteorological drought decreased as monthly precipitation increased and that 10 mm can be regarded as the threshold for triggering extreme drought. From a quantitative perspective, when R ≤ mm, the probabilities of moderate drought, severe drought, and extreme drought were 22.1%, 18%, and 13.6%, respectively. This conditional probability distribution not only revealed the occurrence of meteorological drought in Beijing but also provided a quantitative way to analyse the probability of drought under different precipitation conditions. Furthermore, the results provide a useful reference for future drought prediction.« less

Exploration of Use of Copulas in Analysing the Relationship between Precipitation and Meteorological Drought in Beijing, China

DOE PAGES

Fan, Linlin; Wang, Hongrui; Wang, Cheng; ...

2017-05-16

Drought risk analysis is essential for regional water resource management. In this study, the probabilistic relationship between precipitation and meteorological drought in Beijing, China, was calculated under three different precipitation conditions (precipitation equal to, greater than, or less than a threshold) based on copulas. The Standardized Precipitation Evapotranspiration Index (SPEI) was calculated based on monthly total precipitation and monthly mean temperature data. The trends and variations in the SPEI were analysed using Hilbert-Huang Transform (HHT) and Mann-Kendall (MK) trend tests with a running approach. The results of the HHT and MK test indicated a significant decreasing trend in the SPEI.more » The copula-based conditional probability indicated that the probability of meteorological drought decreased as monthly precipitation increased and that 10 mm can be regarded as the threshold for triggering extreme drought. From a quantitative perspective, when R ≤ mm, the probabilities of moderate drought, severe drought, and extreme drought were 22.1%, 18%, and 13.6%, respectively. This conditional probability distribution not only revealed the occurrence of meteorological drought in Beijing but also provided a quantitative way to analyse the probability of drought under different precipitation conditions. Furthermore, the results provide a useful reference for future drought prediction.« less

A systematic revision of Operclipygus Marseul (Coleoptera, Histeridae, Exosternini)

PubMed Central

Caterino, Michael S.; Tishechkin, Alexey K.

2013-01-01

Abstract We revise the large Neotropical genus Operclipygus Marseul, in the histerid tribe Exosternini (Histeridae: Histerinae). We synonymize 3 species, move 14 species from other genera, sink the genus Tribalister Horn into Operclipygus, and describe 138 species as new, bringing the total to 177 species of Operclipygus. Keys are provided for the identification of all species, and the majority of the species are illustrated by habitus and male genitalia illustrations. The species are diverse throughout tropical South and Central America, with only a few species extending into the temperate parts of North America. The majority of species can be recognized by the presence of a distinct stria or sulcus along the apical margin of the pygidium, though it is not exclusive to the genus. Natural history details for species of Operclipygus are scant, as most specimens have been collected through the use of passive flight interception traps. Many are probably generally associated with decaying vegetation and leaf litter, where they prey on small arthropods. But a small proportion are known inquilines, with social insects such as ants and termites, and also with some burrowing mammals, such as Ctenomys Blainville. The genus now includes the following species groups and species: Operclipygus sulcistrius group [Operclipygus lucanoides sp. n., Operclipygus schmidti sp. n., Operclipygus simplistrius sp. n., Operclipygus sulcistrius Marseul, 1870], Operclipygus mirabilis group [Operclipygus mirabilis (Wenzel & Dybas, 1941) comb. n., Operclipygus pustulifer sp. n., Operclipygus plaumanni sp. n., Operclipygus sinuatus sp. n., Operclipygus mutuca sp. n., Operclipygus carinistrius (Lewis, 1908) comb. n., Operclipygus parensis sp. n., Operclipygus schlingeri sp. n.], Operclipygus kerga group [Operclipygus kerga (Marseul, 1870), Operclipygus planifrons sp. n., Operclipygus punctistrius sp. n.], Operclipygus conquisitus group [Operclipygus bicolor sp. n., Operclipygus conquisitus (Lewis, 1902), Operclipygus friburgius (Marseul, 1864)], Operclipygus impuncticollis group [Operclipygus bickhardti sp. n., Operclipygus britannicus sp. n., Operclipygus impuncticollis (Hinton, 1935)], Operclipygus panamensis group [Operclipygus crenatus (Lewis, 1888), Operclipygus panamensis (Wenzel & Dybas, 1941)], Operclipygus sejunctus group [Operclipygus depressus (Hinton, 1935), Operclipygus itoupe sp. n., Operclipygus juninensis sp. n., Operclipygus pecki sp. n., Operclipygus punctiventer sp. n., Operclipygus sejunctus (Schmidt, 1896) comb. n., Operclipygus setiventrissp. n.], Operclipygus mortavis group [Operclipygus ecitonis sp. n., Operclipygus mortavis sp. n., Operclipygus paraguensis sp. n.], Operclipygus dytiscoides group [Operclipygus carinisternus sp. n., Operclipygus crenulatus sp. n., Operclipygus dytiscoides sp. n., Operclipygus quadratus sp. n.], Operclipygus dubitabilis group [Operclipygus dubitabilis (Marseul, 1889), Operclipygus yasuni sp. n.], Operclipygus angulifer group [Operclipygus angulifer sp. n., Operclipygus impressifrons sp. n.], Operclipygus dubius group [Operclipygus andinus sp. n., Operclipygus dubius (Lewis, 1888), Operclipygus extraneus sp. n., Operclipygus intermissus sp. n., Operclipygus lunulus sp. n., Operclipygus occultus sp. n., Operclipygus perplexus sp. n., Operclipygus remotus sp. n., Operclipygus validus sp. n., Operclipygus variabilis sp. n.], Operclipygus hospes group [Operclipygus assimilis sp. n., Operclipygus belemensis sp. n., Operclipygus bulbistoma sp. n., Operclipygus callifrons sp. n., Operclipygus colombicus sp. n., Operclipygus communis sp. n., Operclipygus confertus sp. n., Operclipygus confluens sp. n., Operclipygus curtistrius sp. n., Operclipygus diffluens sp. n., Operclipygus fusistrius sp. n., Operclipygus gratus sp. n., Operclipygus hospes (Lewis, 1902), Operclipygus ibiscus sp. n., Operclipygus ignifer sp. n., Operclipygus impositus sp. n., Operclipygus incisus sp. n., Operclipygus innocuus sp. n., Operclipygus inquilinus sp. n., Operclipygus minutus sp. n., Operclipygus novateutoniae sp. n., Operclipygus praecinctus sp. n., Operclipygus prominens sp. n., Operclipygus rileyi sp. n., Operclipygus subterraneus sp. n., Operclipygus tenuis sp. n., Operclipygus tiputinus sp. n.], Operclipygus farctus group [Operclipygus atlanticus sp. n., Operclipygus bidessois (Marseul, 1889), Operclipygus distinctus (Hinton, 1935), Operclipygus distractus (Schmidt, 1896) comb. n., Operclipygus farctissimus sp. n., Operclipygus farctus (Marseul, 1864), Operclipygus gilli sp. n., Operclipygus impressistrius sp. n., Operclipygus inflatus sp. n., Operclipygus latemarginatus (Bickhardt, 1920) comb. n., Operclipygus petrovi sp. n., Operclipygus plicatus (Hinton, 1935) comb. n., Operclipygus prolixus sp. n., Operclipygus punctifrons sp. n., Operclipygus proximus sp. n., Operclipygus subrufus sp. n.], Operclipygus hirsutipes group [Operclipygus guianensis sp. n., Operclipygus hirsutipes sp. n.], Operclipygus hamistrius group [Operclipygus arquus sp. n., Operclipygus campbelli sp. n., Operclipygus chiapensis sp. n., Operclipygus dybasi sp. n., Operclipygus geometricus (Casey, 1893) comb. n., Operclipygus hamistrius (Schmidt, 1893) comb. n., Operclipygus impressicollis sp. n., Operclipygus intersectus sp. n., Operclipygus montanus sp. n., Operclipygus nubosus sp. n., Operclipygus pichinchensis sp. n., Operclipygus propinquus sp. n., Operclipygus quinquestriatus sp. n., Operclipygus rubidus (Hinton, 1935) comb. n., Operclipygus rufescens sp. n., Operclipygus troglodytes sp. n.], Operclipygus plicicollis group [Operclipygus cephalicus sp. n., Operclipygus longidens sp. n., Operclipygus plicicollis (Schmidt, 1893)], Operclipygus fossipygus group [Operclipygus disconnectus sp. n., Operclipygus fossipygus (Wenzel, 1944), Operclipygus foveipygus (Bickhardt, 1918), Operclipygus fungicolus (Wenzel & Dybas, 1941), Operclipygus gibbulus (Schmidt, 1889) comb. n., Operclipygus olivensis sp. n., Operclipygus simplicipygus sp. n., Operclipygus subdepressus (Schmidt, 1889), Operclipygus therondi (Wenzel, 1976)], Operclipygus impunctipennis group [Operclipygus chamelensis sp. n., Operclipygus foveiventris sp. n., Operclipygus granulipectus sp. n., Operclipygus impunctipennis (Hinton, 1935) comb. n., Operclipygus latifoveatus sp. n., Operclipygus lissipygus sp. n., Operclipygus maesi sp. n., Operclipygus mangiferus sp. n., Operclipygus marginipennis sp. n., Operclipygus nicodemus sp. n., Operclipygus nitidus sp. n., Operclipygus pacificus sp. n., Operclipygus pauperculus sp. n., Operclipygus punctissipygus sp. n., Operclipygus subviridis sp. n., Operclipygus tripartitus sp. n., Operclipygus vorax sp. n.], Operclipygus marginellus group [Operclipygus ashei sp. n., Operclipygus baylessae sp. n., Operclipygus dentatus sp. n., Operclipygus formicatus sp. n., Operclipygus hintoni sp. n., Operclipygus marginellus (J.E. LeConte, 1860) comb. n., Operclipygus orchidophilus sp. n., Operclipygus selvorum sp. n., Operclipygus striatellus (Fall, 1917) comb. n.], incertae sedis: O. teapensis (Marseul, 1853) comb. n., Operclipygus punctulatus sp. n., Operclipygus lama Mazur, 1988, Operclipygus florifaunensis sp. n., Operclipygus bosquesecus sp. n., Operclipygus arnaudi Dégallier, 1982, Operclipygus subsphaericus sp. n., Operclipygus latipygus sp. n., Operclipygus elongatus sp. n., Operclipygus rupicolus sp. n., Operclipygus punctipleurus sp. n., Operclipygus falini sp. n., Operclipygus peregrinus sp. n., Operclipygus brooksi sp. n., Operclipygus profundipygus sp. n., Operclipygus punctatissimus sp. n., Operclipygus cavisternus sp. n., Operclipygus siluriformis sp. n., Operclipygus parallelus sp. n., Operclipygus abbreviatus sp. n., Operclipygus pygidialis (Lewis, 1908), Operclipygus faltistrius sp. n., Operclipygus limonensis sp. n., Operclipygus wenzeli sp. n., Operclipygus iheringi (Bickhardt, 1917), Operclipygus angustisternus (Wenzel, 1944), Operclipygus shorti sp. n. We establish the following synonymies: Phelisteroides miladae Wenzel & Dybas, 1941 and Pseudister propygidialis Hinton, 1935e = Operclipygus crenatus (Lewis, 1888); Phelister subplicatus Schmidt, 1893b = Operclipygus bidessois (Marseul, 1889). We designate lectotypes for Operclipygus sulcistrius Marseul, 1870, Phelister carinistrius Lewis, 1908, Phelister kerga Marseul, 1870, Phelister friburgius Marseul, 1864, Phelister impuncticollis Hinton, 1935, Phelister crenatus Lewis, 1888, Phelister sejunctus Schmidt, 1896, Pseudister depressus Hinton, 1935, Epierus dubius Lewis, 1888, Phelister hospes Lewis, 1902, Phelister farctus Marseul, 1864, Phelister bidessois Marseul, 1889, Phelister subplicatus Schmidt, 1893, Phelister plicatus Hinton, 1935, Phelister distinctus Hinton, 1935, Phelister distractus Schmidt, 1896, Pseudister latemarginatus Bickhardt, 1920, Phelister hamistrius Schmidt, 1893, Phelister plicicollis Schmidt, 1893, Phelister gibbulus Schmidt, 1889, Phelister subdepressus Schmidt, 1889, Phelister teapensis Marseul, 1853, Phelister pygidialis Lewis, 1908, Phelister iheringi Bickhardt, 1917, and Phelister marginellus J.E. LeConte 1860. We designate a neotype for Operclipygus conquisitus Lewis, replacing its lost type specimen. PMID:23717185

Noise effects on entanglement distribution by separable state

NASA Astrophysics Data System (ADS)

Bordbar, Najmeh Tabe; Memarzadeh, Laleh

2018-02-01

We investigate noise effects on the performance of entanglement distribution by separable state. We consider a realistic situation in which the mediating particle between two distant nodes of the network goes through a noisy channel. For a large class of noise models, we show that the average value of distributed entanglement between two parties is equal to entanglement between particular bipartite partitions of target qubits and exchange qubit in intermediate steps of the protocol. This result is valid for distributing two-qubit/qudit and three-qubit entangled states. In explicit examples of the noise family, we show that there exists a critical value of noise parameter beyond which distribution of distillable entanglement is not possible. Furthermore, we determine how this critical value increases in terms of Hilbert space dimension, when distributing d-dimensional Bell states.

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'.

Airgun inter-pulse noise field during a seismic survey in an Arctic ultra shallow marine environment.

PubMed

Guan, Shane; Vignola, Joseph; Judge, John; Turo, Diego

2015-12-01

Offshore oil and gas exploration using seismic airguns generates intense underwater pulses that could cause marine mammal hearing impairment and/or behavioral disturbances. However, few studies have investigated the resulting multipath propagation and reverberation from airgun pulses. This research uses continuous acoustic recordings collected in the Arctic during a low-level open-water shallow marine seismic survey, to measure noise levels between airgun pulses. Two methods were used to quantify noise levels during these inter-pulse intervals. The first, based on calculating the root-mean-square sound pressure level in various sub-intervals, is referred to as the increment computation method, and the second, which employs the Hilbert transform to calculate instantaneous acoustic amplitudes, is referred to as the Hilbert transform method. Analyses using both methods yield similar results, showing that the inter-pulse sound field exceeds ambient noise levels by as much as 9 dB during relatively quiet conditions. Inter-pulse noise levels are also related to the source distance, probably due to the higher reverberant conditions of the very shallow water environment. These methods can be used to quantify acoustic environment impacts from anthropogenic transient noises (e.g., seismic pulses, impact pile driving, and sonar pings) and to address potential acoustic masking affecting marine mammals.

Online Pairwise Learning Algorithms.

PubMed

Ying, Yiming; Zhou, Ding-Xuan

2016-04-01

Pairwise learning usually refers to a learning task that involves a loss function depending on pairs of examples, among which the most notable ones are bipartite ranking, metric learning, and AUC maximization. In this letter we study an online algorithm for pairwise learning with a least-square loss function in an unconstrained setting of a reproducing kernel Hilbert space (RKHS) that we refer to as the Online Pairwise lEaRning Algorithm (OPERA). In contrast to existing works (Kar, Sriperumbudur, Jain, & Karnick, 2013 ; Wang, Khardon, Pechyony, & Jones, 2012 ), which require that the iterates are restricted to a bounded domain or the loss function is strongly convex, OPERA is associated with a non-strongly convex objective function and learns the target function in an unconstrained RKHS. Specifically, we establish a general theorem that guarantees the almost sure convergence for the last iterate of OPERA without any assumptions on the underlying distribution. Explicit convergence rates are derived under the condition of polynomially decaying step sizes. We also establish an interesting property for a family of widely used kernels in the setting of pairwise learning and illustrate the convergence results using such kernels. Our methodology mainly depends on the characterization of RKHSs using its associated integral operators and probability inequalities for random variables with values in a Hilbert space.

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'.

Documentation for the machine-readable version of A Finding List of Stars of Spectral Type F2 and Earlier in a North Galactic Pole Region

NASA Technical Reports Server (NTRS)

Warren, W. H., Jr.

1982-01-01

The machine-readable data set is the result of an objective-prism survey made with an 80 cm/120 cm Schmidt telescope. The F2 and earlier stars were isolated from later type objects by using the MK classification criteria. The catalog contains 601 stars and includes cross identifications to the BD and HD catalogs, coordinates, photographic magnitudes and spectral types. A separate file contains the remarks from the original data tables merged with those following the data. The machine-readable files are described.

Human telomerase: biogenesis, trafficking, recruitment, and activation.

PubMed

Schmidt, Jens C; Cech, Thomas R

2015-06-01

Telomerase is the ribonucleoprotein enzyme that catalyzes the extension of telomeric DNA in eukaryotes. Recent work has begun to reveal key aspects of the assembly of the human telomerase complex, its intracellular trafficking involving Cajal bodies, and its recruitment to telomeres. Once telomerase has been recruited to the telomere, it appears to undergo a separate activation step, which may include an increase in its repeat addition processivity. This review covers human telomerase biogenesis, trafficking, and activation, comparing key aspects with the analogous events in other species. © 2015 Schmidt and Cech Published by Cold Spring Harbor Laboratory Press.

Measuring qutrit-qutrit entanglement of orbital angular momentum states of an atomic ensemble and a photon.

PubMed

Inoue, R; Yonehara, T; Miyamoto, Y; Koashi, M; Kozuma, M

2009-09-11

Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result confirms that the density matrix cannot be decomposed into an ensemble of pure states of Schmidt rank 1 or 2. That is, the Schmidt number of the density matrix must be equal to or greater than 3.

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.

Beacons in Time: Maarten Schmidt and the Discovery of Quasars.

ERIC Educational Resources Information Center

Preston, Richard

1988-01-01

Tells the story of Maarten Schmidt and the discovery of quasars. Discusses the decomposition of light, crucial observations and solving astronomical mysteries. Describes spectroscopic analysis used in astronomy and its application to quasars. (CW)

Cryogenic solid Schmidt camera as a base for future wide-field IR systems

NASA Astrophysics Data System (ADS)

Yudin, Alexey N.

