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.

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.

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

NASA Technical Reports Server (NTRS)

Huang, Norden E.

1999-01-01

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

Harmonic analysis of electrified railway based on improved HHT

NASA Astrophysics Data System (ADS)

Wang, Feng

2018-04-01

In this paper, the causes and harms of the current electric locomotive electrical system harmonics are firstly studied and analyzed. Based on the characteristics of the harmonics in the electrical system, the Hilbert-Huang transform method is introduced. Based on the in-depth analysis of the empirical mode decomposition method and the Hilbert transform method, the reasons and solutions to the endpoint effect and modal aliasing problem in the HHT method are explored. For the endpoint effect of HHT, this paper uses point-symmetric extension method to extend the collected data; In allusion to the modal aliasing problem, this paper uses the high frequency harmonic assistant method to preprocess the signal and gives the empirical formula of high frequency auxiliary harmonic. Finally, combining the suppression of HHT endpoint effect and modal aliasing problem, an improved HHT method is proposed and simulated by matlab. The simulation results show that the improved HHT is effective for the electric locomotive power supply system.

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.

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.

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.

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.

Applications of Hilbert Spectral Analysis for Speech and Sound Signals

NASA Technical Reports Server (NTRS)

Huang, Norden E.

2003-01-01

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

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.

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.

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.

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.

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.

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.

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.

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.

Comparison of automatic denoising methods for phonocardiograms with extraction of signal parameters via the Hilbert Transform

NASA Astrophysics Data System (ADS)

Messer, Sheila R.; Agzarian, John; Abbott, Derek

2001-05-01

Phonocardiograms (PCGs) have many advantages over traditional auscultation (listening to the heart) because they may be replayed, may be analyzed for spectral and frequency content, and frequencies inaudible to the human ear may be recorded. However, various sources of noise may pollute a PCG including lung sounds, environmental noise and noise generated from contact between the recording device and the skin. Because PCG signals are known to be nonlinear and it is often not possible to determine their noise content, traditional de-noising methods may not be effectively applied. However, other methods including wavelet de-noising, wavelet packet de-noising and averaging can be employed to de-noise the PCG. This study examines and compares these de-noising methods. This study answers such questions as to which de-noising method gives a better SNR, the magnitude of signal information that is lost as a result of the de-noising process, the appropriate uses of the different methods down to such specifics as to which wavelets and decomposition levels give best results in wavelet and wavelet packet de-noising. In general, the wavelet and wavelet packet de-noising performed roughly equally with optimal de-noising occurring at 3-5 levels of decomposition. Averaging also proved a highly useful de- noising technique; however, in some cases averaging is not appropriate. The Hilbert Transform is used to illustrate the results of the de-noising process and to extract instantaneous features including instantaneous amplitude, frequency, and phase.

Symmetries of hyper-Kähler (or Poisson gauge field) hierarchy

NASA Astrophysics Data System (ADS)

Takasaki, K.

1990-08-01

Symmetry properties of the space of complex (or formal) hyper-Kähler metrics are studied in the language of hyper-Kähler hierarchies. The construction of finite symmetries is analogous to the theory of Riemann-Hilbert transformations, loop group elements now taking values in a (pseudo-) group of canonical transformations of a simplectic manifold. In spite of their highly nonlinear and involved nature, infinitesimal expressions of these symmetries are shown to have a rather simple form. These infinitesimal transformations are extended to the Plebanski key functions to give rise to a nonlinear realization of a Poisson loop algebra. The Poisson algebra structure turns out to originate in a contact structure behind a set of symplectic structures inherent in the hyper-Kähler hierarchy. Possible relations to membrane theory are briefly discussed.

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.

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.

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

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).

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.

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.

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.

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.

Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform.

PubMed

Hausel, Tamás

2006-04-18

A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and Hausel-Sturmfels), Poincaré polynomials of Hilbert schemes of points and twisted Atiyah-Drinfeld-Hitchin-Manin (ADHM) spaces of instantons on C2 (recovering results of Nakajima-Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced.

On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

NASA Technical Reports Server (NTRS)

Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Huang; Peng, Chung Kang;

Optimal mode transformations for linear-optical cluster-state generation

DOE PAGES

Uskov, Dmitry B.; Lougovski, Pavel; Alsing, Paul M.; ...

2015-06-15

In this paper, we analyze the generation of linear-optical cluster states (LOCSs) via sequential addition of one and two qubits. Existing approaches employ the stochastic linear-optical two-qubit controlled-Z (CZ) gate with success rate of 1/9 per operation. The question of optimality of the CZ gate with respect to LOCS generation has remained open. We report that there are alternative schemes to the CZ gate that are exponentially more efficient and show that sequential LOCS growth is indeed globally optimal. We find that the optimal cluster growth operation is a state transformation on a subspace of the full Hilbert space. Finally,more » we show that the maximal success rate of postselected entangling n photonic qubits or m Bell pairs into a cluster is (1/2) n-1 and (1/4) m-1, respectively, with no ancilla photons, and we give an explicit optical description of the optimal mode transformations.« less

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.

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.

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.}

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.

A Riemann-Hilbert Approach for the Novikov Equation

NASA Astrophysics Data System (ADS)

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

2016-09-01

We develop the inverse scattering transform method for the Novikov equation u_t-u_{txx}+4u^2u_x=3u u_xu_{xx}+u^2u_{xxx} considered on the line xin(-∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann-Hilbert (RH) problem, which in this case is a 3× 3 matrix problem. The structure of this RH problem shares many common features with the case of the Degasperis-Procesi (DP) equation having quadratic nonlinear terms (see [Boutet de Monvel A., Shepelsky D., Nonlinearity 26 (2013), 2081-2107, arXiv:1107.5995]) and thus the Novikov equation can be viewed as a ''modified DP equation'', in analogy with the relationship between the Korteweg-de Vries (KdV) equation and the modified Korteweg-de Vries (mKdV) equation. We present parametric formulas giving the solution of the Cauchy problem for the Novikov equation in terms of the solution of the RH problem and discuss the possibilities to use the developed formalism for further studying of the Novikov equation.

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

Particle-hole symmetry in generalized seniority, microscopic interacting boson (fermion) model, nucleon-pair approximation, and other models

NASA Astrophysics Data System (ADS)

Jia, L. Y.

2016-06-01

The particle-hole symmetry (equivalence) of the full shell-model Hilbert space is straightforward and routinely used in practical calculations. In this work I show that this symmetry is preserved in the subspace truncated up to a certain generalized seniority and give the explicit transformation between the states in the two types (particle and hole) of representations. Based on the results, I study particle-hole symmetry in popular theories that could be regarded as further truncations on top of the generalized seniority, including the microscopic interacting boson (fermion) model, the nucleon-pair approximation, and other models.

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.

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.

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 .

Rolling Bearing Fault Diagnosis Based on an Improved HTT Transform

PubMed Central

Tang, Guiji; Tian, Tian; Zhou, Chong

2018-01-01

When rolling bearing failure occurs, vibration signals generally contain different signal components, such as impulsive fault feature signals, background noise and harmonic interference signals. One of the most challenging aspects of rolling bearing fault diagnosis is how to inhibit noise and harmonic interference signals, while enhancing impulsive fault feature signals. This paper presents a novel bearing fault diagnosis method, namely an improved Hilbert time–time (IHTT) transform, by combining a Hilbert time–time (HTT) transform with principal component analysis (PCA). Firstly, the HTT transform was performed on vibration signals to derive a HTT transform matrix. Then, PCA was employed to de-noise the HTT transform matrix in order to improve the robustness of the HTT transform. Finally, the diagonal time series of the de-noised HTT transform matrix was extracted as the enhanced impulsive fault feature signal and the contained fault characteristic information was identified through further analyses of amplitude and envelope spectrums. Both simulated and experimental analyses validated the superiority of the presented method for detecting bearing failures. PMID:29662013

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.

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)].

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.

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).

On the Hilbert-Huang Transform Theoretical Developments

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

NASA Technical Reports Server (NTRS)

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

2006-01-01

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

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.

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.

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.

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.

On infinite-dimensional state spaces

NASA Astrophysics Data System (ADS)

Fritz, Tobias

2013-05-01

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

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.

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.

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-04-27

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

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

PubMed

Shahoei, Hiva; Dumais, Patrick; Yao, Jianping

2014-05-01

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

Extraction of microseismic waveforms characteristics prior to rock burst using Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Li, Xuelong; Li, Zhonghui; Wang, Enyuan; Feng, Junjun; Chen, Liang; Li, Nan; Kong, Xiangguo

2016-09-01

This study provides a new research idea concerning rock burst prediction. The characteristics of microseismic (MS) waveforms prior to and during the rock burst were studied through the Hilbert-Huang transform (HHT). In order to demonstrate the advantage of the MS features extraction based on HHT, the conventional analysis method (Fourier transform) was also used to make a comparison. The results show that HHT is simple and reliable, and could extract in-depth information about the characteristics of MS waveforms. About 10 days prior to the rock burst, the main frequency of MS waveforms transforms from the high-frequency to low-frequency. What's more, the waveforms energy also presents accumulation characteristic. Based on our study results, it can be concluded that the MS signals analysis through HHT could provide valuable information about the coal or rock deformation and fracture.

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

NASA Technical Reports Server (NTRS)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

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.

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.

THz-bandwidth photonic Hilbert transformers based on fiber Bragg gratings in transmission.

PubMed

Fernández-Ruiz, María R; Wang, Lixian; Carballar, Alejandro; Burla, Maurizio; Azaña, José; LaRochelle, Sophie

2015-01-01

THz-bandwidth photonic Hilbert transformers (PHTs) are implemented for the first time, to the best of our knowledge, based on fiber Bragg grating (FBG) technology. To increase the practical bandwidth limitation of FBGs (typically <200  GHz), a superstructure based on two superimposed linearly-chirped FBGs operating in transmission has been employed. The use of a transmission FBG involves first a conversion of the non-minimum phase response of the PHT into a minimum-phase response by adding an anticipated instantaneous component to the desired system temporal impulse response. Using this methodology, a 3-THz-bandwidth integer PHT and a fractional (order 0.81) PHT are designed, fabricated, and successfully characterized.

Multichannel photonic Hilbert transformers based on complex modulated integrated Bragg gratings.

PubMed

Cheng, Rui; Chrostowski, Lukas

2018-03-01

Multichannel photonic Hilbert transformers (MPHTs) are reported. The devices are based on single compact spiral integrated Bragg gratings on silicon with coupling coefficients precisely modulated by the phase of each grating period. MPHTs with up to nine wavelength channels and a single-channel bandwidth of up to ∼625  GHz are achieved. The potential of the devices for multichannel single-sideband signal generation is suggested. The work offers a new possibility of utilizing wavelength as an extra degree of freedom in designing radio-frequency photonic signal processors. Such multichannel processors are expected to possess improved capacities and a potential to greatly benefit current widespread wavelength division multiplexed systems.

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

NASA Astrophysics Data System (ADS)

Anderson, B. E.; Sosa-Martinez, H.; Riofrío, C. A.; Deutsch, Ivan H.; Jessen, Poul S.

2015-06-01

Unitary transformations are the most general input-output maps available in closed quantum systems. Good control protocols have been developed for qubits, but questions remain about the use of optimal control theory to design unitary maps in high-dimensional Hilbert spaces, and about the feasibility of their robust implementation in the laboratory. Here we design and implement unitary maps in a 16-dimensional Hilbert space associated with the 6 S1 /2 ground state of 133Cs, achieving fidelities >0.98 with built-in robustness to static and dynamic perturbations. Our work has relevance for quantum information processing and provides a template for similar advances on other physical platforms.

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

PubMed

Chen, Lili; Hao, Yaru

2017-01-01

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

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

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

NASA Technical Reports Server (NTRS)

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

2015-01-01

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

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.

[Realization of Heart Sound Envelope Extraction Implemented on LabVIEW Based on Hilbert-Huang Transform].

PubMed

Tan, Zhixiang; Zhang, Yi; Zeng, Deping; Wang, Hua

2015-04-01

We proposed a research of a heart sound envelope extraction system in this paper. The system was implemented on LabVIEW based on the Hilbert-Huang transform (HHT). We firstly used the sound card to collect the heart sound, and then implemented the complete system program of signal acquisition, pretreatment and envelope extraction on LabVIEW based on the theory of HHT. Finally, we used a case to prove that the system could collect heart sound, preprocess and extract the envelope easily. The system was better to retain and show the characteristics of heart sound envelope, and its program and methods were important to other researches, such as those on the vibration and voice, etc.

Structural stability and chaotic solutions of perturbed Benjamin-Ono equations

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

Birnir, B.; Morrison, P.J.

1986-11-01

A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is verymore » sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform.« less

On infinite-dimensional state spaces

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

Fritz, Tobias

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

Quantum number theoretic transforms on multipartite finite systems.

PubMed

Vourdas, A; Zhang, S

2009-06-01

A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied. A representation of the Heisenberg-Weyl group in this context is also discussed.

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

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.

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

NASA Astrophysics Data System (ADS)

Zhang, Wenjin; Wang, Ming L.

2018-03-01

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

Time-frequency analysis of neuronal populations with instantaneous resolution based on noise-assisted multivariate empirical mode decomposition.

PubMed

Alegre-Cortés, J; Soto-Sánchez, C; Pizá, Á G; Albarracín, A L; Farfán, F D; Felice, C J; Fernández, E

2016-07-15

Linear analysis has classically provided powerful tools for understanding the behavior of neural populations, but the neuron responses to real-world stimulation are nonlinear under some conditions, and many neuronal components demonstrate strong nonlinear behavior. In spite of this, temporal and frequency dynamics of neural populations to sensory stimulation have been usually analyzed with linear approaches. In this paper, we propose the use of Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD), a data-driven template-free algorithm, plus the Hilbert transform as a suitable tool for analyzing population oscillatory dynamics in a multi-dimensional space with instantaneous frequency (IF) resolution. The proposed approach was able to extract oscillatory information of neurophysiological data of deep vibrissal nerve and visual cortex multiunit recordings that were not evidenced using linear approaches with fixed bases such as the Fourier analysis. Texture discrimination analysis performance was increased when Noise-Assisted Multivariate Empirical Mode plus Hilbert transform was implemented, compared to linear techniques. Cortical oscillatory population activity was analyzed with precise time-frequency resolution. Similarly, NA-MEMD provided increased time-frequency resolution of cortical oscillatory population activity. Noise-Assisted Multivariate Empirical Mode Decomposition plus Hilbert transform is an improved method to analyze neuronal population oscillatory dynamics overcoming linear and stationary assumptions of classical methods. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

Wearable Sensor-Based Human Activity Recognition Method with Multi-Features Extracted from Hilbert-Huang Transform.

PubMed

Xu, Huile; Liu, Jinyi; Hu, Haibo; Zhang, Yi

2016-12-02

Wearable sensors-based human activity recognition introduces many useful applications and services in health care, rehabilitation training, elderly monitoring and many other areas of human interaction. Existing works in this field mainly focus on recognizing activities by using traditional features extracted from Fourier transform (FT) or wavelet transform (WT). However, these signal processing approaches are suitable for a linear signal but not for a nonlinear signal. In this paper, we investigate the characteristics of the Hilbert-Huang transform (HHT) for dealing with activity data with properties such as nonlinearity and non-stationarity. A multi-features extraction method based on HHT is then proposed to improve the effect of activity recognition. The extracted multi-features include instantaneous amplitude (IA) and instantaneous frequency (IF) by means of empirical mode decomposition (EMD), as well as instantaneous energy density (IE) and marginal spectrum (MS) derived from Hilbert spectral analysis. Experimental studies are performed to verify the proposed approach by using the PAMAP2 dataset from the University of California, Irvine for wearable sensors-based activity recognition. Moreover, the effect of combining multi-features vs. a single-feature are investigated and discussed in the scenario of a dependent subject. The experimental results show that multi-features combination can further improve the performance measures. Finally, we test the effect of multi-features combination in the scenario of an independent subject. Our experimental results show that we achieve four performance indexes: recall, precision, F-measure, and accuracy to 0.9337, 0.9417, 0.9353, and 0.9377 respectively, which are all better than the achievements of related works.

Wearable Sensor-Based Human Activity Recognition Method with Multi-Features Extracted from Hilbert-Huang Transform

PubMed Central

Xu, Huile; Liu, Jinyi; Hu, Haibo; Zhang, Yi

2016-01-01

Wearable sensors-based human activity recognition introduces many useful applications and services in health care, rehabilitation training, elderly monitoring and many other areas of human interaction. Existing works in this field mainly focus on recognizing activities by using traditional features extracted from Fourier transform (FT) or wavelet transform (WT). However, these signal processing approaches are suitable for a linear signal but not for a nonlinear signal. In this paper, we investigate the characteristics of the Hilbert-Huang transform (HHT) for dealing with activity data with properties such as nonlinearity and non-stationarity. A multi-features extraction method based on HHT is then proposed to improve the effect of activity recognition. The extracted multi-features include instantaneous amplitude (IA) and instantaneous frequency (IF) by means of empirical mode decomposition (EMD), as well as instantaneous energy density (IE) and marginal spectrum (MS) derived from Hilbert spectral analysis. Experimental studies are performed to verify the proposed approach by using the PAMAP2 dataset from the University of California, Irvine for wearable sensors-based activity recognition. Moreover, the effect of combining multi-features vs. a single-feature are investigated and discussed in the scenario of a dependent subject. The experimental results show that multi-features combination can further improve the performance measures. Finally, we test the effect of multi-features combination in the scenario of an independent subject. Our experimental results show that we achieve four performance indexes: recall, precision, F-measure, and accuracy to 0.9337, 0.9417, 0.9353, and 0.9377 respectively, which are all better than the achievements of related works. PMID:27918414

Fast fringe pattern phase demodulation using FIR Hilbert transformers

NASA Astrophysics Data System (ADS)

Gdeisat, Munther; Burton, David; Lilley, Francis; Arevalillo-Herráez, Miguel

2016-01-01

This paper suggests the use of FIR Hilbert transformers to extract the phase of fringe patterns. This method is computationally faster than any known spatial method that produces wrapped phase maps. Also, the algorithm does not require any parameters to be adjusted which are dependent upon the specific fringe pattern that is being processed, or upon the particular setup of the optical fringe projection system that is being used. It is therefore particularly suitable for full algorithmic automation. The accuracy and validity of the suggested method has been tested using both computer-generated and real fringe patterns. This novel algorithm has been proposed for its advantages in terms of computational processing speed as it is the fastest available method to extract the wrapped phase information from a fringe pattern.

Cubic spline interpolation with overlapped window and data reuse for on-line Hilbert Huang transform biomedical microprocessor.

PubMed

Chang, Nai-Fu; Chiang, Cheng-Yi; Chen, Tung-Chien; Chen, Liang-Gee

2011-01-01

On-chip implementation of Hilbert-Huang transform (HHT) has great impact to analyze the non-linear and non-stationary biomedical signals on wearable or implantable sensors for the real-time applications. Cubic spline interpolation (CSI) consumes the most computation in HHT, and is the key component for the HHT processor. In tradition, CSI in HHT is usually performed after the collection of a large window of signals, and the long latency violates the realtime requirement of the applications. In this work, we propose to keep processing the incoming signals on-line with small and overlapped data windows without sacrificing the interpolation accuracy. 58% multiplication and 73% division of CSI are saved after the data reuse between the data windows.

A kernel adaptive algorithm for quaternion-valued inputs.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2015-10-01

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

An Axiom System for High School Geometry Based on Isometrics.

ERIC Educational Resources Information Center

Beard, Earl M. L.

Presented in this report is an approach to Euclidean geometry that makes use of distance preserving transformations as the primary approach in the development of the proposed course. The foundation of the course consists of an axiom set that is a combination of Binkhoff's, Hilbert's, and Klein's. Transformations and distance preserving…

On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data

PubMed Central

Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Hung; Peng, Chung Kang; Meijer, Johanna H.; Wang, Yung-Hung; Long, Steven R.; Wu, Zhauhua

2016-01-01

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time–frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities. PMID:26953180

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

NASA Astrophysics Data System (ADS)

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

2010-12-01

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

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.

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.

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.

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.

Fivebranes and 3-manifold homology

NASA Astrophysics Data System (ADS)

Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun

2017-07-01

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[ M 3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

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

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

NASA Technical Reports Server (NTRS)

Anastasi, Robert F.; Madaras, Eric I.

2005-01-01

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

Induction motor broken rotor bar fault location detection through envelope analysis of start-up current using Hilbert transform

NASA Astrophysics Data System (ADS)

Abd-el-Malek, Mina; Abdelsalam, Ahmed K.; Hassan, Ola E.

2017-09-01

Robustness, low running cost and reduced maintenance lead Induction Motors (IMs) to pioneerly penetrate the industrial drive system fields. Broken rotor bars (BRBs) can be considered as an important fault that needs to be early assessed to minimize the maintenance cost and labor time. The majority of recent BRBs' fault diagnostic techniques focus on differentiating between healthy and faulty rotor cage. In this paper, a new technique is proposed for detecting the location of the broken bar in the rotor. The proposed technique relies on monitoring certain statistical parameters estimated from the analysis of the start-up stator current envelope. The envelope of the signal is obtained using Hilbert Transformation (HT). The proposed technique offers non-invasive, fast computational and accurate location diagnostic process. Various simulation scenarios are presented that validate the effectiveness of the proposed technique.

Phase recovery in temporal speckle pattern interferometry using the generalized S-transform.

PubMed

Federico, Alejandro; Kaufmann, Guillermo H

2008-04-15

We propose a novel approach based on the generalized S-transform to retrieve optical phase distributions in temporal speckle pattern interferometry. The performance of the proposed approach is compared with those given by well-known techniques based on the continuous wavelet, the Hilbert transforms, and a smoothed time-frequency distribution by analyzing interferometric data degraded by noise, nonmodulating pixels, and modulation loss. The advantages and limitations of the proposed phase retrieval approach are discussed.

Spatio-temporal phase retrieval in speckle interferometry with Hilbert transform and two-dimensional phase unwrapping

NASA Astrophysics Data System (ADS)

Li, Xiangyu; Huang, Zhanhua; Zhu, Meng; He, Jin; Zhang, Hao

2014-12-01

Hilbert transform (HT) is widely used in temporal speckle pattern interferometry, but errors from low modulations might propagate and corrupt the calculated phase. A spatio-temporal method for phase retrieval using temporal HT and spatial phase unwrapping is presented. In time domain, the wrapped phase difference between the initial and current states is directly determined by using HT. To avoid the influence of the low modulation intensity, the phase information between the two states is ignored. As a result, the phase unwrapping is shifted from time domain to space domain. A phase unwrapping algorithm based on discrete cosine transform is adopted by taking advantage of the information in adjacent pixels. An experiment is carried out with a Michelson-type interferometer to study the out-of-plane deformation field. High quality whole-field phase distribution maps with different fringe densities are obtained. Under the experimental conditions, the maximum number of fringes resolvable in a 416×416 frame is 30, which indicates a 15λ deformation along the direction of loading.

Linearised dynamics and non-modal instability analysis of an impinging under-expanded supersonic jet

NASA Astrophysics Data System (ADS)

Karami, Shahram; Stegeman, Paul C.; Theofilis, Vassilis; Schmid, Peter J.; Soria, Julio

2018-04-01

Non-modal instability analysis of the shear layer near the nozzle of a supersonic under-expanded impinging jet is studied. The shear layer instability is considered to be one of the main components of the feedback loop in supersonic jets. The feedback loop is observed in instantaneous visualisations of the density field where it is noted that acoustic waves scattered by the nozzle lip internalise as shear layer instabilities. A modal analysis describes the asymptotic limit of the instability disturbances and fails to capture short-time responses. Therefore, a non-modal analysis which allows the quantitative description of the short-time amplification or decay of a disturbance is performed by means of a local far-field pressure pulse. An impulse response analysis is performed which allows a wide range of frequencies to be excited. The temporal and spatial growths of the disturbances in the shear layer near the nozzle are studied by decomposing the response using dynamic mode decomposition and Hilbert transform analysis. The short-time response shows that disturbances with non-dimensionalised temporal frequencies in the range of 1 to 4 have positive growth rates in the shear layer. The Hilbert transform analysis shows that high non-dimensionalised temporal frequencies (>4) are dampened immediately, whereas low non-dimensionalised temporal frequencies (<1) are neutral. Both dynamic mode decomposition and Hilbert transform analysis show that spatial frequencies between 1 and 3 have positive spatial growth rates. Finally, the envelope of the streamwise velocity disturbances reveals the presence of a convective instability.

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.

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

Fivebranes and 3-manifold homology

DOE PAGES

Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun

2017-07-14

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that vebrane compacti cations provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N = 2 theory T[M 3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categori cation of Chern-Simons partition function.more » Finally, some of the new key elements include the explicit form of the S-transform and a novel connection between categori cation and a previously mysterious role of Eichler integrals in Chern-Simons theory.« less

Argyres-Douglas theories, chiral algebras and wild Hitchin characters

NASA Astrophysics Data System (ADS)

Fredrickson, Laura; Pei, Du; Yan, Wenbin; Ye, Ke

2018-01-01

We use Coulomb branch indices of Argyres-Douglas theories on S 1 × L( k, 1) to quantize moduli spaces M_H of wild/irregular Hitchin systems. In particular, we obtain formulae for the "wild Hitchin characters" — the graded dimensions of the Hilbert spaces from quantization — for four infinite families of M_H , giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in M_H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform ST k S in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.

Preconditioned alternating direction method of multipliers for inverse problems with constraints

NASA Astrophysics Data System (ADS)

Jiao, Yuling; Jin, Qinian; Lu, Xiliang; Wang, Weijie

2017-02-01

We propose a preconditioned alternating direction method of multipliers (ADMM) to solve linear inverse problems in Hilbert spaces with constraints, where the feature of the sought solution under a linear transformation is captured by a possibly non-smooth convex function. During each iteration step, our method avoids solving large linear systems by choosing a suitable preconditioning operator. In case the data is given exactly, we prove the convergence of our preconditioned ADMM without assuming the existence of a Lagrange multiplier. In case the data is corrupted by noise, we propose a stopping rule using information on noise level and show that our preconditioned ADMM is a regularization method; we also propose a heuristic rule when the information on noise level is unavailable or unreliable and give its detailed analysis. Numerical examples are presented to test the performance of the proposed method.

Time-domain full waveform inversion using instantaneous phase information with damping

NASA Astrophysics Data System (ADS)

Luo, Jingrui; Wu, Ru-Shan; Gao, Fuchun

2018-06-01

In time domain, the instantaneous phase can be obtained from the complex seismic trace using Hilbert transform. The instantaneous phase information has great potential in overcoming the local minima problem and improving the result of full waveform inversion. However, the phase wrapping problem, which comes from numerical calculation, prevents its application. In order to avoid the phase wrapping problem, we choose to use the exponential phase combined with the damping method, which gives instantaneous phase-based multi-stage inversion. We construct the objective functions based on the exponential instantaneous phase, and also derive the corresponding gradient operators. Conventional full waveform inversion and the instantaneous phase-based inversion are compared with numerical examples, which indicates that in the case without low frequency information in seismic data, our method is an effective and efficient approach for initial model construction for full waveform inversion.

Local quantum measurement and no-signaling imply quantum correlations.

PubMed

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

2010-04-09

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

Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

NASA Astrophysics Data System (ADS)

Zhou, Xin

1990-03-01

For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.

Integrals for IBS and beam cooling

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

Burov, A.; /Fermilab

Simulation of beam cooling usually requires performing certain integral transformations every time step or so, which is a significant burden on the CPU. Examples are the dispersion integrals (Hilbert transforms) in the stochastic cooling, wake fields and IBS integrals. An original method is suggested for fast and sufficiently accurate computation of the integrals. This method is applied for the dispersion integral. Some methodical aspects of the IBS analysis are discussed.

Integrals for IBS and Beam Cooling

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

Burov, A.

Simulation of beam cooling usually requires performing certain integral transformations every time step or so, which is a significant burden on the CPU. Examples are the dispersion integrals (Hilbert transforms) in the stochastic cooling, wake fields and IBS integrals. An original method is suggested for fast and sufficiently accurate computation of the integrals. This method is applied for the dispersion integral. Some methodical aspects of the IBS analysis are discussed.

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.

Multiscale characterization and prediction of monsoon rainfall in India using Hilbert-Huang transform and time-dependent intrinsic correlation analysis

NASA Astrophysics Data System (ADS)

Adarsh, S.; Reddy, M. Janga

2017-07-01

In this paper, the Hilbert-Huang transform (HHT) approach is used for the multiscale characterization of All India Summer Monsoon Rainfall (AISMR) time series and monsoon rainfall time series from five homogeneous regions in India. The study employs the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) for multiscale decomposition of monsoon rainfall in India and uses the Normalized Hilbert Transform and Direct Quadrature (NHT-DQ) scheme for the time-frequency characterization. The cross-correlation analysis between orthogonal modes of All India monthly monsoon rainfall time series and that of five climate indices such as Quasi Biennial Oscillation (QBO), El Niño Southern Oscillation (ENSO), Sunspot Number (SN), Atlantic Multi Decadal Oscillation (AMO), and Equatorial Indian Ocean Oscillation (EQUINOO) in the time domain showed that the links of different climate indices with monsoon rainfall are expressed well only for few low-frequency modes and for the trend component. Furthermore, this paper investigated the hydro-climatic teleconnection of ISMR in multiple time scales using the HHT-based running correlation analysis technique called time-dependent intrinsic correlation (TDIC). The results showed that both the strength and nature of association between different climate indices and ISMR vary with time scale. Stemming from this finding, a methodology employing Multivariate extension of EMD and Stepwise Linear Regression (MEMD-SLR) is proposed for prediction of monsoon rainfall in India. The proposed MEMD-SLR method clearly exhibited superior performance over the IMD operational forecast, M5 Model Tree (MT), and multiple linear regression methods in ISMR predictions and displayed excellent predictive skill during 1989-2012 including the four extreme events that have occurred during this period.

