Power Spectral Density and Hilbert Transform
2016-12-01
the Hilbert transform. 2.3 Hilbert Transform The Hilbert transform is a math function used to convert a real function into an analytic signal...domain function and symmetric Fourier transform) into an analytic signal. We then demonstrate how multiplication by a complex exponential is used...Dirac Delta Function 2 2.2 Fourier Transform 4 2.3 Hilbert Transform 5 3. Digital Signal Processing in a Software-Defined Radio 14 4. Conclusion 20 5
Computing Instantaneous Frequency by normalizing Hilbert Transform
Huang, Norden E. (Inventor)
2005-01-01
This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.
Hilbert transform algorithm in labVIEW
Directory of Open Access Journals (Sweden)
Oana Muntean
2014-12-01
Full Text Available This paper presents an alternative algorithm for Hilbert transform calculation. This algorithm was implemented in LabVIEW software. It was tested for some different elementary signals. The results were compared with the method proposed by LabVIEW programming environment of National Instruments Company.
Using Hilbert transform and classical chains to simulate quantum walks
Xiong, Daxing; Thiel, Felix; Barkai, Eli
2017-08-01
We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular quantum walks. Through this strategy, we obtain the quantum wave function from the classical evolution. Specially, this goal is achieved with the classical momenta of the particles on the chain and their Hilbert transform, from which we construct the many-body momentum and Hilbert transformed momentum pair correlation functions yielding the real and imaginary parts of the wave function, respectively. With such a wave function, we show that the classical chain's energy and heat spreading densities can be related to the wave function's modulus square. This relation provides a new perspective to understand ballistic heat transport. The results here may give a definite answer to Feynman's idea of using a classical device to simulate quantum physics.
Some Definition of Hartley-Hilbert and Fourier-Hilbert Transforms in a Quotient Space of Boehmians
S. K. Q. Al-Omari
2014-01-01
We investigate the Hartley-Hilbert and Fourier-Hilbert transforms on a quotient space of Boehmians. The investigated transforms are well-defined and linear mappings in the space of Boehmians. Further properties are also obtained.
PAIR FRAMES IN HILBERT C∗−MODULES 1. Introduction Frames ...
Indian Academy of Sciences (India)
53
results obtained for Bessel multipliers in Hilbert C∗−modules to pair frames and considering the stability of pair frames under invertible operators, we construct new pair frames and we show that pair frames are stable under small perturbations. 1. Introduction. Frames for Hilbert spaces were first introduced by Duffin and ...
Spectral analysis and Hilbert transform of aeromagnetic data over ...
African Journals Online (AJOL)
... and represents intrusive/extrusive bodies within the tectonic evolution and the preliminary assessment of the hydrocarbon generation and maturation prospects of the Upper Benue Trough. Keywords: Upper Benue trough, Fourier Transform, Hilbert Transform, sediment thickness and Crustal Structure [Global Jnl Geol. Sci.
AN EFFICIENT HILBERT AND INTEGER WAVELET TRANSFORM BASED VIDEO WATERMARKING
Directory of Open Access Journals (Sweden)
AGILANDEESWARI L.
2016-03-01
Full Text Available In this paper, an efficient, highly imperceptible, robust, and secure digital video watermarking technique for content authentication based on Hilbert transform in the Integer Wavelet Transform (IWT domain has been introduced. The Hilbert coefficients of gray watermark image are embedded into the cover video frames Hilbert coefficients on the 2-level IWT decomposed selected block on sub-bands using Principal Component Analysis (PCA technique. The authentication is achieved by using the digital signature mechanism. This mechanism is used to generate and embed a digital signature after embedding the watermarks. Since, the embedding process is done in Hilbert transform domain, the imperceptibility and the robustness of the watermark is greatly improved. At the receiver end, prior to the extraction of watermark, the originality of the content is verified through the authentication test. If the generated and received signature matches, it proves that the received content is original and performs the extraction process, otherwise deny the extraction process due to unauthenticated received content. The proposed method avoids typical degradations in the imperceptibility level of watermarked video in terms of Average Peak Signal – to – Noise Ratio (PSNR value of about 48db, while it is still providing better robustness against common video distortions such as frame dropping, averaging, and various image processing attacks such as noise addition, median filtering, contrast adjustment, and geometrical attacks such as, rotation and cropping in terms of Normalized Correlation Coefficient (NCC value of about nearly 1.
A Generalized Demodulation and Hilbert Transform Based Signal Decomposition Method
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Zhi-Xiang Hu
2017-01-01
Full Text Available This paper proposes a new signal decomposition method that aims to decompose a multicomponent signal into monocomponent signal. The main procedure is to extract the components with frequencies higher than a given bisecting frequency by three steps: (1 the generalized demodulation is used to project the components with lower frequencies onto negative frequency domain, (2 the Hilbert transform is performed to eliminate the negative frequency components, and (3 the inverse generalized demodulation is used to obtain the signal which contains components with higher frequencies only. By running the procedure recursively, all monocomponent signals can be extracted efficiently. A comprehensive derivation of the decomposition method is provided. The validity of the proposed method has been demonstrated by extensive numerical analysis. The proposed method is also applied to decompose the dynamic strain signal of a cable-stayed bridge and the echolocation signal of a bat.
The Hilbert Transform in Analysis of Uterine Contraction Activity
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Borowska Marta
2015-12-01
Full Text Available Prevention and early diagnosis of forthcoming preterm labor is of vital importance in preventing child mortality. To date, our understanding of the coordination of uterine contractions is incomplete. Among the many methods of recording uterine contractility, electrohysterography (EHG – the recording of changes in electrical potential associated with contraction of the uterine muscle, seems to be the most important from a diagnostic point of view. There is some controversy regarding whether EHG may identify patients with a high risk of preterm delivery. There is a need to check various digital signal processing techniques to describe the recorded signals. The study of synchronization of multivariate signals is important from both a theoretical and a practical point of view. Application of the Hilbert transformation seems very promising.
Directory of Open Access Journals (Sweden)
Zhi-Hai Zhuo
2017-01-01
Full Text Available This paper investigates the generalized pattern of Poisson summation formulae from the special affine Fourier transform (SAFT and offset Hilbert transform (OHT points of view. Several novel summation formulae are derived accordingly. Firstly, the relationship between SAFT (or OHT and Fourier transform (FT is obtained. Then, the generalized Poisson sum formulae are obtained based on above relationships. The novel results can be regarded as the generalizations of the classical results in several transform domains such as FT, fractional Fourier transform, and the linear canonical transform.
Noncycling mappings and best proximity pair results in Hilbert and ...
African Journals Online (AJOL)
A new class of noncyclic mappings, called generalized noncyclic relatively nonexpansive, is introduced and used to study the existence of best proximity pairs in the setting of uniformly convex Banach spaces. We also obtain a weak convergence theorem for noncyclic relatively nonexpansive mappings in the setting of ...
Phase retrieval by using the transport-of-intensity equation with Hilbert transform.
Li, Wei-Shuo; Chen, Chun-Wei; Lin, Kuo-Feng; Chen, Hou-Ren; Tsai, Chih-Ya; Chen, Chyong-Hua; Hsieh, Wen-Feng
2016-04-01
Phase recovery by solving the transport-of-intensity equation (TIE) is a non-iterative and non-interferometric phase retrieval technique. From solving the TIE with conventional, one partial derivative and Hilbert transform methods for both the periodic and aperiodic samples, we demonstrate that the Hilbert transform method can provide the smoother phase images with edge enhancement and fine structures. Furthermore, compared with the images measured by optical and atomic force microscopy, the Hilbert transform method has the ability to quantitatively map out the phase images for both the periodic and aperiodic structures.
Single-image structured illumination using Hilbert transform demodulation
Hoffman, Zachary R.; DiMarzio, Charles A.
2017-05-01
Structured illumination microscopy (SIM) achieves sectioning at depth by removing undesired light from out-of-focus planes within a specimen. However, it generally requires at least three modulated images with discrete phase shifts of 0, 120, and 240 deg to produce sectioning. Using a Hilbert transform demodulation, it is possible to produce both sectioning and depth information relative to a reference plane (i.e., a coverslip) using only a single image. The specimen is modulated at a known frequency, and the unmodulated portion of the image is estimated. These two components are used to provide a high-quality sectioned image containing both axial and lateral information of an object. The sectioning resolution with a single image is on par with that of a control three-image SIM. We are also able to show that when used with three images of discrete phase, this method produces better contrast within a turbid media than the traditional SIM technique. Because the traditional SIM requires alignment of three different phases, small differences in optical path length can introduce strong artifacts. Using the single-image technique removes this dependency, greatly improving sectioning in turbid media. Multiple targets with various depths and opaqueness are considered, including human skin in vivo, demonstrating a quick and useful way to provide noninvasive sectioning in real time.
Determination of fundamental asteroseismic parameters using the Hilbert transform
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.
Hilbert-space Karhunen-Loève transform with application to image analysis.
Levy, A; Rubinstein, J
1999-01-01
A generalization of the Karhunen-Loève (KL) transform to Hilbert spaces is developed. It allows one to find the best low-dimensional approximation of an ensemble of images with respect to a variety of distance functions other than the traditional mean square error (L2 norm). A simple and intuitive characterization of the family of Hilbert norms in finite-dimensional spaces leads to an algorithm for calculating the Hilbert-KL expansion. KL approximations of ensembles of objects and faces optimized with respect to a norm based on the modulation transfer function of the human visual system are compared with the standard L2 approximations.
Cutting force response in milling of Inconel: analysis by wavelet and Hilbert-Huang Transforms
Directory of Open Access Journals (Sweden)
Grzegorz Litak
Full Text Available We study the milling process of Inconel. By continuously increasing the cutting depth we follow the system response and appearance of oscillations of larger amplitude. The cutting force amplitude and frequency analysis has been done by means of wavelets and Hilbert-Huang transform. We report that in our system the force oscillations are closely related to the rotational motion of the tool and advocate for a regenerative mechanism of chatter vibrations. To identify vibrations amplitudes occurrence in time scale we apply wavelet and Hilbert-Huang transforms.
Zhuang, L.; Beeker, Willem; Beeker, W.P.; Leinse, Arne; Heideman, Rene; Roeloffzen, C.G.H.
2012-01-01
We propose and demonstrate a wideband photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonators allows variable and arbitrary fractional order of the Hilbert transformer. The implemented all-pass filter
DEFF Research Database (Denmark)
Vincent, Claire Louise; Giebel, Gregor; Pinson, Pierre
2010-01-01
such as the Fourier transform. The Hilbert–Huang transform is a local method based on a nonparametric and empirical decomposition of the data followed by calculation of instantaneous amplitudes and frequencies using the Hilbert transform. The Hilbert–Huang transformed 4-yr time series is averaged and summarized...... a 4-yr time series of 10-min wind speed observations. An adaptive spectral analysis method called the Hilbert–Huang transform is chosen for the analysis, because the nonstationarity of time series of wind speed observations means that they are not well described by a global spectral analysis method...... to show climatological patterns in the relationship between wind variability and time of day. First, by integrating the Hilbert spectrum along the frequency axis, a scalar time series representing the total variability within a given frequency range is calculated. Second, by calculating average spectra...
Bäcklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem
Directory of Open Access Journals (Sweden)
Alexander Sakhnovich
2007-03-01
Full Text Available A GBDT version of the Bäcklund-Darboux transformation is constructed for a non-isospectral canonical system, which plays essential role in the theory of random matrix models. The corresponding Riemann-Hilbert problem is treated and some explicit formulas are obtained. A related inverse problem is formulated and solved.
Topology optimization of pulse shaping filters using the Hilbert transform envelope extraction
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Matzen, René; Elesin, Yuriy
2011-01-01
Time domain topology optimization is applied to design pulse shaping filters. The objective function depends on the pulse envelope, which is extracted by utilizing the Hilbert transform. The gradients with respect to the topology optimization variables are derived, and the optimization methodology...