2011-11-01

Work is focused on study of capability of solid Schmidt camera to serve as a wide-field infrared lens for aircraft system with whole sphere coverage, working in 8-14 um spectral range, coupled with spherical focal array of megapixel class. Designs of 16 mm f/0.2 lens with 60 and 90 degrees sensor diagonal are presented, their image quality is compared with conventional solid design. Achromatic design with significantly improved performance, containing enclosed soft correcting lens behind protective front lens is proposed. One of the main goals of the work is to estimate benefits from curved detector arrays in 8-14 um spectral range wide-field systems. Coupling of photodetector with solid Schmidt camera by means of frustrated total internal reflection is considered, with corresponding tolerance analysis. The whole lens, except front element, is considered to be cryogenic, with solid Schmidt unit to be flown by hydrogen for improvement of bulk transmission.

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.

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.

Deterministic joint remote preparation of an equatorial hybrid state via high-dimensional Einstein-Podolsky-Rosen pairs: active versus passive receiver

NASA Astrophysics Data System (ADS)

Bich, Cao Thi; Dat, Le Thanh; Van Hop, Nguyen; An, Nguyen Ba

2018-04-01

Entanglement plays a vital and in many cases non-replaceable role in the quantum network communication. Here, we propose two new protocols to jointly and remotely prepare a special so-called bipartite equatorial state which is hybrid in the sense that it entangles two Hilbert spaces with arbitrary different dimensions D and N (i.e., a type of entanglement between a quDit and a quNit). The quantum channels required to do that are however not necessarily hybrid. In fact, we utilize four high-dimensional Einstein-Podolsky-Rosen pairs, two of which are quDit-quDit entanglements, while the other two are quNit-quNit ones. In the first protocol the receiver has to be involved actively in the process of remote state preparation, while in the second protocol the receiver is passive as he/she needs to participate only in the final step for reconstructing the target hybrid state. Each protocol meets a specific circumstance that may be encountered in practice and both can be performed with unit success probability. Moreover, the concerned equatorial hybrid entangled state can also be jointly prepared for two receivers at two separated locations by slightly modifying the initial particles' distribution, thereby establishing between them an entangled channel ready for a later use.

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.

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.

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}).

Positions of Asteroids Obtained with the GPO Telescope at ESO, Chile and with the Kvistaberg Schmidt Telescope

NASA Astrophysics Data System (ADS)

Lagerkvist, C.-I.; Olofsson, K.; From, A.; Hammarback, G.; Magnusson, P.; Morell, O.

1985-01-01

In this paper we present 101 positions of asteroids obtained during Augnst 1982 with the GPO astrograph at ESO, Chile and with the Kvistaberg Schmidt telescope during September 1979 and February 1981.

Wash-away of contaminant downstream of a backward-facing step over a range of Schmidt number

NASA Astrophysics Data System (ADS)

Min, Hannah; Fischer, Paul F.; Pearlstein, Arne J.

2017-11-01

We report computations of two-dimensional unsteady convective mass transfer in flow over a backward-facing step, in which a contaminant initially present downstream of the step is ``washed away''. Results are presented for a range of Schmidt numbers, showing how the recirculation region downstream of the step not only serves to retain contaminant near the step, but also transports contaminant upstream towards the step. The results for the highest Schmidt number considered (2650) are relevant to wash-away of low-molecular weight species in liquids, for which some implications are discussed.

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.

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.

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

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.

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.

Orientation in birds. The sun compass.

PubMed

Schmidt-Koenig, K; Ganzhorn, J U; Ranvaud, R

1991-01-01

The sun compass was discovered by G. Kramer in caged birds showing migratory restlessness. Subsequent experiments with caged birds employing directional training and clock shifts, carried out by Hoffman and Schmidt-Koenig, showed that the sun azimuth is used, and the sun altitude ignored. In the laboratory, McDonald found the accuracy to be +/- 3 degrees(-)+/- 5 degrees. According to Hoffmann and Schmidt-Koenig, caged birds trained at medium northern latitudes were able to allow for the sun's apparent movement north of the arctic circle, but not in equatorial and trans-equatorial latitudes. In homing experiments, and employing clock shifts, Schmidt-Koenig demonstrated that the sun compass is used by homing pigeons during initial orientation. This finding is the principal evidence for the existence of a map-and-compass navigational system. Pigeons living in equatorial latitudes utilize the sun compass even under the extreme solar conditions of equinox, achieving angular resolution of about 3 degrees in homing experiments. According to preliminary analyses, the homing pigeons' ephemerides are retarded by several weeks (Ranvaud, Schmidt-Koenig, Ganzhorn et al.).

Extending the length and time scales of Gram-Schmidt Lyapunov vector computations

NASA Astrophysics Data System (ADS)

Costa, Anthony B.; Green, Jason R.

2013-08-01

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram-Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N2 (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram-Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard-Jones fluids from N=100 to 1300 between Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram-Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.

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.

A robotic reflective Schmidt telescope for Dome C

NASA Astrophysics Data System (ADS)

Strassmeier, K. G.; Andersen, M. I.; Steinbach, M.

2004-10-01

This paper lays out a wide-field robotic Schmidt telescope (RST) for the Antarctic site Dome C. The telescope is based on 80/120cm reflective Schmidt optics, built originally for a space project, and a mosaic of four 7.5k×7.5k 8-μm thinned CCDs from the PEPSI/LBT wafer run. The telescope's total field of view (FOV) would be 5o circular (minimum 3o× 3o square) with a plate scale of 0.7 arcsec per pixel. Limiting magnitude is expected to be V=21.5mag in 60 sec for a field of 9 square degrees.

VizieR Online Data Catalog: The USNO-B1.0 Catalog (Monet+ 2003)

NASA Astrophysics Data System (ADS)

Monet, D. G.; Levine, S. E.; Casian, B.; et al.

2002-11-01

The USNO-B1.0 is a catalog that presents positions, proper motions, magnitudes in various optical passbands, and star/galaxy estimators for 1,045,913,669 objects derived from 3,648,832,040 separate observations. The data were taken from scans of 7,435 Schmidt plates taken from various sky surveys during the last 50 years. The catalog is expected to be complete down to V=21; the estimated accuracies are 0.2arcsec for the positions at J2000, 0.3mag in up to 5 colors, and 85% accuracy for distinguishing stars from non-stellar objects. (1 data file).

Quantum finance

NASA Astrophysics Data System (ADS)

Schaden, Martin

2002-12-01

Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding securities and cash is taken as the basis of the Hilbert space of market states. The temporal evolution of an isolated market is unitary in this space. Linear operators representing basic financial transactions such as cash transfer and the buying or selling of securities are constructed and simple model Hamiltonians that generate the temporal evolution due to cash flows and the trading of securities are proposed. The Hamiltonian describing financial transactions becomes local when the profit/loss from trading is small compared to the turnover. This approximation may describe a highly liquid and efficient stock market. The lognormal probability distribution for the price of a stock with a variance that is proportional to the elapsed time is reproduced for an equilibrium market. The asymptotic volatility of a stock in this case is related to the long-term probability that it is traded.

Optimum quantum receiver for detecting weak signals in PAM communication systems

NASA Astrophysics Data System (ADS)

Sharma, Navneet; Rawat, Tarun Kumar; Parthasarathy, Harish; Gautam, Kumar

2017-09-01

This paper deals with the modeling of an optimum quantum receiver for pulse amplitude modulator (PAM) communication systems. The information bearing sequence {I_k}_{k=0}^{N-1} is estimated using the maximum likelihood (ML) method. The ML method is based on quantum mechanical measurements of an observable X in the Hilbert space of the quantum system at discrete times, when the Hamiltonian of the system is perturbed by an operator obtained by modulating a potential V with a PAM signal derived from the information bearing sequence {I_k}_{k=0}^{N-1}. The measurement process at each time instant causes collapse of the system state to an observable eigenstate. All probabilities of getting different outcomes from an observable are calculated using the perturbed evolution operator combined with the collapse postulate. For given probability densities, calculation of the mean square error evaluates the performance of the receiver. Finally, we present an example involving estimating an information bearing sequence that modulates a quantum electromagnetic field incident on a quantum harmonic oscillator.

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.

Fisher metric, geometric entanglement, and spin networks

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Mele, Fabio M.; Oriti, Daniele; Vitale, Patrizia

2018-02-01

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of nonlocal correlations between two nonadjacent regions of a generic spin network graph characterized by the bipartite unfolding of an intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and nonlocal level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.

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

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.

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.

Moral Injury in Military Operations: A Review of the Literature and Key Considerations for the Canadian Armed Forces

DTIC Science & Technology

2015-03-01

Heekeren, Wartenburger, Schmidt, Prehn , Schwintowski, & Villringer 2005; Jones, 1991; Kagan, 2001; Velasuez & Rostankowski, 1985). Our moral foundation...Business Ethics Quarterly, 21(4), 555-578. Heekeren, H. R., Wartenburger, I., Schmidt, H., Prehn , K., Schwintowski, H. P., & Villringer, A. (2005

Clinical Reasoning Skills of Speech and Language Therapy Students

ERIC Educational Resources Information Center

Hoben, Kirsty; Varley, Rosemary; Cox, Richard

2007-01-01

Background: Difficulties experienced by novices in clinical reasoning have been well documented in many professions, especially medicine (Boshuizen and Schmidt 1992, 2000; Elstein, Shulman and Sprafka 1978; Patel and Groen 1986; Rikers, Loyens and Schmidt 2004). These studies have shown that novice clinicians have difficulties with both knowledge…

Golf Instruction. An Application of Schmidt's Generalized Motor Program.

ERIC Educational Resources Information Center

Asbell, Ann C.

1989-01-01

This article describes how application of the generalized motor program, conceptualized by Schmidt, can yield consistent and effective results when teaching students the golf swing. Specific teaching suggestions are given and a brief discussion of the applicability of this program to tennis and swimming is included. (JAH)

Laboratory and numerical simulation of internal wave attractors and their instability.

NASA Astrophysics Data System (ADS)

Brouzet, Christophe; Dauxois, Thierry; Ermanyuk, Evgeny; Joubaud, Sylvain; Sibgatullin, Ilias

2015-04-01

Internal wave attractors are formed as result of focusing of internal gravity waves in a confined domain of stably stratified fluid due to peculiarities of reflections properties [1]. The energy injected into domain due to external perturbation, is concentrated along the path formed by the attractor. The existence of attractors was predicted theoretically and proved both experimentally and numerically [1-4]. Dynamics of attractors is greatly influenced by geometrical focusing, viscous dissipation and nonlinearity. The experimental setup features Schmidt number equal to 700 which impose constraints on resolution in numerical schemes. Also for investigation of stability on large time intervals (about 1000 periods of external forcing) numerical viscosity may have significant impact. For these reasons, we have chosen spectral element method for investigation of this problem, what allows to carefully follow the nonlinear dynamics. We present cross-comparison of experimental observations and numerical simulations of long-term behavior of wave attractors. Fourier analysis and subsequent application of Hilbert transform are used for filtering of spatial components of internal-wave field [5]. The observed dynamics shows a complicated coupling between the effects of local instability and global confinement of the fluid domain. The unstable attractor is shown to act as highly efficient mixing box providing the efficient energy pathway from global-scale excitation to small-scale wave motions and mixing. Acknowledgement, IS has been partially supported by Russian Ministry of Education and Science (agreement id RFMEFI60714X0090) and Russian Foundation for Basic Research, grant N 15-01-06363. EVE gratefully acknowledges his appointment as a Marie Curie incoming fellow at Laboratoire de physique ENS de Lyon. This work has been partially supported by the ONLITUR grant (ANR-2011-BS04-006-01) and achieved thanks to the resources of PSMN from ENS de Lyon 1. Maas, L. R. M. & Lam, F.-P. A., Geometric focusing of internal waves. J. Fluid Mech, 1995,. 300, 1-41 L. R. M. Maas, D. Benielli, J. Sommeria, and F.-P. A. Lam, Nature (London) 388, 557 (1997). 2. Dauxois, Thierry; Young, W., Journal of Fluid Mechanics, 1999, vol. 390, Issue 01, p.271-295 3. Grisouard, N., Staquet, C., Pairaud, I., 2008, Journal of Fluid Mechanics, 614, 1 4. Scolan, H., Ermanyuk, E., Dauxois, T., 2013, Physical Review Letters, 110, 234501 5. Mercier, Matthieu J.; Garnier, Nicolas B.; Dauxois, Thierry Reflection and diffraction of internal waves analyzed with the Hilbert transform Physics of Fluids, Volume 20, Issue 8, pp. 086601-086601-10 (2008).

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.

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

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.

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.

The weakly coupled fractional one-dimensional Schrödinger operator with index 1 < α <= 2

NASA Astrophysics Data System (ADS)

Hatzinikitas, Agapitos N.

2010-12-01

Considering the space fractional Weyl operator hat{P}^{α } on the separable Hilbert space H=L^2({R},dx) we determine the asymptotic behavior of both the free Green's function and its variation with respect to energy in one dimension for bound states. Later, we specify the Birman-Schwinger representation for the Schrödinger operator hat{H}_g=K_{α }hat{P}^{α }+ghat{V} and extract the finite-rank portion which is essential for the asymptotic expansion of the ground state. Finally, we determine necessary and sufficient conditions for there to be a bound state for small coupling constant g.

Geometric multiaxial representation of N -qubit mixed symmetric separable states

NASA Astrophysics Data System (ADS)

SP, Suma; Sirsi, Swarnamala; Hegde, Subramanya; Bharath, Karthik

2017-08-01

The study of N -qubit mixed symmetric separable states is a longstanding challenging problem as no unique separability criterion exists. In this regard, we take up the N -qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer an elegant mathematical analysis since the dimension of the Hilbert space is reduced from 2N to N +1 . Since there exists a one-to-one correspondence between the spin-j system and an N -qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of the spin-density matrix. Further, we use a geometric multiaxial representation (MAR) of the density matrix to characterize the mixed symmetric separable states. Since the separability problem is NP-hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the P -distribution function λ (θ ,ϕ ) . We show that the N -qubit mixed symmetric separable states can be visualized as a uniaxial system if the distribution function is independent of θ and ϕ . We further choose a distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the N -qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two-qubit mixed symmetric separable state. We also observe that there exists a correspondence between the separability and classicality of states.

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

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.

Probing the Rate-Determining Step of the Claisen-Schmidt Condensation by Competition Reactions

ERIC Educational Resources Information Center

Mak, Kendrew K. W.; Chan, Wing-Fat; Lung, Ka-Ying; Lam, Wai-Yee; Ng, Weng-Cheong; Lee, Siu-Fung

2007-01-01

Competition experiments are a useful tool for preliminary study of the linear free energy relationship of organic reactions. This article describes a physical organic experiment for upper-level undergraduates to identify the rate-determining step of the Claisen-Schmidt condensation of benzaldehyde and acetophenone by studying the linear free…

Mathematics Instruction and the Common Core: Where Do We Go from Here? Q&A with William Schmidt, Ph.D. REL Mid-Atlantic Webinar

ERIC Educational Resources Information Center

Regional Educational Laboratory Mid-Atlantic, 2015

2015-01-01

In this webinar, Dr. William Schmidt of Michigan State University discussed helpful instructional tools for promoting the higher order conceptual thinking found in the Common Core Standards. The PowerPoint presentation and webinar recording are also available.

Listening Journals for Extensive and Intensive Listening Practice

ERIC Educational Resources Information Center

Schmidt, Anthony

2016-01-01

In this article, Anthony Schmidt presents results from his research on listening instruction in a second language. Schmidt reveals that throughout the history of English language teaching (ELT), most students have never been taught how to listen. It was not just listening, but the need to do this listening in conjunction with an approach that…

Extending the length and time scales of Gram–Schmidt Lyapunov vector computations

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

Costa, Anthony B., E-mail: acosta@northwestern.edu; Green, Jason R., E-mail: jason.green@umb.edu; Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram–Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N{sup 2} (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram–Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard–Jones fluids from N=100 to 1300 betweenmore » Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram–Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.« less

SNOW LINES AS PROBES OF TURBULENT DIFFUSION IN PROTOPLANETARY DISKS

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

Owen, James E.

2014-07-20

Sharp chemical discontinuities can occur in protoplanetary disks, particularly at ''snow lines'' where a gas-phase species freezes out to form ice grains. Such sharp discontinuities will diffuse out due to the turbulence suspected to drive angular momentum transport in accretion disks. We demonstrate that the concentration gradient—in the vicinity of the snow line—of a species present outside a snow line but destroyed inside is strongly sensitive to the level of turbulent diffusion (provided the chemical and transport timescales are decoupled) and provides a direct measurement of the radial ''Schmidt number'' (the ratio of the angular momentum transport to radial turbulentmore » diffusion). Taking as an example the tracer species N{sub 2}H{sup +}, which is expected to be destroyed inside the CO snow line (as recently observed in TW Hya) we show that ALMA observations possess significant angular resolution to constrain the Schmidt number. Since different turbulent driving mechanisms predict different Schmidt numbers, a direct measurement of the Schmidt number in accretion disks would allow inferences to be made about the nature of the turbulence.« less

Coupled harmonic oscillators and their quantum entanglement.

PubMed

Makarov, Dmitry N

2018-04-01

A system of two coupled quantum harmonic oscillators with the Hamiltonian H[over ̂]=1/2(1/m_{1}p[over ̂]_{1}^{2}+1/m_{2}p[over ̂]_{2}^{2}+Ax_{1}^{2}+Bx_{2}^{2}+Cx_{1}x_{2}) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H[over ̂]Ψ=iℏ∂Ψ/∂t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.

Coupled harmonic oscillators and their quantum entanglement

NASA Astrophysics Data System (ADS)

Makarov, Dmitry N.

2018-04-01

A system of two coupled quantum harmonic oscillators with the Hamiltonian H ̂=1/2 (1/m1p̂1 2+1/m2p̂2 2+A x12+B x22+C x1x2) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H ̂Ψ =i ℏ ∂/Ψ ∂ t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.