Topologies on quantum topoi induced by quantization

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

Nakayama, Kunji

2013-07-15

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

Protecting Location Privacy for Outsourced Spatial Data in Cloud Storage

PubMed Central

Gui, Xiaolin; An, Jian; Zhao, Jianqiang; Zhang, Xuejun

2014-01-01

As cloud computing services and location-aware devices are fully developed, a large amount of spatial data needs to be outsourced to the cloud storage provider, so the research on privacy protection for outsourced spatial data gets increasing attention from academia and industry. As a kind of spatial transformation method, Hilbert curve is widely used to protect the location privacy for spatial data. But sufficient security analysis for standard Hilbert curve (SHC) is seldom proceeded. In this paper, we propose an index modification method for SHC (SHC∗) and a density-based space filling curve (DSC) to improve the security of SHC; they can partially violate the distance-preserving property of SHC, so as to achieve better security. We formally define the indistinguishability and attack model for measuring the privacy disclosure risk of spatial transformation methods. The evaluation results indicate that SHC∗ and DSC are more secure than SHC, and DSC achieves the best index generation performance. PMID:25097865

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.

A framework for the damage evaluation of acoustic emission signals through Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Siracusano, Giulio; Lamonaca, Francesco; Tomasello, Riccardo; Garescì, Francesca; Corte, Aurelio La; Carnì, Domenico Luca; Carpentieri, Mario; Grimaldi, Domenico; Finocchio, Giovanni

2016-06-01

The acoustic emission (AE) is a powerful and potential nondestructive testing method for structural monitoring in civil engineering. Here, we show how systematic investigation of crack phenomena based on AE data can be significantly improved by the use of advanced signal processing techniques. Such data are a fundamental source of information that can be used as the basis for evaluating the status of the material, thereby paving the way for a new frontier of innovation made by data-enabled analytics. In this article, we propose a framework based on the Hilbert-Huang Transform for the evaluation of material damages that (i) facilitates the systematic employment of both established and promising analysis criteria, and (ii) provides unsupervised tools to achieve an accurate classification of the fracture type, the discrimination between longitudinal (P-) and traversal (S-) waves related to an AE event. The experimental validation shows promising results for a reliable assessment of the health status through the monitoring of civil infrastructures.

Image restoration method based on Hilbert transform for full-field optical coherence tomography

NASA Astrophysics Data System (ADS)

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

2008-01-01

A full-field optical coherence tomography (FF-OCT) system utilizing a simple but novel image restoration method suitable for a high-speed system is demonstrated. An en-face image is retrieved from only two phase-shifted interference fringe images through using the mathematical Hilbert transform. With a thermal light source, a high-resolution FF-OCT system having axial and transverse resolutions of 1 and 2.2 μm, respectively, was implemented. The feasibility of the proposed scheme is confirmed by presenting the obtained en-face images of biological samples such as a piece of garlic and a gold beetle. The proposed method is robust to the error in the amount of the phase shift and does not leave residual fringes. The use of just two interference images and the strong immunity to phase errors provide great advantages in the imaging speed and the system design flexibility of a high-speed high-resolution FF-OCT system.

Identification of Velcro rales based on Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Chen, Xue; Shao, Jie; Long, Yingjiao; Que, Chengli; Zhang, Jue; Fang, Jing

2014-05-01

Velcro rales, as a kind of crackles, are relatively specific for lung fibrosis and usually the first clinical clue of interstitial lung disease (ILD). We proposed an automatic analytic tool based on Hilbert-Huang transform (HHT) for the computerized identification of Velcro rales. In particular, HHT was utilized to extract the energy weight in various frequency bands (EW) of crackles and to calculate the portion of crackles during late inspiration. Support vector machine (SVM) based on the HHT-derived measures was used to differentiate Velcro rales from other crackles. We found that there were significant differences in the extracted parameters between Velcro rales and other crackles, including EW, EW and the proportion of crackles that appeared during the late inspiration. The discrimination results obtained from SVM achieved a concordance rate up to 92.20%±1.80% as confirmed by the diagnosis from experienced physicians. For practical purpose, the proposed approach may have potential applications to improve the sensitivity and accuracy of auscultation and conduct automatic ILD diagnose system.

Automated flaw detection scheme for cast austenitic stainless steel weld specimens using Hilbert-Huang transform of ultrasonic phased array data

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

Khan, Tariq; Majumdar, Shantanu; Udpa, Lalita

2012-05-17

The objective of this work is to develop processing algorithms to detect and localize flaws using ultrasonic phased-array data. Data was collected on cast austenitic stainless stell (CASS) weld specimens onloan from the U.S. nuclear power industry' Pressurized Walter Reactor Owners Group (PWROG) traveling specimen set. Each specimen consists of a centrifugally cast stainless stell (CCSS) pipe section welded to a statically cst(SCSS) or wrought (WRSS) section. The paper presents a novel automated flaw detection and localization scheme using low frequency ultrasonic phased array inspection singals from the weld and heat affected zone of the based materials. The major stepsmore » of the overall scheme are preprocessing and region of interest (ROI) detection followed by the Hilbert-Huang transform (HHT) of A-scans in the detected ROIs. HHT offers time-frequency-energy distribution for each ROI. The Accumulation of energy in a particular frequency band is used as a classification feature for the particular ROI.« less

Protecting location privacy for outsourced spatial data in cloud storage.

PubMed

Tian, Feng; Gui, Xiaolin; An, Jian; Yang, Pan; Zhao, Jianqiang; Zhang, Xuejun

2014-01-01

As cloud computing services and location-aware devices are fully developed, a large amount of spatial data needs to be outsourced to the cloud storage provider, so the research on privacy protection for outsourced spatial data gets increasing attention from academia and industry. As a kind of spatial transformation method, Hilbert curve is widely used to protect the location privacy for spatial data. But sufficient security analysis for standard Hilbert curve (SHC) is seldom proceeded. In this paper, we propose an index modification method for SHC (SHC(∗)) and a density-based space filling curve (DSC) to improve the security of SHC; they can partially violate the distance-preserving property of SHC, so as to achieve better security. We formally define the indistinguishability and attack model for measuring the privacy disclosure risk of spatial transformation methods. The evaluation results indicate that SHC(∗) and DSC are more secure than SHC, and DSC achieves the best index generation performance.

Neural network Hilbert transform based filtered backprojection for fast inline x-ray inspection

NASA Astrophysics Data System (ADS)

Janssens, Eline; De Beenhouwer, Jan; Van Dael, Mattias; De Schryver, Thomas; Van Hoorebeke, Luc; Verboven, Pieter; Nicolai, Bart; Sijbers, Jan

2018-03-01

X-ray imaging is an important tool for quality control since it allows to inspect the interior of products in a non-destructive way. Conventional x-ray imaging, however, is slow and expensive. Inline x-ray inspection, on the other hand, can pave the way towards fast and individual quality control, provided that a sufficiently high throughput can be achieved at a minimal cost. To meet these criteria, an inline inspection acquisition geometry is proposed where the object moves and rotates on a conveyor belt while it passes a fixed source and detector. Moreover, for this acquisition geometry, a new neural-network-based reconstruction algorithm is introduced: the neural network Hilbert transform based filtered backprojection. The proposed algorithm is evaluated both on simulated and real inline x-ray data and has shown to generate high quality reconstructions of 400  ×  400 reconstruction pixels within 200 ms, thereby meeting the high throughput criteria.

Ice cream and orbifold Riemann-Roch

NASA Astrophysics Data System (ADS)

Buckley, Anita; Reid, Miles; Zhou, Shengtian

2013-06-01

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

Direct digital RF synthesis and modulation for MSAT mobile applications

NASA Technical Reports Server (NTRS)

Crozier, Stewart; Datta, Ravi; Sydor, John

1993-01-01

A practical method of performing direct digital RF synthesis using the Hilbert transform single sideband (SSB) technique is described. It is also shown that amplitude and phase modulation can be achieved directly at L-band with frequency stability and spurii performance exceeding stringent MSAT system requirements.

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

NASA Astrophysics Data System (ADS)

Franca, Mário J.; Lemmin, Ulrich

2014-05-01

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

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.

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.

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 Hilbert Space Geometric Representation of Shared Awareness and Joint Decision Making

ERIC Educational Resources Information Center

Canan, Mustafa

2017-01-01

Two people in the same situation may ascribe very different meanings to their experiences. They will form different awareness, reacting differently to shared information. Various factors can give rise to this behavior. These factors include, but are not limited to, prior knowledge, training, biases, cultural factors, social factors, team vs.…

Nonstandard Methods in Lie Theory

ERIC Educational Resources Information Center

Goldbring, Isaac Martin

2009-01-01

In this thesis, we apply model theory to Lie theory and geometric group theory. These applications of model theory come via nonstandard analysis. In Lie theory, we use nonstandard methods to prove two results. First, we give a positive solution to the local form of Hilbert's Fifth Problem, which asks whether every locally euclidean local…

Strong Convergence of Iteration Processes for Infinite Family of General Extended Mappings

NASA Astrophysics Data System (ADS)

Hussein Maibed, Zena

2018-05-01

The aim of this paper, we introduce a concept of general extended mapping which is independent of nonexpansive mapping and give an iteration process of families of quasi nonexpansive and of general extended mappings. Also, the existence of common fixed point are studied for these process in the Hilbert spaces.

Device-independent characterizations of a shared quantum state independent of any Bell inequalities

NASA Astrophysics Data System (ADS)

Wei, Zhaohui; Sikora, Jamie

2017-03-01

In a Bell experiment two parties share a quantum state and perform local measurements on their subsystems separately, and the statistics of the measurement outcomes are recorded as a Bell correlation. For any Bell correlation, it turns out that a quantum state with minimal size that is able to produce this correlation can always be pure. In this work, we first exhibit two device-independent characterizations for the pure state that Alice and Bob share using only the correlation data. Specifically, we give two conditions that the Schmidt coefficients must satisfy, which can be tight, and have various applications in quantum tasks. First, one of the characterizations allows us to bound the entanglement between Alice and Bob using Renyi entropies and also to bound the underlying Hilbert space dimension. Second, when the Hilbert space dimension bound is tight, the shared pure quantum state has to be maximally entangled. Third, the second characterization gives a sufficient condition that a Bell correlation cannot be generated by particular quantum states. We also show that our results can be generalized to the case of shared mixed states.

EEG synchronization and migraine

NASA Astrophysics Data System (ADS)

Stramaglia, Sebastiano; Angelini, Leonardo; Pellicoro, Mario; Hu, Kun; Ivanov, Plamen Ch.

2004-03-01

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli.

Solitons of shallow-water models from energy-dependent spectral problems

NASA Astrophysics Data System (ADS)

Haberlin, Jack; Lyons, Tony

2018-01-01

The current work investigates the soliton solutions of the Kaup-Boussinesq equation using the inverse scattering transform method. We outline the construction of the Riemann-Hilbert problem for a pair of energy-dependent spectral problems for the system, which we then use to construct the solution of this hydrodynamic system.

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.

Image processing with the radial Hilbert transform of photo-thermal imaging for carious detection

NASA Astrophysics Data System (ADS)

El-Sharkawy, Yasser H.

2014-03-01

Knowledge of heat transfer in biological bodies has many diagnostic and therapeutic applications involving either raising or lowering of temperature, and often requires precise monitoring of the spatial distribution of thermal histories that are produced during a treatment protocol. The present paper therefore aims to design and implementation of laser therapeutic and imaging system used for carious tracking and drilling by develop a mathematical algorithm using Hilbert transform for edge detection of photo-thermal imaging. photothermal imaging has the ability to penetrate and yield information about an opaque medium well beyond the range of conventional optical imaging. Owing to this ability, Q- switching Nd:YAG laser at wavelength 1064 nm has been extensively used in human teeth to study the sub-surface deposition of laser radiation. The high absorption coefficient of the carious rather than normal region rise its temperature generating IR thermal radiation captured by high resolution thermal camera. Changing the pulse repetition frequency of the laser pulses affects the penetration depth of the laser, which can provide three-dimensional (3D) images in arbitrary planes and allow imaging deep within a solid tissue.

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

PubMed Central

Zhang, Juwei; Tan, Xiaojiang; Zheng, Pengbo

2017-01-01

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

Hilbert-Huang transform analysis of long-term solar magnetic activity

NASA Astrophysics Data System (ADS)

Deng, Linhua

2018-04-01

Astronomical time series analysis is one of the hottest and most important problems, and becomes the suitable way to deal with the underlying dynamical behavior of the considered nonlinear systems. The quasi-periodic analysis of solar magnetic activity has been carried out by various authors during the past fifty years. In this work, the novel Hilbert-Huang transform approach is applied to investigate the yearly numbers of polar faculae in the time interval from 1705 to 1999. The detected periodicities can be allocated to three components: the first one is the short-term variations with periods smaller than 11 years, the second one is the mid- term variations with classical periods from 11 years to 50 years, and the last one is the long-term variations with periods larger than 50 years. The analysis results improve our knowledge on the quasi-periodic variations of solar magnetic activity and could be provided valuable constraints for solar dynamo theory. Furthermore, our analysis results could be useful for understanding the long-term variations of solar magnetic activity, providing crucial information to describe and forecast solar magnetic activity indicators.

Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors

NASA Astrophysics Data System (ADS)

Chen, Xiang; Li, Jingchao; Han, Hui; Ying, Yulong

2018-05-01

Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the Hilbert transform was extracted as the second eigenvector. Finally, the dual improved fractal box-counting dimension eigenvectors formed the multi-dimensional eigenvectors as signal subtle features, which were used for radiation source signal recognition by the grey relation algorithm. The experimental results show that, compared with the traditional fractal box-counting dimension algorithm and the single improved fractal box-counting dimension algorithm, the proposed dual improved fractal box-counting dimension algorithm can better extract the signal subtle distribution characteristics under different reconstruction phase space, and has a better recognition effect with good real-time performance.

Geometric properties of commutative subalgebras of partial differential operators

NASA Astrophysics Data System (ADS)

Zheglov, A. B.; Kurke, H.

2015-05-01

We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k \\lbrack u,t \\rbrack is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.

On using the Hilbert transform for blind identification of complex modes: A practical approach

NASA Astrophysics Data System (ADS)

Antunes, Jose; Debut, Vincent; Piteau, Pilippe; Delaune, Xavier; Borsoi, Laurent

2018-01-01

The modal identification of dynamical systems under operational conditions, when subjected to wide-band unmeasured excitations, is today a viable alternative to more traditional modal identification approaches based on processing sets of measured FRFs or impulse responses. Among current techniques for performing operational modal identification, the so-called blind identification methods are the subject of considerable investigation. In particular, the SOBI (Second-Order Blind Identification) method was found to be quite efficient. SOBI was originally developed for systems with normal modes. To address systems with complex modes, various extension approaches have been proposed, in particular: (a) Using a first-order state-space formulation for the system dynamics; (b) Building complex analytic signals from the measured responses using the Hilbert transform. In this paper we further explore the latter option, which is conceptually interesting while preserving the model order and size. Focus is on applicability of the SOBI technique for extracting the modal responses from analytic signals built from a set of vibratory responses. The novelty of this work is to propose a straightforward computational procedure for obtaining the complex cross-correlation response matrix to be used for the modal identification procedure. After clarifying subtle aspects of the general theoretical framework, we demonstrate that the correlation matrix of the analytic responses can be computed through a Hilbert transform of the real correlation matrix, so that the actual time-domain responses are no longer required for modal identification purposes. The numerical validation of the proposed technique is presented based on time-domain simulations of a conceptual physical multi-modal system, designed to display modes ranging from normal to highly complex, while keeping modal damping low and nearly independent of the modal complexity, and which can prove very interesting in test bench applications. Numerical results for complex modal identifications are presented, and the quality of the identified modal matrix and modal responses, extracted using the complex SOBI technique and implementing the proposed formulation, is assessed.

Analysis of Human's Motions Based on Local Mean Decomposition in Through-wall Radar Detection

NASA Astrophysics Data System (ADS)

Lu, Qi; Liu, Cai; Zeng, Zhaofa; Li, Jing; Zhang, Xuebing

2016-04-01

Observation of human motions through a wall is an important issue in security applications and search-and rescue. Radar has advantages in looking through walls where other sensors give low performance or cannot be used at all. Ultrawideband (UWB) radar has high spatial resolution as a result of employment of ultranarrow pulses. It has abilities to distinguish the closely positioned targets and provide time-lapse information of targets. Moreover, the UWB radar shows good performance in wall penetration when the inherently short pulses spread their energy over a broad frequency range. Human's motions show periodic features including respiration, swing arms and legs, fluctuations of the torso. Detection of human targets is based on the fact that there is always periodic motion due to breathing or other body movements like walking. The radar can gain the reflections from each human body parts and add the reflections at each time sample. The periodic movements will cause micro-Doppler modulation in the reflected radar signals. Time-frequency analysis methods are consider as the effective tools to analysis and extract micro-Doppler effects caused by the periodic movements in the reflected radar signal, such as short-time Fourier transform (STFT), wavelet transform (WT), and Hilbert-Huang transform (HHT).The local mean decomposition (LMD), initially developed by Smith (2005), is to decomposed amplitude and frequency modulated signals into a small set of product functions (PFs), each of which is the product of an envelope signal and a frequency modulated signal from which a time-vary instantaneous phase and instantaneous frequency can be derived. As bypassing the Hilbert transform, the LMD has no demodulation error coming from window effect and involves no negative frequency without physical sense. Also, the instantaneous attributes obtained by LMD are more stable and precise than those obtained by the empirical mode decomposition (EMD) because LMD uses smoothed local means and local magnitudes that facilitate a more natural decomposition than that using the cubic spline approach of EMD. In this paper, we apply the UWB radar system in through-wall human detections and present a method to characterize human's motions. We start with a walker's motion model and periodic motion features are given the analysis of the experimental data based on the combination of the LMT and fast Fourier Transform (FFT). The characteristics of human's motions including respiration, swing arms and legs, and fluctuations of the torso are extracted. At last, we calculate the actual distance between the human and the wall. This work was supported in part by National Natural Science Foundation of China under Grant 41574109 and 41430322.

The Analysis of Eigenstates of a Few Generalized Quantum Baker’s Maps Using Hadamard and Related Transforms

NASA Astrophysics Data System (ADS)

Meenakshisundaram, N.

Application of the Hadamard and related transforms on a few generalized quantum baker’s maps have been studied. Effectiveness of the Hadamard transform and a new transform which combines the Fourier and the Hadamard transforms, for simplifying the eigenstates or resonances of the quantization of a few generalized baker’s map namely tetradic baker and lazy baker’s map when the Hilbert space dimension is power of 2 has been done by comparing the participation ratios in the transformed basis with respect to the position basis. Several special family of states based on their maximal compression in either Hadamard transform or the new transform are identified and they are related to the ubiquitous Thue-Morse and allied sequences. Evidence is provided that these special family of states as well as average over all eigenstates exhibits multifractal nature.

Seizure classification in EEG signals utilizing Hilbert-Huang transform

PubMed Central

2011-01-01

Background Classification method capable of recognizing abnormal activities of the brain functionality are either brain imaging or brain signal analysis. The abnormal activity of interest in this study is characterized by a disturbance caused by changes in neuronal electrochemical activity that results in abnormal synchronous discharges. The method aims at helping physicians discriminate between healthy and seizure electroencephalographic (EEG) signals. Method Discrimination in this work is achieved by analyzing EEG signals obtained from freely accessible databases. MATLAB has been used to implement and test the proposed classification algorithm. The analysis in question presents a classification of normal and ictal activities using a feature relied on Hilbert-Huang Transform. Through this method, information related to the intrinsic functions contained in the EEG signal has been extracted to track the local amplitude and the frequency of the signal. Based on this local information, weighted frequencies are calculated and a comparison between ictal and seizure-free determinant intrinsic functions is then performed. Methods of comparison used are the t-test and the Euclidean clustering. Results The t-test results in a P-value < 0.02 and the clustering leads to accurate (94%) and specific (96%) results. The proposed method is also contrasted against the Multivariate Empirical Mode Decomposition that reaches 80% accuracy. Comparison results strengthen the contribution of this paper not only from the accuracy point of view but also with respect to its fast response and ease to use. Conclusion An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper. The proposed system bears the potential of providing several credible benefits such as fast diagnosis, high accuracy, good sensitivity and specificity, time saving and user friendly. Furthermore, the classification of mode mixing can be achieved using the extracted instantaneous information of every IMF, but it would be most likely a hard task if only the average value is used. Extra benefits of this proposed system include low cost, and ease of interface. All of that indicate the usefulness of the tool and its use as an efficient diagnostic tool. PMID:21609459

Seizure classification in EEG signals utilizing Hilbert-Huang transform.

PubMed

Oweis, Rami J; Abdulhay, Enas W

2011-05-24

Classification method capable of recognizing abnormal activities of the brain functionality are either brain imaging or brain signal analysis. The abnormal activity of interest in this study is characterized by a disturbance caused by changes in neuronal electrochemical activity that results in abnormal synchronous discharges. The method aims at helping physicians discriminate between healthy and seizure electroencephalographic (EEG) signals. Discrimination in this work is achieved by analyzing EEG signals obtained from freely accessible databases. MATLAB has been used to implement and test the proposed classification algorithm. The analysis in question presents a classification of normal and ictal activities using a feature relied on Hilbert-Huang Transform. Through this method, information related to the intrinsic functions contained in the EEG signal has been extracted to track the local amplitude and the frequency of the signal. Based on this local information, weighted frequencies are calculated and a comparison between ictal and seizure-free determinant intrinsic functions is then performed. Methods of comparison used are the t-test and the Euclidean clustering. The t-test results in a P-value < 0.02 and the clustering leads to accurate (94%) and specific (96%) results. The proposed method is also contrasted against the Multivariate Empirical Mode Decomposition that reaches 80% accuracy. Comparison results strengthen the contribution of this paper not only from the accuracy point of view but also with respect to its fast response and ease to use. An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper. The proposed system bears the potential of providing several credible benefits such as fast diagnosis, high accuracy, good sensitivity and specificity, time saving and user friendly. Furthermore, the classification of mode mixing can be achieved using the extracted instantaneous information of every IMF, but it would be most likely a hard task if only the average value is used. Extra benefits of this proposed system include low cost, and ease of interface. All of that indicate the usefulness of the tool and its use as an efficient diagnostic tool.

Type II superstring field theory: geometric approach and operadic description

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Münster, Korbinian

2013-04-01

We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach's construction for the bosonic string. The construction uses the small Hilbert space. Elementary vertices of the non-polynomial action are described with the help of a properly formulated minimal area problem. They give rise to an infinite tower of superstring field products defining a {N} = 1 generalization of a loop homotopy Lie algebra, the genus zero part generalizing a homotopy Lie algebra. Finally, we give an operadic interpretation of the construction.

An Inquiry: Effectiveness of the Complex Empirical Mode Decomposition Method, the Hilbert-Huang Transform, and the Fast-Fourier Transform for Analysis of Dynamic Objects

DTIC Science & Technology

2012-03-01

graphical user interface (GUI) called ALPINE© [18]. Then, it will be converted into a 10 MAT-file that can be read into MATLAB®. At this point...breathing [3]. For comparison purposes, Balocchi et al. recorded the respiratory signal simultaneously with the tachogram (or EKG ) signal. As previously...primary authors, worked to create his own code for implementing the method proposed by Rilling et al. Through reading the BEMD paper and proceeding to

ECG-derived respiration based on iterated Hilbert transform and Hilbert vibration decomposition.

PubMed

Sharma, Hemant; Sharma, K K

2018-06-01

Monitoring of the respiration using the electrocardiogram (ECG) is desirable for the simultaneous study of cardiac activities and the respiration in the aspects of comfort, mobility, and cost of the healthcare system. This paper proposes a new approach for deriving the respiration from single-lead ECG based on the iterated Hilbert transform (IHT) and the Hilbert vibration decomposition (HVD). The ECG signal is first decomposed into the multicomponent sinusoidal signals using the IHT technique. Afterward, the lower order amplitude components obtained from the IHT are filtered using the HVD to extract the respiration information. Experiments are performed on the Fantasia and Apnea-ECG datasets. The performance of the proposed ECG-derived respiration (EDR) approach is compared with the existing techniques including the principal component analysis (PCA), R-peak amplitudes (RPA), respiratory sinus arrhythmia (RSA), slopes of the QRS complex, and R-wave angle. The proposed technique showed the higher median values of correlation (first and third quartile) for both the Fantasia and Apnea-ECG datasets as 0.699 (0.55, 0.82) and 0.57 (0.40, 0.73), respectively. Also, the proposed algorithm provided the lowest values of the mean absolute error and the average percentage error computed from the EDR and reference (recorded) respiration signals for both the Fantasia and Apnea-ECG datasets as 1.27 and 9.3%, and 1.35 and 10.2%, respectively. In the experiments performed over different age group subjects of the Fantasia dataset, the proposed algorithm provided effective results in the younger population but outperformed the existing techniques in the case of elderly subjects. The proposed EDR technique has the advantages over existing techniques in terms of the better agreement in the respiratory rates and specifically, it reduces the need for an extra step required for the detection of fiducial points in the ECG for the estimation of respiration which makes the process effective and less-complex. The above performance results obtained from two different datasets validate that the proposed approach can be used for monitoring of the respiration using single-lead ECG.

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

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

NASA Astrophysics Data System (ADS)

Cai, Jianhua

2017-05-01

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

TIME-FREQUENCY ANALYSIS OF THE SUPERORBITAL MODULATION OF THE X-RAY BINARY SMC X-1 USING THE HILBERT-HUANG TRANSFORM

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

Hu, Chin-Ping; Chou, Yi; Yang, Ting-Chang

2011-10-20

The high-mass X-ray binary SMC X-1 exhibits a superorbital modulation with a dramatically varying period ranging between {approx}40 days and {approx}60 days. This research studies the time-frequency properties of the superorbital modulation of SMC X-1 based on the observations made by the All-Sky Monitor (ASM) onboard the Rossi X-ray Timing Explorer (RXTE). We analyzed the entire ASM database collected since 1996. The Hilbert-Huang transform (HHT), developed for non-stationary and nonlinear time-series analysis, was adopted to derive the instantaneous superorbital frequency. The resultant Hilbert spectrum is consistent with the dynamic power spectrum as it shows more detailed information in both themore » time and frequency domains. The RXTE observations show that the superorbital modulation period was mostly between {approx}50 days and {approx}65 days, whereas it changed to {approx}45 days around MJD 50,800 and MJD 54,000. Our analysis further indicates that the instantaneous frequency changed to a timescale of hundreds of days between {approx}MJD 51,500 and {approx}MJD 53,500. Based on the instantaneous phase defined by HHT, we folded the ASM light curve to derive a superorbital profile, from which an asymmetric feature and a low state with barely any X-ray emissions (lasting for {approx}0.3 cycles) were observed. We also calculated the correlation between the mean period and the amplitude of the superorbital modulation. The result is similar to the recently discovered relationship between the superorbital cycle length and the mean X-ray flux for Her X-1.« less

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

NASA Astrophysics Data System (ADS)

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

2014-06-01

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

Some equalities and inequalities for fusion frames.

PubMed

Guo, Qianping; Leng, Jinsong; Li, Houbiao

2016-01-01

Fusion frames have some properties similar to those of frames in Hilbert spaces, but not all of their properties are similar. Some authors have established some equalities and inequalities for conventional frames. In this paper, we give some equalities and inequalities for fusion frames. Our results generalize and improve the remarkable results which have been obtained by Balan, Casazza and Gǎvruta etc.

Uncertainty relations as Hilbert space geometry

NASA Technical Reports Server (NTRS)

Braunstein, Samuel L.

1994-01-01

Precision measurements involve the accurate determination of parameters through repeated measurements of identically prepared experimental setups. For many parameters there is a 'natural' choice for the quantum observable which is expected to give optimal information; and from this observable one can construct an Heinsenberg uncertainty principle (HUP) bound on the precision attainable for the parameter. However, the classical statistics of multiple sampling directly gives us tools to construct bounds for the precision available for the parameters of interest (even when no obvious natural quantum observable exists, such as for phase, or time); it is found that these direct bounds are more restrictive than those of the HUP. The implication is that the natural quantum observables typically do not encode the optimal information (even for observables such as position, and momentum); we show how this can be understood simply in terms of the Hilbert space geometry. Another striking feature of these bounds to parameter uncertainty is that for a large enough number of repetitions of the measurements all V quantum states are 'minimum uncertainty' states - not just Gaussian wave-packets. Thus, these bounds tell us what precision is achievable as well as merely what is allowed.

A Riemann-Hilbert formulation for the finite temperature Hubbard model

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

Pseudo Wigner-Ville Distribution, Computer Program and its Applications to Time-Frequency Domain Problems

DTIC Science & Technology

1993-03-01

representation is needed to characterize such signature. Pseudo Wigner - Ville distribution is ideally suited for portraying non-stationary signal in the...features jointly in time and frequency. 14, SUBJECT TERIMS 15. NUMBER OF PAGES Pseudo Wigner - Ville Distribution , Analytic Signal, 83 Hilbert Transform...D U C T IO N ............................................................................ . 1 II. PSEUDO WIGNER - VILLE DISTRIBUTION

Steady-State Visual Evoked Potentials and Phase Synchronization in Migraine Patients

NASA Astrophysics Data System (ADS)

Angelini, L.; Tommaso, M. De; Guido, M.; Hu, K.; Ivanov, P. Ch.; Marinazzo, D.; Nardulli, G.; Nitti, L.; Pellicoro, M.; Pierro, C.; Stramaglia, S.

2004-07-01

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in the presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli.

Surface Imaging Skin Friction Instrument and Method

NASA Technical Reports Server (NTRS)

Brown, James L. (Inventor); Naughton, Jonathan W. (Inventor)

1999-01-01

A surface imaging skin friction instrument allowing 2D resolution of spatial image by a 2D Hilbert transform and 2D inverse thin-oil film solver, providing an innovation over prior art single point approaches. Incoherent, monochromatic light source can be used. The invention provides accurate, easy to use, economical measurement of larger regions of surface shear stress in a single test.