Pairs of dual Gabor frames generated by functions of Hilbert-Schmidt type
DEFF Research Database (Denmark)
Christiansen, Lasse Hjuler
2015-01-01
where each member may be written as a linear combination of integer translates of any B-spline. We introduce functions of Hilbert-Schmidt type along with a new method which allows us to associate to certain such functions finite families of recursively defined dual windows of arbitrary smoothness......We show that any two functions which are real-valued, bounded, compactly supported and whose integer translates each form a partition of unity lead to a pair of windows generating dual Gabor frames for (Formula presented.). In particular we show that any such functions have families of dual windows....... As a special case we show that any exponential B-spline has finite families of dual windows, where each member may be conveniently written as a linear combination of another exponential B-spline. Unlike results known from the literature we avoid the usual need for the partition of unity constraint in this case....
Directory of Open Access Journals (Sweden)
Isti Qomah
2017-01-01
Full Text Available Kerusakan batang rotor merupakan salah satu jenis kerusakan pada motor induksi yang dapat menyebabkan masalah serius. Kerusakan tersebut dapat mencapai 5% - 10% dari seluruh kasus gangguan motor induksi. Oleh karena itu, perlu adanya diagnosis awal yang mendeteksi adanya gangguan pada rotor motor induksi, agar dapat dilakukan perbaikan lebih cepat dan tanggap sebelum terjadi gangguan yang lebih besar. Tugas Akhir ini membahas terkait teknik deteksi kerusakan batang rotor pada motor induksi dengan menggunakan analisis arus mula. Sistem yang digunakan berbasis decomposition wavelet transform terlebih dahulu kemudian dilanjutkan dengan analisis berbasis hilbert transform sebagai perangkat pengolahan sinyal sehingga mampu mendeteksi motor dalam keadaan sehat atau mengalami kerusakan. Pengujian sistem dilakukan dalam beberapa kondisi, yaitu kondisi tanpa beban dan berbeban. Selain itu, kondisi yang diberikan adalah kecacatan mulai dai 1BRB hingga 3BRB. Hasil pengujian membuktikan bahwa decomposition wavelet transform dan Hilbert transform mampu mendeteksi perbedaan kondisi pada motor induksi normal ataupun rusak pada batang rotor.
Directory of Open Access Journals (Sweden)
V. I. Nesteruk
2013-06-01
Full Text Available A proof of nondegeneracy of the Tate pairing and Kolyvagin's formula for elliptic curves with good reductions over an $n$-dimensional ($nleq 3$ pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal field and an $n$-dimensional ($nleq 3$ pseudolocal field, and the relations of local Artin map and of the Hilbert symbol for an $n$-dimensional ($nleq 3$ general local field isgiven.
National Aeronautics and Space Administration — The three goals of this IRAD are:1.1 Research and develop the Hilbert-Huang Transform for 2D second and last component – the Hilbert Spectral Analysis for 2D...
Frequency hopping signal detection based on wavelet decomposition and Hilbert-Huang transform
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.
Identifying flight modes of Aerial Planting Projectile using Hilbert-Huang transformation
Goodarzi, H.; Sabzehparvar, M.
2017-11-01
A novel method based on Hilbert Huang Transform (HHT) for analyzing the non-linear and non-stationary of Aerial Planting Projectile (APP) flight data signal is presented. Also an image processing method is used for acquire attitude signals of projectile. Experimental test setup includes an electrical fan, high speed digital camera and projectile that the images of projectile falling down against of fan flow is captured. The frequency components of the projectile attitude signal along separation phase and free falling are complicated. Empirical Mode Decomposition (EMD) can decompose the signal into Intrinsic Mode Functions (IMFs). After a Hilbert transform, the instantaneous frequency and damping ratio of each IMF is obtained to get the physical meaning of each IMF. Analysis results indicate that the flight modes of APP are identified with high accuracy.
DEFF Research Database (Denmark)
Kragh, Knud Abildgaard; Thomsen, Jon Juel; Tcherniak, Dmitri
2010-01-01
exists. The present study suggests a framework for the detection of structural nonlinearities. Two methods for detection are compared, the homogeneity method and a Hilbert transform based method. Based on these two methods, a nonlinearity index is suggested. Through simulations and laboratory experiments......All real structures are inherently nonlinear. Whether a structure exhibits linear or nonlinear behavior, depends mainly on the excitation level. So far no unequivocal framework for experimental detection, localization, and characterization of structural nonlinearities from dynamic measurements...
Directory of Open Access Journals (Sweden)
Xueyong Liu
2014-01-01
Full Text Available Infrasound is a type of low frequency signal that occurs in nature and results from man-made events, typically ranging in frequency from 0.01 Hz to 20 Hz. In this paper, a classification method based on Hilbert-Huang transform (HHT and support vector machine (SVM is proposed to discriminate between three different natural events. The frequency spectrum characteristics of infrasound signals produced by different events, such as volcanoes, are unique, which lays the foundation for infrasound signal classification. First, the HHT method was used to extract the feature vectors of several kinds of infrasound events from the Hilbert marginal spectrum. Then, the feature vectors were classified by the SVM method. Finally, the present of classification and identification accuracy are given. The simulation results show that the recognition rate is above 97.7%, and that approach is effective for classifying event types for small samples.
New approach to ECE measurements based on Hilbert-transform spectral analysis
Directory of Open Access Journals (Sweden)
Pandya Hitesh Kumar B.
2015-01-01
Full Text Available Spectroscopy of Electron Cyclotron Emission (ECE has been established as adequate diagnostic technique for fusion research machines. Among various instruments for ECE diagnostics, only Fourier-transform spectrometers with Martin-Puplett interferometers can measure electron cyclotron radiation in a broadband frequency range from 70 to 1000 GHz. Before these measurements, a complete system including a frontend radiation collector, a transmission line, an interferometer and a radiation detector should be absolutely calibrated. A hot/cold calibration source and data-averaging technique are used to calibrate the total ECE diagnostic system. It takes long time to calibrate the ECE system because of the low power level of the calibration source and high values of the noise equivalent power (NEP of the detection system. A new technique, Hilbert-transform spectral analysis, is proposed for the ITER plasma ECE spectral measurements. An operation principle, characteristics and advantages of the corresponding Hilbert-transform spectrum analyser (HTSA based on a high-Tc Josephson detector are discussed. Due to lower NEP-values of the Josephson detector, this spectrum analyser might demonstrate shorter calibration times than that for the Martin-Puplett interferometer.
Bearing fault detection utilizing group delay and the Hilbert-Huang transform
Energy Technology Data Exchange (ETDEWEB)
Jin, Shuai; Lee, Sang-Kwon [Inha University, Incheon (Korea, Republic of)
2017-03-15
Vibration signals measured from a mechanical system are useful to detect system faults. Signal processing has been used to extract fault information in bearing systems. However, a wide vibration signal frequency band often affects the ability to obtain the effective fault features. In addition, a few oscillation components are not useful at the entire frequency band in a vibration signal. By contrast, useful fatigue information can be embedded in the noise oscillation components. Thus, a method to estimate which frequency band contains fault information utilizing group delay was proposed in this paper. Group delay as a measure of phase distortion can indicate the phase structure relationship in the frequency domain between original (with noise) and denoising signals. We used the empirical mode decomposition of a Hilbert-Huang transform to sift the useful intrinsic mode functions based on the results of group delay after determining the valuable frequency band. Finally, envelope analysis and the energy distribution after the Hilbert transform were used to complete the fault diagnosis. The practical bearing fault data, which were divided into inner and outer race faults, were used to verify the efficiency and quality of the proposed method.
CMF Signal Processing Method Based on Feedback Corrected ANF and Hilbert Transformation
Directory of Open Access Journals (Sweden)
Tu Yaqing
2014-02-01
Full Text Available In this paper, we focus on CMF signal processing and aim to resolve the problems of precision sharp-decline occurrence when using adaptive notch filters (ANFs for tracking the signal frequency for a long time and phase difference calculation depending on frequency by the sliding Goertzel algorithm (SGA or the recursive DTFT algorithm with negative frequency contribution. A novel method is proposed based on feedback corrected ANF and Hilbert transformation. We design an index to evaluate whether the ANF loses the signal frequency or not, according to the correlation between the output and input signals. If the signal frequency is lost, the ANF parameters will be adjusted duly. At the same time, singular value decomposition (SVD algorithm is introduced to reduce noise. And then, phase difference between the two signals is detected through trigonometry and Hilbert transformation. With the frequency and phase difference obtained, time interval of the two signals is calculated. Accordingly, the mass flow rate is derived. Simulation and experimental results show that the proposed method always preserves a constant high precision of frequency tracking and a better performance of phase difference measurement compared with the SGA or the recursive DTFT algorithm with negative frequency contribution
Optimization of the End Effect of Hilbert-Huang transform (HHT)
LV, Chenhuan; ZHAO, Jun; WU, Chao; GUO, Tiantai; CHEN, Hongjiang
2017-05-01
In fault diagnosis of rotating machinery, Hilbert-Huang transform (HHT) is often used to extract the fault characteristic signal and analyze decomposition results in time-frequency domain. However, end effect occurs in HHT, which leads to a series of problems such as modal aliasing and false IMF (Intrinsic Mode Function). To counter such problems in HHT, a new method is put forward to process signal by combining the generalized regression neural network (GRNN) with the boundary local characteristic-scale continuation (BLCC). Firstly, the improved EMD (Empirical Mode Decomposition) method is used to inhibit the end effect problem that appeared in conventional EMD. Secondly, the generated IMF components are used in HHT. Simulation and measurement experiment for the cases of time domain, frequency domain and related parameters of Hilbert-Huang spectrum show that the method described here can restrain the end effect compared with the results obtained through mirror continuation, as the absolute percentage of the maximum mean of the beginning end point offset and the terminal point offset are reduced from 30.113% and 27.603% to 0.510% and 6.039% respectively, thus reducing the modal aliasing, and eliminating the false IMF components of HHT. The proposed method can effectively inhibit end effect, reduce modal aliasing and false IMF components, and show the real structure of signal components accurately.
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.
Li, H. J.; Li, C. Y.; Feng, X. S.; Xiang, J.; Huang, Y. Y.; Zhou, S. D.
2017-04-01
Hilbert transforms (HT) have first been used to build the essential technique of Grad-Shafranov (GS) reconstruction by Li et al. (2013), where the problem of ill posedness in GS reconstruction has been thoroughly investigated. In this study, we present an extended Hilbert transform (EHT) over the plane rectangle. In contrast to previous one (HT over the unit circular region), corner singularities are introduced into these new formulae. It is confronted by problems like the integral with both endpoint singularities, and the semiinfinite integral with one endpoint singularity, as these EHT formulae are used to rebuild the essential technique of GS reconstruction. Two additional mathematic tools are adopted in this study. First, high-accuracy quadrature schemes are constructed for those improper integrals based on the double exponential (DE) transformations. Benchmark testing with the analytic solutions on a rectangular boundary has shown the efficiency and robustness of the EHT formulae. Second, the data completion or the inverse boundary value problem is solved with the help of a truncated Chebyshev series, which approximates the unknown boundary gradients in very high efficiency under the only assumption that they are Lipschitz continuous on each side of the rectangle. Combining the introduced EHT formulae and the two needed mathematic tools, the essential technique of GS reconstruction is formulated into a linear system of Fredholm equations of the first kind. Then a three-parameter Tikhonov regularization scheme is developed to deal with the ill-posed linear operators appearing in the discretized linear system. This new approach for data completion over the plane rectangle is benchmarked with the analytic solutions. Numerical experiments highlight the efficiency and robustness of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Goedbloed, J.P.
1982-11-01
Mathematical techniques are described that facilitate the reduction of the stability problem of a toroidal free-boundary high-..beta.. tokamak equilibrium with skin currents to one that is basically one-dimensional. This includes the conformal mapping of the simply connected plasma region onto a circular disk and the conformal mapping of the doubly connected vacuum region onto an annulus by means of the Theodorsen and Garrick nonlinear integral equations. Henrici's method of constructing the discretized Hilbert transforms for periodic functions on the boundaries of these domains provides both the basis for constructing the mappings and the tool for the study of the perturbations. The methods are applied to problems of two-dimensional potential flow with a discontinuity of which the stability of sharp-boundary high-..beta.. tokamaks is just a special case.