Velocity-Resolved LES (VR-LES) technique for simulating turbulent transport of high Schmidt number passive scalars

NASA Astrophysics Data System (ADS)

Verma, Siddhartha; Blanquart, Guillaume; P. K. Yeung Collaboration

2011-11-01

Accurate simulation of high Schmidt number scalar transport in turbulent flows is essential to studying pollutant dispersion, weather, and several oceanic phenomena. Batchelor's theory governs scalar transport in such flows, but requires further validation at high Schmidt and high Reynolds numbers. To this end, we use a new approach with the velocity field fully resolved, but the scalar field only partially resolved. The grid used is fine enough to resolve scales up to the viscous-convective subrange where the decaying slope of the scalar spectrum becomes constant. This places the cutoff wavenumber between the Kolmogorov scale and the Batchelor scale. The subgrid scale terms, which affect transport at the supergrid scales, are modeled under the assumption that velocity fluctuations are negligible beyond this cutoff wavenumber. To ascertain the validity of this technique, we performed a-priori testing on existing DNS data. This Velocity-Resolved LES (VR-LES) technique significantly reduces the computational cost of turbulent simulations of high Schmidt number scalars, and yet provides valuable information of the scalar spectrum in the viscous-convective subrange.

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.

A fast new cadioptric design for fiber-fed spectrographs

NASA Astrophysics Data System (ADS)

Saunders, Will

2012-09-01

The next generation of massively multiplexed multi-object spectrographs (DESpec, SUMIRE, BigBOSS, 4MOST, HECTOR) demand fast, efficient and affordable spectrographs, with higher resolutions (R = 3000-5000) than current designs. Beam-size is a (relatively) free parameter in the design, but the properties of VPH gratings are such that, for fixed resolution and wavelength coverage, the effect on beam-size on overall VPH efficiency is very small. For alltransmissive cameras, this suggests modest beam-sizes (say 80-150mm) to minimize costs; while for cadioptric (Schmidt-type) cameras, much larger beam-sizes (say 250mm+) are preferred to improve image quality and to minimize obstruction losses. Schmidt designs have benefits in terms of image quality, camera speed and scattered light performance, and recent advances such as MRF technology mean that the required aspherics are no longer a prohibitive cost or risk. The main objections to traditional Schmidt designs are the inaccessibility of the detector package, and the loss in throughput caused by it being in the beam. With expected count rates and current read-noise technology, the gain in camera speed allowed by Schmidt optics largely compensates for the additional obstruction losses. However, future advances in readout technology may erase most of this compensation. A new Schmidt/Maksutov-derived design is presented, which differs from previous designs in having the detector package outside the camera, and adjacent to the spectrograph pupil. The telescope pupil already contains a hole at its center, because of the obstruction from the telescope top-end. With a 250mm beam, it is possible to largely hide a 6cm × 6cm detector package and its dewar within this hole. This means that the design achieves a very high efficiency, competitive with transmissive designs. The optics are excellent, as least as good as classic Schmidt designs, allowing F/1.25 or even faster cameras. The principal hardware has been costed at $300K per arm, making the design affordable.

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.

Quantum computation with coherent spin states and the close Hadamard problem

NASA Astrophysics Data System (ADS)

Adcock, Mark R. A.; Høyer, Peter; Sanders, Barry C.

2016-04-01

We study a model of quantum computation based on the continuously parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close Hadamard problem. We prove that the close Hadamard problem can be solved in the spin system model with arbitrarily small error probability in a constant number of oracle queries. We conclude that this model of quantum computation is suitable for solving certain types of problems. The model is effective for problems where symmetries between the structure of the information associated with the problem and the structure of the unitary operators employed in the quantum algorithm can be exploited.

Testing for entanglement with periodic coarse graining

NASA Astrophysics Data System (ADS)

Tasca, D. S.; Rudnicki, Łukasz; Aspden, R. S.; Padgett, M. J.; Souto Ribeiro, P. H.; Walborn, S. P.

2018-04-01

Continuous-variable systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as entanglement detection. Here we employ the continuous transverse spatial variables of photon pairs to experimentally demonstrate entanglement criteria based on a periodic structure of coarse-grained measurements. The periodization of the measurements allows an efficient evaluation of entanglement using spatial masks acting as mode analyzers over the entire transverse field distribution of the photons and without the need to reconstruct the probability densities of the conjugate continuous variables. Our experimental results demonstrate the utility of the derived criteria with a success rate in entanglement detection of ˜60 % relative to 7344 studied cases.

Probability distributions of the electroencephalogram envelope of preterm infants.

PubMed

Saji, Ryoya; Hirasawa, Kyoko; Ito, Masako; Kusuda, Satoshi; Konishi, Yukuo; Taga, Gentaro

2015-06-01

To determine the stationary characteristics of electroencephalogram (EEG) envelopes for prematurely born (preterm) infants and investigate the intrinsic characteristics of early brain development in preterm infants. Twenty neurologically normal sets of EEGs recorded in infants with a post-conceptional age (PCA) range of 26-44 weeks (mean 37.5 ± 5.0 weeks) were analyzed. Hilbert transform was applied to extract the envelope. We determined the suitable probability distribution of the envelope and performed a statistical analysis. It was found that (i) the probability distributions for preterm EEG envelopes were best fitted by lognormal distributions at 38 weeks PCA or less, and by gamma distributions at 44 weeks PCA; (ii) the scale parameter of the lognormal distribution had positive correlations with PCA as well as a strong negative correlation with the percentage of low-voltage activity; (iii) the shape parameter of the lognormal distribution had significant positive correlations with PCA; (iv) the statistics of mode showed significant linear relationships with PCA, and, therefore, it was considered a useful index in PCA prediction. These statistics, including the scale parameter of the lognormal distribution and the skewness and mode derived from a suitable probability distribution, may be good indexes for estimating stationary nature in developing brain activity in preterm infants. The stationary characteristics, such as discontinuity, asymmetry, and unimodality, of preterm EEGs are well indicated by the statistics estimated from the probability distribution of the preterm EEG envelopes. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

VizieR Online Data Catalog: IRAS Point Source Identifications (MacConnell, 1993; rev. 2009)

NASA Astrophysics Data System (ADS)

MacConnell, D. J.

2010-08-01

Most of the sources are south of the celestial equator and have been classified in increasing galactic longitude over the period Sept. 1985 to May 1992. They have been classified on Kodak I-N objective-prism plates taken primarily with the Curtis Schmidt telescope at Cerro Tololo, but some northern plates taken with the Burrell Schmidt at Kitt Peak were also used for classification. The spectra cover the range 680-880nm at a dispersion of 340nm/mm at the A-band, and the plate scale is 96.6"/mm. They are ideal for classifying M stars of type M3 and cooler (increasing strength of TiO and VO bands) and carbon stars (CN bands), but stars warmer than M2 and most S stars cannot be classified or identified as such. The M stars M3 and cooler can be separated into about five groups. The limiting mag of the deepest plates is I about 13.5. The IRAS PS were identified on transparent overlays made to the plate scale for each plate center, and the association of a spectrum with a given PS is usually unambiguous. In cases of doubt or offset, a comment is made. Note that there are some cases where the PSC gives an incorrect association on the basis of position, and the correct association is with a faint, uncatalogued M star. (3 data files).

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.}

Whitebark pine ecosystem restoration in western Montana

Treesearch

Robert E. Keane; Stephen F. Arno

1996-01-01

Whitebark pine (Pinus albicaulis) is a major tree species of upper subalpine forests of the northern Rocky Mountains (Schmidt and McDonald 1990). It is an important nutritional and structural component of wildlife habitat (Arno and Hoff 1990; Schmidt and McDonald 1990). Its large, nutlike seeds are a major food source for many birds and mammals (...

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

Age of Local Galactic Disk from the Wdlf for Cpmbs

NASA Astrophysics Data System (ADS)

Smith, J. Allyn; Oswalt, Terry D.; Wood, Matt A.; Silvestri, Nicole M.

We present the white dwarf luminosity function (WDLF) for common proper motion systems. This WDLF was derived using the 1/Vmax method pioneered by Schmidt (1975) and detailed by Liebert Dahn and Monet (1988). New cooling models were used to determine the luminosities of the white dwarfs and the age of the local Galactic disk. Comparison to WDLFs developed using older colling models (Wood 1995) will be examined for changes in the derived disk age. Kinematic data is available for a subset of the WDs in the sample. Separate luminosity functions will be examined for each of the statistically significant subsets. JAS acknowledges support from NASA GSRP Fellowship NGT-51086.

Characteristics of an Imaging Polarimeter for the Powell Observatory

NASA Astrophysics Data System (ADS)

Hall, Shannon W.; Henson, Gary D.

2010-07-01

A dual-beam imaging polarimeter has been built for use on the 14-inch Schmidt-Cassegrain telescope at the ETSU Harry D. Powell Observatory. The polarimeter includes a rotating half-wave plate and a Wollaston prism to separate light into two orthogonal linearly polarized rays. A thermoelectrically cooled CCD camera is used to detect the modulated polarized light. We present here measurements of the polarization of polarimetric standard stars. By measuring unpolarized and polarized standard stars we are able to establish the instrumental polarization and the efficiency of the instrument. The polarimeter will initially be used as a dedicated instrument in an ongoing project to monitor the eclipsing binary star, Epsilon Aurigae.

Extremal entanglement witnesses

NASA Astrophysics Data System (ADS)

Hansen, Leif Ove; Hauge, Andreas; Myrheim, Jan; Sollid, Per Øyvind

2015-02-01

We present a study of extremal entanglement witnesses on a bipartite composite quantum system. We define the cone of witnesses as the dual of the set of separable density matrices, thus TrΩρ≥0 when Ω is a witness and ρ is a pure product state, ρ=ψψ† with ψ=ϕ⊗χ. The set of witnesses of unit trace is a compact convex set, uniquely defined by its extremal points. The expectation value f(ϕ,χ)=TrΩρ as a function of vectors ϕ and χ is a positive semidefinite biquadratic form. Every zero of f(ϕ,χ) imposes strong real-linear constraints on f and Ω. The real and symmetric Hessian matrix at the zero must be positive semidefinite. Its eigenvectors with zero eigenvalue, if such exist, we call Hessian zeros. A zero of f(ϕ,χ) is quadratic if it has no Hessian zeros, otherwise it is quartic. We call a witness quadratic if it has only quadratic zeros, and quartic if it has at least one quartic zero. A main result we prove is that a witness is extremal if and only if no other witness has the same, or a larger, set of zeros and Hessian zeros. A quadratic extremal witness has a minimum number of isolated zeros depending on dimensions. If a witness is not extremal, then the constraints defined by its zeros and Hessian zeros determine all directions in which we may search for witnesses having more zeros or Hessian zeros. A finite number of iterated searches in random directions, by numerical methods, leads to an extremal witness which is nearly always quadratic and has the minimum number of zeros. We discuss briefly some topics related to extremal witnesses, in particular the relation between the facial structures of the dual sets of witnesses and separable states. We discuss the relation between extremality and optimality of witnesses, and a conjecture of separability of the so-called structural physical approximation (SPA) of an optimal witness. Finally, we discuss how to treat the entanglement witnesses on a complex Hilbert space as a subset of the witnesses on a real Hilbert space.

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.

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.

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.

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.

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.

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.

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.

Staying Focused on What Really Matters: Further Thoughts on Empowerment Theory for Professional School Counselors

ERIC Educational Resources Information Center

Hipolito-Delgado, Carlos P.; Lee, Courtland C.

2007-01-01

In this article, the authors provide their reactions to the commentaries of Mitcham-Smith and Schmidt on their study. As Mitcham-Smith and Schmidt in their responses both suggest, it is evident that if professional school counselors are to be successful in facilitating the empowerment of students, they must engage in a self-reflective process…

History and Development of the Schmidt-Hunter Meta-Analysis Methods

ERIC Educational Resources Information Center

Schmidt, Frank L.

2015-01-01

In this article, I provide answers to the questions posed by Will Shadish about the history and development of the Schmidt-Hunter methods of meta-analysis. In the 1970s, I headed a research program on personnel selection at the US Office of Personnel Management (OPM). After our research showed that validity studies have low statistical power, OPM…

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.

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.

Turbulence Model Effects on RANS Simulations of the HIFiRE Flight 2 Ground Test Configurations

NASA Technical Reports Server (NTRS)

Georgiadis, Nicholas J.; Mankbadi, Mina R.; Vyas, Manan A.

2014-01-01

The Wind-US Reynolds-averaged Navier-Stokes solver was applied to the Hypersonic International Flight Research Experimentation (HIFiRE) Flight 2 scramjet ground test configuration. Two test points corresponding to flight Mach numbers of 5.9 and 8.9 were examined. The emphasis was examining turbulence model effects on the prediction of flow path pressures. Three variants of the Menter k-omega turbulence model family were investigated. These include the baseline (BSL) and shear stress transport (SST) as well as a modified SST model where the shear stress limiter was altered. Variations in the turbulent Schmidt number were also considered. Choice of turbulence model had a substantial effect on prediction of the flow path pressures. The BSL model produced the highest pressures and the SST model produced the lowest pressures. As expected, the settings for the turbulent Schmidt number also had significant effects on predicted pressures. Small values for the turbulent Schmidt number enabled more rapid mass transfer, faster combustion, and in turn higher flowpath pressures. Optimal settings for turbulence model and turbulent Schmidt number were found to be rather case dependent, as has been concluded in other scramjet investigations.

Intermittency measurement in two-dimensional bacterial turbulence

NASA Astrophysics Data System (ADS)

Qiu, Xiang; Ding, Long; Huang, Yongxiang; Chen, Ming; Lu, Zhiming; Liu, Yulu; Zhou, Quan

2016-06-01

In this paper, an experimental velocity database of a bacterial collective motion, e.g., Bacillus subtilis, in turbulent phase with volume filling fraction 84 % provided by Professor Goldstein at Cambridge University (UK), was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β -limitation. A dual-power-law behavior separated by the viscosity scale ℓν was observed for the q th -order Hilbert moment Lq(k ) . This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R , e.g., the bacterial body length. The measured scaling exponents ζ (q ) of both the small-scale (k >kν ) and large-scale (k

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).

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

Gheorghiu, Vlad; Yu Li; Cohen, Scott M.

We investigate the conditions under which a set S of pure bipartite quantum states on a DxD system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in S must be full Schmidt rank and equally entangled under the G-concurrence measure, and (ii) the set S can be extended to a larger clonable set generated by a finite group G of order |G|=N, the number ofmore » states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides D exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all D; and (ii) local cloning of entangled qubit states with nonvanishing entanglement. In both of these cases, we show that a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary 'shift' operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in D=3 we show that a maximally entangled resource is again necessary and sufficient, while for higher-dimensional systems, we find that the resource state must be strictly more entangled than the states in S. All of our necessary conditions for separable operations are also necessary conditions for local operations and classical communication (LOCC), since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.« less

The Dielectric Permittivity of Crystals in the Reduced Hartree-Fock Approximation

NASA Astrophysics Data System (ADS)

Cancès, Éric; Lewin, Mathieu

2010-07-01

In a recent article (Cancès et al. in Commun Math Phys 281:129-177, 2008), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree-Fock model, the ground state electronic density matrix is decomposed as {γ = γ^0_per + Q_{ν,\\varepsilon_F}}, where {γ^0_per} is the ground state density matrix of the host crystal and {Q_{ν,\\varepsilon_F}} the modification of the electronic density matrix generated by a modification ν of the nuclear charge of the host crystal, the Fermi level ɛ F being kept fixed. The purpose of the present article is twofold. First, we study in more detail the mathematical properties of the density matrix {Q_{ν,\\varepsilon_F}} (which is known to be a self-adjoint Hilbert-Schmidt operator on {L^2(mathbb{R}^3)}). We show in particular that if {int_{mathbb{R}^3} ν neq 0, Q_{ν,\\varepsilon_F}} is not trace-class. Moreover, the associated density of charge is not in {L^1(mathbb{R}^3)} if the crystal exhibits anisotropic dielectric properties. These results are obtained by analyzing, for a small defect ν, the linear and nonlinear terms of the resolvent expansion of {Q_{ν,\\varepsilon_F}}. Second, we show that, after an appropriate rescaling, the potential generated by the microscopic total charge (nuclear plus electronic contributions) of the crystal in the presence of the defect converges to a homogenized electrostatic potential solution to a Poisson equation involving the macroscopic dielectric permittivity of the crystal. This provides an alternative (and rigorous) derivation of the Adler-Wiser formula.

A Possible Operational Motivation for the Orthocomplementation in Quantum Structures

NASA Astrophysics Data System (ADS)

D'Hooghe, Bart

2010-11-01

In the foundations of quantum mechanics Gleason’s theorem dictates the uniqueness of the state transition probability via the inner product of the corresponding state vectors in Hilbert space, independent of which measurement context induces this transition. We argue that the state transition probability should not be regarded as a secondary concept which can be derived from the structure on the set of states and properties, but instead should be regarded as a primitive concept for which measurement context is crucial. Accordingly, we adopt an operational approach to quantum mechanics in which a physical entity is defined by the structure of its set of states, set of properties and the possible (measurement) contexts which can be applied to this entity. We put forward some elementary definitions to derive an operational theory from this State-COntext-Property (SCOP) formalism. We show that if the SCOP satisfies a Gleason-like condition, namely that the state transition probability is independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented, which is one of the ‘quantum axioms’ used in the Piron-Solèr representation theorem for quantum systems. In this sense we obtain a possible physical meaning for the orthocomplementation widely used in quantum structures.

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

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.

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

Thermodynamics and the structure of quantum theory

NASA Astrophysics Data System (ADS)

Krumm, Marius; Barnum, Howard; Barrett, Jonathan; Müller, Markus P.