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

Analysis and Recognition of Traditional Chinese Medicine Pulse Based on the Hilbert-Huang Transform and Random Forest in Patients with Coronary Heart Disease

PubMed Central

Wang, Yiqin; Yan, Hanxia; Yan, Jianjun; Yuan, Fengyin; Xu, Zhaoxia; Liu, Guoping; Xu, Wenjie

2015-01-01

Objective. This research provides objective and quantitative parameters of the traditional Chinese medicine (TCM) pulse conditions for distinguishing between patients with the coronary heart disease (CHD) and normal people by using the proposed classification approach based on Hilbert-Huang transform (HHT) and random forest. Methods. The energy and the sample entropy features were extracted by applying the HHT to TCM pulse by treating these pulse signals as time series. By using the random forest classifier, the extracted two types of features and their combination were, respectively, used as input data to establish classification model. Results. Statistical results showed that there were significant differences in the pulse energy and sample entropy between the CHD group and the normal group. Moreover, the energy features, sample entropy features, and their combination were inputted as pulse feature vectors; the corresponding average recognition rates were 84%, 76.35%, and 90.21%, respectively. Conclusion. The proposed approach could be appropriately used to analyze pulses of patients with CHD, which can lay a foundation for research on objective and quantitative criteria on disease diagnosis or Zheng differentiation. PMID:26180536

Analysis and Recognition of Traditional Chinese Medicine Pulse Based on the Hilbert-Huang Transform and Random Forest in Patients with Coronary Heart Disease.

PubMed

Guo, Rui; Wang, Yiqin; Yan, Hanxia; Yan, Jianjun; Yuan, Fengyin; Xu, Zhaoxia; Liu, Guoping; Xu, Wenjie

2015-01-01

Objective. This research provides objective and quantitative parameters of the traditional Chinese medicine (TCM) pulse conditions for distinguishing between patients with the coronary heart disease (CHD) and normal people by using the proposed classification approach based on Hilbert-Huang transform (HHT) and random forest. Methods. The energy and the sample entropy features were extracted by applying the HHT to TCM pulse by treating these pulse signals as time series. By using the random forest classifier, the extracted two types of features and their combination were, respectively, used as input data to establish classification model. Results. Statistical results showed that there were significant differences in the pulse energy and sample entropy between the CHD group and the normal group. Moreover, the energy features, sample entropy features, and their combination were inputted as pulse feature vectors; the corresponding average recognition rates were 84%, 76.35%, and 90.21%, respectively. Conclusion. The proposed approach could be appropriately used to analyze pulses of patients with CHD, which can lay a foundation for research on objective and quantitative criteria on disease diagnosis or Zheng differentiation.

A Hilbert transform-based smart sensor for detection, classification, and quantification of power quality disturbances.

PubMed

Granados-Lieberman, David; Valtierra-Rodriguez, Martin; Morales-Hernandez, Luis A; Romero-Troncoso, Rene J; Osornio-Rios, Roque A

2013-04-25

Power quality disturbance (PQD) monitoring has become an important issue due to the growing number of disturbing loads connected to the power line and to the susceptibility of certain loads to their presence. In any real power system, there are multiple sources of several disturbances which can have different magnitudes and appear at different times. In order to avoid equipment damage and estimate the damage severity, they have to be detected, classified, and quantified. In this work, a smart sensor for detection, classification, and quantification of PQD is proposed. First, the Hilbert transform (HT) is used as detection technique; then, the classification of the envelope of a PQD obtained through HT is carried out by a feed forward neural network (FFNN). Finally, the root mean square voltage (Vrms), peak voltage (Vpeak), crest factor (CF), and total harmonic distortion (THD) indices calculated through HT and Parseval's theorem as well as an instantaneous exponential time constant quantify the PQD according to the disturbance presented. The aforementioned methodology is processed online using digital hardware signal processing based on field programmable gate array (FPGA). Besides, the proposed smart sensor performance is validated and tested through synthetic signals and under real operating conditions, respectively.

Influence of signals length and noise in power spectral densities computation using Hilbert-Huang Transform in synthetic HRV

NASA Astrophysics Data System (ADS)

Rodríguez, María. G.; Altuve, Miguel; Lollett, Carlos; Wong, Sara

2013-11-01

Among non-invasive techniques, heart rate variability (HRV) analysis has become widely used for assessing the balance of the autonomic nervous system. Research in this area has not stopped and alternative tools for the study and interpretation of HRV, are still being proposed. Nevertheless, frequency-domain analysis of HRV is controversial when the heartbeat sequence is non-stationary. The Hilbert-Huang Transform (HHT) is a relative new technique for timefrequency analyses of non-linear and non-stationary signals. The main purpose of this work is to investigate the influence of time serieś length and noise in HRV from synthetic signals, using HHT and to compare it with Welch method. Synthetic heartbeat time series with different sizes and levels of signal to noise ratio (SNR) were investigated. Results shows i) sequencés length did not affect the estimation of HRV spectral parameter, ii) favorable performance for HHT for different SNR. Additionally, HHT can be applied to non-stationary signals from nonlinear systems and it will be useful to HRV analysis to interpret autonomic activity when acute and transient phenomena are assessed.

Deep Learning Methods for Underwater Target Feature Extraction and Recognition

PubMed Central

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

2018-01-01

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

Segmentation of Killer Whale Vocalizations Using the Hilbert-Huang Transform

NASA Astrophysics Data System (ADS)

Adam, Olivier

2008-12-01

The study of cetacean vocalizations is usually based on spectrogram analysis. The feature extraction is obtained from 2D methods like the edge detection algorithm. Difficulties appear when signal-to-noise ratios are weak or when more than one vocalization is simultaneously emitted. This is the case for acoustic observations in a natural environment and especially for the killer whales which swim in groups. To resolve this problem, we propose the use of the Hilbert-Huang transform. First, we illustrate how few modes (5) are satisfactory for the analysis of these calls. Then, we detail our approach which consists of combining the modes for extracting the time-varying frequencies of the vocalizations. This combination takes advantage of one of the empirical mode decomposition properties which is that the successive IMFs represent the original data broken down into frequency components from highest to lowest frequency. To evaluate the performance, our method is first applied on the simulated chirp signals. This approach allows us to link one chirp to one mode. Then we apply it on real signals emitted by killer whales. The results confirm that this method is a favorable alternative for the automatic extraction of killer whale vocalizations.

Advanced Signal Processing for High Temperatures Health Monitoring of Condensed Water Height in Steam Pipes

NASA Technical Reports Server (NTRS)

Lih, Shyh-Shiuh; Bar-Cohen, Yoseph; Lee, Hyeong Jae; Takano, Nobuyuki; Bao, Xiaoqi

2013-01-01

An advanced signal processing methodology is being developed to monitor the height of condensed water thru the wall of a steel pipe while operating at temperatures as high as 250deg. Using existing techniques, previous study indicated that, when the water height is low or there is disturbance in the environment, the predicted water height may not be accurate. In recent years, the use of the autocorrelation and envelope techniques in the signal processing has been demonstrated to be a very useful tool for practical applications. In this paper, various signal processing techniques including the auto correlation, Hilbert transform, and the Shannon Energy Envelope methods were studied and implemented to determine the water height in the steam pipe. The results have shown that the developed method provides a good capability for monitoring the height in the regular conditions. An alternative solution for shallow water or no water conditions based on a developed hybrid method based on Hilbert transform (HT) with a high pass filter and using the optimized windowing technique is suggested. Further development of the reported methods would provide a powerful tool for the identification of the disturbances of water height inside the pipe.

Antiparallel spin does not always contain more information

NASA Astrophysics Data System (ADS)

Ghosh, Sibasish; Roy, Anirban; Sen, Ujjwal

2001-01-01

We show that the Bloch vectors lying on any great circle comprise the largest set SL for which the parallel states \\|n-->,n-->> can always be exactly transformed into the antiparallel states \\|n-->,-n-->>. Thus more information about n--> is not extractable from \\|n-->,-n-->> than from \\|n-->,n-->> by any measuring strategy, for n-->∈SL. Surprisingly this most general transformation reduces to just a flip operation on the second particle. We also show here that a probabilistic exact parallel to antiparallel transformation is not possible if the corresponding antiparallel states span the whole Hilbert space of the two qubits. These considerations allow us to generalize a conjecture of Gisin and Popescu [Phys. Rev. Lett. 83, 432 (1999)].

Phase synchronization based on a Dual-Tree Complex Wavelet Transform

NASA Astrophysics Data System (ADS)

Ferreira, Maria Teodora; Domingues, Margarete Oliveira; Macau, Elbert E. N.

2016-11-01

In this work, we show the applicability of our Discrete Complex Wavelet Approach (DCWA) to verify the phenomenon of phase synchronization transition in two coupled chaotic Lorenz systems. DCWA is based on the phase assignment from complex wavelet coefficients obtained by using a Dual-Tree Complex Wavelet Transform (DT-CWT). We analyzed two coupled chaotic Lorenz systems, aiming to detect the transition from non-phase synchronization to phase synchronization. In addition, we check how good is the method in detecting periods of 2π phase-slips. In all experiments, DCWA is compared with classical phase detection methods such as the ones based on arctangent and Hilbert transform showing a much better performance.

Qualitative analysis of MTEM response using instantaneous attributes

NASA Astrophysics Data System (ADS)

Fayemi, Olalekan; Di, Qingyun

2017-11-01

This paper introduces new technique for qualitative analysis of multi-transient electromagnetic (MTEM) earth impulse response over complex geological structures. Instantaneous phase and frequency attributes were used in place of the conventional common offset section for improved qualitative interpretation of MTEM data by obtaining more detailed information from the earth impulse response. The instantaneous attributes were used to describe the lateral variation in subsurface resistivity and the visible geological structure with respect to given offsets. Instantaneous phase attribute was obtained by converting the impulse response into a complex form using the Hilbert transform. Conversely, the polynomial phase difference (PPD) estimator was favored over the center finite difference (CFD) approximation method in calculating the instantaneous frequency attribute because it is computationally efficient and has the ability to give a smooth variation of the instantaneous frequency over a common offset section. The observed results from the instantaneous attributes were in good agreement with both the subsurface model used and the apparent resistivity section obtained from the MTEM earth impulse response. Hence, this study confirms the capability of both instantaneous phase and frequency attributes as highly effective tools for MTEM qualitative analysis.

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.

Solitons on Noncommutative Torus as Elliptic Calogero-Gaudin Models, Branes and Laughlin Wave Functions

NASA Astrophysics Data System (ADS)

Hou, Bo-Yu; Peng, Dan-Tao; Shi, Kang-Jie; Yue, Rui-Hong

For the noncommutative torus T, in the case of the noncommutative parameter θ = (Z)/(n), we construct the basis of Hilbert space Hn in terms of θ functions of the positions zi of n solitons. The wrapping around the torus generates the algebra An, which is the Zn × Zn Heisenberg group on θ functions. We find the generators g of a local elliptic su(n), which transform covariantly by the global gauge transformation of An. By acting on Hn we establish the isomorphism of An and g. We embed this g into the L-matrix of the elliptic Gaudin and Calogero-Moser models to give the dynamics. The moment map of this twisted cotangent sunT) bundle is matched to the D-equation with the Fayet-Illiopoulos source term, so the dynamics of the noncommutative solitons become that of the brane. The geometric configuration (k, u) of the spectral curve det|L(u) - k| = 0 describes the brane configuration, with the dynamical variables zi of the noncommutative solitons as the moduli T⊗ n/Sn. Furthermore, in the noncommutative Chern-Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map equation of the noncommutative sunT cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz.

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

2018-01-01

In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

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

NASA Astrophysics Data System (ADS)

Kuai, Ken Z.; Tsai, Christina W.

2012-02-01

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

Hilbert space structure in quantum gravity: an algebraic perspective

DOE PAGES

Giddings, Steven B.

2015-12-16

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of themore » Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.« less

Hilbert space structure in quantum gravity: an algebraic perspective

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

Giddings, Steven B.

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of themore » Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.« less

Riemann-Hilbert technique scattering analysis of metamaterial-based asymmetric 2D open resonators

NASA Astrophysics Data System (ADS)

Kamiński, Piotr M.; Ziolkowski, Richard W.; Arslanagić, Samel

2017-12-01

The scattering properties of metamaterial-based asymmetric two-dimensional open resonators excited by an electric line source are investigated analytically. The resonators are, in general, composed of two infinite and concentric cylindrical layers covered with an infinitely thin, perfect conducting shell that has an infinite axial aperture. The line source is oriented parallel to the cylinder axis. An exact analytical solution of this problem is derived. It is based on the dual-series approach and its transformation to the equivalent Riemann-Hilbert problem. Asymmetric metamaterial-based configurations are found to lead simultaneously to large enhancements of the radiated power and to highly steerable Huygens-like directivity patterns; properties not attainable with the corresponding structurally symmetric resonators. The presented open resonator designs are thus interesting candidates for many scientific and engineering applications where enhanced directional near- and far-field responses, tailored with beam shaping and steering capabilities, are highly desired.

An alternative approach to characterize nonlinear site effects

USGS Publications Warehouse

Zhang, R.R.; Hartzell, S.; Liang, J.; Hu, Y.

2005-01-01

This paper examines the rationale of a method of nonstationary processing and analysis, referred to as the Hilbert-Huang transform (HHT), for its application to a recording-based approach in quantifying influences of soil nonlinearity in site response. In particular, this paper first summarizes symptoms of soil nonlinearity shown in earthquake recordings, reviews the Fourier-based approach to characterizing nonlinearity, and offers justifications for the HHT in addressing nonlinearity issues. This study then uses the HHT method to analyze synthetic data and recordings from the 1964 Niigata and 2001 Nisqually earthquakes. In doing so, the HHT-based site response is defined as the ratio of marginal Hilbert amplitude spectra, alternative to the Fourier-based response that is the ratio of Fourier amplitude spectra. With the Fourier-based approach in studies of site response as a reference, this study shows that the alternative HHT-based approach is effective in characterizing soil nonlinearity and nonlinear site response.

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

Nonparametric Analyses of Log-Periodic Precursors to Financial Crashes

NASA Astrophysics Data System (ADS)

Zhou, Wei-Xing; Sornette, Didier

We apply two nonparametric methods to further test the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The term "parametric" refers here to the use of the log-periodic power law formula to fit the data; in contrast, "nonparametric" refers to the use of general tools such as Fourier transform, and in the present case the Hilbert transform and the so-called (H, q)-analysis. The analysis using the (H, q)-derivative is applied to seven time series ending with the October 1987 crash, the October 1997 correction and the April 2000 crash of the Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq indices. The Hilbert transform is applied to two detrended price time series in terms of the ln(tc-t) variable, where tc is the time of the crash. Taking all results together, we find strong evidence for a universal fundamental log-frequency f=1.02±0.05 corresponding to the scaling ratio λ=2.67±0.12. These values are in very good agreement with those obtained in earlier works with different parametric techniques. This note is extracted from a long unpublished report with 58 figures available at , which extensively describes the evidence we have accumulated on these seven time series, in particular by presenting all relevant details so that the reader can judge for himself or herself the validity and robustness of the results.

A transform from absorption to Raman excitation profile. A time-dependent approach

NASA Astrophysics Data System (ADS)

Lee, Soo-Y.; Yeo, Robert C. K.

1994-04-01

An alternative time-frame approach, which is canonically conjugate to the energy-frame approach, for implementing the transform relations for calculating Raman excitation profiles directly from the optical absorption spectrum is presented. Practical and efficient fast Fourier transformation in the time frame replaces the widely used Chan and Page algorithm for evaluating the Hilbert transform in the energy frame. The time-frame approach is applied to: (a) a two-mode model which illustrates the missing mode effect in both absorption and Raman excitation profiles, (b) carotene, in which both the absorption spectrum and the Raman excitation profile show vibrational structure and (c) hexamethylbenzene: TCNE electron donor—acceptor complex where the same spectra are structureless and the Raman excitation profile for the 168 cm -1 mode poses a problem for the energy-frame approach. A similar time-frame approach can be used for the inverse transform from the Raman excitation profile to the optical absorption spectrum.

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.

Two Dimensional Processing Of Speech And Ecg Signals Using The Wigner-Ville Distribution

NASA Astrophysics Data System (ADS)

Boashash, Boualem; Abeysekera, Saman S.

1986-12-01

The Wigner-Ville Distribution (WVD) has been shown to be a valuable tool for the analysis of non-stationary signals such as speech and Electrocardiogram (ECG) data. The one-dimensional real data are first transformed into a complex analytic signal using the Hilbert Transform and then a 2-dimensional image is formed using the Wigner-Ville Transform. For speech signals, a contour plot is determined and used as a basic feature. for a pattern recognition algorithm. This method is compared with the classical Short Time Fourier Transform (STFT) and is shown, to be able to recognize isolated words better in a noisy environment. The same method together with the concept of instantaneous frequency of the signal is applied to the analysis of ECG signals. This technique allows one to classify diseased heart-beat signals. Examples are shown.

Multimodal Pressure-Flow Analysis: Application of Hilbert Huang Transform in Cerebral Blood Flow Regulation

NASA Astrophysics Data System (ADS)

Lo, Men-Tzung; Hu, Kun; Liu, Yanhui; Peng, C.-K.; Novak, Vera

2008-12-01

Quantification of nonlinear interactions between two nonstationary signals presents a computational challenge in different research fields, especially for assessments of physiological systems. Traditional approaches that are based on theories of stationary signals cannot resolve nonstationarity-related issues and, thus, cannot reliably assess nonlinear interactions in physiological systems. In this review we discuss a new technique called multimodal pressure flow (MMPF) method that utilizes Hilbert-Huang transformation to quantify interaction between nonstationary cerebral blood flow velocity (BFV) and blood pressure (BP) for the assessment of dynamic cerebral autoregulation (CA). CA is an important mechanism responsible for controlling cerebral blood flow in responses to fluctuations in systemic BP within a few heart-beats. The MMPF analysis decomposes BP and BFV signals into multiple empirical modes adaptively so that the fluctuations caused by a specific physiologic process can be represented in a corresponding empirical mode. Using this technique, we showed that dynamic CA can be characterized by specific phase delays between the decomposed BP and BFV oscillations, and that the phase shifts are significantly reduced in hypertensive, diabetics and stroke subjects with impaired CA. Additionally, the new technique can reliably assess CA using both induced BP/BFV oscillations during clinical tests and spontaneous BP/BFV fluctuations during resting conditions.

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.

Terahertz Josephson spectral analysis and its applications

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

A Hilbert Transform-Based Smart Sensor for Detection, Classification, and Quantification of Power Quality Disturbances

PubMed Central

Granados-Lieberman, David; Valtierra-Rodriguez, Martin; Morales-Hernandez, Luis A.; Romero-Troncoso, Rene J.; Osornio-Rios, Roque A.

2013-01-01

Power quality disturbance (PQD) monitoring has become an important issue due to the growing number of disturbing loads connected to the power line and to the susceptibility of certain loads to their presence. In any real power system, there are multiple sources of several disturbances which can have different magnitudes and appear at different times. In order to avoid equipment damage and estimate the damage severity, they have to be detected, classified, and quantified. In this work, a smart sensor for detection, classification, and quantification of PQD is proposed. First, the Hilbert transform (HT) is used as detection technique; then, the classification of the envelope of a PQD obtained through HT is carried out by a feed forward neural network (FFNN). Finally, the root mean square voltage (Vrms), peak voltage (Vpeak), crest factor (CF), and total harmonic distortion (THD) indices calculated through HT and Parseval's theorem as well as an instantaneous exponential time constant quantify the PQD according to the disturbance presented. The aforementioned methodology is processed online using digital hardware signal processing based on field programmable gate array (FPGA). Besides, the proposed smart sensor performance is validated and tested through synthetic signals and under real operating conditions, respectively. PMID:23698264

Consonant identification in noise using Hilbert-transform temporal fine-structure speech and recovered-envelope speech for listeners with normal and impaired hearinga)

PubMed Central

Léger, Agnès C.; Reed, Charlotte M.; Desloge, Joseph G.; Swaminathan, Jayaganesh; Braida, Louis D.

2015-01-01

Consonant-identification ability was examined in normal-hearing (NH) and hearing-impaired (HI) listeners in the presence of steady-state and 10-Hz square-wave interrupted speech-shaped noise. The Hilbert transform was used to process speech stimuli (16 consonants in a-C-a syllables) to present envelope cues, temporal fine-structure (TFS) cues, or envelope cues recovered from TFS speech. The performance of the HI listeners was inferior to that of the NH listeners both in terms of lower levels of performance in the baseline condition and in the need for higher signal-to-noise ratio to yield a given level of performance. For NH listeners, scores were higher in interrupted noise than in steady-state noise for all speech types (indicating substantial masking release). For HI listeners, masking release was typically observed for TFS and recovered-envelope speech but not for unprocessed and envelope speech. For both groups of listeners, TFS and recovered-envelope speech yielded similar levels of performance and consonant confusion patterns. The masking release observed for TFS and recovered-envelope speech may be related to level effects associated with the manner in which the TFS processing interacts with the interrupted noise signal, rather than to the contributions of TFS cues per se. PMID:26233038

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

NASA Astrophysics Data System (ADS)

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

2007-05-01

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

Algorithms and Results of Eye Tissues Differentiation Based on RF Ultrasound

PubMed Central

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

2012-01-01

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

Conformal Nets II: Conformal Blocks

NASA Astrophysics Data System (ADS)

Bartels, Arthur; Douglas, Christopher L.; Henriques, André

2017-08-01

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.

Adaptive spread spectrum receiver using acoustic surface wave technology

NASA Astrophysics Data System (ADS)

Das, P.; Milstein, L. B.

1984-05-01

This technical report summarizes the results of the research we have been engaged in regarding the use of surface acoustic wave devices in direct sequence spread spectrum receivers. The heart of this research has been the use of the device as a real-time Fourier transformer. A system of this type is sometimes referred to as a compressive receiver, and our use of the system has been primarily as a means to implement a narrowband interference rejection filter. In addition, we have studied many other topics such as rapid acquisition, Hilbert transform generation, etc. and these topics are all overviewed in this report.

Exact controllability for a Thermodiffusion System with locally distributed controls

NASA Astrophysics Data System (ADS)

de Moraes, F. G.; Schulz, R. A.; Soriano, J. A.

2018-03-01

In this work we establish a exact controllability result for a thermodiffusion system, modeled by Cattaneo's law, posed in a one-dimensional domain. In the present model the control mechanisms are effective in a small subinterval of the domain. To obtain the desired results, we prove an observability inequality for the adjoint system which, together with the multiplier methods and the Hilbert Uniqueness Method (HUM) developed by J.L. Lions, gives the controllability.

Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

NASA Astrophysics Data System (ADS)

Connes, Alain; Kreimer, Dirk

This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ+ of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. The analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title.

Proposed MIL Standard and Handbook - Flying Qualities of Air Vehicles. Volume 2. Proposed MIL Handbook

DTIC Science & Technology

1982-11-01

model but uses the Hilbert transform to model intermittency as well as Gaussian structure patchiness. Includes University of Washington model features...Requirements for Satisfactory Elevator Control Characteristics, NACA TN 1060, June 1946. 852 - - - - 137. Jones, R. T., and H. Greenberg , Effect of Hinge...Moment Parameters on Elevator Stick Forces in Rapid Maneuvers NACA Report 798, Nov. 1944. 138. Greenberg , H., and L. Sternfield, A Theoretical

Modern Electromagnetic Scattering

DTIC Science & Technology

2013-08-10

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

Axial 3D region of interest reconstruction using weighted cone beam BPF/DBPF algorithm cascaded with adequately oriented orthogonal butterfly filtering

NASA Astrophysics Data System (ADS)

Tang, Shaojie; Tang, Xiangyang

2016-03-01

Axial cone beam (CB) computed tomography (CT) reconstruction is still the most desirable in clinical applications. As the potential candidates with analytic form for the task, the back projection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical and axial reconstruction from CB and fan beam projection data, respectively. These two algorithms have been heuristically extended for axial CB reconstruction via adoption of virtual PI-line segments. Unfortunately, however, streak artifacts are induced along the Hilbert filtering direction, since these algorithms are no longer accurate on the virtual PI-line segments. We have proposed to cascade the extended BPF/DBPF algorithm with orthogonal butterfly filtering for image reconstruction (namely axial CB-BPP/DBPF cascaded with orthogonal butterfly filtering), in which the orientation-specific artifacts caused by post-BP Hilbert transform can be eliminated, at a possible expense of losing the BPF/DBPF's capability of dealing with projection data truncation. Our preliminary results have shown that this is not the case in practice. Hence, in this work, we carry out an algorithmic analysis and experimental study to investigate the performance of the axial CB-BPP/DBPF cascaded with adequately oriented orthogonal butterfly filtering for three-dimensional (3D) reconstruction in region of interest (ROI).

Space Inside a Liquid Sphere Transforms into De Sitter Space by Hilbert Radius

NASA Astrophysics Data System (ADS)

Rabounski, Dmitri; Borissova, Larissa

2010-04-01

Consider space inside a sphere of incompressible liquid, and space surrounding a mass-point. Metrics of the spaces were deduced in 1916 by Karl Schwarzschild. 1) Our calculation shows that a liquid sphere can be in the state of gravitational collapse (g00 = 0) only if its mass and radius are close to those of the Universe (M = 8.7x10^55 g, a = 1.3x10^28 cm). However if the same mass is presented as a mass-point, the radius of collapse rg (Hilbert radius) is many orders lesser: g00 = 0 realizes in a mass-point's space by other conditions. 2) We considered a liquid sphere whose radius meets, formally, the Hilbert radius of a mass-point bearing the same mass: a = rg, however the liquid sphere is not a collapser (see above). We show that in this case the metric of the liquid sphere's internal space can be represented as de Sitter's space metric, wherein λ = 3/a^2 > 0: physical vacuum (due to the λ-term) is the same as the field of an ideal liquid where ρ0 < 0 and p = -ρ0 c^2 > 0 (the mirror world liquid). The gravitational redshift inside the sphere is produced by the non-Newtonian force of repulsion (which is due to the λ-term, λ = 3/a^2 > 0); it is also calculated.

Schwinger-Keldysh superspace in quantum mechanics

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Optically-sectioned two-shot structured illumination microscopy with Hilbert-Huang processing.

PubMed

Patorski, Krzysztof; Trusiak, Maciej; Tkaczyk, Tomasz

2014-04-21

We introduce a fast, simple, adaptive and experimentally robust method for reconstructing background-rejected optically-sectioned images using two-shot structured illumination microscopy. Our innovative data demodulation method needs two grid-illumination images mutually phase shifted by π (half a grid period) but precise phase displacement between two frames is not required. Upon frames subtraction the input pattern with increased grid modulation is obtained. The first demodulation stage comprises two-dimensional data processing based on the empirical mode decomposition for the object spatial frequency selection (noise reduction and bias term removal). The second stage consists in calculating high contrast image using the two-dimensional spiral Hilbert transform. Our algorithm effectiveness is compared with the results calculated for the same input data using structured-illumination (SIM) and HiLo microscopy methods. The input data were collected for studying highly scattering tissue samples in reflectance mode. Results of our approach compare very favorably with SIM and HiLo techniques.

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.

Characterization of large-scale fluctuations and short-term variability of Seine river daily streamflow (France) over the period 1950-2008 by empirical mode decomposition and the Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Massei, N.; Fournier, M.

2010-12-01

Daily Seine river flow from 1950 to 2008 was analyzed using Hilbert-Huang Tranform (HHT). For the last ten years, this method which combines the so-called Empirical Mode Decomposition (EMD) multiresolution analysis and the Hilbert transform has proven its efficiency for the analysis of transient oscillatory signals, although the mathematical definition of the EMD is not totally established yet. HHT also provides an interesting alternative to other time-frequency or time-scale analysis of non-stationary signals, the most famous of which being wavelet-based approaches. In this application of HHT to the analysis of the hydrological variability of the Seine river, we seek to characterize the interannual patterns of daily flow, differenciate them from the short-term dynamics and eventually interpret them in the context of regional climate regime fluctuations. In this aim, HHT is also applied to the North-Atlantic Oscillation (NAO) through the annual winter-months NAO index time series. For both hydrological and climatic signals, dominant variability scales are extracted and their temporal variations analyzed by determination of the intantaneous frequency of each component. When compared to previous ones obtained from continuous wavelet transform (CWT) on the same data, HHT results highlighted the same scales and somewhat the same internal components for each signal. However, HHT allowed the identification and extraction of much more similar features during the 1950-2008 period (e.g., around 7-yr, between NAO and Seine flow than what was obtained from CWT, which comes to say that variability scales in flow likely to originate from climatic regime fluctuations were much properly identified in river flow. In addition, a more accurate determination of singularities in the natural processes analyzed were authorized by HHT compared to CWT, in which case the time-frequency resolution partly depends on the basic properties of the filter (i.e., the reference wavelet chosen initially). Compared to CWT or even to discrete wavelet multiresolution analysis, HHT is auto-adaptive, non-parametric, allows an orthogonal decomposition of the signal analyzed and provides a more accurate estimation of changing variability scales across time for highly transient signals.

Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings

NASA Astrophysics Data System (ADS)

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo; Vernizzi, Filippo

2017-09-01

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlator can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.

An improved method to characterise the modulation of small-scale turbulent by large-scale structures

NASA Astrophysics Data System (ADS)

Agostini, Lionel; Leschziner, Michael; Gaitonde, Datta

2015-11-01

A key aspect of turbulent boundary layer dynamics is ``modulation,'' which refers to degree to which the intensity of coherent large-scale structures (LS) cause an amplification or attenuation of the intensity of the small-scale structures (SS) through large-scale-linkage. In order to identify the variation of the amplitude of the SS motion, the envelope of the fluctuations needs to be determined. Mathis et al. (2009) proposed to define this latter by low-pass filtering the modulus of the analytic signal built from the Hilbert transform of SS. The validity of this definition, as a basis for quantifying the modulated SS signal, is re-examined on the basis of DNS data for a channel flow. The analysis shows that the modulus of the analytic signal is very sensitive to the skewness of its PDF, which is dependent, in turn, on the sign of the LS fluctuation and thus of whether these fluctuations are associated with sweeps or ejections. The conclusion is that generating an envelope by use of a low-pass filtering step leads to an important loss of information associated with the effects of the local skewness of the PDF of the SS on the modulation process. An improved Hilbert-transform-based method is proposed to characterize the modulation of SS turbulence by LS structures

Reconstruction of the in-plane mode shape of a rotating tire with a continuous scanning measurement using the Hilbert-Huang transform.