Goedbloed, J. P.
1982-11-01
Mathematical techniques are described that facilitate the reduction of the stability problem of a toroidal free-boundary high-β tokamak equilibrium with skin currents to one that is basically one-dimensional. This includes the conformal mapping of the simply connected plasma region onto a circular disk and the conformal mapping of the doubly connected vacuum region onto an annulus by means of the Theodorsen and Garrick nonlinear integral equations. Henrici's method of constructing the discretized Hilbert transforms for periodic functions on the boundaries of these domains provides both the basis for constructing the mappings and the tool for the study of the perturbations. The methods are applied to problems of two-dimensional potential flow with a discontinuity of which the stability of sharp-boundary high-β tokamaks is just a special case.
Xiang, Yu; Wang, Xuezhi; He, Lihua; Wang, Wenyong; Moran, William
2016-01-01
Temperature, solar radiation and water are major important variables in ecosystem models which are measurable via wireless sensor networks (WSN). Effective data analysis is necessary to extract significant spatial and temporal information. In this work, information regarding the long term variation of seasonal field environment conditions is explored using Hilbert-Huang transform (HHT) based analysis on the wireless sensor network data collection. The data collection network, consisting of 36 wireless nodes, covers an area of 100 square kilometres in Yanqing, the northwest of Beijing CBD, in China and data collection involves environmental parameter observations taken over a period of three months in 2011. The analysis used the empirical mode decomposition (EMD/EEMD) to break a time sequence of data down to a finite set of intrinsic mode functions (IMFs). Both spatial and temporal properties of data explored by HHT analysis are demonstrated. Our research shows potential for better understanding the spatial-temporal relationships among environmental parameters using WSN and HHT.
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.
Energy spectrum analysis of blast waves based on an improved Hilbert-Huang transform
Li, L.; Wang, F.; Shang, F.; Jia, Y.; Zhao, C.; Kong, D.
2017-05-01
Using the improved Hilbert-Huang transform (HHT), this paper investigates the problems of analysis and interpretation of the energy spectrum of a blast wave. It has been previously established that the energy spectrum is an effective feature by which to characterize a blast wave. In fact, the higher the energy spectra in a frequency band of a blast wave, the greater the damage to a target in the same frequency band. However, most current research focuses on analyzing wave signals in the time domain or frequency domain rather than considering the energy spectrum. We propose here an improved HHT method combined with a wavelet packet to extract the energy spectrum feature of a blast wave. When applying the HHT, the signal is first roughly decomposed into a series of intrinsic mode functions (IMFs) by empirical mode decomposition. The wavelet packet method is then performed on each IMF to eliminate noise on the energy spectrum. Second, a coefficient is introduced to remove unrelated IMFs. The energy of each instantaneous frequency can be derived through the Hilbert transform. The energy spectrum can then be obtained by adding up all the components after the wavelet packet filters and screens them through a coefficient to obtain the effective IMFs. The effectiveness of the proposed method is demonstrated by 12 groups of experimental data, and an energy attenuation model is established based on the experimental data. The improved HHT is a precise method for blast wave signal analysis. For other shock wave signals from blasting experiments, an energy frequency time distribution and energy spectrum can also be obtained through this method, allowing for more practical applications.
Madeiro, João P V; Cortez, Paulo C; Marques, João A L; Seisdedos, Carlos R V; Sobrinho, Carlos R M R
2012-11-01
The QRS detection and segmentation processes constitute the first stages of a greater process, e.g., electrocardiogram (ECG) feature extraction. Their accuracy is a prerequisite to a satisfactory performance of the P and T wave segmentation, and also to the reliability of the heart rate variability analysis. This work presents an innovative approach of QRS detection and segmentation and the detailed results of the proposed algorithm based on First-Derivative, Hilbert and Wavelet Transforms, adaptive threshold and an approach of surface indicator. The method combines the adaptive threshold, Hilbert and Wavelet Transforms techniques, avoiding the whole ECG signal preprocessing. After each QRS detection, the computation of an indicator related to the area covered by the QRS complex envelope provides the detection of the QRS onset and offset. The QRS detection proposed technique is evaluated based on the well-known MIT-BIH Arrhythmia and QT databases, obtaining the average sensitivity of 99.15% and the positive predictability of 99.18% for the first database, and 99.75% and 99.65%, respectively, for the second one. The QRS segmentation approach is evaluated on the annotated QT database with the average segmentation errors of 2.85±9.90ms and 2.83±12.26ms for QRS onset and offset, respectively. Those results demonstrate the accuracy of the developed algorithm for a wide variety of QRS morphology and the adaptation of the algorithm parameters to the existing QRS morphological variations within a single record. Copyright © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.
Fan, Gang; Zhang, Li-Min; Zhang, Jian-Jing; Ouyang, Fang
2017-09-01
Based on the Hilbert-Huang Transform and its marginal spectrum, an energy-based method is proposed to analyse the dynamics of earthquake-induced landslides and a case study is presented to illustrate the proposed method. The results show that the seismic Hilbert energy in the sliding mass of a landslide is larger than that in the sliding bed when subjected to seismic excitations, causing different dynamic responses between the sliding mass and the sliding bed. The seismic Hilbert energy transits from the high-frequency components to the low-frequency components when the seismic waves propagate through the weak zone, causing a nonuniform seismic Hilbert energy distribution in the frequency domain. Shear failure develops first at the crest and toe of the sliding mass due to resonance effects. Meanwhile, the seismic Hilbert energy in the frequency components of 3-5 Hz, which is close to the natural frequency of the slope, is largely dissipated in the initiation and failure processes of the landslide. With the development of dynamic failure, the peak energy transmission ratios in the weak zone decrease gradually. This study offers an energy-based interpretation for the initiation and progression of earthquake-induced landslides with the shattering-sliding failure type.
Multiple Harmonics Fitting Algorithms Applied to Periodic Signals Based on Hilbert-Huang Transform
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Hui Wang
2013-01-01
Full Text Available A new generation of multipurpose measurement equipment is transforming the role of computers in instrumentation. The new features involve mixed devices, such as kinds of sensors, analog-to-digital and digital-to-analog converters, and digital signal processing techniques, that are able to substitute typical discrete instruments like multimeters and analyzers. Signal-processing applications frequently use least-squares (LS sine-fitting algorithms. Periodic signals may be interpreted as a sum of sine waves with multiple frequencies: the Fourier series. This paper describes a new sine fitting algorithm that is able to fit a multiharmonic acquired periodic signal. By means of a “sinusoidal wave” whose amplitude and phase are both transient, the “triangular wave” can be reconstructed on the basis of Hilbert-Huang transform (HHT. This method can be used to test effective number of bits (ENOBs of analog-to-digital converter (ADC, avoiding the trouble of selecting initial value of the parameters and working out the nonlinear equations. The simulation results show that the algorithm is precise and efficient. In the case of enough sampling points, even under the circumstances of low-resolution signal with the harmonic distortion existing, the root mean square (RMS error between the sampling data of original “triangular wave” and the corresponding points of fitting “sinusoidal wave” is marvelously small. That maybe means, under the circumstances of any periodic signal, that ENOBs of high-resolution ADC can be tested accurately.
Liu, J.; Wang, C.
2016-12-01
The Hilbert-Huang transform (HHT) is an adaptive data analysis method that can accommodate variety of data generated by nonlinear and nonstationary processes in nature. We focus on the small geomagnetically induced current (GIC) at the local substations in low-latitude power grid of China, responding to a moderate storm on 14-18 July 2012. The HHT is applied to analyze the neutral point currents (NPCs) of transformers measured at different substations, and the GIC indices converted from local geomagnetic field measurements. The original data are decomposed into intrinsic mode functions (IMFs) using the ensemble empirical mode decomposition. After removal of the quasi-diurnal components related with the solar quiet variation, the IMFs representing storm disturbances are transformed into Hilbert energy spectra. The results show that some transformers have more or less responses to the moderate storm in the form of Hilbert energy spectra with the frequency around 2-3 mHz. A comparison on the amplitude changes of the spectra total energy of NPCs' perturbation during storm time intervals at different sites suggests that a shell type of three-phase single transformer group seems to be more vulnerable in the storm. Although the low-latitude power grids usually show very small GIC, these can be used to investigate the potential risk of space weather to the system.
Slew Bearings Damage Detection using Hilbert Huang Transformation and Acoustic Methods
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P. Nikolakopoulos
2015-06-01
Full Text Available Slow speed slew bearings are widely used in many applications such us radar, aviation and aerospace units, bogie bearings for vehicles, harbor and shipyard cranes. Slew bearings are design to carry out high axial and radial loads, they have high titling rigidity and they lubricated with grease. Slew bearings consist of the rollers, the inner and the outer ring and the gear in general. One of the most common problems arising in such equipments is the vibration levels due to wear of either regarding the rollers or the other components. Actually, it is very critical for his safe operation and reliability to know from where the vibrations come from, and how much severe are. In this article, the acoustic emission method is used in order to excite slew bearings either for laboratory tests or real naval application receiving the sound waves in the time domain. The Hilbert Huang Transformation (HHT with the empirical mode decomposition (EMD is used in order to detect the possible defect and to estimate the healthy state from the measured sound signals of the bearing, through to investigation of the statistical index kurtosis.
PET and MRI image fusion based on combination of 2-D Hilbert transform and IHS method.
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 (Dk) as an assessing spectral features and Average Gradient (AGk) 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 (AGk) and the lowest Discrepancy (Dk) 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 (AGk), Discrepancy (Dk) 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.
Segmentation of Killer Whale Vocalizations Using the Hilbert-Huang Transform
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Olivier Adam
2008-08-01
Full Text Available 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.
Segmentation of Killer Whale Vocalizations Using the Hilbert-Huang Transform
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.
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Roque A. Osornio-Rios
2013-04-01
Full Text Available 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.
Image processing with the radial Hilbert transform of photo-thermal imaging for carious detection
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.
A combinatorial filtering method for magnetotelluric time-series based on Hilbert-Huang transform
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.
Jorgensen, Palle E. T.; Pearse, Erin P. J.
2017-06-01
In a previous paper, the authors introduced the idea of a symmetric pair of operators as a way to compute self-adjoint extensions of symmetric operators. In brief, a symmetric pair consists of two densely defined linear operators A and B, with A \\subseteq B^{\\star } and B \\subseteq A^{\\star }. In this paper, we will show by example that symmetric pairs may be used to deduce closability of operators and sometimes even compute adjoints. In particular, we prove that the Malliavin derivative and Skorokhod integral of stochastic calculus are closable, and the closures are mutually adjoint. We also prove that the basic involutions of Tomita-Takesaki theory are closable and that their closures are mutually adjoint. Applications to functions of finite energy on infinite graphs are also discussed, wherein the Laplace operator and inclusion operator form a symmetric pair.
Benameur, Narjes; Caiani, Enrico Gianluca; Arous, Younes; Abdallah, Nejmeddine Ben; Kraiem, Tarek
2017-08-01
The aim of this study was to test and validate the clinical impact of parametric amplitude images obtained using the Hilbert transform on the regional interpretation of cardiac wall motion abnormalities from cine-MR images by non-expert radiologists compared with expert consensus. Cine-MRI short-axis images obtained in 20 patients (10 with myocardial infarction, 5 with myocarditis and 5 with normal function) were processed to compute a parametric amplitude image for each using the Hilbert transform. Two expert radiologists blindly reviewed the cine-MR images to define a gold standard for wall motion interpretation for each left ventricular sector. Two non-expert radiologists reviewed and graded the same images without and in combination with parametric images. Grades assigned to each segment in the two separate sessions were compared with the gold standard. According to expert interpretation, 264/320 (82.5%) segments were classified as normal and 56/320 (17.5%) were considered abnormal. The accuracy of the non-expert radiologists' grades compared to the gold standard was significantly improved by adding parametric images (from 87.2 to 94.6%) together with sensitivity (from 64.29 to 84.4%) and specificity (from 92 to 96.9%), also resulting in reduced interobserver variability (from 12.8 to 5.6%). The use of parametric amplitude images based on the Hilbert transform in conjunction with cine-MRI was shown to be a promising technique for improvement of the detection of left ventricular wall motion abnormalities in less expert radiologists.