2017-04-01

Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behaviour should arguably satisfy. In the framework of generalised probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechanics. Using a thought experiment by von Neumann, we show that these theories admit a consistent thermodynamic notion of entropy, and prove that the second law holds for projective measurements and mixing procedures. Furthermore, we study additional entropy-like quantities based on measurement probabilities and convex decomposition probabilities, and uncover a relation between one of these quantities and Sorkin’s notion of higher-order interference.

Solar Observations on Magneto-Convection

DTIC Science & Technology

1989-05-31

Technical Library National Solar Observatory Sunspot, NM 88349 Karl - Schwarzschild -Strasse 1 8046 Garching bei Mundhen Solar Observations On Magneto...Schmidt, Hermann-Ulrich Schmidt, Hans-Christoph Thomas (eds.) Max-Planck-Institut fir Physik und Astrophysik Institut fiur Astrophysik Karl ... Schwarzschild -St-. 1 D-8046 Garching, FklG 14TIS CRiA.&l DTIC TA. U~Jar,iou8:ed B ......... ... Distribution I -- Availability COcý----- Avail and or Dist special

Ca2+-induced phase separation in black lipid membranes and its effect on the transport of a hydrophobic ion.

PubMed

Miller, A; Schmidt, G; Eibl, H; Knoll, W

1985-03-14

Voltage jump-current relaxation studies have been performed with dipicrylamine-doped black membranes of binary lipid mixtures. As in the case of the carrier-mediated ion transport (Schmidt, G., Eibl, H. and Knoll, W. (1982) J. Membrane Biol. 70, 147-155) no evidence was found that the neutral lipid phosphatidylcholine (DPMPC) and the charged phosphatidic acid (DPMPA) are heterogeneously distributed in the membrane over the whole range of composition. However, besides a continuous dilution of the surface charges of DPMPA by the addition of DPMPC molecules, different structural properties of mixed membranes influence the kinetics of the dipicrylamine transport. The addition of Ca2+ to the electrolyte induces a lipid phase separation within the membrane into two fluid phases of distinctly different characteristics of the translocation of hydrophobic ions. Thus, it is possible to determine a preliminary composition phase diagram for the DPMPA/DPMPC mixtures as a function of the Ca2+ concentration.

Data and Analysis of the Double Stars STFA 10AB and STFA 1744AB

NASA Astrophysics Data System (ADS)

Arcilla, Marisa; Bowden, Sam; DeBlase, Jacqueline; Hall, Anthony; Hall, Corielyn; Hernandez, Alyssa; Renna, Danielle; Rodriguez, Fatima; Salazar, Cassandra; Sanchez, Andres; Teeter, Dayton; Brewer, Mark; Funk, Benjamin; Gillette, Travis; Sharpe, Scott

2017-04-01

Eighth grade students at Vanguard Preparatory School measured the double stars STFA 10AB and STFA 1744AB. A 22-inch Newtonian Alt/Az telescope and a 14-inch Celestron Schmidt Cassegrain telescope were used. The star Bellatrix was used as the calibration star to determine the scale constant of the 22-inch telescope to be 7.8 “/tick marks. The double star STFA 1744AB was used as the calibration star to determine the scale constant of the 14-inch telescope to be 5.1 “/tick marks. The separation and position angle of STFA 10AB was determined by the 22-inch telescope to be 347.9” and 339.3°. The separation and position angle of STFA 1744AB was determined by the 14-inch telescope to be 3.6” and 158.1°. The measurements that were calculated were compared to the most recent measurements listed in the Washington Double Star Catalog.

A Variable Turbulent Schmidt Number Formulation for Scramjet Application

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.; Cutler, A. D.

2004-01-01

In high speed engines, thorough turbulent mixing of fuel and air is required to obtain high performance and high efficiency. Thus, the ability to predict turbulent mixing is crucial in obtaining accurate numerical simulation of an engine and its performance. Current state of the art in CFD simulation is to assume both turbulent Prandtl number and Schmidt numbers to be constants. However, since the mixing of fuel and air is inversely proportional to the Schmidt number, a value of 0.45 for the Schmidt number will produce twice as much diffusion as that with a value of 0.9. Because of this, current CFD tools and models have not been able to provide the needed guidance required for the efficient design of a scramjet engine. The goal of this investigation is to develop the framework needed to calculate turbulent Prandtl and Schmidt numbers as part of the solution. This requires four additional equations: two for the temperature variance and its dissipation rate and two for the concentration variance and its dissipation rate. In the current investigation emphasis will be placed on studying mixing without reactions. For such flows, variable Prandtl number does not play a major role in determining the flow. This, however, will have to be addressed when combustion is present. The approach to be used is similar to that used to develop the k-zeta model. In this approach, relevant equations are derived from the exact Navier-Stokes equations and each individual correlation is modeled. This ensures that relevant physics is incorporated into the model equations. This task has been accomplished. The final set of equations have no wall or damping functions. Moreover, they are tensorially consistent and Galilean invariant. The derivation of the model equations is rather lengthy and thus will not be incorporated into this abstract, but will be included in the final paper. As a preliminary to formulating the proposed model, the original k-zeta model with constant turbulent Prandtl and Schmidt numbers is used to model the supersonic coaxial jet mixing experiments involving He, O2 and air.

Quantum search algorithms on a regular lattice

NASA Astrophysics Data System (ADS)

Hein, Birgit; Tanner, Gregor

2010-07-01

Quantum algorithms for searching for one or more marked items on a d-dimensional lattice provide an extension of Grover’s search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.

Embedding Quantum Mechanics Into a Broader Noncontextual Theory: A Conciliatory Result

NASA Astrophysics Data System (ADS)

Garola, Claudio; Sozzo, Sandro

2010-12-01

The extended semantic realism ( ESR) model 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 an improved version of this model and show that it predicts that, whenever idealized measurements are performed, a modified Bell-Clauser-Horne-Shimony-Holt ( BCHSH) inequality holds if one takes into account all individual systems that are prepared, standard quantum predictions hold if one considers only the individual systems that are detected, and a standard BCHSH inequality holds at a microscopic (purely theoretical) level. These results admit an intuitive explanation in terms of an unconventional kind of unfair sampling and constitute a first example of the unified perspective that can be attained by adopting the ESR model.

Photodissociation of OCS: deviations between theory and experiment, and the importance of higher order correlation effects.

PubMed

Schmidt, J A; Olsen, J M H

2014-11-14

The photodissociation of carbonyl sulfide (OCS) was investigated theoretically in a series of studies by Schmidt and co-workers. Initial studies [J. A. Schmidt, M. S. Johnson, G. C. McBane, and R. Schinke, J. Chem. Phys. 136, 131101 (2012); J. A. Schmidt, M. S. Johnson, G. C. McBane, and R. Schinke, J. Chem. Phys. 137, 054313 (2012)] found photodissociation in the first UV-band to occur mainly by excitation of the 2(1)A' (A) excited state. However, in a later study [G. C. McBane, J. A. Schmidt, M. S. Johnson, and R. Schinke, J. Chem. Phys. 138, 094314 (2013)] it was found that a significant fraction of photodissociation must occur by excitation of 1(1)A″ (B) excited state to explain the product angular distribution. The branching between excitation of the A and B excited states is determined by the magnitude of the transition dipole moment vectors in the Franck-Condon region. This study examines the sensitivity of these quantities to changes in the employed electronic structure methodology. This study benchmarks the methodology employed in previous studies against highly correlated electronic structure methods (CC3 and MRAQCC) and provide evidence in support of the picture of the OCS photodissociation process presented in [G. C. McBane, J. A. Schmidt, M. S. Johnson, and R. Schinke, J. Chem. Phys. 138, 094314 (2013)] showing that excitation of A and B electronic states both contribute significantly to the first UV absorption band of OCS. In addition, this study presents evidence in support of the assertion that the A state potential energy surface employed in previous studies underestimates the energy at highly bent geometries (γ ∼ 70°) leading to overestimated rotational energy in the product CO.

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.

The Mount Wilson Optical Shop during the Second World War

NASA Astrophysics Data System (ADS)

Abrahams, P.

2004-12-01

During the Second World War, the Optical Shop of Mount Wilson Observatory, located in Pasadena, engaged in a variety of exacting and pioneering ventures in optical design and fabrication. Roof prisms for military optics were produced on a large scale, leading to the production of an instruction manual, for guidance in other workshops. Triple mirrors, or autocollimating corner cubes, were another precision part made in large numbers. Aerial photography was extensively developed. Test procedures for measuring resolution of lenses were researched. Various camera shutters and film sweep mechanisms were devised. The most significant work concerned Schmidt cameras, for possible use in night-time aerial photography. Variations included a solid Schmidt, and the Schmidt Cassegrain, which was fabricated for the first time at MWO. Key figures include Don Hendrix, Roger Hayward, Aden Meinel, and Walter Adams.

Accurate phase extraction algorithm based on Gram–Schmidt orthonormalization and least square ellipse fitting method

NASA Astrophysics Data System (ADS)

Lei, Hebing; Yao, Yong; Liu, Haopeng; Tian, Yiting; Yang, Yanfu; Gu, Yinglong

2018-06-01

An accurate algorithm by combing Gram-Schmidt orthonormalization and least square ellipse fitting technology is proposed, which could be used for phase extraction from two or three interferograms. The DC term of background intensity is suppressed by subtraction operation on three interferograms or by high-pass filter on two interferograms. Performing Gram-Schmidt orthonormalization on pre-processing interferograms, the phase shift error is corrected and a general ellipse form is derived. Then the background intensity error and the corrected error could be compensated by least square ellipse fitting method. Finally, the phase could be extracted rapidly. The algorithm could cope with the two or three interferograms with environmental disturbance, low fringe number or small phase shifts. The accuracy and effectiveness of the proposed algorithm are verified by both of the numerical simulations and experiments.

Divergent Synthesis of Solanidine and 22-epi-Solanidine.

PubMed

Hou, Ling-Li; Shi, Yong; Zhang, Zhi-Dan; Wu, Jing-Jing; Yang, Qing-Xiong; Tian, Wei-Sheng

2017-07-21

A divergent synthesis of solanidine and 22-epi-solanidine, two 25S natural steroidal alkaloids, from 25R-configured diosgenin acetate, is described. Initially, solanidine was synthesized through a series of transformations including a cascade ring-switching process of furostan-26-acid, an epimerization of C25 controlled by the conformation of six-membered lactone ring, an intramolecular Schmidt reaction, and an imine reduction/intramolecular aminolysis process. To address the epimerization issue during Schmidt reaction, an improved synthesis was developed, which also led to a synthesis of 22-epi-solanidine. In this synthesis, selective transformation of azido lactone to azido diol and amino diol was realized through a reduction relay tactic. The azido diol was transformed to solanidine via an intramolecular Schmidt reaction/N-alkylation/reduction process and to 22-epi-solanidine via an intramolecular double N-alkylation process.

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.

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.

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.

Random pure states: Quantifying bipartite entanglement beyond the linear statistics.

PubMed

Vivo, Pierpaolo; Pato, Mauricio P; Oshanin, Gleb

2016-05-01

We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary N≤M, a general relation between the n-point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Schmidt eigenvalues, and the analogous functionals of the eigenvalues of the Wishart-Laguerre ensemble of the random matrix theory. This allows us to derive explicit expressions for two-level densities, and also an exact expression for the variance of von Neumann entropy at finite N,M. Then, we focus on the moments E{K^{a}} of the Schmidt number K, the reciprocal of the purity. This is a random variable supported on [1,N], which quantifies the number of degrees of freedom effectively contributing to the entanglement. We derive a wealth of analytical results for E{K^{a}} for N=2 and 3 and arbitrary M, and also for square N=M systems by spotting for the latter a connection with the probability P(x_{min}^{GUE}≥sqrt[2N]ξ) that the smallest eigenvalue x_{min}^{GUE} of an N×N matrix belonging to the Gaussian unitary ensemble is larger than sqrt[2N]ξ. As a by-product, we present an exact asymptotic expansion for P(x_{min}^{GUE}≥sqrt[2N]ξ) for finite N as ξ→∞. Our results are corroborated by numerical simulations whenever possible, with excellent agreement.

Optimizing Feedback Utilization in Motor Skill Training

DTIC Science & Technology

1988-02-01

Abehiorlemphasis. Champaign, IL: Human Kinetics Press. Schmidt, R.A., & White, J.L. (1972). Evidence for an error-detection mechanism in motor skills...motor program. In D.M. Landers & R.W. Christina (Eds.), Psyc g 2 moto behavior d S (Vol 1). Champaign, IL: Human Kinetics Press. Shapiro, D.C. (1978...and sport research. Champaign, IL: Human Kinetics Press. Schmidt, R.A. (in press). Toward a better understanding of motor learning. Theoretical and

Image Analysis Using Quantum Entropy Scale Space and Diffusion Concepts

DTIC Science & Technology

2009-11-01

images using a combination of analytic methods and prototype Matlab and Mathematica programs. We investigated concepts of generalized entropy and...Schmidt strength from quantum logic gate decomposition. This form of entropy gives a measure of the nonlocal content of an entangling logic gate...11 We recall that the Schmidt number is an indicator of entanglement , but not a measure of entanglement . For instance, let us compare

Report on PDF Models for Turbulence Chemistry Interaction

DTIC Science & Technology

2014-03-01

significantly within the flowfield (like rocket plumes or scramjet combustors). For multi-species flows turbulence can increase the apparent mass...Variable Turbulent Schmidt-Number Formulation for Scramjet Applications, AIAA Journal, 44(3), 593–599. [12] Xiao, X., Hassan, H.A., and Baurle, R.A...2006), Modeling Scramjet Flows with Variable Turbulent Prandtl and Schmidt Numbers. AIAA Paper 2006-128. [13] Xiao, X., Hassan, H.A., and Baurle, R.A

Multimodality Image-Guided HDR/IMRT in Prostate Cancer: Combined Molecular Targeting Using Nanoparticle MR, 3D MRSI, and 11C Acetate PET Imaging

DTIC Science & Technology

2005-08-01

Ph.D. Panos Fatouros, Ph.D. Jerry Hirsch, MSc, PharmD Rhonda Hoyle Kristin Schmidt Dorin Tudor, Ph.D. Jie Liu CONTRACTING ORGANIZATION: Virginia...McClish, Ph.D., Panos Fatouros, Ph.D., Jerry Hirsch, MSc, PharmD, 5e. TASK NUMBER Rhonda Hoyle, Kristin Schmidt, Dorin Tudor, Ph.D., Jie Liu 5f. WORK UNIT

Analyzing Divisia Rules Extracted from a Feedforward Neural Network

DTIC Science & Technology

2006-03-01

assumptions. (Barnett and work, Data Mining, Rule Generation Serletis give a detailed treatment of the the- ory of monetary aggregation [1].) However, 1... Serletis , A. (Eds.) (2000), The The- Swizerland, 1995. ory of Monetary Aggregation, North-H ollandeAmsterdam, Chgaptero , pp.- [11] Vincent A. Schmidt and...gas, Nevada, 2002. sets. Macroeconomic Dynamics, 1:485-512, 1997. Reprinted in Barnett, WA. [12] Vincent A. Schmidt and Jane M. Binner. and Serletis

Robust Sensitivity Analysis of Courses of Action Using an Additive Value Model

DTIC Science & Technology

2008-03-01

According to Clemen , sensitivity analysis answers, “What makes a difference in this decision?” (2001:175). Sensitivity analysis can also indicate...alternative to change. These models look for the new weighting that causes a specific alternative to rank above all others. 19 Barron and Schmidt first... Schmidt , 1988:123). A smaller objective function value indicates greater sensitivity. Wolters and Mareschal propose a similar approach using goal

Cartesian and polar Schmidt bases for down-converted photons. How high dimensional entanglement protects the shared information from non-ideal measurements

NASA Astrophysics Data System (ADS)

Miatto, F. M.; Brougham, T.; Yao, A. M.

2012-07-01

We derive an analytical form of the Schmidt modes of spontaneous parametric down-conversion (SPDC) biphotons in both Cartesian and polar coordinates. We show that these correspond to Hermite-Gauss (HG) or Laguerre-Gauss (LG) modes only for a specific value of their width, and we show how such value depends on the experimental parameters. The Schmidt modes that we explicitly derive allow one to set up an optimised projection basis that maximises the mutual information gained from a joint measurement. The possibility of doing so with LG modes makes it possible to take advantage of the properties of orbital angular momentum eigenmodes. We derive a general entropic entanglement measure using the Rényi entropy as a function of the Schmidt number, K, and then retrieve the von Neumann entropy, S. Using the relation between S and K we show that, for highly entangled states, a non-ideal measurement basis does not degrade the number of shared bits by a large extent. More specifically, given a non-ideal measurement which corresponds to the loss of a fraction of the total number of modes, we can quantify the experimental parameters needed to generate an entangled SPDC state with a sufficiently high dimensionality to retain any given fraction of shared bits.

Two-qubit quantum cloning machine and quantum correlation broadcasting

NASA Astrophysics Data System (ADS)

Kheirollahi, Azam; Mohammadi, Hamidreza; Akhtarshenas, Seyed Javad

2016-11-01

Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: "Is there an optimal quantum cloning machine?" Buzek and Hillery answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.

Cars Gone Wild: The Major Contributor to Unintended Acceleration in Automobiles is Pedal Error.

PubMed

Schmidt, Richard A; Young, Douglas E

2010-01-01

"Unintended-acceleration" automobile accidents typically begin when the driver first enters the car, starts the engine, and intends to press his/her right foot on the brake while shifting from Park to a drive gear (Drive or Reverse). The driver reports an unintended (uncommanded) full-throttle acceleration, coupled with a loss of braking, until the episode ends in a crash. Pedal misapplications - where the right foot contacts the accelerator instead of the brake that was intended - have been linked to these accidents (Schmidt, 1989, 1993) which, in the 1980s, were thought to occur only at the start of a driving cycle (and/or with the car in Park). But, in 1997, we identified over 200 pedal errors as the cause of accidents reported in the North Carolina database; these crashes occurred during the driving cycle (Schmidt et al., 1997), and/or with the vehicle in a gear other than Park. Our present work provides a more thorough analysis of these North Carolina Police Accident Reports from 1979 to 1995. The vast majority of pedal misapplications (over 92%) (a) occurred during the driving cycle, (b) were generally in "unhurried" conditions, and (c) were categorically separate from those events referred to as unintended-acceleration episodes at start-up. These ideas are explanatory for the recent (2009-2010) surge of unintended-acceleration reports, perhaps even suggesting that all of these crashes are caused by pedal errors, and that none of them are based on some vehicle defect(s).