PubMed

Lee, Jongsuh; Wang, Semyung; Pluymers, Bert; Desmet, Wim; Kindt, Peter

2015-02-01

Generally, the dynamic characteristics (natural frequency, damping, and mode shape) of a structure can be estimated by experimental modal analysis. Among these dynamic characteristics, mode shape requires multiple measurements of the structure at different positions, which increases the experimental cost and time. Recently, the Hilbert-Huang transform (HHT) method has been introduced to extract mode-shape information from a continuous measurement, which requires vibration measurements from one position to another position continuously with a non-contact sensor. In this research study, an effort has been made to estimate the mode shapes of a rolling tire with a single measurement instead of using the conventional experimental setup (i.e., measurement of the vibration of a rolling tire at multiple positions similar to the case of a non-rotating structure), which is used to estimate the dynamic behavior of a rolling tire. For this purpose, HHT, which was used in the continuous measurement of a non-rotating structure in previous research studies, has been used for the case of a rotating system in this study. Ambiguous mode combinations can occur in this rotating system, and therefore, a method to overcome this ambiguity is proposed in this study. In addition, the specific phenomenon for a rotating system is introduced, and the effect of this phenomenon with regard to the obtained results through HHT is investigated.

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

A Thin Lens Model for Charged-Particle RF Accelerating Gaps

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

Allen, Christopher K.

Presented is a thin-lens model for an RF accelerating gap that considers general axial fields without energy dependence or other a priori assumptions. Both the cosine and sine transit time factors (i.e., Fourier transforms) are required plus two additional functions; the Hilbert transforms the transit-time factors. The combination yields a complex-valued Hamiltonian rotating in the complex plane with synchronous phase. Using Hamiltonians the phase and energy gains are computed independently in the pre-gap and post-gap regions then aligned using the asymptotic values of wave number. Derivations of these results are outlined, examples are shown, and simulations with the model aremore » presented.« less

Lorentz quantum mechanics

NASA Astrophysics Data System (ADS)

Zhang, Qi; Wu, Biao

2018-01-01

We present a theoretical framework for the dynamics of bosonic Bogoliubov quasiparticles. We call it Lorentz quantum mechanics because the dynamics is a continuous complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary transformation in Hilbert space. In our Lorentz quantum mechanics, three types of state exist: space-like, light-like and time-like. Fundamental aspects are explored in parallel to the usual quantum mechanics, such as a matrix form of a Lorentz transformation, and the construction of Pauli-like matrices for spinors. We also investigate the adiabatic evolution in these mechanics, as well as the associated Berry curvature and Chern number. Three typical physical systems, where bosonic Bogoliubov quasi-particles and their Lorentz quantum dynamics can arise, are presented. They are a one-dimensional fermion gas, Bose-Einstein condensate (or superfluid), and one-dimensional antiferromagnet.

Stability Analysis of Finite Difference Approximations to Hyperbolic Systems,and Problems in Applied and Computational Matrix and Operator Theory

DTIC Science & Technology

1990-12-07

Fundaqao Calouste Gulbenkian, Instituto Gulbenkian de Ci~ncia, Centro de C6lculo Cientifico , Coimbra, 1973. 28, Dirac, P. A. M., Spinors in Hilbert Space...Office of Scientific Research grants 1965 Mathematical Association of America Editorial Prize for the article entitled: "Linear Transformations on...matrices" 1966 L.R. Ford Memorial Prize awarded by the Mathematical Association of America for the article , "Permanents" 1989 Outstanding Computer

Speech Envelope Normalization, a Method to Improve SNR and Suppress Noise in Present and Future Radio Systems.

DTIC Science & Technology

1982-12-01

GRA&IT--4 I DTIC TAB U:.r.nnoincee Distr±iatic !/ KAvnilr,1.llty Codes AvRUJ and/or Dist S pecial 1 AN 𔄃 . .. ACKNOWLEDGEMENTS The success of the...evaluated. Two different approaches emerged, one employing cascaded active all-pass networks, and the other using a charged coupled device sampled data delay...Wideband 900 Phase-Shifters 38 * 5.2 Samples Data Direct Hilbert Transforms 43 5.3 Charge Coupled Device (CCD) Implementation 45 5.4 Digital

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

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2008-01-01

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

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

Asplund, Curtis T., E-mail: ca2621@columbia.edu; Berenstein, David, E-mail: dberens@physics.ucsb.edu

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate themore » dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.« less

BRST detour quantization: Generating gauge theories from constraints

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

Cherney, D.; Waldron, A.; Latini, E.

2010-06-15

We present the Becchi-Rouet-Stora-Tyutin (BRST) cohomologies of a class of constraint (super) Lie algebras as detour complexes. By interpreting the components of detour complexes as gauge invariances, Bianchi identities, and equations of motion, we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric, and Kaehler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-formmore » Kaehler electromagnetism. We also discuss how our results generalize to other special geometries.« less

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

NASA Astrophysics Data System (ADS)

Samsonov, Boris F.

2010-10-01

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

Evaluation of Hydrologic and Meteorological Impacts on Dengue Fever Incidences in Southern Taiwan using Time- Frequency Method

NASA Astrophysics Data System (ADS)

Tsai, Christina; Yeh, Ting-Gu

2017-04-01

Extreme weather events are occurring more frequently as a result of climate change. Recently dengue fever has become a serious issue in southern Taiwan. It may have characteristic temporal scales that can be identified. Some researchers have hypothesized that dengue fever incidences are related to climate change. This study applies time-frequency analysis to time series data concerning dengue fever and hydrologic and meteorological variables. Results of three time-frequency analytical methods - the Hilbert Huang transform (HHT), the Wavelet Transform (WT) and the Short Time Fourier Transform (STFT) are compared and discussed. A more effective time-frequency analysis method will be identified to analyze relevant time series data. The most influential time scales of hydrologic and meteorological variables that are associated with dengue fever are determined. Finally, the linkage between hydrologic/meteorological factors and dengue fever incidences can be established.

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'.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

PubMed

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

2016-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

NASA Astrophysics Data System (ADS)

Yang, Qingsong; Cong, Wenxiang; Wang, Ge

2016-10-01

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

PET and MRI image fusion based on combination of 2-D Hilbert transform and IHS method.

PubMed

Haddadpour, Mozhdeh; Daneshvar, Sabalan; Seyedarabi, Hadi

2017-08-01

The process of medical image fusion is combining two or more medical images such as Magnetic Resonance Image (MRI) and Positron Emission Tomography (PET) and mapping them to a single image as fused image. So purpose of our study is assisting physicians to diagnose and treat the diseases in the least of the time. We used Magnetic Resonance Image (MRI) and Positron Emission Tomography (PET) as input images, so fused them based on combination of two dimensional Hilbert transform (2-D HT) and Intensity Hue Saturation (IHS) method. Evaluation metrics that we apply are Discrepancy (D k ) as an assessing spectral features and Average Gradient (AG k ) as an evaluating spatial features and also Overall Performance (O.P) to verify properly of the proposed method. In this paper we used three common evaluation metrics like Average Gradient (AG k ) and the lowest Discrepancy (D k ) and Overall Performance (O.P) to evaluate the performance of our method. Simulated and numerical results represent the desired performance of proposed method. Since that the main purpose of medical image fusion is preserving both spatial and spectral features of input images, so based on numerical results of evaluation metrics such as Average Gradient (AG k ), Discrepancy (D k ) and Overall Performance (O.P) and also desired simulated results, it can be concluded that our proposed method can preserve both spatial and spectral features of input images. Copyright © 2017 Chang Gung University. Published by Elsevier B.V. All rights reserved.

Canonical field anticommutators in the extended gauged Rarita-Schwinger theory

NASA Astrophysics Data System (ADS)

Adler, Stephen L.; Henneaux, Marc; Pais, Pablo

2017-10-01

We reexamine canonical quantization of the gauged Rarita-Schwinger theory using the extended theory, incorporating a dimension 1/2 auxiliary spin-1/2 field Λ , in which there is an exact off-shell gauge invariance. In Λ =0 gauge, which reduces to the original unextended theory, our results agree with those found by Johnson and Sudarshan, and later verified by Velo and Zwanziger, which give a canonical Rarita-Schwinger field Dirac bracket that is singular for small gauge fields. In gauge covariant radiation gauge, the Dirac bracket of the Rarita-Schwinger fields is nonsingular, but does not correspond to a positive semidefinite anticommutator, and the Dirac bracket of the auxiliary fields has a singularity of the same form as found in the unextended theory. These results indicate that gauged Rarita-Schwinger theory is somewhat pathological, and cannot be canonically quantized within a conventional positive semidefinite metric Hilbert space. We leave open the questions of whether consistent quantizations can be achieved by using an indefinite metric Hilbert space, by path integral methods, or by appropriate couplings to conventional dimension 3/2 spin-1/2 fields.

Eternal non-Markovianity: from random unitary to Markov chain realisations.

PubMed

Megier, Nina; Chruściński, Dariusz; Piilo, Jyrki; Strunz, Walter T

2017-07-25

The theoretical description of quantum dynamics in an intriguing way does not necessarily imply the underlying dynamics is indeed intriguing. Here we show how a known very interesting master equation with an always negative decay rate [eternal non-Markovianity (ENM)] arises from simple stochastic Schrödinger dynamics (random unitary dynamics). Equivalently, it may be seen as arising from a mixture of Markov (semi-group) open system dynamics. Both these approaches lead to a more general family of CPT maps, characterized by a point within a parameter triangle. Our results show how ENM quantum dynamics can be realised easily in the laboratory. Moreover, we find a quantum time-continuously measured (quantum trajectory) realisation of the dynamics of the ENM master equation based on unitary transformations and projective measurements in an extended Hilbert space, guided by a classical Markov process. Furthermore, a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) representation of the dynamics in an extended Hilbert space can be found, with a remarkable property: there is no dynamics in the ancilla state. Finally, analogous constructions for two qubits extend these results from non-CP-divisible to non-P-divisible dynamics.

Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings

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

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlatormore » can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.« less

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

Livine, Etera R.

We introduce the set of framed (convex) polyhedra with N faces as the symplectic quotient C{sup 2N}//SU(2). A framed polyhedron is then parametrized by N spinors living in C{sup 2} satisfying suitable closure constraints and defines a usual convex polyhedron plus extra U(1) phases attached to each face. We show that there is a natural action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any (framed) polyhedron onto any other with the same total (boundary) area. This identifies the space of framed polyhedra to the Grassmannian space U(N)/ (SU(2)×U(N−2)).more » We show how to write averages of geometrical observables (polynomials in the faces' area and the angles between them) over the ensemble of polyhedra (distributed uniformly with respect to the Haar measure on U(N)) as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically. We also use the Itzykson-Zuber formula from matrix models as the generating function for these averages and correlations. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners (or, in other words, SU(2)-invariant states in tensor products of irreducible representations). The total boundary area as well as the individual face areas are quantized as half-integers (spins), and the Hilbert spaces for fixed total area form irreducible representations of U(N). We define semi-classical coherent intertwiner states peaked on classical framed polyhedra and transforming consistently under U(N) transformations. And we show how the U(N) character formula for unitary transformations is to be considered as an extension of the Itzykson-Zuber to the quantum level and generates the traces of all polynomial observables over the Hilbert space of intertwiners. We finally apply the same formalism to two dimensions and show that classical (convex) polygons can be described in a similar fashion trading the unitary group for the orthogonal group. We conclude with a discussion of the possible (deformation) dynamics that one can define on the space of polygons or polyhedra. This work is a priori useful in the context of discrete geometry but it should hopefully also be relevant to (loop) quantum gravity in 2+1 and 3+1 dimensions when the quantum geometry is defined in terms of gluing of (quantized) polygons and polyhedra.« less

Conduction velocity of the uterine contraction in serial magnetomyogram (MMG) data: event based simulation and validation.

PubMed

Furdea, Adrian; Preissl, Hubert; Lowery, Curtis L; Eswaran, Hari; Govindan, Rathinaswamy B

2011-01-01

We propose a novel approach to calculate the conduction velocity (CV) of the uterine contraction bursts in magnetomyogram (MMG) signals measured using a multichannel SQUID array. For this purpose, we partition the sensor coordinates into four different quadrants and identify the contractile bursts using a previously proposed Hilbert-wavelet transform approach. If contractile burst is identified in more than one quadrant, we calculate the center of gravity (CoG) in each quadrant for each time point as the sum of the product of the sensor coordinates with the Hilbert amplitude of the MMG signals normalized by the sum of the Hilbert amplitude of the signals over all sensors. Following this we compute the delay between the CoGs of all (six) possible quadrant pairs combinations. As a first step, we validate this approach by simulating a stochastic model based on independent second-order autoregressive processes (AR2) and we divide them into 30 second disjoint windows and insert burst activity at specific time instances in preselected sensors. Also we introduce a lag of 5 ± 1 seconds between different quadrants. Using our approach we calculate the CoG of the signals in a quadrant. To this end, we compute the delay between CoGs obtained from different quadrants and show that our approach is able to reliably capture the delay incorporated in the model. We apply the proposed approach to 19 serial MMG data obtained from two subjects and show an increase in the CV as the subjects approached labor.

Adaptive fault feature extraction from wayside acoustic signals from train bearings

NASA Astrophysics Data System (ADS)

Zhang, Dingcheng; Entezami, Mani; Stewart, Edward; Roberts, Clive; Yu, Dejie

2018-07-01

Wayside acoustic detection of train bearing faults plays a significant role in maintaining safety in the railway transport system. However, the bearing fault information is normally masked by strong background noises and harmonic interferences generated by other components (e.g. axles and gears). In order to extract the bearing fault feature information effectively, a novel method called improved singular value decomposition (ISVD) with resonance-based signal sparse decomposition (RSSD), namely the ISVD-RSSD method, is proposed in this paper. A Savitzky-Golay (S-G) smoothing filter is used to filter singular vectors (SVs) in the ISVD method as an extension of the singular value decomposition (SVD) theorem. Hilbert spectrum entropy and a stepwise optimisation strategy are used to optimize the S-G filter's parameters. The RSSD method is able to nonlinearly decompose the wayside acoustic signal of a faulty train bearing into high and low resonance components, the latter of which contains bearing fault information. However, the high level of noise usually results in poor decomposition results from the RSSD method. Hence, the collected wayside acoustic signal must first be de-noised using the ISVD component of the ISVD-RSSD method. Next, the de-noised signal is decomposed by using the RSSD method. The obtained low resonance component is then demodulated with a Hilbert transform such that the bearing fault can be detected by observing Hilbert envelope spectra. The effectiveness of the ISVD-RSSD method is verified through both laboratory field-based experiments as described in the paper. The results indicate that the proposed method is superior to conventional spectrum analysis and ensemble empirical mode decomposition methods.

Quantum probability and Hilbert's sixth problem

NASA Astrophysics Data System (ADS)

Accardi, Luigi

2018-04-01

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

Full characterization of modular values for finite-dimensional systems

NASA Astrophysics Data System (ADS)

Ho, Le Bin; Imoto, Nobuyuki

2016-06-01

Kedem and Vaidman obtained a relationship between the spin-operator modular value and its weak value for specific coupling strengths [14]. Here we give a general expression for the modular value in the n-dimensional Hilbert space using the weak values up to (n - 1)th order of an arbitrary observable for any coupling strength, assuming non-degenerated eigenvalues. For two-dimensional case, it shows a linear relationship between the weak value and the modular value. We also relate the modular value of the sum of observables to the weak value of their product.

The energy-momentum tensor(s) in classical gauge theories

DOE PAGES

Blaschke, Daniel N.; Gieres, François; Reboud, Méril; ...

2016-07-12

We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. In conclusion, the relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.

Polarized 3-folds in a codimension 10 weighted homogeneous F4 variety

NASA Astrophysics Data System (ADS)

Qureshi, Muhammad Imran

2017-10-01

We describe the construction of a codimension 10 weighted homogeneous variety wΣF4(μ , u) corresponding to the exceptional Lie group F4 by explicit computation of its graded ring structure. We give a formula for the Hilbert series of the generic weighted wΣF4(μ , u) in terms of representation theoretic data of F4. We also construct some families of polarized 3-folds in codimension 10 whose general member is a weighted complete intersection of some wΣF4(μ , u) .

Initial-boundary value problems associated with the Ablowitz-Ladik system

NASA Astrophysics Data System (ADS)

Xia, Baoqiang; Fokas, A. S.

2018-02-01

We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

High resolution signal-processing method for extrinsic Fabry-Perot interferometric sensors

NASA Astrophysics Data System (ADS)

Xie, Jiehui; Wang, Fuyin; Pan, Yao; Wang, Junjie; Hu, Zhengliang; Hu, Yongming

2015-03-01

In this paper, a signal-processing method for optical fiber extrinsic Fabry-Perot interferometric sensors is presented. It achieves both high resolution and absolute measurement of the dynamic change of cavity length with low sampling points in wavelength domain. In order to improve the demodulation accuracy, the reflected interference spectrum is cleared by Discrete Wavelet Transform and adjusted by the Hilbert transform. Then the cavity length is interrogated by the cross correlation algorithm. The continuous tests show the resolution of cavity length is only 36.7 pm. Moreover, the corresponding resolution of cavity length is only 1 pm on the low frequency range below 420 Hz, and the corresponding power spectrum shows the possibility of detecting the ultra-low frequency signals based on spectra detection.

Signal processing techniques for damage detection with piezoelectric wafer active sensors and embedded ultrasonic structural radar

NASA Astrophysics Data System (ADS)

Yu, Lingyu; Bao, Jingjing; Giurgiutiu, Victor

2004-07-01

Embedded ultrasonic structural radar (EUSR) algorithm is developed for using piezoelectric wafer active sensor (PWAS) array to detect defects within a large area of a thin-plate specimen. Signal processing techniques are used to extract the time of flight of the wave packages, and thereby to determine the location of the defects with the EUSR algorithm. In our research, the transient tone-burst wave propagation signals are generated and collected by the embedded PWAS. Then, with signal processing, the frequency contents of the signals and the time of flight of individual frequencies are determined. This paper starts with an introduction of embedded ultrasonic structural radar algorithm. Then we will describe the signal processing methods used to extract the time of flight of the wave packages. The signal processing methods being used include the wavelet denoising, the cross correlation, and Hilbert transform. Though hardware device can provide averaging function to eliminate the noise coming from the signal collection process, wavelet denoising is included to ensure better signal quality for the application in real severe environment. For better recognition of time of flight, cross correlation method is used. Hilbert transform is applied to the signals after cross correlation in order to extract the envelope of the signals. Signal processing and EUSR are both implemented by developing a graphical user-friendly interface program in LabView. We conclude with a description of our vision for applying EUSR signal analysis to structural health monitoring and embedded nondestructive evaluation. To this end, we envisage an automatic damage detection application utilizing embedded PWAS, EUSR, and advanced signal processing.

Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units.

PubMed

Watanabe, Yuuki; Maeno, Seiya; Aoshima, Kenji; Hasegawa, Haruyuki; Koseki, Hitoshi

2010-09-01

The real-time display of full-range, 2048?axial pixelx1024?lateral pixel, Fourier-domain optical-coherence tomography (FD-OCT) images is demonstrated. The required speed was achieved by using dual graphic processing units (GPUs) with many stream processors to realize highly parallel processing. We used a zero-filling technique, including a forward Fourier transform, a zero padding to increase the axial data-array size to 8192, an inverse-Fourier transform back to the spectral domain, a linear interpolation from wavelength to wavenumber, a lateral Hilbert transform to obtain the complex spectrum, a Fourier transform to obtain the axial profiles, and a log scaling. The data-transfer time of the frame grabber was 15.73?ms, and the processing time, which includes the data transfer between the GPU memory and the host computer, was 14.75?ms, for a total time shorter than the 36.70?ms frame-interval time using a line-scan CCD camera operated at 27.9?kHz. That is, our OCT system achieved a processed-image display rate of 27.23 frames/s.

Operational Axioms for Quantum Mechanics

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

D'Ariano, Giacomo Mauro; Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208

2007-02-21

The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of physical experiment and from five simple Postulates concerning experimental accessibility and simplicity. For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in Ref. [1]. The main ingredient of the axiomatization is the postulated existence of faithful states that allows one to calibrate the experimental apparatus. Such notionmore » is at the basis of the operational definitions of the scalar product and of the transposed of a physical transformation. What is new in the present paper with respect to Ref. [1], is the operational deduction of an involution corresponding to the complex-conjugation for effects, whose extension to transformations allows to define the adjoint of a transformation when the extension is composition-preserving. The existence of such composition-preserving extension among possible extensions is analyzed.« less

Signal quality enhancement using higher order wavelets for ultrasonic TOFD signals from austenitic stainless steel welds.

PubMed

Praveen, Angam; Vijayarekha, K; Abraham, Saju T; Venkatraman, B

2013-09-01

Time of flight diffraction (TOFD) technique is a well-developed ultrasonic non-destructive testing (NDT) method and has been applied successfully for accurate sizing of defects in metallic materials. This technique was developed in early 1970s as a means for accurate sizing and positioning of cracks in nuclear components became very popular in the late 1990s and is today being widely used in various industries for weld inspection. One of the main advantages of TOFD is that, apart from fast technique, it provides higher probability of detection for linear defects. Since TOFD is based on diffraction of sound waves from the extremities of the defect compared to reflection from planar faces as in pulse echo and phased array, the resultant signal would be quite weak and signal to noise ratio (SNR) low. In many cases the defect signal is submerged in this noise making it difficult for detection, positioning and sizing. Several signal processing methods such as digital filtering, Split Spectrum Processing (SSP), Hilbert Transform and Correlation techniques have been developed in order to suppress unwanted noise and enhance the quality of the defect signal which can thus be used for characterization of defects and the material. Wavelet Transform based thresholding techniques have been applied largely for de-noising of ultrasonic signals. However in this paper, higher order wavelets are used for analyzing the de-noising performance for TOFD signals obtained from Austenitic Stainless Steel welds. It is observed that higher order wavelets give greater SNR improvement compared to the lower order wavelets. Copyright © 2013 Elsevier B.V. All rights reserved.

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,…

Chandler wobble: two more large phase jumps revealed

NASA Astrophysics Data System (ADS)

Malkin, Zinovy; Miller, Natalia

2010-12-01

Investigations of the anomalies in the Earth rotation, in particular, the polar motion components, play an important role in our understanding of the processes that drive changes in the Earth's surface, interior, atmosphere, and ocean. This paper is primarily aimed at investigation of the Chandler wobble (CW) at the whole available 163-year interval to search for the major CW amplitude and phase variations. First, the CW signal was extracted from the IERS (International Earth Rotation and Reference Systems Service) Pole coordinates time series using two digital filters: the singular spectrum analysis and Fourier transform. The CW amplitude and phase variations were examined by means of the wavelet transform and Hilbert transform. Results of our analysis have shown that, besides the well-known CW phase jump in the 1920s, two other large phase jumps have been found in the 1850s and 2000s. As in the 1920s, these phase jumps occurred contemporarily with a sharp decrease in the CW amplitude.

Low-derivative operators of the Standard Model effective field theory via Hilbert series methods

NASA Astrophysics Data System (ADS)

Lehman, Landon; Martin, Adam

2016-02-01

In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N f = 1 operators.

Nonequilibrium statistical mechanics Brussels-Austin style

NASA Astrophysics Data System (ADS)

Bishop, Robert C.

The fundamental problem on which Ilya Prigogine and the Brussels-Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels-Austin Group after the mid-1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincaré systems, nonlinear dynamics and the mathematical tools necessary to analyze them.

Dissipation and entropy production in open quantum systems

NASA Astrophysics Data System (ADS)

Majima, H.; Suzuki, A.

2010-11-01

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

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 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.

Coherent multiscale image processing using dual-tree quaternion wavelets.

PubMed

Chan, Wai Lam; Choi, Hyeokho; Baraniuk, Richard G

2008-07-01

The dual-tree quaternion wavelet transform (QWT) is a new multiscale analysis tool for geometric image features. The QWT is a near shift-invariant tight frame representation whose coefficients sport a magnitude and three phases: two phases encode local image shifts while the third contains image texture information. The QWT is based on an alternative theory for the 2-D Hilbert transform and can be computed using a dual-tree filter bank with linear computational complexity. To demonstrate the properties of the QWT's coherent magnitude/phase representation, we develop an efficient and accurate procedure for estimating the local geometrical structure of an image. We also develop a new multiscale algorithm for estimating the disparity between a pair of images that is promising for image registration and flow estimation applications. The algorithm features multiscale phase unwrapping, linear complexity, and sub-pixel estimation accuracy.

Minimal Cohomological Model of a Scalar Field on a Riemannian Manifold

NASA Astrophysics Data System (ADS)

Arkhipov, V. V.

2018-04-01

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

Kato Smoothing and Strichartz Estimates for Wave Equations with Magnetic Potentials

NASA Astrophysics Data System (ADS)

D'Ancona, Piero

2015-04-01

Let H be a selfadjoint operator and A a closed operator on a Hilbert space . If A is H-(super)smooth in the sense of Kato-Yajima, we prove that is -(super)smooth. This allows us to include wave and Klein-Gordon equations in the abstract theory at the same level of generality as Schrödinger equations. We give a few applications and in particular, based on the resolvent estimates of Erdogan, Goldberg and Schlag (Forum Mathematicum 21:687-722, 2009), we prove Strichartz estimates for wave equations perturbed with large magnetic potentials on , n ≥ 3.

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.

Inflation in a renormalizable cosmological model and the cosmic no hair conjecture

NASA Technical Reports Server (NTRS)

Maeda, Kei-Ichi; Stein-Schabes, Jaime A.; Futamase, Toshifumi

1988-01-01

The possibility of having inflation in a renormalizable cosmological model is investigated. The Cosmic No Hair Conjecture is proved to hold for all Bianchi types except Bianchi IX. By the use of a conformal transformation on the metric it is shown that these models are equivalent to the ones described by the Einstein-Hilbert action for gravity minimally coupled to a set of scalar fields with inflationary potentials. Henceforth, it is proven that inflationary solutions behave as attractors in solution space, making it a natural event in the evolution of such models.

The cosmological Slavnov-Taylor identity from BRST symmetry in single-field inflation

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

Binosi, D.; Quadri, A., E-mail: binosi@ectstar.eu, E-mail: andrea.quadri@mi.infn.it

The cosmological Slavnov-Taylor (ST) identity of the Einstein-Hilbert action coupled to a single inflaton field is obtained from the Becchi-Rouet-Stora-Tyutin (BRST) symmetry associated with diffeomorphism invariance in the Arnowitt-Deser-Misner (ADM) formalism. The consistency conditions between the correlators of the scalar and tensor modes in the squeezed limit are then derived from the ST identity, together with the softly broken conformal symmetry. Maldacena's original relations connecting the 2- and 3-point correlators at horizon crossing are recovered, as well as the next-to-leading corrections, controlled by the special conformal transformations.

Artifact removal from EEG data with empirical mode decomposition

NASA Astrophysics Data System (ADS)

Grubov, Vadim V.; Runnova, Anastasiya E.; Efremova, Tatyana Yu.; Hramov, Alexander E.

2017-03-01

In the paper we propose the novel method for dealing with the physiological artifacts caused by intensive activity of facial and neck muscles and other movements in experimental human EEG recordings. The method is based on analysis of EEG signals with empirical mode decomposition (Hilbert-Huang transform). We introduce the mathematical algorithm of the method with following steps: empirical mode decomposition of EEG signal, choosing of empirical modes with artifacts, removing empirical modes with artifacts, reconstruction of the initial EEG signal. We test the method on filtration of experimental human EEG signals from movement artifacts and show high efficiency of the method.

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.

Efficient method for the calculation of mean extinction. II. Analyticity of the complex extinction efficiency of homogeneous spheroids and finite cylinders.

PubMed

Xing, Z F; Greenberg, J M

1994-08-20

The analyticity of the complex extinction efficiency is examined numerically in the size-parameter domain for homogeneous prolate and oblate spheroids and finite cylinders. The T-matrix code, which is the most efficient program available to date, is employed to calculate the individual particle-extinction efficiencies. Because of its computational limitations in the size-parameter range, a slightly modified Hilbert-transform algorithm is required to establish the analyticity numerically. The findings concerning analyticity that we reported for spheres (Astrophys. J. 399, 164-175, 1992) apply equally to these nonspherical particles.

Singularity formations for a surface wave model

NASA Astrophysics Data System (ADS)

Castro, Angel; Córdoba, Diego; Gancedo, Francisco

2010-11-01

In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch (see Biello and Hunter 2010 Commun. Pure Appl. Math. LXIII 0303-36 Marsden and Weinstein 1983 Physica D 7 305-23). We prove blowup in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form ΛαHu for 0 < α < 1, finite time singularity formation is also shown.

Numerical Inverse Scattering for the Toda Lattice

NASA Astrophysics Data System (ADS)

Bilman, Deniz; Trogdon, Thomas

2017-06-01

We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann-Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be evaluated in O(1) operations for arbitrary points in the ( n, t)-domain, including short- and long-time regimes. No time-stepping is required to compute the solution because ( n, t) appear as parameters in the associated RH problem. The solution of the Toda lattice is computed in long-time asymptotic regions where the asymptotics are not known rigorously.

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.

Signal Processing Methods Monitor Cranial Pressure

NASA Technical Reports Server (NTRS)

2010-01-01

Dr. Norden Huang, of Goddard Space Flight Center, invented a set of algorithms (called the Hilbert-Huang Transform, or HHT) for analyzing nonlinear and nonstationary signals that developed into a user-friendly signal processing technology for analyzing time-varying processes. At an auction managed by Ocean Tomo Federal Services LLC, licenses of 10 U.S. patents and 1 domestic patent application related to HHT were sold to DynaDx Corporation, of Mountain View, California. DynaDx is now using the licensed NASA technology for medical diagnosis and prediction of brain blood flow-related problems, such as stroke, dementia, and traumatic brain injury.

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.

Quantum Mechanics and the Principle of Least Radix Economy

NASA Astrophysics Data System (ADS)

Garcia-Morales, Vladimir

2015-03-01

A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.