Hilbert-Huang transform based instrumental assessment of intention tremor in multiple sclerosis
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
Mohammed, Arshed Abdulhamed; Haris, Sallehuddin Mohamed; Nuawi, Mohd Zaki
2016-02-01
This study is one of the first to report on the use of Hilbert-Huang transform (HHT) to determine the modulus of elasticity of a material, which is one of the most important properties of metals. In addition, this study involves an analytical study of the process of transfer of energy, which was represented in the form of intrinsic mode functions (IMFs). Moreover, the distribution of IMFs within the time-frequency-plain was determined by testing eight test specimens. Five test specimens were refractory materials, namely, Ti, Ti6AL4V, Zr, Nb, and Ta, and the other three were non-refractory materials, namely, Al, Brass, and ST4340. The new setup was composed of Mg and involves the use of two piezoelectric transducers, which were used as the emitter and receiver. The setup was designed and implemented in this research based on Mg usage to test the metals. First, a new relationship was derived between the pressure transmission coefficient (PTC) of the transmitted wave (through the emitter-water-test specimen-Mg to the receiver) and the corresponding values of the product of the density (ρ) and the modulus of elasticity (E) for the same test specimen. Another relationship was established between the PTCs and the total energy transmitted at high frequencies. This energy indicates the summation of IMFs that have high frequencies (THIMFs), higher than 10 kHz, can determine E better than TOF for most test specimens. To verify this results, with regard to the second conclusion, a new simulation for this setup was carried out using Simulink in MATLAB. Twelve theoretical tests were done, for high acoustic impedance metals, like Hf, Mo, WNiFe and W in addition to test the same group which was tested experimentally. The results of theoretical tests supported the experimental results except for Nb. Most of the conclusions were obtained through practical results and analytical studies. The results proved that THIMFs can determine the change in the microstructure of the alloys
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.
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.
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Lili Chen
2017-01-01
Full Text Available 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.
Paired Straight Hearth Furnace - Transformational Ironmaking Process
Energy Technology Data Exchange (ETDEWEB)
Lu, Wei-Kao [McMaster Univ., Hamilton, ON (Canada); Debski, Paul [Andritz Metals Inc.,Canonsburg, PA (United States)
2014-11-19
The U. S. steel industry has reduced its energy intensity per ton of steel shipped by 33% since 1990. However, further significant gains in energy efficiency will require the development of new, transformational iron and steelmaking processes. The Paired Straight Hearth Furnace (PSH) process is an emerging alternative high productivity, direct reduced iron (DRI) technology that may achieve very low fuel rates and has the potential to replace blast furnace ironmaking. The PSH furnace can operate independently or may be coupled with other melting technologies to produce liquid hot metal that is both similar to blast furnace iron and suitable as a feedstock for basic oxygen steelmaking furnaces. The PSH process uses non-metallurgical coal as a reductant to convert iron oxides such as iron ore and steelmaking by-product oxides to DRI pellets. In this process, a multi-layer, nominally 120mm tall bed of composite “green balls” made from oxide, coal and binder is built up and contained within a moving refractory hearth. The pellet bed absorbs radiant heat energy during exposure to the high temperature interior refractory surfaces of the PSH while generating a strongly reducing gas atmosphere in the bed that yields a highly metalized DRI product. The PSH concept has been well tested in static hearth experiments. A moving bed design is being developed. The process developers believe that if successful, the PSH process has the potential to replace blast furnaces and coke ovens at a fraction of the operating and capital cost while using about 30% less energy relative to current blast furnace technology. DRI output could also feed electric arc furnaces (EAFs) by displacing a portion of the scrap charge.
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Huile Xu
2016-12-01
Full Text Available 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.
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.
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Unger Laura Anna
2015-09-01
Full Text Available This work aimed at the detection of rotor centers within the atrial cavity during atrial fibrillation on the basis of phase singularities. A voxel based method was established which employs the Hilbert transform and the phase of unipolar electrograms. The method provides a 3D overview of phase singularities at the endocardial surface and within the blood volume. Mapping those phase singularities from the inside of the atria at the endocardium yielded rotor center trajectories. We discuss the results for an unstable and a more stable rotor. The side length of the areas covered by the trajectories varied from 1.5 mm to 10 mm. These results are important for cardiologists who target rotors with RF ablation in order to cure atrial fibrillation.
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.
Ortiz P., D.; Villa, Luisa F.; Salazar, Carlos; Quintero, O. L.
2016-04-01
A simple but efficient voice activity detector based on the Hilbert transform and a dynamic threshold is presented to be used on the pre-processing of audio signals. The algorithm to define the dynamic threshold is a modification of a convex combination found in literature. This scheme allows the detection of prosodic and silence segments on a speech in presence of non-ideal conditions like a spectral overlapped noise. The present work shows preliminary results over a database built with some political speech. The tests were performed adding artificial noise to natural noises over the audio signals, and some algorithms are compared. Results will be extrapolated to the field of adaptive filtering on monophonic signals and the analysis of speech pathologies on futures works.
Wu, Jiandong; Huang, Ruodong; Wan, Jiadong; Chen, Yading; Yin, Yi; Chen, George
2016-04-01
Data processing (i.e. phase identification) using the instantaneous phase φ‧(t) defined by the Hilbert transform is discussed to confirm the detecting phase of the space charge observed by the pulsed electroacoustic method under the periodic wave V a (t). The discrete voltage V a (i) of the periodic wave at the detecting phase φ(i) is used for phase identification, and φ(i) is equally distributed to obtain N p divisions for the phase within one period. The accuracy of the discrete instantaneous phase φ‧(i) is significantly determined by the number of samples N for the discrete voltage V a (i). The instantaneous phase is consistent with the real phase of pure sine and cosine waves, and this phase linearly varies with time. However, the instantaneous phase non-linearly varies with time under the periodic stress of arbitrary waveforms. This limitation can be resolved using the base wave component, i.e. sine or cosine wave of V a (t), which is acquired by the Fourier transform. Finally, the space charge behaviour in low-density polyethylene under square and sine waves with offset is detected to verify the accuracy and effectiveness of the proposed method.
Assessment of vocal cord nodules: a case study in speech processing by using Hilbert-Huang Transform
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.
Sgouros, G.; Helmis, C. G.
2009-04-01
The Low Level Jet (LLJ) is a common feature of the vertical structure of the Atmospheric Boundary Layer (ABL) that affects the meteorology and the local climate of an area, while it is important for aviation safety, wind energy and air quality applications. Low Level Jets have been associated mainly with the local topography and/or a large scale horizontal temperature contrast causing baroclinicity in the ABL, the diurnal heating cycle over sloping terrain, the mid-latitude fronts, the frontogenesis, the baroclinicity near coastal regions and the frictional decoupling. The purpose of this work is to investigate the interaction of the physical processes characterized by different time scales and identify the way they affect the characteristics and the evolution of the LLJ. The complex topographic features of the experimental area (Messogia Plain in Attica, Greece) and the vicinity with the sea, introduces, under favorable synoptic conditions, a variety of local circulations like land - sea breezes, katabatic and anabatic flows, phenomena that could provide a strong imprint on the wind components and affect the shape and behavior of LLJs. The selected event is a representative case of a post-frontal LLJ mainly observed during spring, summer and early autumn days at this area, characterized by clear skies or scattered cloudiness and strong diurnal temperature ranges. It is shown that these LLJ events are a result of the interaction of the synoptic scale with the local diurnal circulations which produces an oscillating core and highly fluxionary depth within the period of the diurnal cycle. In order to reveal the character of the observed wind variations during the LLJ event, the Hilbert-Huang Transform (HHT) algorithm is applied to SODAR wind speed data, at different levels. The HHT algorithm is an adaptive and empirically based data analysis method, well-suited for the study of intermittent and non-stationary processes that take place within the ABL. It consists of
Directory of Open Access Journals (Sweden)
Ning Wu
2013-01-01
Full Text Available Smart wireless sensors have been recognized as a promising technology to overcome many inherent difficulties and limitations associated with traditional wired structural health monitoring (SHM systems. Despite the advances in smart sensor technologies, on-board computing capability of smart sensors has been considered as one of the most difficult challenges in the application of the smart sensors in SHM. Taking the advantage of recent developments in microprocessor which provides powerful on-board computing functionality for smart sensors, this paper presents a new decentralized data processing approach for modal identification using the Hilbert-Huang transform (HHT algorithm, which is based on signal decomposition technique. It is shown that this method is suitable for implementation in the intrinsically distributed computing environment found in wireless smart sensor networks (WSSNs. The HHT-based decentralized data processing is, then, programmed and implemented on the Crossbow IRIS mote sensor platform. The effectiveness of the proposed techniques is demonstrated through a set of numerical studies and experimental validations on an in-house cable-stayed bridge model in terms of the accuracy of identified dynamic properties.
Lee, Jongsuh; Hussain, Syed Hassaan; Wang, Semyung; Park, Kyihwan
2014-09-01
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 analysis 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.
Altan, Gokhan; Kutlu, Yakup; Allahverdi, Novruz
2016-12-01
Congestive heart failure (CHF) is a degree of cardiac disease occurring as a result of the heart's inability to pump enough blood for the human body. In recent studies, coronary artery disease (CAD) is accepted as the most important cause of CHF. This study focuses on the diagnosis of both the CHF and the CAD. The Hilbert-Huang transform (HHT), which is effective on non-linear and non-stationary signals, is used to extract the features from R-R intervals obtained from the raw electrocardiogram data. The statistical features are extracted from instinct mode functions that are obtained applying the HHT to R-R intervals. Classification performance is examined with extracted statistical features using a multilayer perceptron neural network. The designed model classified the CHF, the CAD patients and a normal control group with rates of 97.83%, 93.79% and 100%, accuracy, specificity and sensitivity, respectively. Also, early diagnosis of the CHF was performed by interpretation of the CAD with a classification accuracy rate of 97.53%, specificity of 98.18% and sensitivity of 97.13%. As a result, a single system having the ability of both diagnosis and early diagnosis of CHF is performed by integrating the CAD diagnosis method to the CHF diagnosis method. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Wu, T. Y.; Chen, J. C.; Wang, C. C.
2012-07-01
The objective of this research is to investigate the feasibility of utilizing the instantaneous dimensionless frequency (DLF) normalization and Hilbert-Huang Transform (HHT) to characterize the different gear faults in case of variable rotating speed. The normalized DLF of the vibration signals are calculated based on the rotating speed of shaft and the instantaneous frequencies of Intrinsic Mode Functions (IMFs) which are decomposed by Empirical Mode Decomposition (EMD) process. The faulty gear features on DLF-energy distribution of vibration signal can be extracted without the presence of shaft rotating speed, so that the proposed approach can be applied for characterizing the malfunctions of gearbox system under variable shaft rotating speed. A test rig of gear transmission system is performed to illustrate the gear faults, including worn tooth, broken tooth and gear unbalance. Different methods to determine the instantaneous frequency are employed to verify the consistence of characterization results. The DLF-energy distributions of vibration signals are investigated in different faulty gear conditions. The analysis results demonstrate the capability and effectiveness of the proposed approach for characterizing the gear malfunctions at the DLFs corresponding to the meshing frequency as well as the shaft rotating frequency. The support vector machine (SVM) is then employed to classify the vibration patterns of gear transmission system at different malfunctions. Using the energy distribution at the characteristic DLFs as the features, the different fault types of gear can be identified by SVM with high accuracy.