VizieR Online Data Catalog: CRTS close supermassive black hole binaries (Graham+, 2015)

NASA Astrophysics Data System (ADS)

Graham, M. J.; Djorgovski, S. G.; Stern, D.; Drake, A. J.; Mahabal, A. A.; Donalek, C.; Glikman, E.; Larson, S.; Christensen, E.

2016-02-01

CRTS leverages the Catalina Sky Survey data streams from three telescopes - the 0.7m Catalina Sky Survey Schmidt and 1.5m Mount Lemmon Survey telescopes in Arizona, and the 0.5m Siding Springs Survey Schmidt in Australia - used in a search for Near-Earth Objects, operated by Lunar and Planetary Laboratory at University of Arizona. CRTS covers up to ~2500deg2 per night, with four exposures per visit, separated by 10-min, over 21 nights per lunation. All data are automatically processed in real-time, and optical transients are immediately distributed using a variety of electronic mechanisms. The data are broadly calibrated to Johnson V (see Drake et al., 2013, Cat. J/ApJ/763/32 for details) and the full CRTS data set contains time series for approximately 500 million sources. The Million Quasars (MQ) catalogue v3.7 contains all spectroscopically confirmed type 1 QSOs (309525), AGN (21728) and BL Lacs (1573) in the literature up to 2013 November 26 and formed the basis for the results of Graham et al. (2015Natur.518...74G). We have extended this with 297301 spectroscopically identified quasars in the SDSS Data Release 12 (Paris et al., in preparation). We cross-matched this combined quasar list against the CRTS data set with a 3-arcsec matching radius and find that 334446 confirmed quasars are covered by the full CRTS. Our final sample consists of 111 quasars. (2 data files).

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.

A novel technique for phase synchrony measurement from the complex motor imaginary potential of combined body and limb action

NASA Astrophysics Data System (ADS)

Zhou, Zhong-xing; Wan, Bai-kun; Ming, Dong; Qi, Hong-zhi

2010-08-01

In this study, we proposed and evaluated the use of the empirical mode decomposition (EMD) technique combined with phase synchronization analysis to investigate the human brain synchrony of the supplementary motor area (SMA) and primary motor area (M1) during complex motor imagination of combined body and limb action. We separated the EEG data of the SMA and M1 into intrinsic mode functions (IMFs) using the EMD method and determined the characteristic IMFs by power spectral density (PSD) analysis. Thereafter, the instantaneous phases of the characteristic IMFs were obtained by the Hilbert transformation, and the single-trial phase-locking value (PLV) features for brain synchrony measurement between the SMA and M1 were investigated separately. The classification performance suggests that the proposed approach is effective for phase synchronization analysis and is promising for the application of a brain-computer interface in motor nerve reconstruction of the lower limbs.

Multi-component separation and analysis of bat echolocation calls.

PubMed

DiCecco, John; Gaudette, Jason E; Simmons, James A

2013-01-01

The vast majority of animal vocalizations contain multiple frequency modulated (FM) components with varying amounts of non-linear modulation and harmonic instability. This is especially true of biosonar sounds where precise time-frequency templates are essential for neural information processing of echoes. Understanding the dynamic waveform design by bats and other echolocating animals may help to improve the efficacy of man-made sonar through biomimetic design. Bats are known to adapt their call structure based on the echolocation task, proximity to nearby objects, and density of acoustic clutter. To interpret the significance of these changes, a method was developed for component separation and analysis of biosonar waveforms. Techniques for imaging in the time-frequency plane are typically limited due to the uncertainty principle and interference cross terms. This problem is addressed by extending the use of the fractional Fourier transform to isolate each non-linear component for separate analysis. Once separated, empirical mode decomposition can be used to further examine each component. The Hilbert transform may then successfully extract detailed time-frequency information from each isolated component. This multi-component analysis method is applied to the sonar signals of four species of bats recorded in-flight by radiotelemetry along with a comparison of other common time-frequency representations.

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.

(Never) Mind your p's and q's: Von Neumann versus Jordan on the foundations of quantum theory

NASA Astrophysics Data System (ADS)

Duncan, A.; Janssen, M.

2013-03-01

In 1927, in two papers entitled "On a new foundation [Neue Begründung] of quantum mechanics," Pascual Jordan presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. Jordan and Paul Dirac arrived at essentially the same theory independently of one another at around the same time. Later in 1927, partly in response to Jordan and Dirac and avoiding the mathematical difficulties facing their approach, John von Neumann developed the modern Hilbert space formalism of quantum mechanics. We focus on Jordan and von Neumann. Central to the formalisms of both are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in quantum mechanics. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p's and q's. For von Neumann, not constrained by the analogy to classical mechanics, it required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p's and q's. Jordan and von Neumann also stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan and Dirac were the first to state those rules in full generality. Von Neumann rephrased them and, in a paper published a few months later, sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by Hilbert, von Neumann, and Nordheim. We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics. This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin.

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.

Ice under cover: Using bulk spatial and physical properties of probable ground ice driven mass wasting features on Ceres to better understand its surface

NASA Astrophysics Data System (ADS)

Hughson, K.; Russell, C.; Schmidt, B. E.; Chilton, H.; Scully, J. E. C.; Castillo, J. C.; Combe, J. P.; Ammannito, E.; Sizemore, H.; Platz, T.; Byrne, S.; Nathues, A.; Raymond, C. A.

2016-12-01

NASA's Dawn spacecraft arrived at Ceres on March 6, 2015, and has been studying the dwarf planet through a series of successively lower orbits, obtaining morphological and topographical image, mineralogical, elemental composition, and gravity data (Russell et al., 2016). Images taken by Dawn's Framing Camera show a multitude of flow features that were broadly interpreted as ground ice related structures either similar to ice cored/ice cemented flows (as seen on Earth and Mars), long run-out landslides, or fluidized ejecta (as seen on Mars) by Schmidt et al. (2016a and 2016b) and Buczkowski et al. (2016). The aforementioned ice cored/ice cemented-like flows are present only at high latitudes. Results from Dawn's Gamma Ray and Neutron Detector (GRaND) indicate a shallow ice table on Ceres above 45-50°N/S, which supports the interpretation that these flows are ice-rich (Prettyman et al., 2016). A near coincident spectral detection of H2O ice with one of these ice cored/ice cemented-like flows in Oxo crater by Dawn's Visual and Infrared spectrometer (VIR) further bolsters this claim (Combe et al., 2016). We use aggregate spatial and physical properties of these ice attributed cerean flows, such as flow orientation, inclination, preference for north or south facing slopes, drop height to run-out length ratio, geographical location, and areal number density to better understand the rheology and distribution of ground ice in Ceres' uppermost layer. By combining these data with local spectroscopic, global elemental abundance, experimentally derived physical properties of cerean analogue material, and other morphological information (such as the morphologies of flow hosting craters) we intend to further test the ground ice hypothesis for the formation of these flows and constrain the global distribution of near surface ground ice on Ceres to a higher fidelity than what would be possible using GRaND and VIR observations alone. References: Buczkowski et al., (2016) Science, AcceptedCombe, J-P., et al. (2016) Science, AcceptedPrettyman, T. H., et al. (2016) LPSC XVII, Abstract #2228 Russell, et al. (2016) Science, AcceptedSchmidt, B. E., et al. (2016a) LPSC XVII, Abstract #2677 Schmidt, B. E., et al. (2016b), Nature Geoscience, In Review

Quantum entanglement of a harmonic oscillator with an electromagnetic field.

PubMed

Makarov, Dmitry N

2018-05-29

At present, there are many methods for obtaining quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of the Schrodinger equation. There is a need for new methods for obtaining quantum-entangled particles and mathematically accurate studies of such methods. In this paper, a quantum harmonic oscillator (for example, an electron in a magnetic field) interacting with a quantized electromagnetic field is considered. Based on the exact solution of the Schrodinger equation for this system, it is shown that for certain parameters there can be a large quantum entanglement between the electron and the electromagnetic field. Quantum entanglement is analyzed on the basis of a mathematically exact expression for the Schmidt modes and the Von Neumann entropy.

Documentation for the machine-readable version of a deep objective-prism survey for large Magellanic cloud members

NASA Technical Reports Server (NTRS)

Warren, W. H., Jr.

1982-01-01

This catalog contains 1273 proven or probable Large Magellanic Cloud (LMC) members, as found on deep objective-prism plates taken with the Curtis Schmidt telescope at Cerro Tololo Inter-American Observatory in Chile. The stars are generally brighter than about photographic magnitude 14. Approximate spectral types were determined by examination of the 580 A/mm objective-prism spectra; approximate 1975 positions were obtained by measuring relative to the 1975 coordinate grids on the Uppsala-Mount Stromlo Atlas of the LMC (Gascoigne and Westerlund 1961), and approximate photographic magnitudes were determined by averaging image density measures from the plates and image-diameter measures on the 'B' charts. The machine-readable version of the LMC survey catalog is described to enable users to read and process the tape file without problems or guesswork.

Faint blue objects at high Galactic latitude. V - Palomar Schmidt field centered on selected area 71

NASA Technical Reports Server (NTRS)

Usher, Peter D.; Mitchell, Kenneth J.; Warnock, Archibald, III

1988-01-01

Starlike objects with both blue and ultraviolet excess have been selected from a Palomar 1.2 m Schmidt field centered on Kapteyn selected area 71. The method of selection is that used in the previous papers of this series, but modified to account for the differential reddening that occurs across the field. The color classes, color subclasses, positions, and magnitudes of the selected objects are listed.

Improved Schmidt Conversion of Aldehydes to Nitriles Using Azidotrimethylsilane in 1,1,1,3,3,3-Hexafluoro-2-propanol.

PubMed

Motiwala, Hashim F; Yin, Qin; Aubé, Jeffrey

2015-12-29

The Schmidt reaction of aromatic aldehydes using a substoichiometric amount (40 mol %) of triflic acid is described. Low catalyst loading was enabled by a strong hydrogen-bond-donating solvent hexafluoro-2-propanol (HFIP). This improved protocol tolerates a broad scope of aldehydes with diverse functional groups and the corresponding nitriles were obtained in good to high yields without the need for aqueous work up.

Significant Findings from a Water-Quality Study on Prairie Band Potawatomi Reservation, Northeastern Kansas, June 1996 through August 2006

USGS Publications Warehouse

Mehl, Heidi E.; Schmidt, Heather C. Ross; Pope, Larry M.

2007-01-01

Water-quality samples were collected from surface- (stream-) and ground-water sites on and near the Prairie Band Potawatomi Reservation in northeastern Kansas (fig. 1) from June 1996 through August 2006 as part of a cooperative study between the U.S. Geological Survey (USGS) and the Prairie Band Potawatomi Nation (Schmidt and others, 2007). Surface- and ground-water quality were evaluated using applicable drinking-water standards to consider whether these resources can be used in the future to supply drinking water for the reservation. Presently (2007), drinking water on the reservation is purchased from Rural Water District #3 in Jackson County (Sharon Bosse, Prairie Band Potawatomi Nation Department of Planning and Environmental Protection, oral commun., 2007). Results of water-quality analyses are summarized in the following sections. Water-quality activities for this study are documented in several reports (Trombley, 1999, 2001; Schmidt, 2004; Schmidt and others, 2007).

The Liverpool-Edinburgh high proper motion catalogue

NASA Astrophysics Data System (ADS)

Pokorny, R. S.; Jones, H. R. A.; Hambly, N. C.; Pinfield, D. J.

2004-07-01

We present a machine selected catalogue of 11 289 objects with proper motions exceeding 0.18 arcsec yr-1 and an R-band faint magnitude limit of 19.5 mag. The catalogue was produced using SuperCOSMOS digitized R-Band ESO and UK Schmidt Plates in 287 Schmidt fields covering almost 7000 square degrees (˜17% of the whole sky) at the South Galactic Cap. The catalogue includes UK Schmidt BJ and I magnitudes for all of the stars as well as 2MASS magnitudes for 10,447 of the catalogue stars. We also show that the NLTT is ˜95% complete for Dec > -32.5°. The full Table \\ref{tab1} is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/421/763

Beyond the Fermi liquid paradigm: Hidden Fermi liquids

PubMed Central

Jain, J. K.; Anderson, P. W.

2009-01-01

An intense investigation of possible non-Fermi liquid states of matter has been inspired by two of the most intriguing phenomena discovered in the past quarter century, namely, high-temperature superconductivity and the fractional quantum Hall effect. Despite enormous conceptual strides, these two fields have developed largely along separate paths. Two widely employed theories are the resonating valence bond theory for high-temperature superconductivity and the composite fermion theory for the fractional quantum Hall effect. The goal of this perspective article is to note that they subscribe to a common underlying paradigm: They both connect these exotic quantum liquids to certain ordinary Fermi liquids residing in unphysical Hilbert spaces. Such a relation yields numerous nontrivial experimental consequences, exposing these theories to rigorous and definitive tests. PMID:19506260

Length filtration of the separable states.

PubMed

Chen, Lin; Ðoković, Dragomir Ž

2016-11-01

We investigate the separable states ρ of an arbitrary multi-partite quantum system with Hilbert space [Formula: see text] of dimension d . The length L ( ρ ) of ρ is defined as the smallest number of pure product states having ρ as their mixture. The length filtration of the set of separable states, [Formula: see text], is the increasing chain [Formula: see text], where [Formula: see text]. We define the maximum length, [Formula: see text], critical length, L crit , and yet another special length, L c , which was defined by a simple formula in one of our previous papers. The critical length indicates the first term in the length filtration whose dimension is equal to [Formula: see text]. We show that in general d ≤ L c ≤ L crit ≤ L max ≤ d 2 . We conjecture that the equality L crit = L c holds for all finite-dimensional multi-partite quantum systems. Our main result is that L crit = L c for the bipartite systems having a single qubit as one of the parties. This is accomplished by computing the rank of the Jacobian matrix of a suitable map having [Formula: see text] as its range.

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.

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.

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.

Brorfelde Schmidt CCD Catalog (BSCC)

DTIC Science & Technology

2010-06-23

reference stars. Errors of individual positions are about 20 to 200 mas for stars in the R = 10 to 18 mag range. External comparisons with 2MASS and SDSS...reveal possible small systematic errors in the BSCC of up to about 30 mas. The catalog is supplemented with J, H, and Ks magnitudes from the 2MASS ...Survey ( 2MASS ) near-infrared photometry added to the catalog (2). The fil- ters used at the Brorfelde Schmidt for this project are approximating the

Mathematical approach to recover EEG brain signals with artifacts by means of Gram-Schmidt transform

NASA Astrophysics Data System (ADS)

Runnova, A. E.; Zhuravlev, M. O.; Koronovskiy, A. A.; Hramov, A. E.

2017-04-01

A novel method for removing oculomotor artifacts on electroencephalographical signals is proposed and based on the orthogonal Gram-Schmidt transform using electrooculography data. The method has shown high efficiency removal of artifacts caused by spontaneous movements of the eyeballs (about 95-97% correct remote oculomotor artifacts). This method may be recommended for multi-channel electroencephalography data processing in an automatic on-line in a variety of psycho-physiological experiments.

Numerical simulation of a plane turbulent mixing layer, with applications to isothermal, rapid reactions

NASA Technical Reports Server (NTRS)

Lin, P.; Pratt, D. T.

1987-01-01

A hybrid method has been developed for the numerical prediction of turbulent mixing in a spatially-developing, free shear layer. Most significantly, the computation incorporates the effects of large-scale structures, Schmidt number and Reynolds number on mixing, which have been overlooked in the past. In flow field prediction, large-eddy simulation was conducted by a modified 2-D vortex method with subgrid-scale modeling. The predicted mean velocities, shear layer growth rates, Reynolds stresses, and the RMS of longitudinal velocity fluctuations were found to be in good agreement with experiments, although the lateral velocity fluctuations were overpredicted. In scalar transport, the Monte Carlo method was extended to the simulation of the time-dependent pdf transport equation. For the first time, the mixing frequency in Curl's coalescence/dispersion model was estimated by using Broadwell and Breidenthal's theory of micromixing, which involves Schmidt number, Reynolds number and the local vorticity. Numerical tests were performed for a gaseous case and an aqueous case. Evidence that pure freestream fluids are entrained into the layer by large-scale motions was found in the predicted pdf. Mean concentration profiles were found to be insensitive to Schmidt number, while the unmixedness was higher for higher Schmidt number. Applications were made to mixing layers with isothermal, fast reactions. The predicted difference in product thickness of the two cases was in reasonable quantitative agreement with experimental measurements.

Probability density function of a puff dispersing from the wall of a turbulent channel

NASA Astrophysics Data System (ADS)

Nguyen, Quoc; Papavassiliou, Dimitrios

2015-11-01

Study of dispersion of passive contaminants in turbulence has proved to be helpful in understanding fundamental heat and mass transfer phenomena. Many simulation and experimental works have been carried out to locate and track motions of scalar markers in a flow. One method is to combine Direct Numerical Simulation (DNS) and Lagrangian Scalar Tracking (LST) to record locations of markers. While this has proved to be useful, high computational cost remains a concern. In this study, we develop a model that could reproduce results obtained by DNS and LST for turbulent flow. Puffs of markers with different Schmidt numbers were released into a flow field at a frictional Reynolds number of 150. The point of release was at the channel wall, so that both diffusion and convection contribute to the puff dispersion pattern, defining different stages of dispersion. Based on outputs from DNS and LST, we seek the most suitable and feasible probability density function (PDF) that represents distribution of markers in the flow field. The PDF would play a significant role in predicting heat and mass transfer in wall turbulence, and would prove to be helpful where DNS and LST are not always available.