Universal Barenco quantum gates via a tunable noncollinear interaction

NASA Astrophysics Data System (ADS)

Shi, Xiao-Feng

2018-03-01

The Barenco gate (B ) is a type of two-qubit quantum gate based on which alone universal quantum computation can be achieved. Each B is characterized by three angles (α , θ , and ϕ ), though it works in a two-qubit Hilbert space. Here we design B via a noncollinear interaction V | r1r2>< r1r3|+H .c . , where | ri> is a state that can be excited from a qubit state and V is adjustable. We present two protocols for B . The first (second) protocol consists of two (six) pulses and one (two) wait period(s), where the former causes rotations between qubit states and excited states, and the latter induces gate transformation via the noncollinear interaction. In the first protocol, the variable ϕ can be tuned by varying the phases of external controls, and the other two variables α and θ , tunable via adjustment of the wait duration, have a linear dependence on each other. Meanwhile, the first protocol can give rise to cnot and controlled-y gates. In the second protocol, α ,θ , and ϕ can be varied by changing the interaction amplitudes and wait durations, and the latter two are dependent on α nonlinearly. Both protocols can also lead to another universal gate when {α ,ϕ }={1 /4 ,1 /2 }π with appropriate parameters. Implementation of these universal gates is analyzed based on the van der Waals interaction of neutral Rydberg atoms.

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.

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

PubMed

Vallicrosa, Guillem; Ridao, Pere

2018-05-01

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

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

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

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

Experimental realization of non-Abelian non-adiabatic geometric gates.

PubMed

Abdumalikov, A A; Fink, J M; Juliusson, K; Pechal, M; Berger, S; Wallraff, A; Filipp, S

2013-04-25

The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies--the effect of which depends on the order of two consecutive paths--can be obtained. They are important, for example, for the creation of synthetic gauge fields in cold atomic gases or the description of non-Abelian anyon statistics. Moreover, there are proposals to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations, non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature. Here we realize non-Abelian non-adiabatic holonomic quantum operations on a single, superconducting, artificial three-level atom by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing.

Accurate derivation of heart rate variability signal for detection of sleep disordered breathing in children.

PubMed

Chatlapalli, S; Nazeran, H; Melarkod, V; Krishnam, R; Estrada, E; Pamula, Y; Cabrera, S

2004-01-01

The electrocardiogram (ECG) signal is used extensively as a low cost diagnostic tool to provide information concerning the heart's state of health. Accurate determination of the QRS complex, in particular, reliable detection of the R wave peak, is essential in computer based ECG analysis. ECG data from Physionet's Sleep-Apnea database were used to develop, test, and validate a robust heart rate variability (HRV) signal derivation algorithm. The HRV signal was derived from pre-processed ECG signals by developing an enhanced Hilbert transform (EHT) algorithm with built-in missing beat detection capability for reliable QRS detection. The performance of the EHT algorithm was then compared against that of a popular Hilbert transform-based (HT) QRS detection algorithm. Autoregressive (AR) modeling of the HRV power spectrum for both EHT- and HT-derived HRV signals was achieved and different parameters from their power spectra as well as approximate entropy were derived for comparison. Poincare plots were then used as a visualization tool to highlight the detection of the missing beats in the EHT method After validation of the EHT algorithm on ECG data from the Physionet, the algorithm was further tested and validated on a dataset obtained from children undergoing polysomnography for detection of sleep disordered breathing (SDB). Sensitive measures of accurate HRV signals were then derived to be used in detecting and diagnosing sleep disordered breathing in children. All signal processing algorithms were implemented in MATLAB. We present a description of the EHT algorithm and analyze pilot data for eight children undergoing nocturnal polysomnography. The pilot data demonstrated that the EHT method provides an accurate way of deriving the HRV signal and plays an important role in extraction of reliable measures to distinguish between periods of normal and sleep disordered breathing (SDB) in children.

An improved EMD method for modal identification and a combined static-dynamic method for damage detection

NASA Astrophysics Data System (ADS)

Yang, Jinping; Li, Peizhen; Yang, Youfa; Xu, Dian

2018-04-01

Empirical mode decomposition (EMD) is a highly adaptable signal processing method. However, the EMD approach has certain drawbacks, including distortions from end effects and mode mixing. In the present study, these two problems are addressed using an end extension method based on the support vector regression machine (SVRM) and a modal decomposition method based on the characteristics of the Hilbert transform. The algorithm includes two steps: using the SVRM, the time series data are extended at both endpoints to reduce the end effects, and then, a modified EMD method using the characteristics of the Hilbert transform is performed on the resulting signal to reduce mode mixing. A new combined static-dynamic method for identifying structural damage is presented. This method combines the static and dynamic information in an equilibrium equation that can be solved using the Moore-Penrose generalized matrix inverse. The combination method uses the differences in displacements of the structure with and without damage and variations in the modal force vector. Tests on a four-story, steel-frame structure were conducted to obtain static and dynamic responses of the structure. The modal parameters are identified using data from the dynamic tests and improved EMD method. The new method is shown to be more accurate and effective than the traditional EMD method. Through tests with a shear-type test frame, the higher performance of the proposed static-dynamic damage detection approach, which can detect both single and multiple damage locations and the degree of the damage, is demonstrated. For structures with multiple damage, the combined approach is more effective than either the static or dynamic method. The proposed EMD method and static-dynamic damage detection method offer improved modal identification and damage detection, respectively, in structures.

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

PubMed

Stöltzner, Michael

2015-10-01

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

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

NASA Astrophysics Data System (ADS)

Verburgt, Lukas M.

2016-02-01

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

The Ising model coupled to 2d orders

NASA Astrophysics Data System (ADS)

Glaser, Lisa

2018-04-01

In this article we make first steps in coupling matter to causal set theory in the path integral. We explore the case of the Ising model coupled to the 2d discrete Einstein Hilbert action, restricted to the 2d orders. We probe the phase diagram in terms of the Wick rotation parameter β and the Ising coupling j and find that the matter and the causal sets together give rise to an interesting phase structure. The couplings give rise to five different phases. The causal sets take on random or crystalline characteristics as described in Surya (2012 Class. Quantum Grav. 29 132001) and the Ising model can be correlated or uncorrelated on the random orders and correlated, uncorrelated or anti-correlated on the crystalline orders. We find that at least one new phase transition arises, in which the Ising spins push the causal set into the crystalline phase.

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.

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

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

Degroote, M.; Henderson, T. M.; Zhao, J.

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero.more » Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.« less

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.

dRGT theory of massive gravity from spontaneous symmetry breaking

NASA Astrophysics Data System (ADS)

Torabian, Mahdi

2018-05-01

In this note we propose a topological action for a Poincare times diffeomorphism invariant gauge theory. We show that there is Higgs phase where the gauge symmetry is spontaneous broken to a diagonal Lorentz subgroup and gives the Einstein-Hilbert action plus the dRGT potential terms. In this vacuum, there are five (three from Goldstone modes) propagating degrees of freedom which form polarizations of a massive spin 2 particle, an extra healthy heavy scalar (Higgs) mode and no Boulware-Deser ghost mode. We further show that the action can be derived in a limit from a topological de Sitter invariant gauge theory in 4 dimensions.

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.

Almost all quantum channels are equidistant

NASA Astrophysics Data System (ADS)

Nechita, Ion; Puchała, Zbigniew; Pawela, Łukasz; Życzkowski, Karol

2018-05-01

In this work, we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant value as the dimension of the system grows larger. As a measure of the distance we use the diamond norm. In the case of a flat Hilbert-Schmidt distribution on quantum channels, we obtain that the distance converges to 1/2 +2/π , giving also an estimate for the maximum success probability for distinguishing the channels. We also consider the problem of distinguishing two random unitary rotations.

Noncommuting observables in quantum detection and estimation theory

NASA Technical Reports Server (NTRS)

Helstrom, C. W.

1972-01-01

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

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.

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.

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

NASA Astrophysics Data System (ADS)

Busemeyer, Brian; Wagner, Lucas K.

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

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

PubMed

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

2007-10-01

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

Single shot white light interference microscopy with colour fringe analysis for quantitative phase imaging of biological cells

NASA Astrophysics Data System (ADS)

Srivastava, Vishal; Mehta, D. S.

2013-02-01

To quantitatively obtain the phase map of Onion and human red blood cell (RBC) from white light interferogram we used Hilbert transform color fringe analysis technique. The three Red, Blue and Green color components are decomposed from single white light interferogram and Refractive index profile for Red, Blue and Green colour were computed in a completely non-invasive manner for Onion and human RBC. The present technique might be useful for non-invasive determination of the refractive index variation within cells and tissues and morphological features of sample with ease of operation and low cost.

Expressions for tidal conversion at seafloor topography using physical space integrals

NASA Astrophysics Data System (ADS)

Schorghofer, Norbert

2010-12-01

The barotropic tide interacts with seafloor topography to generate internal gravity waves. Equations for streamfunction and power conversion are derived in terms of integrals over the topography in spatial coordinates. The slope of the topography does not need to be small. Explicit equations are derived up to second order in slope for general topography, and conversion by a bell-shaped topography is calculated analytically to this order. A concise formalism using Hilbert transforms is developed, the minimally converting topographic shape is discussed, and a numerical scheme for the evaluation of power conversion is designed that robustly deals with the singular integrand.

Simulation of ultrasonic and EMAT arrays using FEM and FDTD.

PubMed

Xie, Yuedong; Yin, Wuliang; Liu, Zenghua; Peyton, Anthony

2016-03-01

This paper presents a method which combines electromagnetic simulation and ultrasonic simulation to build EMAT array models. For a specific sensor configuration, Lorentz forces are calculated using the finite element method (FEM), which then can feed through to ultrasonic simulations. The propagation of ultrasound waves is numerically simulated using finite-difference time-domain (FDTD) method to describe their propagation within homogenous medium and their scattering phenomenon by cracks. Radiation pattern obtained with Hilbert transform on time domain waveforms is proposed to characterise the sensor in terms of its beam directivity and field distribution along the steering angle. Copyright © 2015 Elsevier B.V. All rights reserved.

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'.

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

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.

On the physical Hilbert space of loop quantum cosmology

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

Noui, Karim; Perez, Alejandro; Vandersloot, Kevin

2005-02-15

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

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

DTIC Science & Technology

1998-05-01

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

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

NASA Astrophysics Data System (ADS)

Gao, Gan; Wang, Li-Ping

2010-11-01

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

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.

LORETA EEG phase reset of the default mode network.

PubMed

Thatcher, Robert W; North, Duane M; Biver, Carl J

2014-01-01

The purpose of this study was to explore phase reset of 3-dimensional current sources in Brodmann areas located in the human default mode network (DMN) using Low Resolution Electromagnetic Tomography (LORETA) of the human electroencephalogram (EEG). The EEG was recorded from 19 scalp locations from 70 healthy normal subjects ranging in age from 13 to 20 years. A time point by time point computation of LORETA current sources were computed for 14 Brodmann areas comprising the DMN in the delta frequency band. The Hilbert transform of the LORETA time series was used to compute the instantaneous phase differences between all pairs of Brodmann areas. Phase shift and lock durations were calculated based on the 1st and 2nd derivatives of the time series of phase differences. Phase shift duration exhibited three discrete modes at approximately: (1) 25 ms, (2) 50 ms, and (3) 65 ms. Phase lock duration present primarily at: (1) 300-350 ms and (2) 350-450 ms. Phase shift and lock durations were inversely related and exhibited an exponential change with distance between Brodmann areas. The results are explained by local neural packing density of network hubs and an exponential decrease in connections with distance from a hub. The results are consistent with a discrete temporal model of brain function where anatomical hubs behave like a "shutter" that opens and closes at specific durations as nodes of a network giving rise to temporarily phase locked clusters of neurons for specific durations.

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

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

Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu; Salgado, Abner J., E-mail: asalgad1@utk.edu; Wang, Cheng, E-mail: cwang1@umassd.edu

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a generalmore » framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.« less

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Salgado, Abner J.; Wang, Cheng; Wise, Steven M.

2017-04-01

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems - including thin film epitaxy with slope selection and the square phase field crystal model - are carried out to verify the efficiency of the scheme.

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

PLQP & Company: Decidable Logics for Quantum Algorithms

NASA Astrophysics Data System (ADS)

Baltag, Alexandru; Bergfeld, Jort; Kishida, Kohei; Sack, Joshua; Smets, Sonja; Zhong, Shengyang

2014-10-01

We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as of a quantum protocol known to solve one of the paradigmatic tasks from classical distributed computing (the leader election problem). We also provide a general method (extending an idea employed in the decidability proof in Dunn et al. (J. Symb. Log. 70:353-359, 2005)) for proving the decidability of a range of quantum logics, interpreted on finite-dimensional Hilbert spaces. We give general conditions for the applicability of this method, and in particular we apply it to prove the decidability of PLQP.

Norms of certain Jordan elementary operators

NASA Astrophysics Data System (ADS)

Zhang, Xiaoli; Ji, Guoxing

2008-10-01

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

Object Classification Based on Analysis of Spectral Characteristics of Seismic Signal Envelopes

NASA Astrophysics Data System (ADS)

Morozov, Yu. V.; Spektor, A. A.

2017-11-01

A method for classifying moving objects having a seismic effect on the ground surface is proposed which is based on statistical analysis of the envelopes of received signals. The values of the components of the amplitude spectrum of the envelopes obtained applying Hilbert and Fourier transforms are used as classification criteria. Examples illustrating the statistical properties of spectra and the operation of the seismic classifier are given for an ensemble of objects of four classes (person, group of people, large animal, vehicle). It is shown that the computational procedures for processing seismic signals are quite simple and can therefore be used in real-time systems with modest requirements for computational resources.

OMA analysis of a launcher under operational conditions with time-varying properties

NASA Astrophysics Data System (ADS)

Eugeni, M.; Coppotelli, G.; Mastroddi, F.; Gaudenzi, P.; Muller, S.; Troclet, B.

2018-05-01

The objective of this paper is the investigation of the capability of operational modal analysis approaches to deal with time-varying system in the low-frequency domain. Specifically, the problem of the identification of the dynamic properties of a launch vehicle, working under actual operative conditions, is studied. Two OMA methods are considered: the frequency-domain decomposition and the Hilbert transform method. It is demonstrated that both OMA approaches allow the time-tracking of modal parameters, namely, natural frequencies, damping ratios, and mode shapes, from the response accelerations only recorded during actual flight tests of a launcher characterized by a large mass variation due to fuel burning typical of the first phase of the flight.

Statistical Interior Tomography

PubMed Central

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

2011-01-01

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

Nonlinear, non-stationary image processing technique for eddy current NDE

NASA Astrophysics Data System (ADS)

Yang, Guang; Dib, Gerges; Kim, Jaejoon; Zhang, Lu; Xin, Junjun; Udpa, Lalita

2012-05-01

Automatic analysis of eddy current (EC) data has facilitated the analysis of large volumes of data generated in the inspection of steam generator tubes in nuclear power plants. The traditional procedure for analysis of EC data includes data calibration, pre-processing, region of interest (ROI) detection, feature extraction and classification. Accurate ROI detection has been enhanced by pre-processing, which involves reducing noise and other undesirable components as well as enhancing defect indications in the raw measurement. This paper presents the Hilbert-Huang Transform (HHT) for feature extraction and support vector machine (SVM) for classification. The performance is shown to significantly better than the existing rule based classification approach used in industry.

Dynamics identification of a piezoelectric vibrational energy harvester by image analysis with a high speed camera

NASA Astrophysics Data System (ADS)

Wolszczak, Piotr; Łygas, Krystian; Litak, Grzegorz

2018-07-01

This study investigates dynamic responses of a nonlinear vibration energy harvester. The nonlinear mechanical resonator consists of a flexible beam moving like an inverted pendulum between amplitude limiters. It is coupled with a piezoelectric converter, and excited kinematically. Consequently, the mechanical energy input is converted into the electrical power output on the loading resistor included in an electric circuit attached to the piezoelectric electrodes. The curvature of beam mode shapes as well as deflection of the whole beam are examined using a high speed camera. The visual identification results are compared with the voltage output generated by the piezoelectric element for corresponding frequency sweeps and analyzed by the Hilbert transform.

Dealing with noise and physiological artifacts in human EEG recordings: empirical mode methods

NASA Astrophysics Data System (ADS)

Runnova, Anastasiya E.; Grubov, Vadim V.; Khramova, Marina V.; Hramov, Alexander E.

2017-04-01

In the paper we propose the new method for removing noise and physiological artifacts in human EEG recordings based on empirical mode decomposition (Hilbert-Huang transform). As physiological artifacts we consider specific oscillatory patterns that cause problems during EEG analysis and can be detected with additional signals recorded simultaneously with EEG (ECG, EMG, EOG, etc.) We introduce the algorithm of the proposed method with steps including empirical mode decomposition of EEG signal, choosing of empirical modes with artifacts, removing these empirical modes and reconstructing of initial EEG signal. We show the efficiency of the method on the example of filtration of human EEG signal from eye-moving artifacts.

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.

Analysis of nonlinear modulation between sound and vibrations in metallic structure and its use for damage detection

NASA Astrophysics Data System (ADS)

Liu, Bin; Gang, Tie; Wan, Chuhao; Wang, Changxi; Luo, Zhiwei

2015-07-01

Vibro-acoustic modulation technique is a nonlinear ultrasonic method in nondestructive testing. This technique detects the defects by monitoring the modulation components generated by the interaction between the vibration and the ultrasound wave due to the nonlinear material behaviour caused by the damage. In this work, a swept frequency signal was used as high frequency excitation, then the Hilbert transform based amplitude and phase demodulation and synchronous demodulation (SD) were used to extract the modulation information from the received signal, the results were graphed in the time-frequency domain after the short time Fourier transform. The demodulation results were quite different from each other. The reason for the difference was investigated by analysing the demodulation process of the two methods. According to the analysis and the subsequent verification test, it was indicated that the SD method was more proper for the test and a new index called MISD was defined to evaluate the structure quality in the Vibro-acoustic modulation test with swept probing excitation.

Joint Bearing and Range Estimation of Multiple Objects from Time-Frequency Analysis.

PubMed

Liu, Jeng-Cheng; Cheng, Yuang-Tung; Hung, Hsien-Sen

2018-01-19

Direction-of-arrival (DOA) and range estimation is an important issue of sonar signal processing. In this paper, a novel approach using Hilbert-Huang transform (HHT) is proposed for joint bearing and range estimation of multiple targets based on a uniform linear array (ULA) of hydrophones. The structure of this ULA based on micro-electro-mechanical systems (MEMS) technology, and thus has attractive features of small size, high sensitivity and low cost, and is suitable for Autonomous Underwater Vehicle (AUV) operations. This proposed target localization method has the following advantages: only a single snapshot of data is needed and real-time processing is feasible. The proposed algorithm transforms a very complicated nonlinear estimation problem to a simple nearly linear one via time-frequency distribution (TFD) theory and is verified with HHT. Theoretical discussions of resolution issue are also provided to facilitate the design of a MEMS sensor with high sensitivity. Simulation results are shown to verify the effectiveness of the proposed method.

Research on vibration signal analysis and extraction method of gear local fault

NASA Astrophysics Data System (ADS)

Yang, X. F.; Wang, D.; Ma, J. F.; Shao, W.

2018-02-01

Gear is the main connection parts and power transmission parts in the mechanical equipment. If the fault occurs, it directly affects the running state of the whole machine and even endangers the personal safety. So it has important theoretical significance and practical value to study on the extraction of the gear fault signal and fault diagnosis of the gear. In this paper, the gear local fault as the research object, set up the vibration model of gear fault vibration mechanism, derive the vibration mechanism of the gear local fault and analyzes the similarities and differences of the vibration signal between the gear non fault and the gears local faults. In the MATLAB environment, the wavelet transform algorithm is used to denoise the fault signal. Hilbert transform is used to demodulate the fault vibration signal. The results show that the method can denoise the strong noise mechanical vibration signal and extract the local fault feature information from the fault vibration signal..

Double-path acquisition of pulse wave transit time and heartbeat using self-mixing interferometry

NASA Astrophysics Data System (ADS)

Wei, Yingbin; Huang, Wencai; Wei, Zheng; Zhang, Jie; An, Tong; Wang, Xiulin; Xu, Huizhen

2017-06-01

We present a technique based on self-mixing interferometry for acquiring the pulse wave transit time (PWTT) and heartbeat. A signal processing method based on Continuous Wavelet Transform and Hilbert Transform is applied to extract potentially useful information in the self-mixing interference (SMI) signal, including PWTT and heartbeat. Then, some cardiovascular characteristics of the human body are easily acquired without retrieving the SMI signal by complicated algorithms. Experimentally, the PWTT is measured on the finger and the toe of the human body using double-path self-mixing interferometry. Experimental statistical data show the relation between the PWTT and blood pressure, which can be used to estimate the systolic pressure value by fitting. Moreover, the measured heartbeat shows good agreement with that obtained by a photoplethysmography sensor. The method that we demonstrate, which is based on self-mixing interferometry with significant advantages of simplicity, compactness and non-invasion, effectively illustrates the viability of the SMI technique for measuring other cardiovascular signals.

Data-driven mono-component feature identification via modified nonlocal means and MEWT for mechanical drivetrain fault diagnosis

NASA Astrophysics Data System (ADS)

Pan, Jun; Chen, Jinglong; Zi, Yanyang; Yuan, Jing; Chen, Binqiang; He, Zhengjia

2016-12-01

It is significant to perform condition monitoring and fault diagnosis on rolling mills in steel-making plant to ensure economic benefit. However, timely fault identification of key parts in a complicated industrial system under operating condition is still a challenging task since acquired condition signals are usually multi-modulated and inevitably mixed with strong noise. Therefore, a new data-driven mono-component identification method is proposed in this paper for diagnostic purpose. First, the modified nonlocal means algorithm (NLmeans) is proposed to reduce noise in vibration signals without destroying its original Fourier spectrum structure. During the modified NLmeans, two modifications are investigated and performed to improve denoising effect. Then, the modified empirical wavelet transform (MEWT) is applied on the de-noised signal to adaptively extract empirical mono-component modes. Finally, the modes are analyzed for mechanical fault identification based on Hilbert transform. The results show that the proposed data-driven method owns superior performance during system operation compared with the MEWT method.

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

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.

Wavelet-based study of valence-arousal model of emotions on EEG signals with LabVIEW.

PubMed

Guzel Aydin, Seda; Kaya, Turgay; Guler, Hasan

2016-06-01

This paper illustrates the wavelet-based feature extraction for emotion assessment using electroencephalogram (EEG) signal through graphical coding design. Two-dimensional (valence-arousal) emotion model was studied. Different emotions (happy, joy, melancholy, and disgust) were studied for assessment. These emotions were stimulated by video clips. EEG signals obtained from four subjects were decomposed into five frequency bands (gamma, beta, alpha, theta, and delta) using "db5" wavelet function. Relative features were calculated to obtain further information. Impact of the emotions according to valence value was observed to be optimal on power spectral density of gamma band. The main objective of this work is not only to investigate the influence of the emotions on different frequency bands but also to overcome the difficulties in the text-based program. This work offers an alternative approach for emotion evaluation through EEG processing. There are a number of methods for emotion recognition such as wavelet transform-based, Fourier transform-based, and Hilbert-Huang transform-based methods. However, the majority of these methods have been applied with the text-based programming languages. In this study, we proposed and implemented an experimental feature extraction with graphics-based language, which provides great convenience in bioelectrical signal processing.

Multimodal Pressure Flow Analysis: Application of Hilbert Huang Transform in Cerebral Blood Flow Regulation

PubMed Central

Lo, Men-Tzung; Hu, Kun; Liu, Yanhui; Peng, C.-K.; Novak, Vera

2008-01-01

Quantification of nonlinear interactions between two nonstationary signals presents a computational challenge in different research fields, especially for assessments of physiological systems. Traditional approaches that are based on theories of stationary signals cannot resolve nonstationarity-related issues and, thus, cannot reliably assess nonlinear interactions in physiological systems. In this review we discuss a new technique “Multi-Modal Pressure Flow method (MMPF)” that utilizes Hilbert-Huang transformation to quantify dynamic cerebral autoregulation (CA) by studying interaction between nonstationary cerebral blood flow velocity (BFV) and blood pressure (BP). CA is an important mechanism responsible for controlling cerebral blood flow in responses to fluctuations in systemic BP within a few heart-beats. The influence of CA is traditionally assessed from the relationship between the well-pronounced systemic BP and BFV oscillations induced by clinical tests. Reliable noninvasive assessment of dynamic CA, however, remains a challenge in clinical and diagnostic medicine. In this brief review we: 1) present an overview of transfer function analysis (TFA) that is traditionally used to quantify CA; 2) describe the a MMPF method and its modifications; 3) introduce a newly developed automatic algorithm and engineering aspects of the improved MMPF method; and 4) review clinical applications of MMPF and its sensitivity for detection of CA abnormalities in clinical studies. The MMPF analysis decomposes complex nonstationary BP and BFV signals into multiple empirical modes adaptively so that the fluctuations caused by a specific physiologic process can be represented in a corresponding empirical mode. Using this technique, we recently showed that dynamic CA can be characterized by specific phase delays between the decomposed BP and BFV oscillations, and that the phase shifts are significantly reduced in hypertensive, diabetics and stroke subjects with impaired CA. In addition, the new technique enables reliable assessment of CA using both data collected during clinical test and spontaneous BP/BFV fluctuations during baseline resting conditions. PMID:18725996

A Novel Characteristic Frequency Bands Extraction Method for Automatic Bearing Fault Diagnosis Based on Hilbert Huang Transform.

PubMed

Yu, Xiao; Ding, Enjie; Chen, Chunxu; Liu, Xiaoming; Li, Li

2015-11-03

Because roller element bearings (REBs) failures cause unexpected machinery breakdowns, their fault diagnosis has attracted considerable research attention. Established fault feature extraction methods focus on statistical characteristics of the vibration signal, which is an approach that loses sight of the continuous waveform features. Considering this weakness, this article proposes a novel feature extraction method for frequency bands, named Window Marginal Spectrum Clustering (WMSC) to select salient features from the marginal spectrum of vibration signals by Hilbert-Huang Transform (HHT). In WMSC, a sliding window is used to divide an entire HHT marginal spectrum (HMS) into window spectrums, following which Rand Index (RI) criterion of clustering method is used to evaluate each window. The windows returning higher RI values are selected to construct characteristic frequency bands (CFBs). Next, a hybrid REBs fault diagnosis is constructed, termed by its elements, HHT-WMSC-SVM (support vector machines). The effectiveness of HHT-WMSC-SVM is validated by running series of experiments on REBs defect datasets from the Bearing Data Center of Case Western Reserve University (CWRU). The said test results evidence three major advantages of the novel method. First, the fault classification accuracy of the HHT-WMSC-SVM model is higher than that of HHT-SVM and ST-SVM, which is a method that combines statistical characteristics with SVM. Second, with Gauss white noise added to the original REBs defect dataset, the HHT-WMSC-SVM model maintains high classification accuracy, while the classification accuracy of ST-SVM and HHT-SVM models are significantly reduced. Third, fault classification accuracy by HHT-WMSC-SVM can exceed 95% under a Pmin range of 500-800 and a m range of 50-300 for REBs defect dataset, adding Gauss white noise at Signal Noise Ratio (SNR) = 5. Experimental results indicate that the proposed WMSC method yields a high REBs fault classification accuracy and a good performance in Gauss white noise reduction.

Hilbert-Huang transform based instrumental assessment of intention tremor in multiple sclerosis

NASA Astrophysics Data System (ADS)

Carpinella, Ilaria; Cattaneo, Davide; Ferrarin, Maurizio

2015-08-01

Objective. This paper describes a method to extract upper limb intention tremor from gyroscope data, through the Hilbert-Huang transform (HHT), a technique suitable for the study of nonlinear and non-stationary processes. The aims of the study were to: (i) evaluate the method’s ability to discriminate between healthy controls and MS subjects; (ii) validate the proposed procedure against clinical tremor scores assigned using Fahn’s tremor rating scale (FTRS); and (iii) compare the performance of the HHT-based method with that of linear band-pass filters. Approach. HHT was applied on gyroscope data collected on 20 MS subjects and 13 healthy controls (CO) during finger-to-nose tests (FNTs) instrumented with an inertial sensor placed on the hand. The results were compared to those obtained after traditional linear filtering. The tremor amplitude was quantified with instrumental indexes (TIs) and clinical FTRS ratings. Main results. The TIs computed after HHT-based filtering discriminated between CO and MS subjects with clinically-detected intention tremor (MS_T). In particular, TIs were significantly higher in the final part of the movement (TI2) with respect to the first part (TI1), and, for all components (X, Y, Z), MST showed a TI2 significantly higher than in CO subjects. Moreover, the HHT detected subtle alterations not visible from clinical ratings, as TI2 (Z-component) was significantly increased in MS subjects without clinically-detected tremor (MS_NT). The method’s validity was demonstrated by significant correlations between clinical FTRS scores and TI2 related to X (rs = 0.587, p = 0.006) and Y (rs = 0.682, p < 0.001) components. Contrarily, fewer differences among the groups and no correlation between instrumental and clinical indexes emerged after traditional filtering. Significance. The present results supported the use of the HHT-based procedure for a fully-automated quantitative and objective measure of intention tremor in MS, which can overcome the limitations of clinical scales and provide supplementary information about this sign.

Time Frequency Analysis of The Land Subsidence Monitored Data with Exploration Geophysics

NASA Astrophysics Data System (ADS)

Wang, Shang-Wei

2014-05-01

Taiwan geographic patterns and various industry water, caused Zhuoshui River Fan groundwater extraction of excess leads to land subsidence, affect the safety of high-speed railway traffic and public construction. It is necessary to do the deeply research on the reason and behavior of subsidence. All the related element will be confer including the water extracted groundwater that be used on each industry or the impact of climate change rainfall and the ground formation characteristics. Conducted a series of in situ measurements and monitoring data with Hilbert Huang Transform. Discussion of subsidence mechanism and estimate the future high-speed rail traffic may affect the extent of providing for future reference remediation. We investigate and experiment on the characteristic of land subsidence in Yun Lin area. The Hilbert-Huang Transform (HHT) and signal normalized are be used to discuss the physical meanings and interactions among the time series data of settlement, groundwater, pumping, rainfall and micro-tremor of ground. The broadband seismic signals of the Broadband Array in Taiwan for Seismology, (BATS) obtained near the Zhuoshui River (WLGB in Chia Yi, WGKB in Yun Lin and RLNB in Zhang Hua) were analyzed by using HHT and empirical mode decomposition (EMD) to discuss the micro-tremor characteristics of the settled ground. To compare among ten years series data of micro-tremor, groundwater and land subsidence monitoring wells, we can get more information about land subsidence. The electrical resistivity tomography (ERT) were performed to correlate the resistivity profile and borehole logging data at the test area. The relationships among resistivity, groundwater variation, and ground subsidence obtained from the test area have been discussed. Active and passive multichannel analysis of surface waves method (MASW) can calculate Poisson's ratio by using shear velocity and pressure velocity. The groundwater level can be presumed when Poisson's ratio arrive 0.5. We can know about undulate groundwater stages and variation of ground by more times measurements.