Tong, Jian-Hua; Chiu, Chin-Lung; Wang, Chung-Yue
2010-11-01
A useful nondestructive testing tool for civil engineering should immediately reveal defects inside concrete structures at the construction sites. To date, there are few effective methods to image defects inside concrete structures. In this paper, a new nondestructive testing method using elastic waves for imaging possible defects inside concrete is developed. This method integrates the point-source/point receiver scheme with the synthetic aperture focusing technique (SAFT) to increase functioning depth and enhance received signals. To improve image quality, received signals are processed by Hilbert-Huang transform (HHT) to get time-frequency curves for the SAFT process. Compared with conventional SAFT method processing with time-amplitude signals, this new method is capable of providing a better image of defects not only in the numerical simulation but also in the experimental result. The image can reveal the number of defects and their locations and front-end profiles. The results shown in this paper indicate that this new elastic-wave-based method exhibits high capability in imaging the defects of in situ concrete structures.
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
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Wei-Ren Chuang
2010-01-01
Full Text Available Effects of continuous low-dose epidural bupivacaine (0.05-0.1% infusion on the Doppler velocimetry for labor analgesia have been well documented. The aim of this study was to monitor the activity of the autonomic nervous system (ANS for women in labor based on Hilbert Huang transform (HHT, which performs signal processing for nonlinear systems, such as human cardiac systems. Thirteen pregnant women were included in the experimental group for labor analgesia. They received continuous epidural bupivacaine 0.075% infusion. The normal-to-normal intervals (NN-interval were downloaded from an ECG holter. Another 20 pregnant women in non-anesthesia labor (average gestation age was 38.6 weeks were included in the comparison group. In this study, HHT was used to decompose components of ECG signals, which reflect three different frequency bands of a person's heart rate spectrum (viz. high frequency (HF, low frequency (LF and very low frequency (VLF. It was found that the change of energy in subjects without anesthesia was more active than that with continuous epidural bupivacaine 0.075% infusion. The energy values of the experimental group (i.e., labor analgesia of HF and LF of ANS activities were significantly lower (P < 0.05 than the values of the comparison group (viz. labor without analgesia, but the trend of energy ratio of LF/HF was opposite. In conclusion, the sympathetic and parasympathetic components of ANS are all suppressed by continuous low-dose epidural bupivacaine 0.075% infusion, but parasympathetic power is suppressed more than sympathetic power.
Determination of phase derivatives from a single fringe pattern using Teager Hilbert Huang transform
Deepan, B.; Quan, C.; Tay, C. J.
2016-01-01
In this paper, a novel sequential algorithm for the estimation of phase derivatives from a single fringe pattern using electronic speckle pattern interferometry (ESPI) is proposed. The algorithm is based on empirical mode decomposition (EMD), vortex operator (VO) and Teager-Kaiser energy operator (TKEO). The empirical mode decomposition normalizes the fringe pattern; while vortex operator provides a 2D complex image and the phase derivatives are obtained using a novel image demodulation method called discrete higher order image demodulation algorithm (DHODA). Unlike phase shifting and Fourier transform methods, the proposed method does not require complex experimental setup or more than one fringe pattern for each deformation state. The proposed method is also able to provide phase derivatives in both the x and ydirections from a single fringe pattern, which is difficult to achieve using shearography. Since the algorithm provides unwrapped phase derivatives directly, it does not require separate phase unwrapping process. Hence it is suitable for dynamic strain and curvature measurement. The proposed algorithm is validated by both simulation and experiment. The results are found to be accurate and the method requires less computation time than existing phase demodulation techniques.
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Morteza Behnam
2015-08-01
Full Text Available Seizure detection using brain signal (EEG analysis is the important clinical methods in drug therapy and the decisions before brain surgery. In this paper, after signal conditioning using suitable filtering, the Gamma frequency band has been extracted and the other brain rhythms, ambient noises and the other bio-signal are canceled. Then, the wavelet transform of brain signal and the map of wavelet transform in multi levels are computed. By dividing the color map to different epochs, the histogram of each sub-image is obtained and the statistics of it based on statistical momentums and Negentropy values are calculated. Statistical feature vector using Principle Component Analysis (PCA is reduced to one dimension. By EMD algorithm and sifting procedure for analyzing the data by Intrinsic Mode Function (IMF and computing the residues of brain signal using spectrum of Hilbert transform and Hilbert – Huang spectrum forming, one spatial feature based on the Euclidian distance for signal classification is obtained. By K-Nearest Neighbor (KNN classifier and by considering the optimal neighbor parameter, EEG signals are classified in two classes, seizure and non-seizure signal, with the rate of accuracy 76.54% and with variance of error 0.3685 in the different tests.
Boehm, Kevin M.; Wang, Shijun; Burtt, Karen E.; Turkbey, Baris; Weisenthal, Samuel; Pinto, Peter; Choyke, Peter; Wood, Bradford J.; Petrick, Nicholas; Sahiner, Berkman; Summers, Ronald M.
2015-03-01
In computer-aided diagnosis (CAD) systems for prostate cancer, dynamic contrast enhanced (DCE) magnetic resonance imaging is useful for distinguishing cancerous and benign tissue. The Tofts physiological model is a commonly used representation of the DCE image data, but the parameters require extensive computation. Hence, we developed an alternative representation based on the Hilbert transform of the DCE images. The time maximum of the Hilbert transform, a binary metric of early enhancement, and a pre-DCE value was assigned to each voxel and appended to a standard feature set derived from T2-weighted images and apparent diffusion coefficient maps. A cohort of 40 patients was used for training the classifier, and 20 patients were used for testing. The AUC was calculated by pooling the voxel-wise prediction values and comparing with the ground truth. The resulting AUC of 0.92 (95% CI [0.87 0.97]) is not significantly different from an AUC calculated using Tofts physiological models of 0.92 (95% CI [0.87 0.97]), as validated by a Wilcoxon signed rank test on each patient's AUC (p = 0.19). The time required for calculation and feature extraction is 11.39 seconds (95% CI [10.95 11.82]) per patient using the Hilbert-based feature set, two orders of magnitude faster than the 1319 seconds (95% CI [1233 1404]) required for the Tofts parameter-based feature set (p<0.001). Hence, the features proposed herein appear useful for CAD systems integrated into clinical workflows where efficiency is important.
Sun, Hong-Mei; Jia, Rui-Sheng; Du, Qian-Qian; Fu, You
2016-06-01
A micro-seismic signal's transient features are non-stationary. The traditional weighted generalized cross-correlation (GCC) algorithm is based on the cross-power spectrum density. This algorithm diminishes the performance of the time delay estimation for homologous micro-seismic signals. This paper analyzed the influence of calculation error on the cross-power spectrum density of a non-stationary signal and proposed a new cross-correlation analysis and time delay estimation method for homologous micro-seismic signals based on the Hilbert-Huang transform (HHT). First, the original signals are decomposed into intrinsic mode function (IMF) components using empirical mode decomposition (EMD) for de-noising. Subsequently, the IMF components and the original signals are analyzed using a cross-correlation analysis. The IMF components are subsequently remodeled at different scales using the Hilbert transform. The marginal spectrum density is obtained via a time integration of the remodeled components. The cross-marginal spectrum density of the two signals can also be obtained. Finally, the cross-marginal spectrum density is used in the weighted GCC algorithm for time delay estimation instead of the cross-power spectrum density. The time delay estimation is determined by searching for the weighted GCC function peak. The experiments demonstrated the superior time delay estimation performance of the new method for non-stationary transient signals. Therefore, a new time delay estimation method for non-stationary random signals is presented in this paper.
Continuous unitary transformation approach to pairing interactions in statistical physics
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T.Domański
2008-06-01
Full Text Available We apply the flow equation method to the study of the fermion systems with pairing interactions which lead to the BCS instability signalled by the appearance of the off-diagonal order parameter. For this purpose we rederive the continuous Bogoliubov transformation in a fashion of renormalization group procedure where the low and high energy sectors are treated subsequently. We further generalize this procedure to the case of fermions interacting with the discrete boson mode. Andreev-type interactions are responsible for developing a gap in the excitation spectrum. However, the long-range coherence is destroyed due to strong quantum fluctuations.
Lin, Chin-Feng; Su, Jiun-Yi; Wang, Hao-Min
2015-09-01
Chronic alcoholism may damage the central nervous system, causing imbalance in the excitation-inhibition homeostasis in the cortex, which may lead to hyper-arousal of the central nervous system, and impairments in cognitive function. In this paper, we use the Hilbert-Huang transformation (HHT) method to analyze the electroencephalogram (EEG) signals from control and alcoholic observers who watched two different pictures. We examined the intrinsic mode function (IMF) based energy distribution features of FP1, FP2, and Fz EEG signals in the time and frequency domains for alcoholics. The HHT-based characteristics of the IMFs, the instantaneous frequencies, and the time-frequency-energy distributions of the IMFs of the clinical FP1, FP2, and Fz EEG signals recorded from normal and alcoholic observers who watched two different pictures were analyzed. We observed that the number of peak amplitudes of the alcoholic subjects is larger than that of the control. In addition, the Pearson correlation coefficients of the IMFs, and the energy-IMF distributions of the clinical FP1, FP2, and Fz EEG signals recorded from normal and alcoholic observers were analyzed. The analysis results show that the energy ratios of IMF4, IMF5, and IMF7 waves of the normal observers to the refereed total energy were larger than 10 %, respectively. In addition, the energy ratios of IMF3, IMF4, and IMF5 waves of the alcoholic observers to the refereed total energy were larger than 10 %. The FP1 and FP2 waves of the normal observers, the FP1 and FP2 waves of the alcoholic observers, and the FP1 and Fz waves of the alcoholic observers demonstrated extremely high correlations. On the other hand, the FP1 waves of the normal and alcoholic observers, the FP1 wave of the normal observer and the FP2 wave of the alcoholic observer, the FP1 wave of the normal observer and the Fz wave of the alcoholic observer, the FP2 waves of the normal and alcoholic FP2 observers, and the FP2 wave of the normal observer and
Evolving matched filter transform pairs for satellite image processing
Peterson, Michael R.; Horner, Toby; Moore, Frank
2011-06-01
Wavelets provide an attractive method for efficient image compression. For transmission across noisy or bandwidth limited channels, a signal may be subjected to quantization in which the signal is transcribed onto a reduced alphabet in order to save bandwidth. Unfortunately, the performance of the discrete wavelet transform (DWT) degrades at increasing levels of quantization. In recent years, evolutionary algorithms (EAs) have been employed to optimize wavelet-inspired transform filters to improve compression performance in the presence of quantization. Wavelet filters consist of a pair of real-valued coefficient sets; one set represents the compression filter while the other set defines the image reconstruction filter. The reconstruction filter is defined as the biorthogonal inverse of the compression filter. Previous research focused upon two approaches to filter optimization. In one approach, the original wavelet filter is used for image compression while the reconstruction filter is evolved by an EA. In the second approach, both the compression and reconstruction filters are evolved. In both cases, the filters are not biorthogonally related to one another. We propose a novel approach to filter evolution. The EA optimizes a compression filter. Rather than using a wavelet filter or evolving a second filter for reconstruction, the reconstruction filter is computed as the biorthogonal inverse of the evolved compression filter. The resulting filter pair retains some of the mathematical properties of wavelets. This paper compares this new approach to existing filter optimization approaches to determine its suitability for the optimization of image filters appropriate for defense applications of image processing.
Hilbert space theory of classical electrodynamics
Indian Academy of Sciences (India)
... prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commutingobservables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of the much recent work on quantum-like features exhibited ...