Work distributions for random sudden quantum quenches

NASA Astrophysics Data System (ADS)

Łobejko, Marcin; Łuczka, Jerzy; Talkner, Peter

2017-05-01

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.

How the Hilbert integral theorem inspired flow lines

NASA Astrophysics Data System (ADS)

Winston, Roland; Jiang, Lun

2017-09-01

Nonimaging Optics has been shown to achieve the theoretical limits constrained only by thermodynamic principles. The designing principles of nonimaging optics allow a non-conventional way of thinking about and generating new optical devices. Compared to conventional imaging optics which rarely utilizes the framework of thermodynamic arguments, nonimaging optics chooses to map etendue instead of rays. This fundamental shift of design paradigm frees the optics design from ray based designs which heavily relies on error tolerance analysis. Instead, the underlying thermodynamic principles guide the nonimaging design to be naturally constructed for extended light source for illumination, non-tracking concentrators and sensors that require sharp cut-off angles. We argue in this article that such optical devices which has enabled a multitude of applications depends on probabilities, geometric flux field and radiative heat transfer while "optics" in the conventional sense recedes into the background.

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.

Debris-flow deposits and watershed erosion rates near southern Death Valley, CA, United States

USGS Publications Warehouse

Schmidt, K.M.; Menges, C.M.; ,

2003-01-01

Debris flows from the steep, granitic hillslopes of the Kingston Range, CA are commensurate in age with nearby fluvial deposits. Quaternary chronostratigraphic differentiation of debris-flow deposits is based upon time-dependent characteristics such as relative boulder strength, derived from Schmidt Hammer measurements, degree of surface desert varnish, pedogenesis, and vertical separation. Rock strength is highest for Holocene-aged boulders and decreases for Pleistocene-aged boulders weathering to grus. Volumes of age-stratified debris-flow deposits, constrained by deposit thickness above bedrock, GPS surveys, and geologic mapping, are greatest for Pleistocene deposits. Shallow landslide susceptibility, derived from a topographically based GIS model, in conjunction with deposit volumes produces watershed-scale erosion rates of ???2-47 mm ka-1, with time-averaged Holocene rates exceeding Pleistocene rates. ?? 2003 Millpress.

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

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

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

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.

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.

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).

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.

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.

Reducing Projection Calculation in Quantum Teleportation by Virtue of the IWOP Technique and Schmidt Decomposition of |η〉 State

NASA Astrophysics Data System (ADS)

Fan, Hong-Yi; Fan, Yue

2002-01-01

By virtue of the technique of integration within an ordered product of operators and the Schmidt decomposition of the entangled state |η〉, we reduce the general projection calculation in the theory of quantum teleportation to a as simple as possible form and present a general formalism for teleportating quantum states of continuous variable. The project supported by National Natural Science Foundation of China and Educational Ministry Foundation of China

Muzzle Blast Pressure Loadings upon Aircraft Surfaces

DTIC Science & Technology

1984-02-01

0.02 m Aluminum plate. The plate is instrumented with a linear array of ten piezoelectric pressure transducers, Kistler Model 201B5. The plate is...maintained to insure compatibility of the various sets of 7. E. M. Schmidt, E. J. Gion, and D. D. Shear, "Acoustic Thermometric Measurements of...s -’-’»VA»’ ^I*T^^,*^^T^7.^ MVV-V-VV VV-V-V’-T-^ *7»T REFERENCES 7. E. M. Schmidt, E. J. Gion, and D. D. Shear, "Acoustic Thermometric

Surface colour photometry of galaxies with Schmidt telescopes.

NASA Technical Reports Server (NTRS)

Wray, J. D.

1972-01-01

A method is described which owes its practicality to the capability of Schmidt telescopes to record a number of galaxy images on a single plate and to the existence of high speed computer controlled area-scanning precision microdensitometers such as the Photometric Data Systems model 1010. The method of analysis results in quantitative color-index information which is displayed in a manner that allows any user to effectively study the morphological properties of the distribution of color-index in galaxies.

Local Gram-Schmidt and covariant Lyapunov vectors and exponents for three harmonic oscillator problems

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.

2012-02-01

We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved analytically. The three-dimensional and four-dimensional problems studied here are simultaneously chaotic, time-reversible, and dissipative. Our treatment is intended to be pedagogical, for use in an updated version of our book on Time Reversibility, Computer Simulation, and Chaos. Comments are very welcome.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes.

PubMed

Cafaro, Carlo; Alsing, Paul M

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes

NASA Astrophysics Data System (ADS)

Cafaro, Carlo; Alsing, Paul M.

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

A model of adaptive decision-making from representation of information environment by quantum fields.

PubMed

Bagarello, F; Haven, E; Khrennikov, A

2017-11-13

We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).

A model of adaptive decision-making from representation of information environment by quantum fields

NASA Astrophysics Data System (ADS)

Bagarello, F.; Haven, E.; Khrennikov, A.

2017-10-01

We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme. This article is part of the themed issue `Second quantum revolution: foundational questions'.

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.

Cars Gone Wild: The Major Contributor to Unintended Acceleration in Automobiles is Pedal Error

PubMed Central

Schmidt, Richard A.; Young, Douglas E.

2010-01-01

“Unintended-acceleration” automobile accidents typically begin when the driver first enters the car, starts the engine, and intends to press his/her right foot on the brake while shifting from Park to a drive gear (Drive or Reverse). The driver reports an unintended (uncommanded) full-throttle acceleration, coupled with a loss of braking, until the episode ends in a crash. Pedal misapplications – where the right foot contacts the accelerator instead of the brake that was intended – have been linked to these accidents (Schmidt, 1989, 1993) which, in the 1980s, were thought to occur only at the start of a driving cycle (and/or with the car in Park). But, in 1997, we identified over 200 pedal errors as the cause of accidents reported in the North Carolina database; these crashes occurred during the driving cycle (Schmidt et al., 1997), and/or with the vehicle in a gear other than Park. Our present work provides a more thorough analysis of these North Carolina Police Accident Reports from 1979 to 1995. The vast majority of pedal misapplications (over 92%) (a) occurred during the driving cycle, (b) were generally in “unhurried” conditions, and (c) were categorically separate from those events referred to as unintended-acceleration episodes at start-up. These ideas are explanatory for the recent (2009–2010) surge of unintended-acceleration reports, perhaps even suggesting that all of these crashes are caused by pedal errors, and that none of them are based on some vehicle defect(s). PMID:21833265

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

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.

Discussion of ``Is there a close spatial relationship between faults and plutons?'' by S.R. Paterson and K.L. Schmidt

NASA Astrophysics Data System (ADS)

Richards, Jeremy P.

2001-12-01

Paterson and Schmidt (1999) and Schmidt and Paterson (2000) presented statistical analyses of spatial relationships between faults and plutons from which they ;see no evidence that magma is channeled along faults; (Paterson and Schmidt, 1999, p. 1140). If anything, they conclude, there is an antithetic relationship. As an economic geologist familiar with intrusion-related hydrothermal ore deposits, I was at first surprised by these statements and the bold title of the EOS article: ;Analyses fail to find coupling between deformation and magmatism.; However, after reading the articles I came to understand that these conclusions applied only to plutons emplaced within compressional orogenic belts. Fortunately, most hypabyssal plutons related to magmatic hydrothermal ore deposits are emplaced in tensional or transtensional arc environments, albeit perhaps within a broadly compressional regime. In such settings, structural controls on the localization of ore-forming magmatism are evident, as illustrated by the restriction of several of the world's largest porphyry copper deposits to a single ∼30 km×∼1000 km fault belt (the West Fissure Zone) in northern Chile and southern Peru (Fig. 1; Baker and Guilbert, 1987; Richards et al., 1999, 2001), and more specifically to lineament intersections along its length (Salfity, 1985; Richards, 2000; Richards et al., 2001). Other examples have been provided by Rehrig and Heidrick (1972), Seraphim and Hollister (1976), Titley (1981), Heidrick and Titley (1982), Sylvester and Linke (1993), Sapiie and Cloos (1995), and Cornejo et al. (1997).

Direct numerical simulation of an isothermal reacting turbulent wall-jet

NASA Astrophysics Data System (ADS)

Pouransari, Zeinab; Brethouwer, Geert; Johansson, Arne V.

2011-08-01

In the present investigation, Direct Numerical Simulation (DNS) is used to study a binary irreversible and isothermal reaction in a plane turbulent wall-jet. The flow is compressible and a single-step global reaction between an oxidizer and a fuel species is solved. The inlet based Reynolds, Schmidt, and Mach numbers of the wall-jet are Re = 2000, Sc = 0.72, and M = 0.5, respectively, and a constant coflow velocity is applied above the jet. At the inlet, fuel and oxidizer enter the domain separately in a non-premixed manner. The turbulent structures of the velocity field show the common streaky patterns near the wall, while a somewhat patchy or spotty pattern is observed for the scalars and the reaction rate fluctuations in the near-wall region. The reaction mainly occurs in the upper shear layer in thin highly convoluted reaction zones, but it also takes place close to the wall. Analysis of turbulence and reaction statistics confirms the observations in the instantaneous snapshots, regarding the intermittent character of the reaction rate near the wall. A detailed study of the probability density functions of the reacting scalars and comparison to that of the passive scalar throughout the domain reveals the significance of the reaction influence as well as the wall effects on the scalar distributions. The higher order moments of both the velocities and the scalar concentrations are analyzed and show a satisfactory agreement with experiments. The simulations show that the reaction can both enhance and reduce the dissipation of fuel scalar, since there are two competing effects; on the one hand, the reaction causes sharper scalar gradients and thus a higher dissipation rate, on the other hand, the reaction consumes the fuel scalar thereby reducing the scalar dissipation.

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.

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.

Soft and hard classification by reproducing kernel Hilbert space methods.

PubMed

Wahba, Grace

2002-12-24

Reproducing kernel Hilbert space (RKHS) methods provide a unified context for solving a wide variety of statistical modelling and function estimation problems. We consider two such problems: We are given a training set [yi, ti, i = 1, em leader, n], where yi is the response for the ith subject, and ti is a vector of attributes for this subject. The value of y(i) is a label that indicates which category it came from. For the first problem, we wish to build a model from the training set that assigns to each t in an attribute domain of interest an estimate of the probability pj(t) that a (future) subject with attribute vector t is in category j. The second problem is in some sense less ambitious; it is to build a model that assigns to each t a label, which classifies a future subject with that t into one of the categories or possibly "none of the above." The approach to the first of these two problems discussed here is a special case of what is known as penalized likelihood estimation. The approach to the second problem is known as the support vector machine. We also note some alternate but closely related approaches to the second problem. These approaches are all obtained as solutions to optimization problems in RKHS. Many other problems, in particular the solution of ill-posed inverse problems, can be obtained as solutions to optimization problems in RKHS and are mentioned in passing. We caution the reader that although a large literature exists in all of these topics, in this inaugural article we are selectively highlighting work of the author, former students, and other collaborators.

Mapping the Braiding Properties of Non-Abelian FQHE Liquids.

NASA Astrophysics Data System (ADS)

Prodan, Emil; Haldane, F. D. M.

2007-03-01

Non-Abelian FQHE (NAFQHE) states have elementary excitations that cannot be individually locally-created. When widely separated, they give rise to topological (quasi-)degeneracy of the quantum states; braiding of such non-Abelian quasiparticles (NAQP's) implements unitary transformations among the degenerate states that may be useful for ``topological quantum computing'' (TQC). We have developed a new technique for explicit computation of NAQP braiding in models exhibiting ideal NAFQHE behavior (where the topological degeneracy is exact), in particular the Moore-Read ν = 5/2 state. For systems of small numbers of NAQP's on a sphere, we have computed the non-Abelian Berry curvature and Hilbert space metric, as one NAQP is moved relative to a fixed configuration of the others, showing how the topological properties develop as the system size (NAQP separation) increases. We also studied the effect of perturbations (Coulomb interaction and substrate potentials) that lift the exact degeneracy, and become the dominant corrections when NAQP's are brought together so that quantum measurements can be made; these effects are likely to be crucial in determining whether TQC is viable in NAFQHE systems.

Comprehensive comparisons of geodesic acoustic mode characteristics and dynamics between Tore Supra experiments and gyrokinetic simulations

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

Storelli, A., E-mail: alexandre.storelli@lpp.polytechnique.fr; Vermare, L.; Hennequin, P.

2015-06-15

In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation timemore » are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.« less

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.

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.

A Lower Bound for the Norm of the Solution of a Nonlinear Volterra Equation in One-Dimensional Viscoelasticity.

DTIC Science & Technology

1980-12-09

34, Symp. on Non-well-posed Problems and Logarithmic Convexity (Lecture Notes on Math. #316), pp. 31-5h, Springer, 1973. 3. Greenberg , J.M., MacCamy, R.C...34Continuous Data Dependence for an Abstract Volterra Integro- Differential Equation in Hilbert Space with Applications to Viscoelasticity", Annali Scuola... Hilbert Space", to appear in the J. Applicable Analysis. 8. Slemrod, M., "Instability of Steady Shearing Flows in a Nonlinear Viscoelastic Fluid", Arch

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.

Monte Carlo study for physiological interference reduction in near-infrared spectroscopy based on empirical mode decomposition

NASA Astrophysics Data System (ADS)

Zhang, Yan; Sun, JinWei; Rolfe, Peter

2010-12-01

Near-infrared spectroscopy (NIRS) can be used as the basis of non-invasive neuroimaging that may allow the measurement of haemodynamic changes in the human brain evoked by applied stimuli. Since this technique is very sensitive, physiological interference arising from the cardiac cycle and breathing can significantly affect the signal quality. Such interference is difficult to remove by conventional techniques because it occurs not only in the extracerebral layer but also in the brain tissue itself. Previous work on this problem employing temporal filtering, spatial filtering, and adaptive filtering have exhibited good performance for recovering brain activity data in evoked response studies. However, in this study, we present a time-frequency adaptive method for physiological interference reduction based on the combination of empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). Monte Carlo simulations based on a five-layered slab model of a human adult head were implemented to evaluate our methodology. We applied an EMD algorithm to decompose the NIRS time series derived from Monte Carlo simulations into a series of intrinsic mode functions (IMFs). In order to identify the IMFs associated with symmetric interference, the extracted components were then Hilbert transformed from which the instantaneous frequencies could be acquired. By reconstructing the NIRS signal by properly selecting IMFs, we determined that the evoked brain response is effectively filtered out with even higher signal-to-noise ratio (SNR). The results obtained demonstrated that EMD, combined with HSA, can effectively separate, identify and remove the contamination from the evoked brain response obtained with NIRS using a simple single source-detector pair.

The Quest for Relevant Air Power: Continental European Responses to the Air Power Challenges of the Post-Cold War Era

DTIC Science & Technology

2011-08-01

Air Power Centre]), Col (GS) Thomas Lorber, FüAk (Führungsakademie); Lt Col Dr. Wolfgang Schmidt, Military- Historical Research Office, Potsdam; Lt Gen...Col (GS) Dr. Michael Wolfgang Romba, Col (GS) Hans-Dieter Schön and his staff, Col (GS) Lothar Schmidt, and Lt Col (GS) Michael Trautermann. In the...Multinational Air Wing (DMAW) Project,” accessed 2 March 2007, http://www.euroairgroup.org/act_DMAW.htm. 75. Wolfgang Lange, “Lufttransport—Ansätze

TAUKAM: a new prime-focus camera for the Tautenburg Schmidt Telescope

NASA Astrophysics Data System (ADS)

Stecklum, Bringfried; Eislöffel, Jochen; Klose, Sylvio; Laux, Uwe; Löwinger, Tom; Meusinger, Helmut; Pluto, Michael; Winkler, Johannes; Dionies, Frank

2016-08-01

TAUKAM stands for "TAUtenburg KAMera", which will become the new prime-focus imager for the Tautenburg Schmidt telescope. It employs an e2v 6kx6k CCD and is under manufacture by Spectral Instruments Inc. We describe the design of the instrument and the auxiliary components, its specifications as well as the concept for integrating the device into the telescope infrastructure. First light is foreseen in 2017. TAUKAM will boost the observational capabilities of the telescope for what concerns optical wide-field surveys.

Analysis of turbulent heat transfer, mass transfer, and friction in smooth tubes at high Prandtl and Schmidt numbers

NASA Technical Reports Server (NTRS)

Deissler, Robert G

1955-01-01

The expression for eddy diffusivity from a previous analysis was modified in order to account for the effect of kinematic viscosity on the turbulence in the region close to a wall. By using the modified expression, good agreement was obtained between predicted and experimental results for heat and mass transfer at Prandtl and Schmidt numbers between 0.5 and 3000. The effects of length-to-diameter ratio and of variable viscosity were also investigated for a wide range of Prandtl numbers.

Variational calculations of subbands in a quantum well with uniform electric field - Gram-Schmidt orthogonalization approach

NASA Technical Reports Server (NTRS)

Ahn, Doyeol; Chuang, S. L.

1986-01-01

Variational calculations of subband eigenstates in an infinite quantum well with an applied electric field using Gram-Schmidt orthogonalized trial wave functions are presented. The results agree very well with the exact numerical solutions even up to 1200 kV/cm. It is also shown that, for increasing electric fields, the energy of the ground state decreases, while that of higher subband states increases slightly up to 1000 kV/cm and then decreases for a well size of 100 A.

A Battalion Staff Prepared for War: The Key to Combined Arms Success on the Modern Tactical Battlefield,

DTIC Science & Technology

1988-03-10

comoat sunort Droblems put the 3d Battalion in a Drecarious Dosition On 4 November. First, the Kall River trail, the major route from the division to...was to maintain one- way traffic through to the Kall River bridge while Company A did the same from the bridge to Schmidt. C Company, in reserve...supply weasels from the 3d Battalion crossed the Kall . (52) Meanwhile, in Schmidt the 3d Battalion prepared to defend. * The battalion had no combined arms

My Visit to La Silla

NASA Astrophysics Data System (ADS)

Muller, A.