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.

The Riesz transform and simultaneous representations of phase, energy and orientation in spatial vision.

PubMed

Langley, Keith; Anderson, Stephen J

2010-08-06

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz transform. For spatial images there exist two Riesz transformed signals and one original signal from which orientation, phase and energy may be represented as a vector in 3-D signal space. We show that these image properties may be represented by a Singular Value Decomposition (SVD) of the higher-order derivatives of the original and the Riesz transformed signals. We further show that the expected responses of even and odd symmetric filters from the Riesz transform may be represented by a single signal autocorrelation function, which is beneficial in simplifying Bayesian computations for spatial orientation. Importantly, the Riesz transform allows one to weight linearly across orientation using both symmetric and asymmetric filters to account for some perceptual phase distortions observed in image signals - notably one's perception of edge structure within plaid patterns whose component gratings are either equal or unequal in contrast. Finally, exploiting the benefits that arise from the Riesz definition of local energy as a scalar quantity, we demonstrate the utility of Riesz signal representations in estimating the spatial orientation of second-order image signals. We conclude that the Riesz transform may be employed as a general tool for 2-D visual pattern recognition by its virtue of representing phase, orientation and energy as orthogonal signal quantities.

Time-frequency techniques in biomedical signal analysis. a tutorial review of similarities and differences.

PubMed

Wacker, M; Witte, H

2013-01-01

This review outlines the methodological fundamentals of the most frequently used non-parametric time-frequency analysis techniques in biomedicine and their main properties, as well as providing decision aids concerning their applications. The short-term Fourier transform (STFT), the Gabor transform (GT), the S-transform (ST), the continuous Morlet wavelet transform (CMWT), and the Hilbert transform (HT) are introduced as linear transforms by using a unified concept of the time-frequency representation which is based on a standardized analytic signal. The Wigner-Ville distribution (WVD) serves as an example of the 'quadratic transforms' class. The combination of WVD and GT with the matching pursuit (MP) decomposition and that of the HT with the empirical mode decomposition (EMD) are explained; these belong to the class of signal-adaptive approaches. Similarities between linear transforms are demonstrated and differences with regard to the time-frequency resolution and interference (cross) terms are presented in detail. By means of simulated signals the effects of different time-frequency resolutions of the GT, CMWT, and WVD as well as the resolution-related properties of the interference (cross) terms are shown. The method-inherent drawbacks and their consequences for the application of the time-frequency techniques are demonstrated by instantaneous amplitude, frequency and phase measures and related time-frequency representations (spectrogram, scalogram, time-frequency distribution, phase-locking maps) of measured magnetoencephalographic (MEG) signals. The appropriate selection of a method and its parameter settings will ensure readability of the time-frequency representations and reliability of results. When the time-frequency characteristics of a signal strongly correspond with the time-frequency resolution of the analysis then a method may be considered 'optimal'. The MP-based signal-adaptive approaches are preferred as these provide an appropriate time-frequency resolution for all frequencies while simultaneously reducing interference (cross) terms.

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.

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.

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.

The New Quantum Logic

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2014-06-01

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics.

Spin Path Integrals and Generations

NASA Astrophysics Data System (ADS)

Brannen, Carl

2010-11-01

The spin of a free electron is stable but its position is not. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have shown that the Feynman position path integral can be mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). Since the more common use of MUBs is in finite dimensional Hilbert spaces, this raises the question “what happens when spin path integrals are computed over products of MUBs?” Such an assumption makes spin no longer stable. We show that the usual spin-1/2 is obtained in the long-time limit in three orthogonal solutions that we associate with the three elementary particle generations. We give applications to the masses of the elementary leptons.

BRST symmetry for a torus knot

NASA Astrophysics Data System (ADS)

Pandey, Vipul Kumar; Prasad Mandal, Bhabani

2017-08-01

We develop BRST symmetry for the first time for a particle on the surface of a torus knot by analyzing the constraints of the system. The theory contains 2nd-class constraints and has been extended by introducing the Wess-Zumino term to convert it into a theory with first-class constraints. BFV analysis of the extended theory is performed to construct BRST/anti-BRST symmetries for the particle on a torus knot. The nilpotent BRST/anti-BRST charges which generate such symmetries are constructed explicitly. The states annihilated by these nilpotent charges consist of the physical Hilbert space. We indicate how various effective theories on the surface of the torus knot are related through the generalized version of the BRST transformation with finite-field-dependent parameters.

Exaggerated heart rate oscillations during two meditation techniques.

PubMed

Peng, C K; Mietus, J E; Liu, Y; Khalsa, G; Douglas, P S; Benson, H; Goldberger, A L

1999-07-31

We report extremely prominent heart rate oscillations associated with slow breathing during specific traditional forms of Chinese Chi and Kundalini Yoga meditation techniques in healthy young adults. We applied both spectral analysis and a novel analytic technique based on the Hilbert transform to quantify these heart rate dynamics. The amplitude of these oscillations during meditation was significantly greater than in the pre-meditation control state and also in three non-meditation control groups: i) elite athletes during sleep, ii) healthy young adults during metronomic breathing, and iii) healthy young adults during spontaneous nocturnal breathing. This finding, along with the marked variability of the beat-to-beat heart rate dynamics during such profound meditative states, challenges the notion of meditation as only an autonomically quiescent state.

Automatic loudness control in short-form content for broadcasting.

PubMed

Pires, Leandro da S; Vieira, Maurílio N; Yehia, Hani C

2017-03-01

During the early years of the International Telecommunication Union (ITU) loudness calculation standard for sound broadcasting [ITU-R (2006), Rec. BS Series, 1770], the need for additional loudness descriptors to evaluate short-form content, such as commercials and live inserts, was identified. This work proposes a loudness control scheme to prevent loudness jumps, which can bother audiences. It employs short-form content audio detection and dynamic range processing methods for the maximum loudness level criteria. Detection is achieved by combining principal component analysis for dimensionality reduction and support vector machines for binary classification. Subsequent processing is based on short-term loudness integrators and Hilbert transformers. The performance was assessed using quality classification metrics and demonstrated through a loudness control example.

Analyze the beta waves of electroencephalogram signals from young musicians and non-musicians in major scale working memory task.

PubMed

Hsu, Chien-Chang; Cheng, Ching-Wen; Chiu, Yi-Shiuan

2017-02-15

Electroencephalograms can record wave variations in any brain activity. Beta waves are produced when an external stimulus induces logical thinking, computation, and reasoning during consciousness. This work uses the beta wave of major scale working memory N-back tasks to analyze the differences between young musicians and non-musicians. After the feature analysis uses signal filtering, Hilbert-Huang transformation, and feature extraction methods to identify differences, k-means clustering algorithm are used to group them into different clusters. The results of feature analysis showed that beta waves significantly differ between young musicians and non-musicians from the low memory load of working memory task. Copyright © 2017 Elsevier B.V. All rights reserved.

Tracking and recognition of multiple human targets moving in a wireless pyroelectric infrared sensor network.

PubMed

Xiong, Ji; Li, Fangmin; Zhao, Ning; Jiang, Na

2014-04-22

With characteristics of low-cost and easy deployment, the distributed wireless pyroelectric infrared sensor network has attracted extensive interest, which aims to make it an alternate infrared video sensor in thermal biometric applications for tracking and identifying human targets. In these applications, effectively processing signals collected from sensors and extracting the features of different human targets has become crucial. This paper proposes the application of empirical mode decomposition and the Hilbert-Huang transform to extract features of moving human targets both in the time domain and the frequency domain. Moreover, the support vector machine is selected as the classifier. The experimental results demonstrate that by using this method the identification rates of multiple moving human targets are around 90%.

Phase gradient algorithm based on co-axis two-step phase-shifting interferometry and its application

NASA Astrophysics Data System (ADS)

Wang, Yawei; Zhu, Qiong; Xu, Yuanyuan; Xin, Zhiduo; Liu, Jingye

2017-12-01

A phase gradient method based on co-axis two-step phase-shifting interferometry, is used to reveal the detailed information of a specimen. In this method, the phase gradient distribution can only be obtained by calculating both the first-order derivative and the radial Hilbert transformation of the intensity difference between two phase-shifted interferograms. The feasibility and accuracy of this method were fully verified by the simulation results for a polystyrene sphere and a red blood cell. The empirical results demonstrated that phase gradient is sensitive to changes in the refractive index and morphology. Because phase retrieval and tedious phase unwrapping are not required, the calculation speed is faster. In addition, co-axis interferometry has high spatial resolution.

Improved Reconstruction of Radio Holographic Signal for Forward Scatter Radar Imaging

PubMed Central

Hu, Cheng; Liu, Changjiang; Wang, Rui; Zeng, Tao

2016-01-01

Forward scatter radar (FSR), as a specially configured bistatic radar, is provided with the capabilities of target recognition and classification by the Shadow Inverse Synthetic Aperture Radar (SISAR) imaging technology. This paper mainly discusses the reconstruction of radio holographic signal (RHS), which is an important procedure in the signal processing of FSR SISAR imaging. Based on the analysis of signal characteristics, the method for RHS reconstruction is improved in two parts: the segmental Hilbert transformation and the reconstruction of mainlobe RHS. In addition, a quantitative analysis of the method’s applicability is presented by distinguishing between the near field and far field in forward scattering. Simulation results validated the method’s advantages in improving the accuracy of RHS reconstruction and imaging. PMID:27164114

A fully reconfigurable photonic integrated signal processor

NASA Astrophysics Data System (ADS)

Liu, Weilin; Li, Ming; Guzzon, Robert S.; Norberg, Erik J.; Parker, John S.; Lu, Mingzhi; Coldren, Larry A.; Yao, Jianping

2016-03-01

Photonic signal processing has been considered a solution to overcome the inherent electronic speed limitations. Over the past few years, an impressive range of photonic integrated signal processors have been proposed, but they usually offer limited reconfigurability, a feature highly needed for the implementation of large-scale general-purpose photonic signal processors. Here, we report and experimentally demonstrate a fully reconfigurable photonic integrated signal processor based on an InP-InGaAsP material system. The proposed photonic signal processor is capable of performing reconfigurable signal processing functions including temporal integration, temporal differentiation and Hilbert transformation. The reconfigurability is achieved by controlling the injection currents to the active components of the signal processor. Our demonstration suggests great potential for chip-scale fully programmable all-optical signal processing.

Comparisons between real and complex Gauss wavelet transform methods of three-dimensional shape reconstruction

NASA Astrophysics Data System (ADS)

Xu, Luopeng; Dan, Youquan; Wang, Qingyuan

2015-10-01

The continuous wavelet transform (CWT) introduces an expandable spatial and frequency window which can overcome the inferiority of localization characteristic in Fourier transform and windowed Fourier transform. The CWT method is widely applied in the non-stationary signal analysis field including optical 3D shape reconstruction with remarkable performance. In optical 3D surface measurement, the performance of CWT for optical fringe pattern phase reconstruction usually depends on the choice of wavelet function. A large kind of wavelet functions of CWT, such as Mexican Hat wavelet, Morlet wavelet, DOG wavelet, Gabor wavelet and so on, can be generated from Gauss wavelet function. However, so far, application of the Gauss wavelet transform (GWT) method (i.e. CWT with Gauss wavelet function) in optical profilometry is few reported. In this paper, the method using GWT for optical fringe pattern phase reconstruction is presented first and the comparisons between real and complex GWT methods are discussed in detail. The examples of numerical simulations are also given and analyzed. The results show that both the real GWT method along with a Hilbert transform and the complex GWT method can realize three-dimensional surface reconstruction; and the performance of reconstruction generally depends on the frequency domain appearance of Gauss wavelet functions. For the case of optical fringe pattern of large phase variation with position, the performance of real GWT is better than that of complex one due to complex Gauss series wavelets existing frequency sidelobes. Finally, the experiments are carried out and the experimental results agree well with our theoretical analysis.

Seismic instantaneous frequency extraction based on the SST-MAW

NASA Astrophysics Data System (ADS)

Liu, Naihao; Gao, Jinghuai; Jiang, Xiudi; Zhang, Zhuosheng; Wang, Ping

2018-06-01

The instantaneous frequency (IF) extraction of seismic data has been widely applied to seismic exploration for decades, such as detecting seismic absorption and characterizing depositional thicknesses. Based on the complex-trace analysis, the Hilbert transform (HT) can extract the IF directly, which is a traditional method and susceptible to noise. In this paper, a robust approach based on the synchrosqueezing transform (SST) is proposed to extract the IF from seismic data. In this process, a novel analytical wavelet is developed and chosen as the basic wavelet, which is called the modified analytical wavelet (MAW) and comes from the three parameter wavelet. After transforming the seismic signal into a sparse time-frequency domain via the SST taking the MAW (SST-MAW), an adaptive threshold is introduced to improve the noise immunity and accuracy of the IF extraction in a noisy environment. Note that the SST-MAW reconstructs a complex trace to extract seismic IF. To demonstrate the effectiveness of the proposed method, we apply the SST-MAW to synthetic data and field seismic data. Numerical experiments suggest that the proposed procedure yields the higher resolution and the better anti-noise performance compared to the conventional IF extraction methods based on the HT method and continuous wavelet transform. Moreover, geological features (such as the channels) are well characterized, which is insightful for further oil/gas reservoir identification.

LORETA EEG phase reset of the default mode network

PubMed Central

Thatcher, Robert W.; North, Duane M.; Biver, Carl J.

2014-01-01

Objectives: The purpose of this study was to explore phase reset of 3-dimensional current sources in Brodmann areas located in the human default mode network (DMN) using Low Resolution Electromagnetic Tomography (LORETA) of the human electroencephalogram (EEG). Methods: The EEG was recorded from 19 scalp locations from 70 healthy normal subjects ranging in age from 13 to 20 years. A time point by time point computation of LORETA current sources were computed for 14 Brodmann areas comprising the DMN in the delta frequency band. The Hilbert transform of the LORETA time series was used to compute the instantaneous phase differences between all pairs of Brodmann areas. Phase shift and lock durations were calculated based on the 1st and 2nd derivatives of the time series of phase differences. Results: Phase shift duration exhibited three discrete modes at approximately: (1) 25 ms, (2) 50 ms, and (3) 65 ms. Phase lock duration present primarily at: (1) 300–350 ms and (2) 350–450 ms. Phase shift and lock durations were inversely related and exhibited an exponential change with distance between Brodmann areas. Conclusions: The results are explained by local neural packing density of network hubs and an exponential decrease in connections with distance from a hub. The results are consistent with a discrete temporal model of brain function where anatomical hubs behave like a “shutter” that opens and closes at specific durations as nodes of a network giving rise to temporarily phase locked clusters of neurons for specific durations. PMID:25100976

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

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

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

De Sitter Space Without Dynamical Quantum Fluctuations

NASA Astrophysics Data System (ADS)

Boddy, Kimberly K.; Carroll, Sean M.; Pollack, Jason

2016-06-01

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no dynamical quantum fluctuations. Such fluctuations require either an evolving microstate, or time-dependent histories of out-of-equilibrium recording devices, which we argue are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincaré recurrences and dynamical Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence, nor does it affect the existence of non-dynamical vacuum fluctuations such as those that give rise to the Casimir effect.

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

NASA Astrophysics Data System (ADS)

Its, Alexander; Its, Elizabeth

2018-04-01

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

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

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

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

2011-06-15

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

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

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

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

A New Instantaneous Frequency Measure Based on The Stockwell Transform

NASA Astrophysics Data System (ADS)

yedlin, M. J.; Ben-Horrin, Y.; Fraser, J. D.

2011-12-01

We propose the use of a new transform, the Stockwell transform[1], as a means of creating time-frequency maps and applying them to distinguish blasts from earthquakes. This new transform, the Stockwell transform can be considered as a variant of the continuous wavelet transform, that preserves the absolute phase.The Stockwell transform employs a complex Morlet mother wavelet. The novelty of this transform lies in its resolution properties. High frequencies in the candidate signal are well-resolved in time but poorly resolved in frequency, while the converse is true for low frequency signal components. The goal of this research is to obtain the instantaneous frequency as a function of time for both the earthquakes and the blasts. Two methods will be compared. In the first method, we will compute the analytic signal, the envelope and the instantaneous phase as a function of time[2]. The instantaneous phase derivative will yield the instantaneous angular frequency. The second method will be based on time-frequency analysis using the Stockwell transform. The Stockwell transform will be computed in non-redundant fashion using a dyadic representation[3]. For each time-point, the frequency centroid will be computed -- a representation for the most likely frequency at that time. A detailed comparison will be presented for both approaches to the computation of the instantaneous frequency. An advantage of the Stockwell approach is that no differentiation is applied. The Hilbert transform method can be less sensitive to edge effects. The goal of this research is to see if the new Stockwell-based method could be used as a discriminant between earthquakes and blasts. References [1] Stockwell, R.G., Mansinha, L. and Lowe, R.P. "Localization of the complex spectrum: the S transform", IEEE Trans. Signal Processing, vol.44, no.4, pp.998-1001, (1996). [2]Taner, M.T., Koehler, F. "Complex seismic trace analysis", Geophysics, vol. 44, Issue 6, pp. 1041-1063 (1979). [3] Brown, R.A., Lauzon, M.L. and Frayne, R. "General Description of Linear Time-Frequency Transforms and Formulation of a Fast, Invertible Transform That Samples the Continuous S-Transform Spectrum Nonredundantly", IEEE Transactions on Signal Processing, 1:281-90 (2010).

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.

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.

On the deep structure of the blowing-up of curve singularities

NASA Astrophysics Data System (ADS)

Elias, Juan

2001-09-01

Let C be a germ of curve singularity embedded in (kn, 0). It is well known that the blowing-up of C centred on its closed ring, Bl(C), is a finite union of curve singularities. If C is reduced we can iterate this process and, after a finite number of steps, we find only non-singular curves. This is the desingularization process. The main idea of this paper is to linearize the blowing-up of curve singularities Bl(C) [rightward arrow] C. We perform this by studying the structure of [script O]Bl(C)/[script O]C as W-module, where W is a discrete valuation ring contained in [script O]C. Since [script O]Bl(C)/[script O]C is a torsion W-module, its structure is determined by the invariant factors of [script O]C in [script O]Bl(C). The set of invariant factors is called in this paper as the set of micro-invariants of C (see Definition 1·2).In the first section we relate the micro-invariants of C to the Hilbert function of C (Proposition 1·3), and we show how to compute them from the Hilbert function of some quotient of [script O]C (see Proposition 1·4).The main result of this paper is Theorem 3·3 where we give upper bounds of the micro-invariants in terms of the regularity, multiplicity and embedding dimension. As a corollary we improve and we recover some results of [6]. These bounds can be established as a consequence of the study of the Hilbert function of a filtration of ideals g = {g[r,i+1]}i [gt-or-equal, slanted] 0 of the tangent cone of [script O]C (see Section 2). The main property of g is that the ideals g[r,i+1] have initial degree bigger than the Castelnuovo-Mumford regularity of the tangent cone of [script O]C.Section 4 is devoted to computation the micro-invariants of branches; we show how to compute them from the semigroup of values of C and Bl(C) (Proposition 4·3). The case of monomial curve singularities is especially studied; we end Section 4 with some explicit computations.In the last section we study some geometric properties of C that can be deduced from special values of the micro-invariants, and we specially study the relationship of the micro-invariants with the Hilbert function of [script O]Bl(C). We end the paper studying the natural equisingularity criteria that can be defined from the micro-invariants and its relationship with some of the known equisingularity criteria.

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

Gadella, M.; Negro, J.; Santander, M.

In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra of the system plus a subalgebra of operators that give the spectrum of the system and connects the eigenfunctions of the Hamiltonian among themselves. In our case, the geometrical symmetry algebra is so(3,1) and the SGA is so(4,2). We start with a representation of so(4,2) by functions on a realization of the Lobachevski space given by a two-sheeted hyperboloid, where the Lie algebramore » commutators are the usual Poisson-Dirac brackets. Then, we introduce a quantized version of the representation in which functions are replaced by operators on a Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the Hamiltonian are given and 'naive' ladder operators are identified. The previously defined 'naive' ladder operators shift the eigenvalues by a complex number so that an alternative approach is necessary. This is obtained by a non-self-adjoint function of a linear combination of the ladder operators, which gives the correct relation among the eigenfunctions of the Hamiltonian. We give an eigenfunction expansion of functions over the upper sheet of a two-sheeted hyperboloid in terms of the eigenfunctions of the Hamiltonian.« less

Fault detection in rotor bearing systems using time frequency techniques

NASA Astrophysics Data System (ADS)

Chandra, N. Harish; Sekhar, A. S.

2016-05-01

Faults such as misalignment, rotor cracks and rotor to stator rub can exist collectively in rotor bearing systems. It is an important task for rotor dynamic personnel to monitor and detect faults in rotating machinery. In this paper, the rotor startup vibrations are utilized to solve the fault identification problem using time frequency techniques. Numerical simulations are performed through finite element analysis of the rotor bearing system with individual and collective combinations of faults as mentioned above. Three signal processing tools namely Short Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT) and Hilbert Huang Transform (HHT) are compared to evaluate their detection performance. The effect of addition of Signal to Noise ratio (SNR) on three time frequency techniques is presented. The comparative study is focused towards detecting the least possible level of the fault induced and the computational time consumed. The computation time consumed by HHT is very less when compared to CWT based diagnosis. However, for noisy data CWT is more preferred over HHT. To identify fault characteristics using wavelets a procedure to adjust resolution of the mother wavelet is presented in detail. Experiments are conducted to obtain the run-up data of a rotor bearing setup for diagnosis of shaft misalignment and rotor stator rubbing faults.

Determination of accuracy of winding deformation method using kNN based classifier used for 3 MVA transformer

NASA Astrophysics Data System (ADS)

Ahmed, Mustafa Wasir; Baishya, Manash Jyoti; Sharma, Sasanka Sekhor; Hazarika, Manash

2018-04-01

This paper presents a detecting system on power transformer in transformer winding, core and on load tap changer (OLTC). Accuracy of winding deformation is determined using kNN based classifier. Winding deformation in power transformer can be measured using sweep frequency response analysis (SFRA), which can enhance the diagnosis accuracy to a large degree. It is suggested that in the results minor deformation faults can be detected at frequency range of 1 mHz to 2 MHz. The values of RCL parameters are changed when faults occur and hence frequency response of the winding will change accordingly. The SFRA data of tested transformer is compared with reference trace. The difference between two graphs indicate faults in the transformer. The deformation between 1 mHz to 1kHz gives winding deformation, 1 kHz to 100 kHz gives core deformation and 100 kHz to 2 MHz gives OLTC deformation.

Acoustic emission analysis for the detection of appropriate cutting operations in honing processes

NASA Astrophysics Data System (ADS)

Buj-Corral, Irene; Álvarez-Flórez, Jesús; Domínguez-Fernández, Alejandro

2018-01-01

In the present paper, acoustic emission was studied in honing experiments obtained with different abrasive densities, 15, 30, 45 and 60. In addition, 2D and 3D roughness, material removal rate and tool wear were determined. In order to treat the sound signal emitted during the machining process, two methods of analysis were compared: Fast Fourier Transform (FFT) and Hilbert Huang Transform (HHT). When density 15 is used, the number of cutting grains is insufficient to provide correct cutting, while clogging appears with densities 45 and 60. The results were confirmed by means of treatment of the sound signal. In addition, a new parameter S was defined as the relationship between energy in low and high frequencies contained within the emitted sound. The selected density of 30 corresponds to S values between 0.1 and 1. Correct cutting operations in honing processes are dependent on the density of the abrasive employed. The density value to be used can be selected by means of measurement and analysis of acoustic emissions during the honing operation. Thus, honing processes can be monitored without needing to stop the process.

Experimental analysis of synchronization and dynamics in an automobile as a complex system

NASA Astrophysics Data System (ADS)

González-Cruz, C. A.; Jáuregui-Correa, J. C.; López-Cajún, C.; Sen, M.; Domínguez-González, A.

2015-08-01

A complex system is composed of many interacting elements, and its behavior, as a whole, can be quite different from that of the individual elements. An automobile is an example of a common mechanical system composed of a large number of individual elements. These elements are connected through soft and hard linkages that transmit motion to each other. This paper proposes a variety of analytical tools to study experimental data from complex systems using two elements of an automobile as an example. Accelerometer measurements were taken from two elements within an automobile: the door and the dashboard. Two types of data were collected: response to impact loading, and response to road excitation of the automobile driven at different speeds. The signals were processed via Fourier and wavelet transforms, cross-correlation coefficients, Hilbert transform, and Kuramoto order parameters. A new parameter, called the order-deficit parameter, is introduced. Considerable, but not complete, synchronization can be found between the accelerations measured at these two locations in the automobile, and the degree of synchronization is quantified using the order-deficit parameter.

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

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.

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

NASA Astrophysics Data System (ADS)

Jahanipur, Ruhollah

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

Linear optics only allows every possible quantum operation for one photon or one port

NASA Astrophysics Data System (ADS)

Moyano-Fernández, Julio José; Garcia-Escartin, Juan Carlos

2017-01-01

We study the evolution of the quantum state of n photons in m different modes when they go through a lossless linear optical system. We show that there are quantum evolution operators U that cannot be built with linear optics alone unless the number of photons or the number of modes is equal to one. The evolution for single photons can be controlled with the known realization of any unitary proved by Reck, Zeilinger, Bernstein and Bertani. The evolution for a single mode corresponds to the trivial evolution in a phase shifter. We analyze these two cases and prove that any other combination of the number of photons and modes produces a Hilbert state too large for the linear optics system to give any desired evolution.

Observation of entanglement witnesses for orbital angular momentum states

NASA Astrophysics Data System (ADS)

Agnew, M.; Leach, J.; Boyd, R. W.

2012-06-01

Entanglement witnesses provide an efficient means of determining the level of entanglement of a system using the minimum number of measurements. Here we demonstrate the observation of two-dimensional entanglement witnesses in the high-dimensional basis of orbital angular momentum (OAM). In this case, the number of potentially entangled subspaces scales as d(d - 1)/2, where d is the dimension of the space. The choice of OAM as a basis is relevant as each subspace is not necessarily maximally entangled, thus providing the necessary state for certain tests of nonlocality. The expectation value of the witness gives an estimate of the state of each two-dimensional subspace belonging to the d-dimensional Hilbert space. These measurements demonstrate the degree of entanglement and therefore the suitability of the resulting subspaces for quantum information applications.

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

Determination of displacements and their derivatives from 3D fringe patterns via extended monogenic phasor method

NASA Astrophysics Data System (ADS)

Sciammarella, Cesar A.; Lamberti, Luciano

2018-05-01

For 1D signals, it is necessary to resort to a 2D abstract space because the concept of phase utilized in the retrieval of fringe pattern analysis information relies on the use of a vectorial function. Fourier and Hilbert transforms provide in-quadrature signals that lead to the very important basic concept of local phase. A 3D abstract space must hence be generated in order to analyze 2D signals. A 3D vector space in a Cartesian complex space is graphically represented by a Poincare sphere. In this study, the extension of the associated spaces is extended to 3D. A 4D hypersphere is defined for that purpose. The proposed approach is illustrated by determining the deformations of the heart left ventricle.

Noether’s second theorem and Ward identities for gauge symmetries

DOE PAGES

Avery, Steven G.; Schwab, Burkhard U. W.

2016-02-04

Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s secondmore » theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.« less

Tracking and Recognition of Multiple Human Targets Moving in a Wireless Pyroelectric Infrared Sensor Network

PubMed Central

Xiong, Ji; Li, Fangmin; Zhao, Ning; Jiang, Na

2014-01-01

With characteristics of low-cost and easy deployment, the distributed wireless pyroelectric infrared sensor network has attracted extensive interest, which aims to make it an alternate infrared video sensor in thermal biometric applications for tracking and identifying human targets. In these applications, effectively processing signals collected from sensors and extracting the features of different human targets has become crucial. This paper proposes the application of empirical mode decomposition and the Hilbert-Huang transform to extract features of moving human targets both in the time domain and the frequency domain. Moreover, the support vector machine is selected as the classifier. The experimental results demonstrate that by using this method the identification rates of multiple moving human targets are around 90%. PMID:24759117

Study of Composite Plate Damages Using Embedded PZT Sensors with Various Center Frequency

NASA Astrophysics Data System (ADS)

Kang, Kyoung-Tak; Chun, Heoung-Jae; Son, Ju-Hyun; Byun, Joon-Hyung; Um, Moon-Kwang; Lee, Sang-Kwan

This study presents part of an experimental and analytical survey of candidate methods for damage detection of composite structural. Embedded piezoceramic (PZT) sensors were excited with the high power ultrasonic wave generator generating a propagation of stress wave along the composite plate. The same embedded piezoceramic (PZT) sensors are used as receivers for acquiring stress signals. The effects of center frequency of embedded sensor were evaluated for the damage identification capability with known localized defects. The study was carried out to assess damage in composite plate by fusing information from multiple sensing paths of the embedded network. It was based on the Hilbert transform, signal correlation and probabilistic searching. The obtained results show that satisfactory detection of defects could be achieved by proposed method.

Ultrastable light sources in the crossover from superradiance to lasing

NASA Astrophysics Data System (ADS)

Xu, Minghui; Tieri, David; Holland, Murray

2013-05-01

We theoretically investigate the crossover from steady-state superradiance to optical lasing. An exact solution of the quantum master equation is difficult to obtain due to the exponential scaling of the Hilbert space dimension with system size. However, since Lindblad operators in the master equation are invariant under SU(4) transformations, we are able to reduce the exponential scaling of the problem to cubic by expanding the density matrix in terms of an SU(4) basis. In this way, we obtain exact quantum solutions of the superradiance-laser crossover. We use this theory to investigate the potential for ultrastable lasers in the millihertz linewidth regime, and find the behavior of important observables, such as intensity, linewidth, spin-correlation, and entanglement. This work was supported by the DARPA QUASAR program and NSF.