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Chin-Ping Hu
2013-06-01
Full Text Available We present the Hilbert-Huang transform (HHT analysis on the quasi-periodic modulation of SMC X-1. SMC X-1, consisting of a neutron star and a massive companion, exhibits superorbital modulation with a period varying between ~40 d and ~65 d. We applied the HHT on the light curve observed by the All-Sky Monitor onboard Rossi X-ray Timing Explorer (RXTE to obtain the instantaneous frequency of the superorbital modulation of SMC X-1. The resultant Hilbert spectrum is consistent with the dynamic power spectrum while it shows more detailed information in both the time and frequency domains. According to the instantaneous frequency, we found a correlation between the superorbital period and the modulation amplitude. Combining the spectral observation made by the Proportional Counter Array onboard RXTE and the superorbital phase derived in the HHT, we performed a superorbital phase-resolved spectral analysis of SMC X-1. An analysis of the spectral parameters versus the orbital phase for different superorbital states revealed that the diversity of nH has an orbital dependence. Furthermore, we obtained the variation in the eclipse profiles by folding the All Sky Monitor light curve with orbital period for different superorbital states. A dip feature, similar to the pre-eclipse dip of Her X-1, can be observed only in the superorbital ascending and descending states, while the width is anti-correlated with the X-ray flux.
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.
Zhang, Juwei; Tan, Xiaojiang; Zheng, Pengbo
2017-03-16
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.
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Juwei Zhang
2017-03-01
Full Text Available 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.
Iqbal, M.
2002-01-01
In this paper we have converted the Laplace transform into an integral equation of the first kind of convolution type, which is an ill-posed problem, and used a statistical regularization method to solve it. The method is applied to three examples. It gives a good approximation to the true solution and compares well with the method given by…
Rigged Hilbert spaces and contractive families of Hilbert spaces
Bellomonte, Giorgia; Trapani, Camillo
2013-01-01
The existence of a rigged Hilbert space whose extreme spaces are, respectively, the projective and the inductive limit of a directed contractive family of Hilbert spaces is investigated. It is proved that, when it exists, this rigged Hilbert space is the same as the canonical rigged Hilbert space associated to a family of closable operators in the central Hilbert space.
Tool Wear Feature Extraction Based on Hilbert Marginal Spectrum
Guan, Shan; Song, Weijie; Pang, Hongyang
2017-09-01
In the metal cutting process, the signal contains a wealth of tool wear state information. A tool wear signal’s analysis and feature extraction method based on Hilbert marginal spectrum is proposed. Firstly, the tool wear signal was decomposed by empirical mode decomposition algorithm and the intrinsic mode functions including the main information were screened out by the correlation coefficient and the variance contribution rate. Secondly, Hilbert transform was performed on the main intrinsic mode functions. Hilbert time-frequency spectrum and Hilbert marginal spectrum were obtained by Hilbert transform. Finally, Amplitude domain indexes were extracted on the basis of the Hilbert marginal spectrum and they structured recognition feature vector of tool wear state. The research results show that the extracted features can effectively characterize the different wear state of the tool, which provides a basis for monitoring tool wear condition.
Sheen, Yuh-Tay
2009-07-01
In this paper, the Morlet wavelet is studied to apply in the envelope analysis for the bearing vibration and, in practice, would be easier to apply in the real-time vibration analyses. The parameter designation of Morlet wavelet is proposed to filter out and demodulate one of the resonance modes of a bearing vibration, but the designation of the filtering passband would not be required. Therefore, the mode vibration and its corresponding envelope could be derived from the real part and the absolute value of the wavelet transform, respectively. In addition, the Morlet wavelet with properly designating the parameters possesses a very excellent property of fast waveform convergence and could effectively reduce the computing burden. From theoretical and experimental studies, it is shown that the designation of Morlet wavelet could be effectively applied in the envelope detection for the vibration signals and could be useful in the defect diagnosis of bearing vibrations.
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Amauri Amorin Assef
2018-01-01
Full Text Available Abstract Introduction Although the envelope detection is a widely used method in medical ultrasound (US imaging to demodulate the amplitude of the received echo signal before any back-end processing, novel hardware-based approaches have been proposed for reducing its computational cost and complexity. In this paper, we present the modeling and FPGA implementation of an efficient envelope detector based on a Hilbert Transform (HT approximation for US imaging applications. Method The proposed model exploits both the symmetry and the alternating zero-valued coefficients of a HT finite impulse response (FIR filter to generate the in-phase and quadrature components that are necessary for the envelope computation. The hardware design was synthesized for a Stratix IV FPGA, by using the Simulink and the integrated DSP Builder toolbox, and implemented on a Terasic DE4-230 board. The accuracy of our algorithm was evaluated by the normalized root mean square error (NRMSE cost function in comparison with the conventional method based on the absolute value of the discrete-time analytic signal via FFT. Results An excellent agreement was achieved between the theoretical simulations with the experimental result. The NRMSE was 0.42% and the overall FPGA utilization was less than 1.5%. Additionally, the proposed envelope detector is capable of generating envelope data at every FPGA clock cycle after 19 (0.48 µs cycles of latency. Conclusion The presented results corroborate the simplicity, flexibility and efficiency of our model for generating US envelope data in real-time, while reducing the hardware cost by up to 75%.
Nested Hilbert schemes on surfaces: Virtual fundamental class
DEFF Research Database (Denmark)
Gholampour, Amin; Sheshmani, Artan; Yau, Shing-Tung
We construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants of Durr-Kabanov-Okonek and the stable pair invariants of Kool......-Thomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial...
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Xiao Yu
2015-11-01
Full Text Available 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
Yu, Xiao; Ding, Enjie; Chen, Chunxu; Liu, Xiaoming; Li, Li
2015-01-01
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
Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm
Brenner, Martin J.; Prazenica, Chad
2006-01-01
This report investigates the utility of the Hilbert Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this report is to demonstrate the potential applications of the Hilbert Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F-18 Active Aeroelastic Wing airplane, an Aerostructures Test Wing, and pitch plunge simulation.
2013-01-01
David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations. Ten essays are devoted to the analysis of classical as well as modern proof theory; three papers on the mathematical roots of Hilbert's work precede the analytical core, and three final essays exploit an open philosophical horizon for reflection on the nature of mathematics in the 21st century.
Hilbert Spaces from Path Integrals
Dowker, Fay; Johnston, Steven; Sorkin, Rafael D.
2010-01-01
It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown that the History Hilbert space is the standard Hilbert space in the case of non-relativistic quantum mechanics.
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.
Frames and bases in tensor products of Hilbert spaces and Hilbert C ...
Indian Academy of Sciences (India)
In this article, we study tensor product of Hilbert *-modules and Hilbert spaces. We show that if is a Hilbert -module and is a Hilbert -module, then tensor product of frames (orthonormal bases) for and produce frames (orthonormal bases) for Hilbert A ⊗ B -module E ⊗ F , and we get more results. For Hilbert ...
Hilbert-type inequalities for Hilbert space operators | Krnic ...
African Journals Online (AJOL)
In this paper we establish a general form of the Hilbert inequality for positive invertible operators on a Hilbert space. Special emphasis is given to such inequalities with homogeneous kernels. In some general cases the best possible constant factors are also derived. Finally, we obtain the improvement of previously deduced ...
Basis-neutral Hilbert-space analyzers.
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
2017-03-27
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.
Skilling, John
2004-04-01
The aim is to compute random samples from the posterior probability distribution for some object, modelled as a mixture distribution with a variable number of component "atoms", usually having relatively few attributes. We use a space-filling curve (specifically the Hilbert curve) to parameterise an atom's attributes by a single number, This simplifies the geometry, and we describe seven "engines" (LifeStory1&2, GuidedWalk, Leapfrog1&2, Chameleon1&2) for driving a MCMC exploration program. A binary variant of slice sampling underlies the engines.
The Ubiquity of Smooth Hilbert Schemes
Staal, Andrew P.
2017-01-01
We investigate the geography of Hilbert schemes that parametrize closed subschemes of projective space with a specified Hilbert polynomial. We classify Hilbert schemes with unique Borel-fixed points via combinatorial expressions for their Hilbert polynomials. We realize the set of all nonempty Hilbert schemes as a probability space and prove that Hilbert schemes are irreducible and nonsingular with probability greater than $0.5$.
Gamow, not Hilbert: The Architect of Hilbert's Grand Hotel
Kragh, Helge
2014-01-01
What is known as "Hilbert's hotel" is a story of an imaginary hotel with infinitely many rooms that illustrates the bizarre consequences of assuming an actual infinity of objects or events. Since the 1970s it has been used in a variety of arguments, some of them relating to cosmology and others to philosophy and theology. It turns out that the name is a misnomer, as Hilbert was not responsible for the story. The originator was George Gamow, who invented the hotel in 1947, jokingly attributing it to Hilbert. Although well known, the counter-intuitive hotel only attracted wide interest in the 1970s, first in philosophical and theological contexts. The paper outlines the origin and early history of what might be called the Gamow-Hilbert hotel paradox.
Li, Jingsong; Yu, Benli; Fischer, Horst
2015-04-01
This paper presents a novel methodology-based discrete wavelet transform (DWT) and the choice of the optimal wavelet pairs to adaptively process tunable diode laser absorption spectroscopy (TDLAS) spectra for quantitative analysis, such as molecular spectroscopy and trace gas detection. The proposed methodology aims to construct an optimal calibration model for a TDLAS spectrum, regardless of its background structural characteristics, thus facilitating the application of TDLAS as a powerful tool for analytical chemistry. The performance of the proposed method is verified using analysis of both synthetic and observed signals, characterized with different noise levels and baseline drift. In terms of fitting precision and signal-to-noise ratio, both have been improved significantly using the proposed method.
Extensions of Bessel sequences to dual pairs of frames
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2013-01-01
Tight frames in Hilbert spaces have been studied intensively for the past years. In this paper we demonstrate that it often is an advantage to use pairs of dual frames rather than tight frames. We show that in any separable Hilbert space, any pairs of Bessel sequences can be extended to a pair...
A Novel Construction Method for n-Dimensional Hilbert Space-Filling Curves
Chen, Chih-Sheng; Lin, Shen-Yi; Fan, Min-Hsuan; Huang, Chua-Huang
We develop a novel construction method forn-dimensional Hilbert space-filling curves. The construction method includes four steps: block allocation, Gray permutation, coordinate transformation and recursive construction. We use the tensor product theory to formulate the method. Ann-dimensional Hilbert space-filling curve of 2r elements on each dimension is specified as a permutation which rearranges 2rn data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing ann-dimensional Hilbert space-filling curve. The tensor product formulation ofn-dimensional Hilbert space-filling curves uses stride permutation, reverse permutation, and Gray permutation. We present both recursive and iterative tensor product formulas ofn-dimensional Hilbert space-filling curves. The tensor product formulas are directly translated into computer programs which can be used in various applications. The process of program generation is explained in the paper.
Instantaneous frequency estimate of nonstationary phonocardiograph signals using hilbert spectrum.
Sun, L; Shen, M; Chan, F H Y; Beadel, P J
2005-01-01
A method for analyzing the nonlinear and non-stationary processes and investigating the instantaneous frequency of the practical medical signals is presented. The aim of this contribution is to explore the role that both empirical mode decomposition and Hilbert transform can be applied to play in phonocardiograph (PCG) signals. Hilbert transform is used to each intrinsic mode function to obtain the global time-frequency distribution of the underlying signal with a point of view of instantaneous frequency. Two kinds of clinical phonocardiograph signals with normal and abnormal cardiac functions were analyzed by using the proposed approach. The instantaneous frequency distributions of the PCG signals were also compared with the results by using the Morlet wavelet transform. Both simulation and experimental results were presented and discussed to demonstrate the power and effectiveness of the proposed approach.
Empirical Mode Decomposition and Hilbert Spectral Analysis
Huang, Norden E.
1998-01-01
The difficult facing data analysis is the lack of method to handle nonlinear and nonstationary time series. Traditional Fourier-based analyses simply could not be applied here. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data. This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency 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. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. The classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and nonstationary effects in the energy-frequency-time distribution.
Equivalence of quotient Hilbert modules
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
in principle may be used, to construct a set of complete unitary invariants for quotient modules Q = M ⊖ M0. The invariants are given explicitly in the particular case of k = 2. Keywords. Hilbert modules; function algebra; quotient module; longitudinal and transversal curvature; kernel function; jet and angle. 1. Preliminaries. Let.