1988-09-01

The Director General of ESO, Harry van der Laan, invited me to La Silla as consultant during the realuminization and the optical trimming of the ESO Schmidt telescope. I was very happy with this invitation because it gave me an opportunity not only to spend some time at the Schmidt, but also to meet with many friends in Chile. At La Silla I had the good luck to meet Richard West who suggested to me to write a short contribution for the Messenger about my stay in Chile which I have done with pleasure.

Quasi-probabilities in conditioned quantum measurement and a geometric/statistical interpretation of Aharonov's weak value

NASA Astrophysics Data System (ADS)

Lee, Jaeha; Tsutsui, Izumi

2017-05-01

We show that the joint behavior of an arbitrary pair of (generally noncommuting) quantum observables can be described by quasi-probabilities, which are an extended version of the standard probabilities used for describing the outcome of measurement for a single observable. The physical situations that require these quasi-probabilities arise when one considers quantum measurement of an observable conditioned by some other variable, with the notable example being the weak measurement employed to obtain Aharonov's weak value. Specifically, we present a general prescription for the construction of quasi-joint probability (QJP) distributions associated with a given combination of observables. These QJP distributions are introduced in two complementary approaches: one from a bottom-up, strictly operational construction realized by examining the mathematical framework of the conditioned measurement scheme, and the other from a top-down viewpoint realized by applying the results of the spectral theorem for normal operators and their Fourier transforms. It is then revealed that, for a pair of simultaneously measurable observables, the QJP distribution reduces to the unique standard joint probability distribution of the pair, whereas for a noncommuting pair there exists an inherent indefiniteness in the choice of such QJP distributions, admitting a multitude of candidates that may equally be used for describing the joint behavior of the pair. In the course of our argument, we find that the QJP distributions furnish the space of operators in the underlying Hilbert space with their characteristic geometric structures such that the orthogonal projections and inner products of observables can be given statistical interpretations as, respectively, “conditionings” and “correlations”. The weak value Aw for an observable A is then given a geometric/statistical interpretation as either the orthogonal projection of A onto the subspace generated by another observable B, or equivalently, as the conditioning of A given B with respect to the QJP distribution under consideration.

Studying Weather and Climate Extremes in a Non-stationary Framework

NASA Astrophysics Data System (ADS)

Wu, Z.

2010-12-01

The study of weather and climate extremes often uses the theory of extreme values. Such a detection method has a major problem: to obtain the probability distribution of extremes, one has to implicitly assume the Earth’s climate is stationary over a long period within which the climatology is defined. While such detection makes some sense in a purely statistical view of stationary processes, it can lead to misleading statistical properties of weather and climate extremes caused by long term climate variability and change, and may also cause enormous difficulty in attributing and predicting these extremes. To alleviate this problem, here we report a novel non-stationary framework for studying weather and climate extremes in a non-stationary framework. In this new framework, the weather and climate extremes will be defined as timescale-dependent quantities derived from the anomalies with respect to non-stationary climatologies of different timescales. With this non-stationary framework, the non-stationary and nonlinear nature of climate system will be taken into account; and the attribution and the prediction of weather and climate extremes can then be separated into 1) the change of the statistical properties of the weather and climate extremes themselves and 2) the background climate variability and change. The new non-stationary framework will use the ensemble empirical mode decomposition (EEMD) method, which is a recent major improvement of the Hilbert-Huang Transform for time-frequency analysis. Using this tool, we will adaptively decompose various weather and climate data from observation and climate models in terms of the components of the various natural timescales contained in the data. With such decompositions, the non-stationary statistical properties (both spatial and temporal) of weather and climate anomalies and of their corresponding climatologies will be analyzed and documented.

Entanglement spectrum as a generalization of entanglement entropy: identification of topological order in non-Abelian fractional quantum Hall effect states.

PubMed

Li, Hui; Haldane, F D M

2008-07-04

We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wave function for the nu=5/2 fractional quantum Hall state with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model state, these are the only levels, while in the "generic" case, they are separated from the rest of the spectrum by a clear "entanglement gap", which appears to remain finite in the thermodynamic limit. We propose that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order.

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.

Multi-fluid Dynamics for Supersonic Jet-and-Crossflows and Liquid Plug Rupture

NASA Astrophysics Data System (ADS)

Hassan, Ezeldin A.

Multi-fluid dynamics simulations require appropriate numerical treatments based on the main flow characteristics, such as flow speed, turbulence, thermodynamic state, and time and length scales. In this thesis, two distinct problems are investigated: supersonic jet and crossflow interactions; and liquid plug propagation and rupture in an airway. Gaseous non-reactive ethylene jet and air crossflow simulation represents essential physics for fuel injection in SCRAMJET engines. The regime is highly unsteady, involving shocks, turbulent mixing, and large-scale vortical structures. An eddy-viscosity-based multi-scale turbulence model is proposed to resolve turbulent structures consistent with grid resolution and turbulence length scales. Predictions of the time-averaged fuel concentration from the multi-scale model is improved over Reynolds-averaged Navier-Stokes models originally derived from stationary flow. The response to the multi-scale model alone is, however, limited, in cases where the vortical structures are small and scattered thus requiring prohibitively expensive grids in order to resolve the flow field accurately. Statistical information related to turbulent fluctuations is utilized to estimate an effective turbulent Schmidt number, which is shown to be highly varying in space. Accordingly, an adaptive turbulent Schmidt number approach is proposed, by allowing the resolved field to adaptively influence the value of turbulent Schmidt number in the multi-scale turbulence model. The proposed model estimates a time-averaged turbulent Schmidt number adapted to the computed flowfield, instead of the constant value common to the eddy-viscosity-based Navier-Stokes models. This approach is assessed using a grid-refinement study for the normal injection case, and tested with 30 degree injection, showing improved results over the constant turbulent Schmidt model both in mean and variance of fuel concentration predictions. For the incompressible liquid plug propagation and rupture study, numerical simulations are conducted using an Eulerian-Lagrangian approach with a continuous-interface method. A reconstruction scheme is developed to allow topological changes during plug rupture by altering the connectivity information of the interface mesh. Rupture time is shown to be delayed as the initial precursor film thickness increases. During the plug rupture process, a sudden increase of mechanical stresses on the tube wall is recorded, which can cause tissue damage.

Blessing of dimensionality: mathematical foundations of the statistical physics of data.

PubMed

Gorban, A N; Tyukin, I Y

2018-04-28

The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Blessing of dimensionality: mathematical foundations of the statistical physics of data

NASA Astrophysics Data System (ADS)

Gorban, A. N.; Tyukin, I. Y.

2018-04-01

The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality. This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction. This article is part of the theme issue `Hilbert's sixth problem'.

Three dimensional empirical mode decomposition analysis apparatus, method and article manufacture

NASA Technical Reports Server (NTRS)

Gloersen, Per (Inventor)

2004-01-01

An apparatus and method of analysis for three-dimensional (3D) physical phenomena. The physical phenomena may include any varying 3D phenomena such as time varying polar ice flows. A repesentation of the 3D phenomena is passed through a Hilbert transform to convert the data into complex form. A spatial variable is separated from the complex representation by producing a time based covariance matrix. The temporal parts of the principal components are produced by applying Singular Value Decomposition (SVD). Based on the rapidity with which the eigenvalues decay, the first 3-10 complex principal components (CPC) are selected for Empirical Mode Decomposition into intrinsic modes. The intrinsic modes produced are filtered in order to reconstruct the spatial part of the CPC. Finally, a filtered time series may be reconstructed from the first 3-10 filtered complex principal components.

Uniform sparse bounds for discrete quadratic phase Hilbert transforms

NASA Astrophysics Data System (ADS)

Kesler, Robert; Arias, Darío Mena

2017-09-01

For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form < H^{α } f , g > for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.

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.

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.

Psychological aspects of retirement: About Schmidt (2002), and Everybody's Fine (2009).

PubMed

Wolman, Thomas

2011-06-01

With the films About Schmidt and Everybody's Fine as his main point of reference, the author elucidates the complex and often melancholic sojourn that follows ordinary men's retirement from their jobs. As this usually occurs during late middle age, the complicating variable of spousal loss, departure of children from the family home, a failing body, and social marginalization also get added to the picture. The vicissitudes of the resulting intrapsychic and interpersonal upheaval can lead to depressive withdrawal or a renewed effort at finding meaning in life. Ego resilience is tested and sublimation and creativity, if possible, save the day.

The Tidbinbilla-U.K. Schmidt radio quasar identification program

NASA Technical Reports Server (NTRS)

Jauncey, D. L.; Batty, M. J.; Savage, A.; Gulkis, S.

1983-01-01

A program is under way at Tidbinbilla to measure accurate (up to 2 arcsec r.m.s) radio positions for compact sources in the Parkes 2.7 GHz survey south of declination -30 deg. Optical identifications are being made on the basis of radio-optical position coincidence alone, without regard to colour or morphology, using the U.K. Schmidt IIIa-J sky survey to a limiting magnitude of 22.5. This program is aimed at producing an evaluation of the radio quasar redshift distribution with particular emphasis on those objects with redshifts greater than 3.0.

Syntheses of the Stemona Alkaloids (±)-Stenine, (±)-Neostenine, and (±)-13-Epineostenine Using a Stereodivergent Diels-Alder/Azido-Schmidt Reaction

PubMed Central

Frankowski, Kevin J.; Golden, Jennifer E.; Zeng, Yibin; Lei, Yao; Aubé, Jeffrey

2009-01-01

A tandem Diels-Alder/azido Schmidt reaction sequence provides rapid access to the core skeleton shared by several Stemona alkaloids including stenine, neostenine, tuberstemonine, and neotubererostemonine. The discovery and evolution of inter- and intramolecular variations of this process and their applications to total syntheses of (±)–stenine and (±)–neostenine is described. The stereochemical outcome of the reaction depends on both substrate type and reaction condition, enabling the preparation of both (±)–stenine and (±)–neostenine from the same diene/dienophile combination. PMID:18396881

Quantum mechanics of Klein-Gordon fields I: Hilbert Space, localized states, and chiral symmetry

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

Mostafazadeh, A.; Zamani, F.

2006-09-15

We derive an explicit manifestly covariant expression for the most general positive-definite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. This expression involves a one-parameter family of conserved current densities J{sub a}{sup {mu}}, with a-bar (-1,1), that are analogous to the chiral current density for spin half fields. The conservation of J{sub a}{sup {mu}} is related to a global gauge symmetry of the Klein-Gordon fields whose gauge group is U(1) for rational a and the multiplicative group of positive real numbers for irrational a. We show that the associated gauge symmetry is responsible for themore » conservation of the total probability of the localization of the field in space. This provides a simple resolution of the paradoxical situation resulting from the fact that the probability current density for free scalar fields is neither covariant nor conserved. Furthermore, we discuss the implications of our approach for free real scalar fields offering a direct proof of the uniqueness of the relativistically invariant positive-definite inner product on the space of real Klein-Gordon fields. We also explore an extension of our results to scalar fields minimally coupled to an electromagnetic field.« less

What killed Karl Patterson Schmidt? Combined venom gland transcriptomic, venomic and antivenomic analysis of the South African green tree snake (the boomslang), Dispholidus typus.

PubMed

Pla, Davinia; Sanz, Libia; Whiteley, Gareth; Wagstaff, Simon C; Harrison, Robert A; Casewell, Nicholas R; Calvete, Juan J

2017-04-01

Non-front-fanged colubroid snakes comprise about two-thirds of extant ophidian species. The medical significance of the majority of these snakes is unknown, but at least five species have caused life-threatening or fatal human envenomings. However, the venoms of only a small number of species have been explored. A combined venomic and venom gland transcriptomic approach was employed to characterise of venom of Dispholidus typus (boomslang), the snake that caused the tragic death of Professor Karl Patterson Schmidt. The ability of CroFab™ antivenom to immunocapture boomslang venom proteins was investigated using antivenomics. Transcriptomic-assisted proteomic analysis identified venom proteins belonging to seven protein families: three-finger toxin (3FTx); phospholipase A 2 (PLA 2 ); cysteine-rich secretory proteins (CRISP); snake venom (SV) serine proteinase (SP); C-type lectin-like (CTL); SV metalloproteinases (SVMPs); and disintegrin-like/cysteine-rich (DC) proteolytic fragments. CroFab™ antivenom efficiently immunodepleted some boomslang SVMPs. The present work is the first to address the overall proteomic profile of D. typus venom. This study allowed us to correlate the toxin composition with the toxic activities of the venom. The antivenomic analysis suggested that the antivenom available at the time of the unfortunate accident could have exhibited at least some immunoreactivity against the boomslang SVMPs responsible for the disseminated intravascular coagulation syndrome that caused K.P. Schmidt's fatal outcome. This study may stimulate further research on other non-front-fanged colubroid snake venoms capable of causing life-threatening envenomings to humans, which in turn should contribute to prevent fatal human accidents, such as that unfortunately suffered by K.P. Schmidt. Copyright © 2017 The Author(s). Published by Elsevier B.V. All rights reserved.

Understanding Spatial and Temporal Variations of Arctic Circulation Using Oxygen Isotopes of Seawater

NASA Astrophysics Data System (ADS)

Yin, L.; Kopans-Johnson, C. R.; LeGrande, A. N.; Kelly, S.

2015-12-01

The isotopic ratio of 18O to 16O in seawater (2005ppm in ocean water is defined as 𝛿18Oseawater≡0 permil or 0‰) is a fundamental ocean tracer due to its distinct linear relationship with salinity(𝛿18O -S) from regional inland freshwater sources. As opposed to salinity alone, 𝛿18O distinguishes river runoff from sea-ice melt and traces ocean circulation pathways from coastal to open waters and surface to deep waters. Observations from the past 60 years of 𝛿18O seawater were compiled into a database by Schimdt et al. (1999), and subsequently used to calculate a 3-dimensional 1°x1° 𝛿18O global gridded dataset by LeGrande and Schmidt (2006). Although the Schmidt et al. (1999) Global Seawater Oxygen-18 Database (𝛿18Oobs) contains 25,514 measurements used to calculate the global gridded dataset, LeGrande and Schmidt (2006) point out that, "data coverage varies greatly from region to region," with seasonal variability creating biases in areas where sea ice is present. Python Pandas is used to automate the addition of 2,942 records to the Schmidt et al. (1999) Global Seawater Oxygen-18 Database (𝛿18Oobs), and examine the spatial and temporal distributions of 18O in the Arctic Ocean. 10 initial water masses are defined using spatial and temporal trends, clusters of observations, and Arctic surface circulation. Jackknife slope analysis of water mass 𝛿18O -S is used to determine anomalous data points and regional hydrology, resulting in 4 distinct Arctic water masses. These techniques are used to improve the gridded 𝛿18Oseawater dataset by distinguishing unique water masses, and accounting for seasonal variability of complex high latitude areas.

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.

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.

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.

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)].

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.

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.

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.

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.

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.

A medium-bright quasar sample - New quasar surface densities in the magnitude range from 16.4 to 17.65 for B

NASA Technical Reports Server (NTRS)

Mitchell, K. J.; Warnock, A., III; Usher, P. D.

1984-01-01

A new medium-bright quasar sample (MBQS) is constructed from spectroscopic observations of 140 bright objects selected for varying degrees of blue and ultraviolet excess (B-UVX) in five Palomar 1.2 m Schmidt fields. The MBQS contains 32 quasars with B less than 17.65 mag. The new integral surface densities in the B range from 16.45 to 17.65 mag are approximately 40 percent (or more) higher than expected. The MBQS and its redshift distribution increase the area of the Hubble diagram covered by complete samples of quasars. The general spectroscopic results indicate that the three-color classification process used to catalog the spectroscopic candidates (1) has efficiently separated the intrinsically B-UVX stellar objects from the Population II subdwarfs and (2) has produced samples of B-UVX objects which are more complete than samples selected by (U - B) color alone.

Development of the Subaru-Mitaka-Okayama-Kiso Archive System

NASA Astrophysics Data System (ADS)

Baba, Hajime; Yasuda, Naoki; Ichikawa, Shin-Ichi; Yagi, Masafumi; Iwamoto, Nobuyuki; Takata, Tadafumi; Horaguchi, Toshihiro; Taga, Masatoshi; Watanabe, Masaru; Ozawa, Tomohiko; Hamabe, Masaru

We have developed the Subaru-Mitaka-Okayama-Kiso-Archive (SMOKA) public science archive system which provides access to the data of the Subaru Telescope, the 188 cm telescope at Okayama Astrophysical Observatory, and the 105 cm Schmidt telescope at Kiso Observatory/University of Tokyo. SMOKA is the successor of the MOKA3 system. The user can browse the Quick-Look Images, Header Information (HDI) and the ASCII Table Extension (ATE) of each frame from the search result table. A request for data can be submitted in a simple manner. The system is developed with Java Servlet for the back-end, and Java Server Pages (JSP) for content display. The advantage of JSP's is the separation of the front-end presentation from the middle- and back-end tiers which led to an efficient development of the system. The SMOKA homepage is available at SMOKA

VizieR Online Data Catalog: Binary white dwarfs atmospheric parameters (Gianninas+, 2014)

NASA Astrophysics Data System (ADS)

Gianninas, A.; Dufour, P.; Kilic, M.; Brown, W. R.; Bergeron, P.; Hermes, J. J.

2017-04-01

The sample that we analyze includes a total of 61 ELM WD binaries from the ELM Survey (Brown et al. 2013, J/ApJ/769/66). The bulk of this sample is comprised of the 58 ELM WDs listed in Table 3 of Brown et al. (2013, J/ApJ/769/66), but also includes three additional ELM WDs that have been published in separate papers since then. The spectra of these 61 ELM WDs were obtained using five distinct setups on two different telescopes. A total of 57 targets were observed with the 6.5m MMT telescope with the Blue Channel spectrograph (Schmidt et al. 1989PASP..101..713S). The four remaining targets were observed using the Fred Lawrence Whipple Observatory's (FLWO) 1.5m Tilinghast telescope equipped with the FAST spectrograph (Fabricant et al. 1998PASP..110...79F) and the 600 line/mm grating. (2 data files).