Temporal structure of neuronal population oscillations with empirical model decomposition

NASA Astrophysics Data System (ADS)

Li, Xiaoli

2006-08-01

Frequency analysis of neuronal oscillation is very important for understanding the neural information processing and mechanism of disorder in the brain. This Letter addresses a new method to analyze the neuronal population oscillations with empirical mode decomposition (EMD). Following EMD of neuronal oscillation, a series of intrinsic mode functions (IMFs) are obtained, then Hilbert transform of IMFs can be used to extract the instantaneous time frequency structure of neuronal oscillation. The method is applied to analyze the neuronal oscillation in the hippocampus of epileptic rats in vivo, the results show the neuronal oscillations have different descriptions during the pre-ictal, seizure onset and ictal periods of the epileptic EEG at the different frequency band. This new method is very helpful to provide a view for the temporal structure of neural oscillation.

Robust Magnetotelluric Impedance Estimation

NASA Astrophysics Data System (ADS)

Sutarno, D.

2010-12-01

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

Research on the fault diagnosis of bearing based on wavelet and demodulation

NASA Astrophysics Data System (ADS)

Li, Jiapeng; Yuan, Yu

2017-05-01

As a most commonly-used machine part, antifriction bearing is extensively used in mechanical equipment. Vibration signal analysis is one of the methods to monitor and diagnose the running status of antifriction bearings. Therefore, using wavelet analysis for demising is of great importance in the engineering practice. This paper firstly presented the basic theory of wavelet analysis to study the transformation, decomposition and reconstruction of wavelet. In addition, edition software LabVIEW was adopted to conduct wavelet and demodulation upon the vibration signal of antifriction bearing collected. With the combination of Hilbert envelop demodulation analysis, the fault character frequencies of the demised signal were extracted to conduct fault diagnosis analysis, which serves as a reference for the wavelet and demodulation of the vibration signal in engineering practice.

Complex correlation approach for high frequency financial data

NASA Astrophysics Data System (ADS)

Wilinski, Mateusz; Ikeda, Yuichi; Aoyama, Hideaki

2018-02-01

We propose a novel approach that allows the calculation of a Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.

Filtration of human EEG recordings from physiological artifacts with empirical mode method

NASA Astrophysics Data System (ADS)

Grubov, Vadim V.; Runnova, Anastasiya E.; Khramova, Marina V.

2017-03-01

In the paper we propose the new method for dealing with noise and physiological artifacts in experimental human EEG recordings. The method is based on analysis of EEG signals with empirical mode decomposition (Hilbert-Huang transform). We consider noises and physiological artifacts on EEG as specific oscillatory patterns that cause problems during EEG analysis and can be detected with additional signals recorded simultaneously with EEG (ECG, EMG, EOG, etc.) We introduce the algorithm of the method with following steps: empirical mode decomposition of EEG signal, choosing of empirical modes with artifacts, removing empirical modes with artifacts, reconstruction of the initial EEG signal. We test the method on filtration of experimental human EEG signals from eye-moving artifacts and show high efficiency of the method.

Biological applications of phase-contrast electron microscopy.

PubMed

Nagayama, Kuniaki

2014-01-01

Here, I review the principles and applications of phase-contrast electron microscopy using phase plates. First, I develop the principle of phase contrast based on a minimal model of microscopy, introducing a double Fourier-transform process to mathematically formulate the image formation. Next, I explain four phase-contrast (PC) schemes, defocus PC, Zernike PC, Hilbert differential contrast, and schlieren optics, as image-filtering processes in the context of the minimal model, with particular emphases on the Zernike PC and corresponding Zernike phase plates. Finally, I review applications of Zernike PC cryo-electron microscopy to biological systems such as protein molecules, virus particles, and cells, including single-particle analysis to delineate three-dimensional (3D) structures of protein and virus particles and cryo-electron tomography to reconstruct 3D images of complex protein systems and cells.

Canonical transformation path to gauge theories of gravity

NASA Astrophysics Data System (ADS)

Struckmeier, J.; Muench, J.; Vasak, D.; Kirsch, J.; Hanauske, M.; Stoecker, H.

2017-06-01

In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime. A term that describes the dynamics of the "free" gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics" Hamiltonian is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields—this is beyond the Einstein-Hilbert theory of general relativity.

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.

QWT: Retrospective and New Applications

NASA Astrophysics Data System (ADS)

Xu, Yi; Yang, Xiaokang; Song, Li; Traversoni, Leonardo; Lu, Wei

Quaternion wavelet transform (QWT) achieves much attention in recent years as a new image analysis tool. In most cases, it is an extension of the real wavelet transform and complex wavelet transform (CWT) by using the quaternion algebra and the 2D Hilbert transform of filter theory, where analytic signal representation is desirable to retrieve phase-magnitude description of intrinsically 2D geometric structures in a grayscale image. In the context of color image processing, however, it is adapted to analyze the image pattern and color information as a whole unit by mapping sequential color pixels to a quaternion-valued vector signal. This paper provides a retrospective of QWT and investigates its potential use in the domain of image registration, image fusion, and color image recognition. It is indicated that it is important for QWT to induce the mechanism of adaptive scale representation of geometric features, which is further clarified through two application instances of uncalibrated stereo matching and optical flow estimation. Moreover, quaternionic phase congruency model is defined based on analytic signal representation so as to operate as an invariant feature detector for image registration. To achieve better localization of edges and textures in image fusion task, we incorporate directional filter bank (DFB) into the quaternion wavelet decomposition scheme to greatly enhance the direction selectivity and anisotropy of QWT. Finally, the strong potential use of QWT in color image recognition is materialized in a chromatic face recognition system by establishing invariant color features. Extensive experimental results are presented to highlight the exciting properties of QWT.

Complete set of invariants of a 4th order tensor: the 12 tasks of HARDI from ternary quartics.

PubMed

Papadopoulo, Théo; Ghosh, Aurobrata; Deriche, Rachid

2014-01-01

Invariants play a crucial role in Diffusion MRI. In DTI (2nd order tensors), invariant scalars (FA, MD) have been successfully used in clinical applications. But DTI has limitations and HARDI models (e.g. 4th order tensors) have been proposed instead. These, however, lack invariant features and computing them systematically is challenging. We present a simple and systematic method to compute a functionally complete set of invariants of a non-negative 3D 4th order tensor with respect to SO3. Intuitively, this transforms the tensor's non-unique ternary quartic (TQ) decomposition (from Hilbert's theorem) to a unique canonical representation independent of orientation - the invariants. The method consists of two steps. In the first, we reduce the 18 degrees-of-freedom (DOF) of a TQ representation by 3-DOFs via an orthogonal transformation. This transformation is designed to enhance a rotation-invariant property of choice of the 3D 4th order tensor. In the second, we further reduce 3-DOFs via a 3D rotation transformation of coordinates to arrive at a canonical set of invariants to SO3 of the tensor. The resulting invariants are, by construction, (i) functionally complete, (ii) functionally irreducible (if desired), (iii) computationally efficient and (iv) reversible (mappable to the TQ coefficients or shape); which is the novelty of our contribution in comparison to prior work. Results from synthetic and real data experiments validate the method and indicate its importance.

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.

Classical and special relativity in four steps

NASA Astrophysics Data System (ADS)

Browne, K. M.

2018-03-01

The most fundamental and pedagogically useful path to the space-time transformations of both classical and special relativity is to postulate the principle of relativity, derive the generalised or Ignatowsky transformation which contains both, then apply two different second postulates that give either the Galilean or Lorentz transformation. What is new here is (a) a simple two-step derivation of the Ignatowsky transformation, (b) a second postulate of universal time which yields the Galilean transformation, and (c) a different second postulate of finite universal lightspeed to give the Lorentz transformation using a simple Ignatowsky transformation of a light wave. This method demonstrates that the fundamental difference between Galilean and Lorentz transformations is not that lightspeed is universal (which is true for both) but whether the model requires lightspeed to be infinite or finite (as once mentioned by Einstein).

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.

On-Line Monitoring and Diagnostics of the Integrity of Nuclear Plant Steam Generators and Heat Exchangers

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

Belle R. Upadhyaya; J. Wesley Hines

2004-09-27

Integrity monitoring and flaw diagnostics of flat beams and tubular structures was investigated in this research task using guided acoustic signals. A piezo-sensor suite was deployed to activate and collect Lamb wave signals that propagate along metallic specimens. The dispersion curves of Lamb waves along plate and tubular structures are generated through numerical analysis. Several advanced techniques were explored to extract representative features from acoustic time series. Among them, the Hilbert-Huang transform (HHT) is a recently developed technique for the analysis of non-linear and transient signals. A moving window method was introduced to generate the local peak characters from acousticmore » time series, and a zooming window technique was developed to localize the structural flaws. The time-frequency analysis and pattern recognition techniques were combined for classifying structural defects in brass tubes. Several types of flaws in brass tubes were tested, both in the air and in water. The techniques also proved to be effective under background/process noise. A detailed theoretical analysis of Lamb wave propagation was performed and simulations were carried out using the finite element software system ABAQUS. This analytical study confirmed the behavior of the acoustic signals acquired from the experimental studies. The report presents the background the analysis of acoustic signals acquired from piezo-electric transducers for structural defect monitoring. A comparison of the use of time-frequency techniques, including the Hilbert-Huang transform, is presented. The report presents the theoretical study of Lamb wave propagation in flat beams and tubular structures, and the need for mode separation in order to effectively perform defect diagnosis. The results of an extensive experimental study of detection, location, and isolation of structural defects in flat aluminum beams and brass tubes are presented. The results of this research show the feasibility of on-line monitoring of small structural flaws by the use of transient and nonlinear acoustic signal analysis, and its implementation by the proper design of a piezo-electric transducer suite.« less

The canonical quantization of chaotic maps on the torus

NASA Astrophysics Data System (ADS)

Rubin, Ron Shai

In this thesis, a quantization method for classical maps on the torus is presented. The quantum algebra of observables is defined as the quantization of measurable functions on the torus with generators exp (2/pi ix) and exp (2/pi ip). The Hilbert space we use remains the infinite-dimensional L2/ (/IR, dx). The dynamics is given by a unitary quantum propagator such that as /hbar /to 0, the classical dynamics is returned. We construct such a quantization for the Kronecker map, the cat map, the baker's map, the kick map, and the Harper map. For the cat map, we find the same for the propagator on the plane the same integral kernel conjectured in (HB) using semiclassical methods. We also define a quantum 'integral over phase space' as a trace over the quantum algebra. Using this definition, we proceed to define quantum ergodicity and mixing for maps on the torus. We prove that the quantum cat map and Kronecker map are both ergodic, but only the cat map is mixing, true to its classical origins. For Planck's constant satisfying the integrality condition h = 1/N, with N/in doubz+, we construct an explicit isomorphism between L2/ (/IR, dx) and the Hilbert space of sections of an N-dimensional vector bundle over a θ-torus T2 of boundary conditions. The basis functions are distributions in L2/ (/IR, dx), given by an infinite comb of Dirac δ-functions. In Bargmann space these distributions take on the form of Jacobi ϑ-functions. Transformations from position to momentum representation can be implemented via a finite N-dimensional discrete Fourier transform. With the θ-torus, we provide a connection between the finite-dimensional quantum maps given in the physics literature and the canonical quantization presented here and found in the language of pseudo-differential operators elsewhere in mathematics circles. Specifically, at a fixed point of the dynamics on the θ-torus, we return a finite-dimensional matrix propagator. We present this connection explicitly for several examples.

Hilbert-Huang spectral analysis for characterizing the intrinsic time-scales of variability in decennial time-series of surface solar radiation

NASA Astrophysics Data System (ADS)

Bengulescu, Marc; Blanc, Philippe; Wald, Lucien

2016-04-01

An analysis of the variability of the surface solar irradiance (SSI) at different local time-scales is presented in this study. Since geophysical signals, such as long-term measurements of the SSI, are often produced by the non-linear interaction of deterministic physical processes that may also be under the influence of non-stationary external forcings, the Hilbert-Huang transform (HHT), an adaptive, noise-assisted, data-driven technique, is employed to extract locally - in time and in space - the embedded intrinsic scales at which a signal oscillates. The transform consists of two distinct steps. First, by means of the Empirical Mode Decomposition (EMD), the time-series is "de-constructed" into a finite number - often small - of zero-mean components that have distinct temporal scales of variability, termed hereinafter the Intrinsic Mode Functions (IMFs). The signal model of the components is an amplitude modulation - frequency modulation (AM - FM) one, and can also be thought of as an extension of a Fourier series having both time varying amplitude and frequency. Following the decomposition, Hilbert spectral analysis is then employed on the IMFs, yielding a time-frequency-energy representation that portrays changes in the spectral contents of the original data, with respect to time. As measurements of surface solar irradiance may possibly be contaminated by the manifestation of different type of stochastic processes (i.e. noise), the identification of real, physical processes from this background of random fluctuations is of interest. To this end, an adaptive background noise null hypothesis is assumed, based on the robust statistical properties of the EMD when applied to time-series of different classes of noise (e.g. white, red or fractional Gaussian). Since the algorithm acts as an efficient constant-Q dyadic, "wavelet-like", filter bank, the different noise inputs are decomposed into components having the same spectral shape, but that are translated to the next lower octave in the spectral domain. Thus, when the sampling step is increased, the spectral shape of IMFs cannot remain at its original position, due to the new lower Nyquist frequency, and is instead pushed toward the lower scaled frequency. Based on these features, the identification of potential signals within the data should become possible without any prior knowledge of the background noises. When applying the above outlined procedure to decennial time-series of surface solar irradiance, only the component that has an annual time-scale of variability is shown to have statistical properties that diverge from those of noise. Nevertheless, the noise-like components are not completely devoid of information, as it is found that their AM components have a non-null rank correlation coefficient with the annual mode, i.e. the background noise intensity seems to be modulated by the seasonal cycle. The findings have possible implications on the modelling and forecast of the surface solar irradiance, by discriminating its deterministic from its quasi-stochastic constituents, at distinct local time-scales.

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.

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.

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

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

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

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

Semiclassical propagation: Hilbert space vs. Wigner representation

NASA Astrophysics Data System (ADS)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

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

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

First law of black hole mechanics as a condition for stationarity

NASA Astrophysics Data System (ADS)

McCormick, Stephen

2014-11-01

In earlier work, we provided a Hilbert manifold structure for the phase space for the Einstein-Yang-Mills equations, and used this to prove a condition for initial data to be stationary [S. McCormick, Adv. Theor. Math. Phys. 18, 799 (2014)]. Here we use the same phase space to consider the evolution of initial data exterior to some closed 2-surface boundary, and establish a condition for stationarity in this case. It is shown that the differential relationship given in the first law of black hole mechanics is exactly the condition required for the initial data to be stationary; this was first argued nonrigorously by Sudarsky and Wald [Phys. Rev. D 46, 1453 (1992)]. Furthermore, we give evidence to suggest that if this differential relationship holds then the boundary surface is the bifurcation surface of a bifurcate Killing horizon.

A fast numerical method for ideal fluid flow in domains with multiple stirrers

NASA Astrophysics Data System (ADS)

Nasser, Mohamed M. S.; Green, Christopher C.

2018-03-01

A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the mathematical problem of resolving the flow field—given a particular distribution of any finite number of stirrers of specified shape and speed—can be formulated as a Riemann-Hilbert (R-H) problem. We show that this R-H problem can be solved numerically using a fast and accurate algorithm for any finite number of stirrers based around a boundary integral equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, and our numerical scheme is shown to handle highly multiply connected domains (i.e. systems of many fluid stirrers) with minimal computational expense.

Natural inflation from polymer quantization

NASA Astrophysics Data System (ADS)

Ali, Masooma; Seahra, Sanjeev S.

2017-11-01

We study the polymer quantization of a homogeneous massive scalar field in the early Universe using a prescription inequivalent to those previously appearing in the literature. Specifically, we assume a Hilbert space for which the scalar field momentum is well defined but its amplitude is not. This is closer in spirit to the quantization scheme of loop quantum gravity, in which no unique configuration operator exists. We show that in the semiclassical approximation, the main effect of this polymer quantization scheme is to compactify the phase space of chaotic inflation in the field amplitude direction. This gives rise to an effective scalar potential closely resembling that of hybrid natural inflation. Unlike polymer schemes in which the scalar field amplitude is well defined, the semiclassical dynamics involves a past cosmological singularity; i.e., this approach does not mitigate the big bang.

Cosmological models in energy-momentum-squared gravity

NASA Astrophysics Data System (ADS)

Board, Charles V. R.; Barrow, John D.

2017-12-01

We study the cosmological effects of adding terms of higher order in the usual energy-momentum tensor to the matter Lagrangian of general relativity. This is in contrast to most studies of higher-order gravity which focus on generalizing the Einstein-Hilbert curvature contribution to the Lagrangian. The resulting cosmological theories give rise to field equations of similar form to several particular theories with different fundamental bases, including bulk viscous cosmology, loop quantum gravity, k -essence, and brane-world cosmologies. We find a range of exact solutions for isotropic universes, discuss their behaviors with reference to the early- and late-time evolution, accelerated expansion, and the occurrence or avoidance of singularities. We briefly discuss extensions to anisotropic cosmologies and delineate the situations where the higher-order matter terms will dominate over anisotropies on approach to cosmological singularities.

Traces on orbifolds: anomalies and one-loop amplitudes

NASA Astrophysics Data System (ADS)

Groot Nibbelink, Stefan

2003-07-01

In the recent literature one can find calculations of various one-loop amplitudes, like anomalies, tadpoles and vacuum energies, on specific types of orbifolds, like S1/Bbb Z2. This work aims to give a general description of such one-loop computations for a large class of orbifold models. In order to achieve a high degree of generality, we formulate these calculations as evaluations of traces of operators over orbifold Hilbert spaces. We find that in general the result is expressed as a sum of traces over hyper surfaces with local projections, and the derivatives perpendicular to these hyper surfaces are rescaled. These local projectors naturally takes into account possible non-periodic boundary conditions. As the examples T6/Bbb Z4 and T4/D4 illustrate, the methods can be applied to non-prime as well as non-abelian orbifolds.

SIC-POVMS and MUBS: Geometrical Relationships in Prime Dimension

NASA Astrophysics Data System (ADS)

Appleby, D. M.

2009-03-01

The paper concerns Weyl-Heisenberg covariant SIC-POVMs (symmetric informationally complete positive operator valued measures) and full sets of MUBs (mutually unbiased bases) in prime dimension. When represented as vectors in generalized Bloch space a SIC-POVM forms a d2-1 dimensional regular simplex (d being the Hilbert space dimension). By contrast, the generalized Bloch vectors representing a full set of MUBs form d+1 mutually orthogonal d-1 dimensional regular simplices. In this paper we show that, in the Weyl-Heisenberg case, there are some simple geometrical relationships between the single SIC-POVM simplex and the d+1 MUB simplices. We go on to give geometrical interpretations of the minimum uncertainty states introduced by Wootters and Sussman, and by Appleby, Dang and Fuchs, and of the fiduciality condition given by Appleby, Dang and Fuchs.

On an open question of V. Colao and G. Marino presented in the paper "Krasnoselskii-Mann method for non-self mappings".

PubMed

Guo, Meifang; Li, Xia; Su, Yongfu

2016-01-01

Let H be a Hilbert space and let C be a closed convex nonempty subset of H and [Formula: see text] a non-self nonexpansive mapping. A map [Formula: see text] defined by [Formula: see text]. Then, for a fixed [Formula: see text] and for [Formula: see text], Krasnoselskii-Mann algorithm is defined by [Formula: see text] where [Formula: see text]. Recently, Colao and Marino (Fixed Point Theory Appl 2015:39, 2015) have proved both weak and strong convergence theorems when C is a strictly convex set and T is an inward mapping. Meanwhile, they proposed a open question for a countable family of non-self nonexpansive mappings. In this article, authors will give an answer and will prove the further generalized results with the examples to support them.

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.

Democratic Superstring Field Theory and Its Gauge Fixing

NASA Astrophysics Data System (ADS)

Kroyter, M.

This work is my contribution to the proceedings of the conference``SFT2010 -- the third international conference on string field theory and related topics'' and it reflects my talk there, which described the democratic string field theory and its gauge fixing. The democratic string field theory is the only fully RNS string field theory to date. It lives in the large Hilbert space and includes all picture numbers. Picture changing amounts in this formalism to a gauge transformation. We describe the theory and its properties and show that when partially gauge fixed it can be reduced to the modified theory and to the non-polynomial theory. In the latter case we can even include the Ramond sector in the picture-fixed action. We also show that another partial gauge-fixing leads to a new consistent string field theory at picture number -1.

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.

Signal processing methods for in-situ creep specimen monitoring

NASA Astrophysics Data System (ADS)

Guers, Manton J.; Tittmann, Bernhard R.

2018-04-01

Previous work investigated using guided waves for monitoring creep deformation during accelerated life testing. The basic objective was to relate observed changes in the time-of-flight to changes in the environmental temperature and specimen gage length. The work presented in this paper investigated several signal processing strategies for possible application in the in-situ monitoring system. Signal processing methods for both group velocity (wave-packet envelope) and phase velocity (peak tracking) time-of-flight were considered. Although the Analytic Envelope found via the Hilbert transform is commonly applied for group velocity measurements, erratic behavior in the indicated time-of-flight was observed when this technique was applied to the in-situ data. The peak tracking strategies tested had generally linear trends, and tracking local minima in the raw waveform ultimately showed the most consistent results.

Stability evaluation of short-circuiting gas metal arc welding based on ensemble empirical mode decomposition

NASA Astrophysics Data System (ADS)

Huang, Yong; Wang, Kehong; Zhou, Zhilan; Zhou, Xiaoxiao; Fang, Jimi

2017-03-01

The arc of gas metal arc welding (GMAW) contains abundant information about its stability and droplet transition, which can be effectively characterized by extracting the arc electrical signals. In this study, ensemble empirical mode decomposition (EEMD) was used to evaluate the stability of electrical current signals. The welding electrical signals were first decomposed by EEMD, and then transformed to a Hilbert-Huang spectrum and a marginal spectrum. The marginal spectrum is an approximate distribution of amplitude with frequency of signals, and can be described by a marginal index. Analysis of various welding process parameters showed that the marginal index of current signals increased when the welding process was more stable, and vice versa. Thus EEMD combined with the marginal index can effectively uncover the stability and droplet transition of GMAW.

Exponential instability in the fractional Calderón problem

NASA Astrophysics Data System (ADS)

Rüland, Angkana; Salo, Mikko

2018-04-01

In this paper we prove the exponential instability of the fractional Calderón problem and thus prove the optimality of the logarithmic stability estimate from Rüland and Salo (2017 arXiv:1708.06294). In order to infer this result, we follow the strategy introduced by Mandache in (2001 Inverse Problems 17 1435) for the standard Calderón problem. Here we exploit a close relation between the fractional Calderón problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in Rüland and Salo (2017 arXiv:1708.06294). Finally, in one dimension, we show a close relation between the fractional Calderón problem and the truncated Hilbert transform.

Combustion of bulk titanium in oxygen

NASA Technical Reports Server (NTRS)

Clark, A. F.; Moulder, J. C.; Runyan, C. C.

1975-01-01

The combustion of bulk titanium in one atmosphere oxygen is studied using laser ignition and several analytical techniques. These were high-speed color cinematography, time and space resolved spectra in the visible region, metallography (including SEM) of specimens quenched in argon gas, X-ray and chemical product analyses, and a new optical technique, the Hilbert transform method. The cinematographic application of this technique for visualizing phase objects in the combustion zone is described. The results indicate an initial vapor phase reaction immediately adjacent to the molten surface but as the oxygen uptake progresses the evaporation approaches the point of congruency and a much reduced evaporation rate. This and the accumulation of the various soluble oxides soon drive the reaction zone below the surface where gas formation causes boiling and ejection of particles. The buildup of rutile cuts off the oxygen supply and the reaction ceases.

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.

Detecting and characterizing high-frequency oscillations in epilepsy: a case study of big data analysis

NASA Astrophysics Data System (ADS)

Huang, Liang; Ni, Xuan; Ditto, William L.; Spano, Mark; Carney, Paul R.; Lai, Ying-Cheng

2017-01-01

We develop a framework to uncover and analyse dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive datasets to eliminate erroneous data segments, application of the empirical mode decomposition and Hilbert transform paradigm to obtain the fundamental components embedded in the time series at distinct time scales, and statistical/scaling analysis of the components. As a case study, we apply our framework to detecting and characterizing high-frequency oscillations (HFOs) from a big database of rat electroencephalogram recordings. We find a striking phenomenon: HFOs exhibit on-off intermittency that can be quantified by algebraic scaling laws. Our framework can be generalized to big data-related problems in other fields such as large-scale sensor data and seismic data analysis.

Wavelet-frequency analysis for the detection of discontinuities in switched system models of human balance.

PubMed

Nema, Salam; Kowalczyk, Piotr; Loram, Ian

2017-01-01

This paper is concerned with detecting the presence of switching behavior in experimentally obtained posturographic data sets by means of a novel algorithm that is based on a combination of wavelet analysis and Hilbert transform. As a test-bed for the algorithm, we first use a switched model of human balance control during quiet standing with known switching behavior in four distinct configurations. We obtain a time-frequency representation of a signal generated by our model system. We are then able to detect manifestations of discontinuities (switchings) in the signal as spiking behavior. The frequency of switchings, measured by means of our algorithm and detected in our models systems, agrees with the frequency of spiking behavior found in the experimentally obtained posturographic data. Copyright © 2016. Published by Elsevier B.V.

Comparison of Signals from Gravitational Wave Detectors with Instantaneous Time-Frequency Maps

NASA Technical Reports Server (NTRS)

Stroeer, A.; Blackburn, L.; Camp, J.

2011-01-01

Gravitational wave astronomy relies on the use of multiple detectors, so that coincident detections may distinguish real signals from instrumental artifacts, and also so that relative timing of signals can provide the sky position of sources. We show that the comparison of instantaneous time-frequency and time-amplitude maps provided by the Hilbert-Huang Transform (HHT) can be used effectively for relative signal timing of common signals, to discriminate between the case of identical coincident signals and random noise coincidences and to provide a classification of signals based on their time-frequency trajectories. The comparison is done with a X(sup 2) goodness-offit method which includes contributions from both the instantaneous amplitude and frequency components of the HHT to match two signals in the time domain. This approach naturally allows the analysis of waveforms with strong frequency modulation.

Advanced optical manufacturing and testing; Proceedings of the Meeting, San Diego, CA, July 9-11, 1990

NASA Astrophysics Data System (ADS)

Sanger, Gregory M.; Reid, Paul B.; Baker, Lionel R.

1990-11-01

Consideration is given to advanced optical fabrication, profilometry and thin films, and metrology. Particular attention is given to automation for optics manufacturing, 3D contouring on a numerically controlled grinder, laser-scanning lens configurations, a noncontact precision measurement system, novel noncontact profiler design for measuring synchrotron radiation mirrors, laser-diode technologies for in-process metrology, measurements of X-ray reflectivities of Au-coatings at several energies, platinum coating of an X-ray mirror for SR lithography, a Hilbert transform algorithm for fringe-pattern analysis, structural error sources during fabrication of the AXAF optical elements, an in-process mirror figure qualification procedure for large deformable mirrors, interferometric evaluation of lenslet arrays for 2D phase-locked laser diode sources, and manufacturing and metrology tooling for the solar-A soft X-ray telescope.

Quantum state matching of qubits via measurement-induced nonlinear transformations

NASA Astrophysics Data System (ADS)

Kálmán, Orsolya; Kiss, Tamás

2018-03-01

We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined with a postselection scheme conditioned on the measurement result obtained on one of the qubits of the pair. The resulting transformation is a deterministic, nonlinear, chaotic map in the Hilbert space. We derive a class of these transformations capable of orthogonalizing nonorthogonal qubit states after a few iterations. These nonlinear maps orthogonalize states which correspond to the two different convergence regions of the nonlinear map. Based on the analysis of the border (the so-called Julia set) between the two regions of convergence, we show that it is always possible to find a map capable of deciding whether an unknown state is within a neighborhood of fixed radius around a desired quantum state. We analyze which one- and two-qubit operations would physically realize the scheme. It is possible to find a single two-qubit unitary gate for each map or, alternatively, a universal special two-qubit gate together with single-qubit gates in order to carry out the task. We note that it is enough to have a single physical realization of the required gates due to the iterative nature of the scheme.

Exploring Algorithms for Stellar Light Curves With TESS

NASA Astrophysics Data System (ADS)

Buzasi, Derek

2018-01-01

The Kepler and K2 missions have produced tens of thousands of stellar light curves, which have been used to measure rotation periods, characterize photometric activity levels, and explore phenomena such as differential rotation. The quasi-periodic nature of rotational light curves, combined with the potential presence of additional periodicities not due to rotation, complicates the analysis of these time series and makes characterization of uncertainties difficult. A variety of algorithms have been used for the extraction of rotational signals, including autocorrelation functions, discrete Fourier transforms, Lomb-Scargle periodograms, wavelet transforms, and the Hilbert-Huang transform. In addition, in the case of K2 a number of different pipelines have been used to produce initial detrended light curves from the raw image frames.In the near future, TESS photometry, particularly that deriving from the full-frame images, will dramatically further expand the number of such light curves, but details of the pipeline to be used to produce photometry from the FFIs remain under development. K2 data offers us an opportunity to explore the utility of different reduction and analysis tool combinations applied to these astrophysically important tasks. In this work, we apply a wide range of algorithms to light curves produced by a number of popular K2 pipeline products to better understand the advantages and limitations of each approach and provide guidance for the most reliable and most efficient analysis of TESS stellar data.

An analytical SMASH procedure (ASP) for sensitivity-encoded MRI.