Unveiling signatures of interdecadal climate changes by Hilbert analysis
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
Reproducing pairs and the continuous nonstationary Gabor transform on LCA groups
Speckbacher, Michael; Balazs, Peter
2015-10-01
In this paper we introduce and investigate the concept of reproducing pairs as a generalization of continuous frames. Reproducing pairs yield a bounded analysis and synthesis process while the frame condition can be omitted at both stages. Moreover, we will investigate certain continuous frames (resp. reproducing pairs) on LCA groups, which can be described as a continuous version of nonstationary Gabor systems and state sufficient conditions for these systems to form a continuous frame (resp. reproducing pair). As a byproduct we identify the structure of the frame operator (resp. resolution operator). We will apply our results to systems generated by a unitary action of a subset of the affine Weyl-Heisenberg group in {L}2({{R}}). This setup will also serve as a nontrivial example of a system for which, whereas continuous frames exist, no dual system with the same structure exists even if we drop the frame property.
Functional Analysis: Entering Hilbert Space
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces, since this is important for applications of the theory. The more general setting with Banach spaces requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators...... between Hilbert spaces. Fredholm operators are of interest far beyond mathematical analysis, they also play a significant role in theoretical physics, differential geometry and topology with the famous Index Theorem proved by Michael Atiyah and Isadore Singer in 1963 as a highlight. With the addition......In the second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Map-ping Theorem, the Closed Graph Theorem and the Hahn-Banach The orem. The material on operators between normed vector spaces is further expanded...
Functional Analysis: Entering Hilbert Space
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
between Hilbert spaces. Fredholm operators are of interest far beyond mathematical analysis, they also play a significant role in theoretical physics, differential geometry and topology with the famous Index Theorem proved by Michael Atiyah and Isadore Singer in 1963 as a highlight. With the addition...... of the new material on normed vector spaces and their operators, the book can hopefully serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them....
Lin, Ji; Ren, Bo; Li, Hua-mei; Li, Yi-Shen
2008-03-01
Two Darboux transformations of the (1+1) -dimensional Wu-Zhang (WZ) equation and the two-component Camassa-Holm (2CH) system with the reciprocal transformation are obtained. One-loop and two-loop soliton solutions and multisoliton(like) solutions of the 2CH system are obtained by using the Darboux transformations and selecting different seed solutions of the corresponding equations. The bidirectional soliton solutions of the (1+1) -dimensional WZ equation are also obtained. The interactions of two-soliton head-on and overtaking collisions for the WZ equation and the evolution of the two-soliton(-like) solutions for the 2CH system are studied.
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
Quantum Hilbert matrices and orthogonal polynomials
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Berg, Christian
2009-01-01
Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|... of reciprocal Fibonacci numbers called Filbert matrices. We find a formula for the entries of the inverse quantum Hilbert matrix....
Linear systems and operators in Hilbert space
Fuhrmann, Paul A
2014-01-01
A treatment of system theory within the context of finite dimensional spaces, this text is appropriate for students with no previous experience of operator theory. The three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.
Functional Analysis: Entering Hilbert Space
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
in a new chapter on Fredholm theory (Chapter 6). Fredholm theory originates in pioneering work of the Swedish mathematician Erik Ivar Fred-holm on integral equations, which inspired the study of a new class of bounded linear operators, known as Fredholm operators. Chapter 6 presents the basic elements...... between Hilbert spaces. Fredholm operators are of interest far beyond mathematical analysis, they also play a significant role in theoretical physics, differential geometry and topology with the famous Index Theorem proved by Michael Atiyah and Isadore Singer in 1963 as a highlight. With the addition...... of the new material on normed vector spaces and their operators, the book can hopefully serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them....
Functional Analysis: Entering Hilbert Space
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
In the second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Map-ping Theorem, the Closed Graph Theorem and the Hahn-Banach The orem. The material on operators between normed vector spaces is further expanded...... in a new chapter on Fredholm theory (Chapter 6). Fredholm theory originates in pioneering work of the Swedish mathematician Erik Ivar Fred-holm on integral equations, which inspired the study of a new class of bounded linear operators, known as Fredholm operators. Chapter 6 presents the basic elements...... of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces, since this is important for applications of the theory. The more general setting with Banach spaces requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators...
Quantum Search in Hilbert Space
Zak, Michail
2003-01-01
A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.
Introduction to spectral theory in Hilbert space
Helmberg, Gilbert; Koiter, W T
1969-01-01
North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of lin
On orthogonal systems in Hilbert C*-modules
Landi, Giovanni; Pavlov, Alexander
2009-01-01
Analogues for Hilbert C*-modules of classical results of Fourier series theory in Hilbert spaces are considered. Relations between different properties of orthogonal and orthonormal systems for Hilbert C*-modules are studied with special attention paid on the differences with the well-known Hilbert space situation.
Hilbert space methods in partial differential equations
Showalter, Ralph E
1994-01-01
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Local spins: improved Hilbert-space analysis.
Ramos-Cordoba, Eloy; Matito, Eduard; Salvador, Pedro; Mayer, István
2012-11-28
The decomposition of for a general wave function has been carried out in the framework of the Hilbert-space analysis. The one and two-center components fulfill all physical requirements imposed to date. An inherent ambiguity of the Hilbert-space decomposition of a two-electron quantity, in particular using a Mulliken-type scheme, is also discussed in detail. The formalism of effective atomic densities has allowed us to derive in a simple manner appropriate expressions for the decomposition of in the framework of Hilbert space analysis that are consistent with Mulliken population analysis and related quantities. Using a particular mapping we have derived the Hilbert-space expressions also in the framework of Löwdin population analysis in a straightforward manner. The numerical results obtained with the latter formalism have proved to be more robust and reliable.
Testing the dimension of Hilbert spaces.
Brunner, Nicolas; Pironio, Stefano; Acin, Antonio; Gisin, Nicolas; Méthot, André Allan; Scarani, Valerio
2008-05-30
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.
Theory of linear operators in Hilbert space
Akhiezer, N I
1993-01-01
This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.
DEFF Research Database (Denmark)
Christensen, Ole; Goh, Say Song
2012-01-01
is needed. The purpose of the present paper is to provide constructions of dual pairs of frames in the setting of the Hilbert space of periodic functions L2(0,2π). The frames constructed are given explicitly as trigonometric polynomials, which allows for an efficient calculation of the coefficients...
Direct integrals and Hilbert W*-modules
Frank, M
1993-01-01
Investigating the direct integral decomposition of von Neumann algebras of bounded module operators on self-dual Hilbert W*-moduli an equivalence principle is obtained which connects the theory of direct disintegration of von Neumann algebras on separable Hilbert spaces and the theory of von Neumann representations on self-dual Hilbert {\\bf A}-moduli with countably generated {\\bf A}-pre-dual Hilbert {\\bf A}-module over commutative separable W*-algebras {\\bf A}. Examples show posibilities and bounds to find more general relations between these two theories, (cf. R. Schaflitzel's results). As an application we prove a Weyl-Berg-Murphy type theorem: for each given commutative W*-algebra {\\bf A} with a special approximation property (*) every normal bounded {\\bf A}-linear operator on a self-dual Hilbert {\\bf A}-module with countably generated {\\bf A}-pre-dual Hilbert {\\bf A}-module is decomposable into the sum of a diagonalizable normal and of a "compact" bounded {\\bf A}-linear operator on that module.
Chen, T; Beu, S C; Kaiser, N K; Hendrickson, C L
2014-06-01
A conventional Fourier transform-Ion Cyclotron Resonance (ICR) detection cell is azimuthally divided into four equal sections. One pair of opposed electrodes is used for ion cyclotron excitation, and the other pair for ion image charge detection. In this work, we demonstrate that an appropriate electrical circuit facilitates excitation and detection on one pair of opposed electrodes. The new scheme can be used to minimize the number of electrically independent ICR cell electrodes and/or improve the electrode geometry for simultaneously increased ICR signal magnitude and optimal post-excitation radius, which results in higher signal-to-noise ratio and decreased space-charge effects.
Homborg, A.M.; Westing, E.P.M.; Tinga, Tiedo; Zhang, X; Oonincx, P.J.; Ferrari, G.M.; de Wit, J.H.W.; Mol, J.M.C.
2013-01-01
Hilbert spectra, calculated with the Hilbert–Huang transform, are presented here as an analysis technique for the characterization of electrochemical noise data in corrosion studies. A highly detailed decomposition of the original current and potential data is provided in time and frequency
Applications of Hilbert Spectral Analysis for Speech and Sound Signals
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.
Discretization of quaternionic continuous wavelet transforms
Askari Hemmat, A.; Thirulogasanthar, K.; Krzyżak, A.
2017-07-01
A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the discretization techniques for 2D-continuous wavelet transform of the SIM(2) group, the quaternionic continuous wavelet transform, living in a complex valued Hilbert space of square integrable functions, of the quaternion wavelet group is discretized, and thereby, a discrete frame for quaternion valued Hilbert space of square integrable functions is obtained.
Commentaries on Hilbert's Basis Theorem | Apine | Science World ...
African Journals Online (AJOL)
The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...
Directory of Open Access Journals (Sweden)
Imaouchen Yacine
2015-01-01
Full Text Available To detect rolling element bearing defects, many researches have been focused on Motor Current Signal Analysis (MCSA using spectral analysis and wavelet transform. This paper presents a new approach for rolling element bearings diagnosis without slip estimation, based on the wavelet packet decomposition (WPD and the Hilbert transform. Specifically, the Hilbert transform first extracts the envelope of the motor current signal, which contains bearings fault-related frequency information. Subsequently, the envelope signal is adaptively decomposed into a number of frequency bands by the WPD algorithm. Two criteria based on the energy and correlation analyses have been investigated to automate the frequency band selection. Experimental studies have confirmed that the proposed approach is effective in diagnosing rolling element bearing faults for improved induction motor condition monitoring and damage assessment.
EEG classification of imagined syllable rhythm using Hilbert spectrum methods
Deng, Siyi; Srinivasan, Ramesh; Lappas, Tom; D'Zmura, Michael
2010-08-01
We conducted an experiment to determine whether the rhythm with which imagined syllables are produced may be decoded from EEG recordings. High density EEG data were recorded for seven subjects while they produced in imagination one of two syllables in one of three different rhythms. We used a modified second-order blind identification (SOBI) algorithm to remove artefact signals and reduce data dimensionality. The algorithm uses the consistent temporal structure along multi-trial EEG data to blindly decompose the original recordings. For the four primary SOBI components, joint temporal and spectral features were extracted from the Hilbert spectra (HS) obtained by a Hilbert-Huang transformation (HHT). The HS provide more accurate time-spectral representations of non-stationary data than do conventional techniques like short-time Fourier spectrograms and wavelet scalograms. Classification of the three rhythms yields promising results for inter-trial transfer, with performance for all subjects significantly greater than chance. For comparison, we tested classification performance of three averaging-based methods, using features in the temporal, spectral and time-frequency domains, respectively, and the results are inferior to those of the SOBI-HHT-based method. The results suggest that the rhythmic structure of imagined syllable production can be detected in non-invasive brain recordings and provide a step towards the development of an EEG-based system for communicating imagined speech.
Hilbert Statistics of Vorticity Scaling in Two-Dimensional Turbulence
Tan, H S; Meng, Jianping
2014-01-01
In this paper, the scaling property of the inverse energy cascade and forward enstrophy cascade of the vorticity filed $\\omega(x,y)$ in two-dimensional (2D) turbulence is analyzed. This is accomplished by applying a Hilbert-based technique, namely Hilbert-Huang Transform, to a vorticity field obtained from a $8192^2$ grid-points direct numerical simulation of the 2D turbulence with a forcing scale $k_f=100$ and an Ekman friction. The measured joint probability density function $p(C,k)$ of mode $C_i(x)$ of the vorticity $\\omega$ and instantaneous wavenumber $k(x)$ is separated by the forcing scale $k_f$ into two parts, which corresponding to the inverse energy cascade and the forward enstrophy cascade. It is found that all conditional pdf $p(C\\vert k)$ at given wavenumber $k$ has an exponential tail. In the inverse energy cascade, the shape of $p(C\\vert k)$ does collapse with each other, indicating a nonintermittent cascade. The measured scaling exponent $\\zeta_{\\omega}^I(q)$ is linear with the statistical ord...