Characteristics of an Imaging Polarimeter for the Powell Observatory

NASA Astrophysics Data System (ADS)

Hall, Shannon; Henson, G.

2010-01-01

A dual-beam imaging polarimeter has been built for use on the 14 inch Schmidt-Cassegrain telescope at the ETSU Harry D. Powell Observatory. The polarimeter includes a rotating half-wave plate and a Wollaston prism to separate light into two orthogonal linearly polarized rays. A TEC cooled CCD camera is used to detect the modulated polarized light. We present here measurements of the polarization of polarimetric standard stars. By measuring unpolarized and polarized standard stars we are able to establish the instrumental polarization and the efficiency of the instrument. The polarimeter will initially be used as a dedicated instrument in an ongoing project to monitor the eclipsing binary star, Epsilon Aurigae. This project was funded by a partnership between the National Science Foundation (NSF AST-0552798), Research Experience for Undergraduates (REU), and the Department of Defense (DoD) ASSURE (Awards to Stimulate and Support Undergraduate Research Experiences) programs.

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.

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.

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

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.

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 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.

WHAT? A Large Reflective Schmidt Telescope for the Antarctic Plateau

NASA Astrophysics Data System (ADS)

Saunders, W.; McGrath, A. J.

We present a design concept for WHAT the Wide-field Antarctic Horizontal Telescope to take advantage of the unique possibilities of Antarctica for both optical and near infrared astronomy. The design is an 8 metre, wide-field, fixed-axis, all-reflective, f/4 Schmidt telescope. Prime and Cassegrain (or Gregorian) foci are provided, giving plate scales 150-1500 μ m/'', over fields of view 3'-3circ. Diffraction limited, NGSAO-corrected K_dark images are possible over arc-minute sized fields, over most of the sky. The sensitivity, resolution, field of view and cost all compare favourably with current or proposed space or ground-based telescopes.

VizieR Online Data Catalog: Ultraviolet Excess Galaxies (Mitchell+ 1982)

NASA Astrophysics Data System (ADS)

Mitchell, K. J.; Brotzman, L. E.; Warnock, A.; Usher, P. D.

2015-05-01

The catalog contains a list of 412 faint galaxies selected for their apparent ultraviolet excess. The galaxies were selected from a 3-color (UBV) plate taken with the Palomar 48-inch Schmidt telescope. The 14-inch-square plates cover an area of 30 square degrees centered on Kapteyn Selected Area 28. The catalog includes running numbers, coordinates, color codes, magnitude codes, morphologies, diameters, and notes. The catalogued galaxies were selected by eye from the Palomar Schmidt 3-color (UBV) plate PS24771, centered on Kapteyn Selexted Area 28 and taken by Usher under conditions of good seeing and transparency. (1 data file).

Modeling Turbulent Combustion for Variable Prandtl and Schmidt Number

NASA Technical Reports Server (NTRS)

Hassan, H. A.

2004-01-01

This report consists of two abstracts submitted for possible presentation at the AIAA Aerospace Science Meeting to be held in January 2005. Since the submittal of these abstracts we are continuing refinement of the model coefficients derived for the case of a variable Turbulent Prandtl number. The test cases being investigated are a Mach 9.2 flow over a degree ramp and a Mach 8.2 3-D calculation of crossing shocks. We have developed an axisymmetric code for treating axisymmetric flows. In addition the variable Schmidt number formulation was incorporated in the code and we are in the process of determining the model constants.

Undersized description on motile gyrotactic micro-organisms individualities in MHD stratified water-based Newtonian nanofluid

NASA Astrophysics Data System (ADS)

Rehman, Khalil Ur; Malik, Aneeqa Ashfaq; Tahir, M.; Malik, M. Y.

2018-03-01

The current pagination summarized the influence of bio-convection Schmidt number, bio-convection Peclet number and micro-organisms concentration difference parameter on the density of motile gyrotactic micro-organisms when they have interaction with the thermally stratified magneto-nanofluid flow past a vertical stretching surface. It is observed that the density of motile microorganisms is the decreasing function of the bio-convection Schmidt and Peclet numbers. It is trusted that the outcomes of present analysis will serve as a helping source for the upcoming developments regarding individualities of motile gyrotactic micro-organisms subject to boundary layer flows induced by stretching surfaces.

The Wide-Field Infrared Survey Explorer (WISE): Mission Description and Initial On-Orbit Performance

NASA Technical Reports Server (NTRS)

Wright, Edward L.; Eisenhardt, Peter R. M.; Mainzer, Amy; Ressler, Michael E.; Cutri, Roc M.; Jarrett, Thomas; Kirkpatrick, J. Davy; Padgett, Deborah; McMillan, Robert S.; Skrutskie,Michael;

Effect of Schmidt number on mass transfer across a sheared gas-liquid interface in a wind-driven turbulence.

PubMed

Takagaki, Naohisa; Kurose, Ryoichi; Kimura, Atsushi; Komori, Satoru

2016-11-14

The mass transfer across a sheared gas-liquid interface strongly depends on the Schmidt number. Here we investigate the relationship between mass transfer coefficient on the liquid side, k L , and Schmidt number, Sc, in the wide range of 0.7 ≤ Sc ≤ 1000. We apply a three-dimensional semi direct numerical simulation (SEMI-DNS), in which the mass transfer is solved based on an approximated deconvolution model (ADM) scheme, to wind-driven turbulence with mass transfer across a sheared wind-driven wavy gas-liquid interface. In order to capture the deforming gas-liquid interface, an arbitrary Lagrangian-Eulerian (ALE) method is employed. Our results show that similar to the case for flat gas-liquid interfaces, k L for the wind-driven wavy gas-liquid interface is generally proportional to Sc -0.5 , and can be roughly estimated by the surface divergence model. This trend is endorsed by the fact that the mass transfer across the gas-liquid interface is controlled mainly by streamwise vortices on the liquid side even for the wind-driven turbulence under the conditions of low wind velocities without wave breaking.

Effect of Schmidt number on mass transfer across a sheared gas-liquid interface in a wind-driven turbulence

PubMed Central

Takagaki, Naohisa; Kurose, Ryoichi; Kimura, Atsushi; Komori, Satoru

2016-01-01

The mass transfer across a sheared gas-liquid interface strongly depends on the Schmidt number. Here we investigate the relationship between mass transfer coefficient on the liquid side, kL, and Schmidt number, Sc, in the wide range of 0.7 ≤ Sc ≤ 1000. We apply a three-dimensional semi direct numerical simulation (SEMI-DNS), in which the mass transfer is solved based on an approximated deconvolution model (ADM) scheme, to wind-driven turbulence with mass transfer across a sheared wind-driven wavy gas-liquid interface. In order to capture the deforming gas-liquid interface, an arbitrary Lagrangian-Eulerian (ALE) method is employed. Our results show that similar to the case for flat gas-liquid interfaces, kL for the wind-driven wavy gas-liquid interface is generally proportional to Sc−0.5, and can be roughly estimated by the surface divergence model. This trend is endorsed by the fact that the mass transfer across the gas-liquid interface is controlled mainly by streamwise vortices on the liquid side even for the wind-driven turbulence under the conditions of low wind velocities without wave breaking. PMID:27841325

Contribution to knowledge of the genus Chydaeus in Xizang Autonomous Region [Tibet] and Yunnan Province, China (Coleoptera, Carabidae, Harpalini)

PubMed Central

Kataev, Boris M.; Liang, Hongbin; Kavanaugh, David H.

2012-01-01

Abstract Five new species of the genus Chydaeus Chaudoir, 1854 are described from China: Chydaeus fugongensis sp. n. (Shibali, Fugong County, Yunnan Province), Chydaeus gutangensis sp. n. (Gutang, Medog County, Xizang Autonomous Region [Tibet]), Chydaeus hanmiensis sp. n. (Hanmi, Medog County, Xizang Autonomous Region [Tibet]), Chydaeus asetosus sp. n. (NE of Fugong, Yunnan Province), and Chydaeus baoshanensis sp. n. (N of Baoshan, Yunnan Province). Taxonomic and faunistic notes on eleven other species occurring in Xizang and Yunnan are also provided. Chydaeus shunichii Ito, 2006 is re-described, based on specimens from Lushui County, Yunnan. Chydaeus kumei Ito, 1992 is treated as a subspecies of Chydaeus andrewesi Schauberger, 1932 [NEW STATUS]. The taxonomic status of Chydaeus guangxiensis Ito, 2006 is discussed. The following taxa are recorded from China for the first time: Chydaeus obtusicollis Schauberger, 1932 (Xizang and Yunnan), Chydaeus malaisei Kataev & Schmidt, 2006 (Yunnan), Chydaeus semenowi (Tschitschérine, 1899) (Xizang and Yunnan), Chydaeus andrewesi andrewesi Schauberger, 1932 (Xizang and Yunnan), Chydaeus andrewesi kumei Ito (Yunnan), Chydaeus bedeli interjectus Kataev & Schmidt, 2002 (Xizang), and Chydaeus bedeli vietnamensis Kataev & Schmidt, 2002 (Yunnan). PMID:22423195

PKP Waveform Complexity and Its Implications to Fine Structure Near the Edge of African Large Low Shear Velocity Province

NASA Astrophysics Data System (ADS)

Song, Teh-Ru Alex; Tanaka, Satoru; Takeuchi, Nozomu

2010-05-01

P wave traveling through the Earth's core typically includes three distinct phases, PKPdf (or PKIKP), PKPbc and PKPab and these waves have been frequently analyzed to study the structure of the outer-core and inner-core. It is well known that PKPab waveform suffers a 90-degree phase shift when encountering an internal acoustics in the outer-core and it is theoretically equivalent to Hilbert-transformed PKPbc (or PKPdf) waveform. Here, we report a dataset from an intermediate-depth earthquake in Vanuatu Islands recorded by a PASSCAL broadband array in Cameroon, West Africa. Two anomalous features stand out in this record section. First, in the period of a few seconds and longer, most PKPab waveforms recorded by this array are anomalous in a way that they do not display a 90-degree phase shift that is observed in other stations in Europe. Secondly, in the high frequency band of 0.5 Hz to 2 Hz, two large arrivals separated by about 3.4 seconds are observed in the time window of PKPab phase and they are often absent in the time window of PKPdf and PKPbc phases. In addition, the second arrival seems suffer some degree of phase shift relative to the first arrival. We examine several other record sections from nearby events in Tonga and they do not show such an anomalous feature, suggesting that receiver structures are probably not the cause of this observation. Note that the take-off angle of PKPab is typically 9-12 degrees shallower than that of PKPdf and PKPbc and it is possible that near-source scattering from the slab may account for such an anomalous feature. We make Hilbert transform of P waveforms recorded at shorter range of less than 90 degrees and compare them with these anomalous PKPab waveforms. However, these Hilbert-transformed P wave show a clear 90-degree phase shift relative to PKPdf and PKPbc and they are different from PKPab waveforms, despite a difference in take-off angles of less than 5 degrees in some cases. It appears that near-source scatterings and receiver-side structure do not play a predominant role in generating these anomalous PKPab waveforms. We then look into structural anomaly near the core-mantle-boundary (CMB) since PKPab grazes the CMB at a very shallow angle and it can effectively interact with it and possibly produce anomalous PKPab waveforms. We first explore 1-D model space by introducing velocity anomaly directly above the CMB, with a velocity perturbation up to a few tens of percents in S wave velocity and P wave velocity. We calculate synthetics up to 2 Hz by Direct Solution Method (DSM) and Reflectivity Method to examine waveform anomaly at long period band (0.01-0.2 Hz) as well as short-period band (0.5-2 Hz). Our preliminary result indicates that the model with a thin (~ 15 km) ultra-low velocity zone (ULVZ, 30% reduction in P wave and S wave velocity) is capable of reproducing characteristics of these anomalous PKPab waveforms at both frequency bands. The pierce points of PKPab in the source side at CMB are near the southeast Indian Ocean where S wave velocity is only slightly faster than PREM. On the other hand, the pierce points in the receiver side are at the eastern edge of the African Large Low Shear Velocity Province (LLSVP). One interesting feature of our ULVZ model is that dlnVs/dlnVp is about 1, which is different from most ULVZ models where dlnVs/dlnVp is about 3.

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.

Quantifying entanglement properties of qudit mixed states with incomplete permutation symmetry

NASA Astrophysics Data System (ADS)

Barasiński, Artur; Nowotarski, Mateusz

2017-04-01

The characterization of entanglement properties in mixed states is important from both a theoretical and a practical point of view. While the estimation of entanglement of bipartite pure states is well established, for mixed states it is a considerably much harder task. The key elements of the mixed-state entanglement theory are given by the exact solutions which sometimes are possible for special states of high symmetry problems. In this paper, we present the exact investigation on the entanglement properties for a five-parameter family of highly symmetric two-qudit mixed states with equal but arbitrary finite local Hilbert space dimension. We achieve this by extensive analysis of various conditions of separability and the entanglement classification with respect to stochastic local operations and classical communication. Furthermore, our results can be used for an arbitrary state by proper application of the proposed twirling operator.

Dynamics for a 2-vertex quantum gravity model

NASA Astrophysics Data System (ADS)

Borja, Enrique F.; Díaz-Polo, Jacobo; Garay, Iñaki; Livine, Etera R.

2010-12-01

We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N)-invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.

Fast underdetermined BSS architecture design methodology for real time applications.

PubMed

Mopuri, Suresh; Reddy, P Sreenivasa; Acharyya, Amit; Naik, Ganesh R

2015-01-01

In this paper, we propose a high speed architecture design methodology for the Under-determined Blind Source Separation (UBSS) algorithm using our recently proposed high speed Discrete Hilbert Transform (DHT) targeting real time applications. In UBSS algorithm, unlike the typical BSS, the number of sensors are less than the number of the sources, which is of more interest in the real time applications. The DHT architecture has been implemented based on sub matrix multiplication method to compute M point DHT, which uses N point architecture recursively and where M is an integer multiples of N. The DHT architecture and state of the art architecture are coded in VHDL for 16 bit word length and ASIC implementation is carried out using UMC 90 - nm technology @V DD = 1V and @ 1MHZ clock frequency. The proposed architecture implementation and experimental comparison results show that the DHT design is two times faster than state of the art architecture.

Mesoscopic Fluctuations for the Thinned Circular Unitary Ensemble

NASA Astrophysics Data System (ADS)

Berggren, Tomas; Duits, Maurice

2017-09-01

In this paper we study the asymptotic behavior of mesoscopic fluctuations for the thinned Circular Unitary Ensemble. The effect of thinning is that the eigenvalues start to decorrelate. The decorrelation is stronger on the larger scales than on the smaller scales. We investigate this behavior by studying mesoscopic linear statistics. There are two regimes depending on the scale parameter and the thinning parameter. In one regime we obtain a CLT of a classical type and in the other regime we retrieve the CLT for CUE. The two regimes are separated by a critical line. On the critical line the limiting fluctuations are no longer Gaussian, but described by infinitely divisible laws. We argue that this transition phenomenon is universal by showing that the same transition and their laws appear for fluctuations of the thinned sine process in a growing box. The proofs are based on a Riemann-Hilbert problem for integrable operators.

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.

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.

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

Method and device for landing aircraft dependent on runway occupancy time

NASA Technical Reports Server (NTRS)

Ghalebsaz Jeddi, Babak (Inventor)

2012-01-01

A technique for landing aircraft using an aircraft landing accident avoidance device is disclosed. The technique includes determining at least two probability distribution functions; determining a safe lower limit on a separation between a lead aircraft and a trail aircraft on a glide slope to the runway; determining a maximum sustainable safe attempt-to-land rate on the runway based on the safe lower limit and the probability distribution functions; directing the trail aircraft to enter the glide slope with a target separation from the lead aircraft corresponding to the maximum sustainable safe attempt-to-land rate; while the trail aircraft is in the glide slope, determining an actual separation between the lead aircraft and the trail aircraft; and directing the trail aircraft to execute a go-around maneuver if the actual separation approaches the safe lower limit. Probability distribution functions include runway occupancy time, and landing time interval and/or inter-arrival distance.

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.

Study of recreational land and open space using Skylab imagery

NASA Technical Reports Server (NTRS)

Sattinger, I. J. (Principal Investigator)

1975-01-01

The author has identified the following significant results. An analysis of the statistical uniqueness of each of the signatures of the Gratiot-Saginaw State Game Area was made by computing a matrix of probabilities of misclassification for all possible signature pairs. Within each data set, the 35 signatures were then aggregated into a smaller set of composite signatures by combining groups of signatures having high probabilities of misclassification. Computer separation of forest denisty classes was poor with multispectral scanner data collected on 5 August 1973. Signatures from the scanner data were further analyzed to determine the ranking of spectral channels for computer separation of the scene classes. Probabilities of misclassification were computed for composite signatures using four separate combinations of data source and channel selection.

Quantitative evaluation of Alzheimer's disease

NASA Astrophysics Data System (ADS)

Duchesne, S.; Frisoni, G. B.

2009-02-01

We propose a single, quantitative metric called the disease evaluation factor (DEF) and assess its efficiency at estimating disease burden in normal, control subjects (CTRL) and probable Alzheimer's disease (AD) patients. The study group consisted in 75 patients with a diagnosis of probable AD and 75 age-matched normal CTRL without neurological or neuropsychological deficit. We calculated a reference eigenspace of MRI appearance from reference data, in which our CTRL and probable AD subjects were projected. We then calculated the multi-dimensional hyperplane separating the CTRL and probable AD groups. The DEF was estimated via a multidimensional weighted distance of eigencoordinates for a given subject and the CTRL group mean, along salient principal components forming the separating hyperplane. We used quantile plots, Kolmogorov-Smirnov and χ2 tests to compare the DEF values and test that their distribution was normal. We used a linear discriminant test to separate CTRL from probable AD based on the DEF factor, and reached an accuracy of 87%. A quantitative biomarker in AD would act as an important surrogate marker of disease status and progression.

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.

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.