PubMed

Lee, R F; Westgate, C R; Weiss, R G; Bottomley, P A

2000-05-01

The simultaneous acquisition of spatial harmonics (SMASH) method of imaging with detector arrays can reduce the number of phase-encoding steps, and MRI scan time several-fold. The original approach utilized numerical gradient-descent fitting with the coil sensitivity profiles to create a set of composite spatial harmonics to replace the phase-encoding steps. Here, an analytical approach for generating the harmonics is presented. A transform is derived to project the harmonics onto a set of sensitivity profiles. A sequence of Fourier, Hilbert, and inverse Fourier transform is then applied to analytically eliminate spatially dependent phase errors from the different coils while fully preserving the spatial-encoding. By combining the transform and phase correction, the original numerical image reconstruction method can be replaced by an analytical SMASH procedure (ASP). The approach also allows simulation of SMASH imaging, revealing a criterion for the ratio of the detector sensitivity profile width to the detector spacing that produces optimal harmonic generation. When detector geometry is suboptimal, a group of quasi-harmonics arises, which can be corrected and restored to pure harmonics. The simulation also reveals high-order harmonic modulation effects, and a demodulation procedure is presented that enables application of ASP to a large numbers of detectors. The method is demonstrated on a phantom and humans using a standard 4-channel phased-array MRI system. Copyright 2000 Wiley-Liss, Inc.

Impact damage imaging in a curved composite panel with wavenumber index via Riesz transform

NASA Astrophysics Data System (ADS)

Chang, Huan-Yu; Yuan, Fuh-Gwo

2018-03-01

The barely visible impact damages reduce the strength of composite structures significantly; however, they are difficult to be detected during regular visual inspection. A guided wave based damage imaging condition method is developed and applied on a curved composite panel, which is a part of an aileron from a retired Boeing C-17 Globemaster III. Ultrasonic guided waves are excited by a piezoelectric transducer (PZT) and then captured by a laser Doppler vibrometer (LDV). The wavefield images are constructed by measuring the out-of-plane velocity point by point within interrogation region, and the anomalies at the damage area can be observed with naked eye. The discontinuities of material properties leads to the change of wavenumber while the wave propagating through the damaged area. These differences in wavenumber can be observed by deriving instantaneous wave vector via Riesz transform (RT), and then be shown and highlighted with the proposed imaging condition named wavenumber index (WI). RT can be introduced as a two-dimensional (2-D) generalization of Hilbert transform (HT) to derive instantaneous phases, amplitudes, orientations of a guided-wave field. WI employs the instantaneous wave vector and weighted instantaneous wave energy computed from the instantaneous amplitudes, yielding high sensitivity and sharp damage image with computational efficiency. The BVID of the composite structure becomes therefore "visible" with the developed technique.

On reliable time-frequency characterization and delay estimation of stimulus frequency otoacoustic emissions

NASA Astrophysics Data System (ADS)

Biswal, Milan; Mishra, Srikanta

2018-05-01

The limited information on origin and nature of stimulus frequency otoacoustic emissions (SFOAEs) necessitates a thorough reexamination into SFOAE analysis procedures. This will lead to a better understanding of the generation of SFOAEs. The SFOAE response waveform in the time domain can be interpreted as a summation of amplitude modulated and frequency modulated component waveforms. The efficiency of a technique to segregate these components is critical to describe the nature of SFOAEs. Recent advancements in robust time-frequency analysis algorithms have staked claims on the more accurate extraction of these components, from composite signals buried in noise. However, their potential has not been fully explored for SFOAEs analysis. Indifference to distinct information, due to nature of these analysis techniques, may impact the scientific conclusions. This paper attempts to bridge this gap in literature by evaluating the performance of three linear time-frequency analysis algorithms: short-time Fourier transform (STFT), continuous Wavelet transform (CWT), S-transform (ST) and two nonlinear algorithms: Hilbert-Huang Transform (HHT), synchrosqueezed Wavelet transform (SWT). We revisit the extraction of constituent components and estimation of their magnitude and delay, by carefully evaluating the impact of variation in analysis parameters. The performance of HHT and SWT from the perspective of time-frequency filtering and delay estimation were found to be relatively less efficient for analyzing SFOAEs. The intrinsic mode functions of HHT does not completely characterize the reflection components and hence IMF based filtering alone, is not recommended for segregating principal emission from multiple reflection components. We found STFT, WT, and ST to be suitable for canceling multiple internal reflection components with marginal altering in SFOAE.

Eisenhart lifts and symmetries of time-dependent systems

NASA Astrophysics Data System (ADS)

Cariglia, M.; Duval, C.; Gibbons, G. W.; Horváthy, P. A.

2016-10-01

Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with n degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in n + 2 dimensions, equipped with its covariantly constant null Killing vector field. Reparametrisation of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrödinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaître and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit.

Quantum Foundations of Quantum Information

NASA Astrophysics Data System (ADS)

Griffiths, Robert

2009-03-01

The main foundational issue for quantum information is: What is quantum information about? What does it refer to? Classical information typically refers to physical properties, and since classical is a subset of quantum information (assuming the world is quantum mechanical), quantum information should--and, it will be argued, does--refer to quantum physical properties represented by projectors on appropriate subspaces of a quantum Hilbert space. All sorts of microscopic and macroscopic properties, not just measurement outcomes, can be represented in this way, and are thus a proper subject of quantum information. The Stern-Gerlach experiment illustrates this. When properties are compatible, which is to say their projectors commute, Shannon's classical information theory based on statistical correlations extends without difficulty or change to the quantum case. When projectors do not commute, giving rise to characteristic quantum effects, a foundation for the subject can still be constructed by replacing the ``measurement and wave-function collapse'' found in textbooks--an efficient calculational tool, but one giving rise to numerous conceptual difficulties--with a fully consistent and paradox free stochastic formulation of standard quantum mechanics. This formulation is particularly helpful in that it contains no nonlocal superluminal influences; the reason the latter carry no information is that they do not exist.

Quantum Measurement, Correlation, and Contextuality

NASA Astrophysics Data System (ADS)

Ozawa, Masanao

2011-03-01

The problem has long been discussed as to whether non-commuting observables are simultaneously measurable, since Heisenberg introduced the uncertainty principle in 1927. The problem was settled state-independently: Two observables are simultaneously measurable in every state if and only if the corresponding operators commute. However, the problem has been open for state-dependent formulation. Saying that two observables are nowhere commuting if there exist no common eigenstates, the problem at stake is whether nowhere commuting observable can be simultaneously measurable in a certain state. There have been two historical arguments claiming the case: (i) In an eigenstate of an observable A one can determine both the values of A and any other observable B . (ii) In an EPR state one can determine both the values of Q ⊗ 1 and P ⊗ 1 . In this talk, we give a necessary and sufficient condition for two observables to be simultaneously measurable in a given state, show that the above two cases actually satisfy the required mathematical conditions, and give a classification of all the possible simultaneous measurements of nowhere commuting observables for the Hilbert space with dimension 2. Related problems on quantum contextuality will also be discussed using a linguistic method based on quantum logic and quantum set theory.

On Birman's sequence of Hardy-Rellich-type inequalities

NASA Astrophysics Data System (ADS)

Gesztesy, Fritz; Littlejohn, Lance L.; Michael, Isaac; Wellman, Richard

2018-02-01

In 1961, Birman proved a sequence of inequalities {In }, for n ∈ N, valid for functions in C0n ((0 , ∞)) ⊂L2 ((0 , ∞)). In particular, I1 is the classical (integral) Hardy inequality and I2 is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space Hn ([ 0 , ∞)) of functions defined on [ 0 , ∞). Moreover, f ∈Hn ([ 0 , ∞)) implies f‧ ∈Hn-1 ([ 0 , ∞)); as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite b > 0, these inequalities hold on the standard Sobolev space H0n ((0 , b)). Furthermore, in all cases, the Birman constants [ (2 n - 1) ! ! ] 2 /22n in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in L2 ((0 , ∞)) (resp., L2 ((0 , b))). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail.

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.

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.

Independence and totalness of subspaces in phase space methods

NASA Astrophysics Data System (ADS)

Vourdas, A.

2018-04-01

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

Diurnal characteristics of turbulent intermittency in the Taklimakan Desert

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Enhancement of security using structured phase masked in optical image encryption on Fresnel transform domain

NASA Astrophysics Data System (ADS)

Yadav, Poonam Lata; Singh, Hukum

2018-05-01

To enhance the security in optical image encryption system and to protect it from the attackers, this paper proposes new digital spiral phase mask based on Fresnel Transform. In this cryptosystem the Spiral Phase Mask (SPM) used is a hybrid of Fresnel Zone Plate (FZP) and Radial Hilbert Mask (RHM) which makes the key strong and enhances the security. The different keys used for encryption and decryption purposed make the system much more secure. Proposed scheme uses various structured phase mask which increases the key space also it increases the number of parameters which makes it difficult for the attackers to exactly find the key to recover the original image. We have also used different keys for encryption and decryption purpose to make the system much more secure. The strength of the proposed cryptosystem has been analyzed by simulating on MATLAB 7.9.0(R2008a). Mean Square Errors (MSE) and Peak Signal to Noise Ratio (PSNR) are calculated for the proposed algorithm. The experimental results are provided to highlight the effectiveness and sustainability of proposed cryptosystem and to prove that the cryptosystem is secure for usage.

Observation of photonic states dynamics in 3-D integrated Fourier circuits

NASA Astrophysics Data System (ADS)

Flamini, Fulvio; Viggianiello, Niko; Giordani, Taira; Bentivegna, Marco; Spagnolo, Nicolò; Crespi, Andrea; Corrielli, Giacomo; Osellame, Roberto; Martin-Delgado, Miguel Angel; Sciarrino, Fabio

2018-07-01

Entanglement is a fundamental resource at the basis of quantum-enhanced performances in several applications, such as quantum algorithms and quantum metrology. In these contexts, Fourier interferometers implement a relevant class of unitary evolutions which can be embedded in a large variety of protocols. For instance, in the single-particle regime it can be adopted to implement the quantum Fourier transform, while in the multi-particle scenario it can be employed to generate quantum states possessing useful entanglement for quantum phase estimation purposes, or as a tool to verify genuine multi-photon interference. In this article, we study experimentally the dynamics of single-photon and two-photon input states during the evolution provided by a 8-mode Fourier transformation, implemented by exploiting a three-dimensional architecture enabled by the femtosecond laser micromachining technology. In such a way, we fabricated three devices to study the evolution after each step of the decomposition. We observe that the probability distributions obey a step-by-step majorization relationship, where the quantum state occupies a progressively larger portion of the Hilbert space. Such behaviour can be related to the majorization principle, which has been conjectured as a necessary condition for quantum speedup.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Empirical Wavelet Transform Based Features for Classification of Parkinson's Disease Severity.

PubMed

Oung, Qi Wei; Muthusamy, Hariharan; Basah, Shafriza Nisha; Lee, Hoileong; Vijean, Vikneswaran

2017-12-29

Parkinson's disease (PD) is a type of progressive neurodegenerative disorder that has affected a large part of the population till now. Several symptoms of PD include tremor, rigidity, slowness of movements and vocal impairments. In order to develop an effective diagnostic system, a number of algorithms were proposed mainly to distinguish healthy individuals from the ones with PD. However, most of the previous works were conducted based on a binary classification, with the early PD stage and the advanced ones being treated equally. Therefore, in this work, we propose a multiclass classification with three classes of PD severity level (mild, moderate, severe) and healthy control. The focus is to detect and classify PD using signals from wearable motion and audio sensors based on both empirical wavelet transform (EWT) and empirical wavelet packet transform (EWPT) respectively. The EWT/EWPT was applied to decompose both speech and motion data signals up to five levels. Next, several features are extracted after obtaining the instantaneous amplitudes and frequencies from the coefficients of the decomposed signals by applying the Hilbert transform. The performance of the algorithm was analysed using three classifiers - K-nearest neighbour (KNN), probabilistic neural network (PNN) and extreme learning machine (ELM). Experimental results demonstrated that our proposed approach had the ability to differentiate PD from non-PD subjects, including their severity level - with classification accuracies of more than 90% using EWT/EWPT-ELM based on signals from motion and audio sensors respectively. Additionally, classification accuracy of more than 95% was achieved when EWT/EWPT-ELM is applied to signals from integration of both signal's information.

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.

Enhancing Understanding of Transformation Matrices

ERIC Educational Resources Information Center

Dick, Jonathan; Childrey, Maria

2012-01-01

With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding. Teaching matrix transformations by focusing on row vectors gives students tools to create matrices to perform transformations. This empowerment opens many doors: Students are able to create the matrices for…

Dualities and Topological Field Theories from Twisted Geometries

NASA Astrophysics Data System (ADS)

Markov, Ruza

I will present three studies of string theory on twisted geometries. In the first calculation included in this dissertation we use gauge/gravity duality to study the Coulomb branch of an unusual type of nonlocal field theory, called Puff Field Theory. On the gravity side, this theory is given in terms of D3-branes in type IIB string theory with a geometric twist. While the field theory description, available in the IR limit, is a deformation of Yang-Mills gauge theory by an order seven operator which we here compute. In the rest of this dissertation we explore N = 4 super Yang-Mills (SYM) theory compactied on a circle with S-duality and R-symmetry twists that preserve N = 6 supersymmetry in 2 + 1D. It was shown that abelian theory on a flat manifold gives Chern-Simons theory in the low-energy limit and here we are interested in the non-abelian counterpart. To that end, we introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a two-torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory. The last result discussed in this dissertation demonstrates a connection between gravitational Chern-Simons theory and N = 4 four-dimensional SYM theory compactified on a circle twisted by S-duality where the remaining three-manifold is not flat starting with the explicit geometric realization of S-duality in terms of (2, 0) theory.

Optical sectioning microscopy using two-frame structured illumination and Hilbert-Huang data processing

NASA Astrophysics Data System (ADS)

Trusiak, M.; Patorski, K.; Tkaczyk, T.

2014-12-01

We propose a fast, simple and experimentally robust method for reconstructing background-rejected optically-sectioned microscopic images using two-shot structured illumination approach. Innovative data demodulation technique requires two grid-illumination images mutually phase shifted by π (half a grid period) but precise phase displacement value is not critical. Upon subtraction of the two frames the input pattern with increased grid modulation is computed. The proposed demodulation procedure comprises: (1) two-dimensional data processing based on the enhanced, fast empirical mode decomposition (EFEMD) method for the object spatial frequency selection (noise reduction and bias term removal), and (2) calculating high contrast optically-sectioned image using the two-dimensional spiral Hilbert transform (HS). The proposed algorithm effectiveness is compared with the results obtained for the same input data using conventional structured-illumination (SIM) and HiLo microscopy methods. The input data were collected for studying highly scattering tissue samples in reflectance mode. In comparison with the conventional three-frame SIM technique we need one frame less and no stringent requirement on the exact phase-shift between recorded frames is imposed. The HiLo algorithm outcome is strongly dependent on the set of parameters chosen manually by the operator (cut-off frequencies for low-pass and high-pass filtering and η parameter value for optically-sectioned image reconstruction) whereas the proposed method is parameter-free. Moreover very short processing time required to efficiently demodulate the input pattern predestines proposed method for real-time in-vivo studies. Current implementation completes full processing in 0.25s using medium class PC (Inter i7 2,1 GHz processor and 8 GB RAM). Simple modification employed to extract only first two BIMFs with fixed filter window size results in reducing the computing time to 0.11s (8 frames/s).

A real-time approach for heart rate monitoring using a Hilbert transform in seismocardiograms.

PubMed

Jafari Tadi, Mojtaba; Lehtonen, Eero; Hurnanen, Tero; Koskinen, Juho; Eriksson, Jonas; Pänkäälä, Mikko; Teräs, Mika; Koivisto, Tero

2016-11-01

Heart rate monitoring helps in assessing the functionality and condition of the cardiovascular system. We present a new real-time applicable approach for estimating beat-to-beat time intervals and heart rate in seismocardiograms acquired from a tri-axial microelectromechanical accelerometer. Seismocardiography (SCG) is a non-invasive method for heart monitoring which measures the mechanical activity of the heart. Measuring true beat-to-beat time intervals from SCG could be used for monitoring of the heart rhythm, for heart rate variability analysis and for many other clinical applications. In this paper we present the Hilbert adaptive beat identification technique for the detection of heartbeat timings and inter-beat time intervals in SCG from healthy volunteers in three different positions, i.e. supine, left and right recumbent. Our method is electrocardiogram (ECG) independent, as it does not require any ECG fiducial points to estimate the beat-to-beat intervals. The performance of the algorithm was tested against standard ECG measurements. The average true positive rate, positive prediction value and detection error rate for the different positions were, respectively, supine (95.8%, 96.0% and ≃0.6%), left (99.3%, 98.8% and ≃0.001%) and right (99.53%, 99.3% and ≃0.01%). High correlation and agreement was observed between SCG and ECG inter-beat intervals (r  >  0.99) for all positions, which highlights the capability of the algorithm for SCG heart monitoring from different positions. Additionally, we demonstrate the applicability of the proposed method in smartphone based SCG. In conclusion, the proposed algorithm can be used for real-time continuous unobtrusive cardiac monitoring, smartphone cardiography, and in wearable devices aimed at health and well-being applications.

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.

Is Logic in the Mind or in the World? Why a Philosophical Question can Affect the Understanding of Intelligence

NASA Astrophysics Data System (ADS)

Sommer, Hanns; Schreiber, Lothar

2012-05-01

Dreyfus' call ‘to make artificial intelligence (AI) more Heideggerian‘ echoes Heidegger's affirmation that pure calculations produce no ‘intelligence’ (Dreyfus, 2007). But what exactly is it that AI needs more than mathematics? The question in the title gives rise to a reexamination of the basic principles of cognition in Husserl's Phenomenology. Using Husserl's Phenomenological Method, a formalization of these principles is presented that provides the principal idea of cognition, and as a consequence, a ‘natural logic’. Only in a second step, mathematics is obtained from this natural logic by abstraction. The limitations of pure reasoning are demonstrated for fundamental considerations (Hilbert's ‘finite Einstellung’) as well as for the task of solving practical problems. Principles will be presented for the design of general intelligent systems, which make use of a natural logic.

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

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

Bouncing and emergent cosmologies from Arnowitt–Deser–Misner RG flows

NASA Astrophysics Data System (ADS)

Bonanno, Alfio; Gionti, S. J. Gabriele; Platania, Alessia

2018-03-01

Asymptotically safe gravity provides a framework for the description of gravity from the trans-Planckian regime to cosmological scales. According to this scenario, the cosmological constant and Newton’s coupling are functions of the energy scale whose evolution is dictated by the renormalization group (RG) equations. The formulation of the RG equations on foliated spacetimes, based on the Arnowitt–Deser–Misner (ADM) formalism, furnishes a natural way to construct the RG energy scale from the spectrum of the Laplacian operator on the spatial slices. Combining this idea with an RG improvement procedure, in this work we study quantum gravitational corrections to the Einstein–Hilbert action on Friedmann–Lemaître–Robertson–Walker backgrounds. The resulting quantum-corrected Friedmann equations can give rise to both bouncing cosmologies and emergent Universe solutions. Our bouncing models do not require the presence of exotic matter and emergent Universe solutions can be constructed for any allowed topology of the spatial slices.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

On 3-gauge transformations, 3-curvatures, and Gray-categories

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

Wang, Wei, E-mail: wwang@zju.edu.cn

In the 3-gauge theory, a 3-connection is given by a 1-form A valued in the Lie algebra g, a 2-form B valued in the Lie algebra h, and a 3-form C valued in the Lie algebra l, where (g,h,l) constitutes a differential 2-crossed module. We give the 3-gauge transformations from one 3-connection to another, and show the transformation formulae of the 1-curvature 2-form, the 2-curvature 3-form, and the 3-curvature 4-form. The gauge configurations can be interpreted as smooth Gray-functors between two Gray 3-groupoids: the path 3-groupoid P{sub 3}(X) and the 3-gauge group G{sup L} associated to the 2-crossed module L,more » whose differential is (g,h,l). The derivatives of Gray-functors are 3-connections, and the derivatives of lax-natural transformations between two such Gray-functors are 3-gauge transformations. We give the 3-dimensional holonomy, the lattice version of the 3-curvature, whose derivative gives the 3-curvature 4-form. The covariance of 3-curvatures easily follows from this construction. This Gray-categorical construction explains why 3-gauge transformations and 3-curvatures have the given forms. The interchanging 3-arrows are responsible for the appearance of terms with the Peiffer commutator (, )« less

Time frequency analysis for automated sleep stage identification in fullterm and preterm neonates.

PubMed

Fraiwan, Luay; Lweesy, Khaldon; Khasawneh, Natheer; Fraiwan, Mohammad; Wenz, Heinrich; Dickhaus, Hartmut

2011-08-01

This work presents a new methodology for automated sleep stage identification in neonates based on the time frequency distribution of single electroencephalogram (EEG) recording and artificial neural networks (ANN). Wigner-Ville distribution (WVD), Hilbert-Hough spectrum (HHS) and continuous wavelet transform (CWT) time frequency distributions were used to represent the EEG signal from which features were extracted using time frequency entropy. The classification of features was done using feed forward back-propagation ANN. The system was trained and tested using data taken from neonates of post-conceptual age of 40 weeks for both preterm (14 recordings) and fullterm (15 recordings). The identification of sleep stages was successfully implemented and the classification based on the WVD outperformed the approaches based on CWT and HHS. The accuracy and kappa coefficient were found to be 0.84 and 0.65 respectively for the fullterm neonates' recordings and 0.74 and 0.50 respectively for preterm neonates' recordings.

Calibration and compensation method of three-axis geomagnetic sensor based on pre-processing total least square iteration

NASA Astrophysics Data System (ADS)

Zhou, Y.; Zhang, X.; Xiao, W.

2018-04-01

As the geomagnetic sensor is susceptible to interference, a pre-processing total least square iteration method is proposed for calibration compensation. Firstly, the error model of the geomagnetic sensor is analyzed and the correction model is proposed, then the characteristics of the model are analyzed and converted into nine parameters. The geomagnetic data is processed by Hilbert transform (HHT) to improve the signal-to-noise ratio, and the nine parameters are calculated by using the combination of Newton iteration method and the least squares estimation method. The sifter algorithm is used to filter the initial value of the iteration to ensure that the initial error is as small as possible. The experimental results show that this method does not need additional equipment and devices, can continuously update the calibration parameters, and better than the two-step estimation method, it can compensate geomagnetic sensor error well.

Generalized quantum no-go theorems of pure states

NASA Astrophysics Data System (ADS)

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

2018-07-01

Various results of the no-cloning theorem, no-deleting theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. First, we prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes the no-cloning theorem, no-anticloning theorem, no-partial-erasure theorem, no-splitting theorem, no-superposing theorem or no-encoding theorem as a special case. Moreover, it implies various new results. Third, we extend the new theorem into another form that includes the no-deleting theorem as a special case.

Fringe-projection profilometry based on two-dimensional empirical mode decomposition.

PubMed

Zheng, Suzhen; Cao, Yiping

2013-11-01

In 3D shape measurement, because deformed fringes often contain low-frequency information degraded with random noise and background intensity information, a new fringe-projection profilometry is proposed based on 2D empirical mode decomposition (2D-EMD). The fringe pattern is first decomposed into numbers of intrinsic mode functions by 2D-EMD. Because the method has partial noise reduction, the background components can be removed to obtain the fundamental components needed to perform Hilbert transformation to retrieve the phase information. The 2D-EMD can effectively extract the modulation phase of a single direction fringe and an inclined fringe pattern because it is a full 2D analysis method and considers the relationship between adjacent lines of a fringe patterns. In addition, as the method does not add noise repeatedly, as does ensemble EMD, the data processing time is shortened. Computer simulations and experiments prove the feasibility of this method.

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

The Ablowitz–Ladik system on a finite set of integers

NASA Astrophysics Data System (ADS)

Xia, Baoqiang

2018-07-01

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

Quadrature rules with multiple nodes for evaluating integrals with strong singularities

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2006-05-01

We present a method based on the Chakalov-Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turan quadrature rules, Numer. Algorithms 10 (1995), 27-39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhauser, Basel, 1999, pp. 109-119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.

An efficient method for the calculation of mean extinction. I - The analyticity of the complex extinction efficiency of homogeneous spheres

NASA Astrophysics Data System (ADS)

Xing, Zhang-Fan; Greenberg, J. M.

1992-11-01

Results of an investigation of the analyticity of the complex extinction efficiency Q-tilde(ext) in different parameter domains are presented. In the size parameter domain, x = omega(a/c), numerical Hilbert transforms are used to study the analyticity properties of Q-tilde(ext) for homogeneous spheres. Q-tilde(ext) is found to be analytic in the entire lower complex x-tilde-plane when the refractive index, m, is fixed as a real constant (pure scattering) or infinity (perfect conductor); poles, however, appear in the left side of the lower complex x-tilde-plane as m becomes complex. The computation of the mean extinction produced by an extended size distribution of particles may be conveniently and accurately approximated using only a few values of the complex extinction evaluated in the complex plane.

An improved principal component analysis based region matching method for fringe direction estimation

NASA Astrophysics Data System (ADS)

He, A.; Quan, C.

2018-04-01

The principal component analysis (PCA) and region matching combined method is effective for fringe direction estimation. However, its mask construction algorithm for region matching fails in some circumstances, and the algorithm for conversion of orientation to direction in mask areas is computationally-heavy and non-optimized. We propose an improved PCA based region matching method for the fringe direction estimation, which includes an improved and robust mask construction scheme, and a fast and optimized orientation-direction conversion algorithm for the mask areas. Along with the estimated fringe direction map, filtered fringe pattern by automatic selective reconstruction modification and enhanced fast empirical mode decomposition (ASRm-EFEMD) is used for Hilbert spiral transform (HST) to demodulate the phase. Subsequently, windowed Fourier ridge (WFR) method is used for the refinement of the phase. The robustness and effectiveness of proposed method are demonstrated by both simulated and experimental fringe patterns.

Generalized thermalization for integrable system under quantum quench.

PubMed

Muralidharan, Sushruth; Lochan, Kinjalk; Shankaranarayanan, S

2018-01-01

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the generalized Gibbs ensemble description for this infinite-dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve toward the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a generalized Gibbs ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states that would potentially not be described by the generalized Gibbs ensemble description.

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.

A rigorous approach to the formulation of extended Born-Oppenheimer equation for a three-state system

NASA Astrophysics Data System (ADS)

Sarkar, Biplab; Adhikari, Satrajit

If a coupled three-state electronic manifold forms a sub-Hilbert space, it is possible to express the non-adiabatic coupling (NAC) elements in terms of adiabatic-diabatic transformation (ADT) angles. Consequently, we demonstrate: (a) Those explicit forms of the NAC terms satisfy the Curl conditions with non-zero Divergences; (b) The formulation of extended Born-Oppenheimer (EBO) equation for any three-state BO system is possible only when there exists coordinate independent ratio of the gradients for each pair of ADT angles leading to zero Curls at and around the conical intersection(s). With these analytic advancements, we formulate a rigorous EBO equation and explore its validity as well as necessity with respect to the approximate one (Sarkar and Adhikari, J Chem Phys 2006, 124, 074101) by performing numerical calculations on two different models constructed with different chosen forms of the NAC elements.

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.

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

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

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.

Taking Successful Programs to Scale and Creating Lasting Results

ERIC Educational Resources Information Center

National Math and Science Initiative, 2008

2008-01-01

Scaling Effective Programs is a category of giving that is quite unique. Philanthropists have many different interests that guide their giving, but Scaling Effective Programs offers an approach that can produce lasting transformation. This guide speaks to funders who: (1) view their giving as venture capital that stimulates other giving; (2) want…

From the Meticulous to the Sublime: Transformations in Ink.

ERIC Educational Resources Information Center

King, Steve

1998-01-01

Provides a lesson that gives students the opportunity to master the medium of pen and ink through a project called "Transformations." Explains that students choose two pictures, copying each one, and then combine them to create a transformation where one object transforms into the other, such as a bolt with butterfly wings. (CMK)

A hybrid approach to fault diagnosis of roller bearings under variable speed conditions

NASA Astrophysics Data System (ADS)

Wang, Yanxue; Yang, Lin; Xiang, Jiawei; Yang, Jianwei; He, Shuilong

2017-12-01

Rolling element bearings are one of the main elements in rotating machines, whose failure may lead to a fatal breakdown and significant economic losses. Conventional vibration-based diagnostic methods are based on the stationary assumption, thus they are not applicable to the diagnosis of bearings working under varying speeds. This constraint limits the bearing diagnosis to the industrial application significantly. A hybrid approach to fault diagnosis of roller bearings under variable speed conditions is proposed in this work, based on computed order tracking (COT) and variational mode decomposition (VMD)-based time frequency representation (VTFR). COT is utilized to resample the non-stationary vibration signal in the angular domain, while VMD is used to decompose the resampled signal into a number of band-limited intrinsic mode functions (BLIMFs). A VTFR is then constructed based on the estimated instantaneous frequency and instantaneous amplitude of each BLIMF. Moreover, the Gini index and time-frequency kurtosis are both proposed to quantitatively measure the sparsity and concentration measurement of time-frequency representation, respectively. The effectiveness of the VTFR for extracting nonlinear components has been verified by a bat signal. Results of this numerical simulation also show the sparsity and concentration of the VTFR are better than those of short-time Fourier transform, continuous wavelet transform, Hilbert-Huang transform and Wigner-Ville distribution techniques. Several experimental results have further demonstrated that the proposed method can well detect bearing faults under variable speed conditions.

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.

Extracting Micro-Doppler Radar Signatures from Rotating Targets Using Fourier-Bessel Transform and Time-Frequency Analysis

DTIC Science & Technology

2014-10-16

Time-Frequency analysis, Short-Time Fourier Transform, Wigner Ville Distribution, Fourier Bessel Transform, Fractional Fourier Transform. I...INTRODUCTION Most widely used time-frequency transforms are short-time Fourier Transform (STFT) and Wigner Ville distribution (WVD). In STFT, time and...frequency resolutions are limited by the size of window function used in calculating STFT. For mono-component signals, WVD gives the best time and frequency

From Winning-at-All-Costs to Give Us Back Our Game: Perspective Transformation in Youth Sport Coaches

ERIC Educational Resources Information Center

Fenoglio, Rick; Taylor, William

2014-01-01

Background: Drawing upon concepts from Mezirow's transformative learning theory, this research investigated the process of perspective transformation in three purposively sampled youth sport coaches in the UK. Perspective transformation is the process by which adults revise their culturally defined frames of reference which have arisen out of…

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.