Hilbert space theory of classical electrodynamics
Indian Academy of Sciences (India)
Abstract. Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics.
Vertical integration from the large Hilbert space
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.
On typical properties of Hilbert space operators
Eisner, T.; Mátrai, T.
2013-01-01
We study the typical behavior of bounded linear operators on infinite-dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral properties, the problem of unitary equivalence of typical
Quasistationary sequences in Hilbert spaces | Muriuki | African ...
African Journals Online (AJOL)
In this paper the concept of covariance differences of a sequence is introduced and its relationship with the covariance function is established. The criteria of linear representability of sequences in Hilbert space are proved. The necessary and sufficient conditions for a linearly representable sequence to be quasistationary ...
Signal detection theory in Hilbert space.
Baldo, Marcus Vinícius C
2013-06-01
The Hilbert space formalism is a powerful language to express many cognitive phenomena. Here, relevant concepts from signal detection theory are recast in that language, allowing an empirically testable extension of the quantum probability formalism to psychophysical measures, such as detectability and discriminability.
A relative Hilbert-Mumford criterion
DEFF Research Database (Denmark)
Gulbrandsen, Martin G.; Halle, Lars Halvard; Hulek, Klaus
2015-01-01
We generalize the classical Hilbert-Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism X -> Spec A to a noetherian k-algebra A. We also extend the classical...
Fluxes, bundle gerbes and 2-Hilbert spaces
Bunk, Severin; Szabo, Richard J.
2017-10-01
We elaborate on the construction of a prequantum 2-Hilbert space from a bundle gerbe over a 2-plectic manifold, providing the first steps in a programme of higher geometric quantisation of closed strings in flux compactifications and of M5-branes in C-fields. We review in detail the construction of the 2-category of bundle gerbes and introduce the higher geometrical structures necessary to turn their categories of sections into 2-Hilbert spaces. We work out several explicit examples of 2-Hilbert spaces in the context of closed strings and M5-branes on flat space. We also work out the prequantum 2-Hilbert space associated with an M-theory lift of closed strings described by an asymmetric cyclic orbifold of the SU(2) WZW model, providing an example of sections of a torsion gerbe on a curved background. We describe the dimensional reduction of M-theory to string theory in these settings as a map from 2-isomorphism classes of sections of bundle gerbes to sections of corresponding line bundles, which is compatible with the respective monoidal structures and module actions.
General construction of reproducing kernels on a quaternionic Hilbert space
Thirulogasanthar, K.; Ali, S. Twareque
A general theory of reproducing kernels and reproducing kernel Hilbert spaces on a right quaternionic Hilbert space is presented. Positive operator-valued measures and their connection to a class of generalized quaternionic coherent states are examined. A Naimark type extension theorem associated with the positive operator-valued measures is proved in a right quaternionic Hilbert space. As illustrative examples, real, complex and quaternionic reproducing kernels and reproducing kernel Hilbert spaces arising from Hermite and Laguerre polynomials are presented. In particular, in the Laguerre case, the Naimark type extension theorem on the associated quaternionic Hilbert space is indicated.
Compact Hilbert Curve Index Algorithm Based on Gray Code
Directory of Open Access Journals (Sweden)
CAO Xuefeng
2016-12-01
Full Text Available Hilbert curve has best clustering in various kinds of space filling curves, and has been used as an important tools in discrete global grid spatial index design field. But there are lots of redundancies in the standard Hilbert curve index when the data set has large differences between dimensions. In this paper, the construction features of Hilbert curve is analyzed based on Gray code, and then the compact Hilbert curve index algorithm is put forward, in which the redundancy problem has been avoided while Hilbert curve clustering preserved. Finally, experiment results shows that the compact Hilbert curve index outperforms the standard Hilbert index, their 1 computational complexity is nearly equivalent, but the real data set test shows the coding time and storage space decrease 40%, the speedup ratio of sorting speed is nearly 4.3.
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.
Xu, Wenjun; Tang, Chen; Su, Yonggang; Li, Biyuan; Lei, Zhenkun
2018-02-01
In this paper, we propose an image decomposition model Shearlet-Hilbert-L 2 with better performance for denoising in electronic speckle pattern interferometry (ESPI) fringe patterns. In our model, the low-density fringes, high-density fringes, and noise are, respectively, described by shearlet smoothness spaces, adaptive Hilbert space, and L 2 space and processed individually. Because the shearlet transform has superior directional sensitivity, our proposed Shearlet-Hilbert-L 2 model achieves commendable filtering results for various types of ESPI fringe patterns, including uniform density fringe patterns, moderately variable density fringe patterns, and greatly variable density fringe patterns. We evaluate the performance of our proposed Shearlet-Hilbert-L 2 model via application to two computer-simulated and nine experimentally obtained ESPI fringe patterns with various densities and poor quality. Furthermore, we compare our proposed model with windowed Fourier filtering and coherence-enhancing diffusion, both of which are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. We also compare our proposed model with the previous image decomposition model BL-Hilbert-L 2 .
The Canonical Structure of the First Order Einstein-Hilbert Action with a Flat Background
Chishtie, Farrukh
2013-01-01
It has been shown that the canonical structure of the first order Einstein-Hilbert (1EH) action involves three generations of constraints and that these can be used to find the generator of a gauge transformation which leaves the action invariant; this transformation is a diffeomorphism with field-dependent gauge function while on shell. In this paper we examine the relationship between the canonical structure of this action and that of the first order spin-2 (1S2) action, which is the weak field limit of the Einstein-Hilbert action. We find that the weak field limit of the Possion Brackets (PB) algebra of first class constraints associated with the 1EH action is not that of the 1S2 action.
Transverse Hilbert schemes and completely integrable systems
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Donin Niccolò Lora Lamia
2017-12-01
Full Text Available In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial and show it has the maximal number of commuting Hamiltonians.We then provide the inverse construction, starting from a 2ddimensional holomorphic integrable system W which has an endomorphism A: TW → TW satisfying the above properties and recover our initial surface S with W ≌ Sp[d].
Elements of Hilbert spaces and operator theory
Vasudeva, Harkrishan Lal
2017-01-01
The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compressio...
Simulating quantum systems using real Hilbert spaces.
McKague, Matthew; Mosca, Michele; Gisin, Nicolas
2009-01-16
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends previous results which were unable to simulate local evolution and measurements with local operators and was limited to discrete evolution. We also detail applications to Bell inequalities and self-testing of the quantum apparatus.
Robust Adaptive Control In Hilbert Space
Wen, John Ting-Yung; Balas, Mark J.
1990-01-01
Paper discusses generalization of scheme for adaptive control of finite-dimensional system to infinite-dimensional Hilbert space. Approach involves generalization of command-generator tracker (CGT) theory. Does not require reference model to be same order as that of plant, and knowledge of order of plant not needed. Suitable for application to high-order systems, main emphasis on adjustment of low-order feedback-gain matrix. Analysis particularly relevant to control of large, flexible structures.
Hyperorthogonal well-folded Hilbert curves
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Arie Bos
2016-03-01
Full Text Available R-trees can be used to store and query sets of point data in two or more dimensions. An easy way to construct and maintain R-trees for two-dimensional points, due to Kamel and Faloutsos, is to keep the points in the order in which they appear along the Hilbert curve. The R-tree will then store bounding boxes of points along contiguous sections of the curve, and the efficiency of the R-tree depends on the size of the bounding boxes---smaller is better. Since there are many different ways to generalize the Hilbert curve to higher dimensions, this raises the question which generalization results in the smallest bounding boxes. Familiar methods, such as the one by Butz, can result in curve sections whose bounding boxes are a factor $\\Omega(2^{d/2}$ larger than the volume traversed by that section of the curve. Most of the volume bounded by such bounding boxes would not contain any data points. In this paper we present a new way of generalizing Hilbert's curve to higher dimensions, which results in much tighter bounding boxes: they have at most 4 times the volume of the part of the curve covered, independent of the number of dimensions. Moreover, we prove that a factor 4 is asymptotically optimal.
Espectro de un operador acotado en espacios de Hilbert
Duran Quiñones, Sofia Irena
2015-01-01
En el presente Trabajo de Investigación demos desarrollado en forma clara los conceptos básicos de los Espacios de Hilbert, la norma definida a partir de un producto interno, el ortogonal de un conjunto, funcional acotada, reflexividad en Espacios de Hilbert, bases ortogonales y ortonormales, separabilidad. Luego estudiaremos los Operadores Lineales Acotados en los Espacios de Hilbert, veremos las propiedades que relacionan a los Operadores: acotado, adjunto, normal, unitario, proyección y po...
Riemann-Hilbert problem and the discrete Bessel kernel
Borodin, Alexei
1999-01-01
We use discrete analogs of Riemann-Hilbert problem's methods to derive the discrete Bessel kernel which describes the poissonized Plancherel measures for symmetric groups. To do this we define discrete analogs of a Riemann-Hilbert problem and of an integrable integral operator and show that computing the resolvent of a discrete integrable operator can be reduced to solving a corresponding discrete Riemann-Hilbert problem. We also give an example, explicitly solvable in terms of classical spec...
Pang, Shuping; Zhou, Yuanyuan; Wang, Zaiwei; Yang, Mengjin; Krause, Amanda R; Zhou, Zhongmin; Zhu, Kai; Padture, Nitin P; Cui, Guanglei
2016-01-27
We demonstrate the feasibility of a nonsalt-based precursor pair--inorganic HPbI3 solid and organic CH3NH2 gas--for the deposition of uniform CH3NH3PbI3 perovskite thin films. The strong room-temperature solid-gas interaction between HPbI3 and CH3NH2 induces transformative evolution of ultrasmooth, full-coverage perovskite thin films at a rapid rate (in seconds) from nominally processed rough, partial-coverage HPbI3 thin films. The chemical origin of this behavior is elucidated via in situ experiments. Perovskite solar cells, fabricated using MAPbI3 thin films thus deposited, deliver power conversion efficiencies up to 18.2%, attesting to the high quality of the perovskite thin films deposited using this transformative process.
a Norm Pairing in Formal Modules
Vostokov, S. V.
1980-02-01
A pairing of the multiplicative group of a local field (a finite extension of the field of p-adic numbers Qp) with the group of points of a Lubin-Tate formal group is defined explicitly. The values of the pairing are roots of an isogeny of the formal group. The main properties of this pairing are established: bilinearity, invariance under the choice of a local uniformizing element, and independence of the method of expanding elements into series with respect to this uniformizing element. These properties of the pairing are used to prove that it agrees with the generalized Hilbert norm residue symbol when the field over whose ring of integers the formal group is defined is totally ramified over Qp. This yields an explicit expression for the generalized Hilbert symbol on the group of points of the formal group. Bibliography: 12 titles.
Ranganadh Narayanam; Grigoryan, Artyom M.; Bindu Tushara D
2013-01-01
Discrete Fourier Transform is principal mathematical method for the frequency analysis and is having wide applications in Engineering and Sciences. Because the DFT is so ubiquitous, fast methods for computing DFT have been studied extensively, and continuous to be an active research. The way of splitting the DFT gives out various fast algorithms. In this paper, we present the implementation of two fast algorithms for the DFT for evaluating their performance. One of them is the popular radix-2...
Huang, Y X; Hermand, J -P; Gagne, Y; Lu, Z M; Liu, Y L; 10.1103/PhysRevE.84.016208
2011-01-01
In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter {\\mu} = 0.15. We find that the SF underestimates scaling e...
Energy Technology Data Exchange (ETDEWEB)
LACKS,S.A.
2003-10-09
Transformation, which alters the genetic makeup of an individual, is a concept that intrigues the human imagination. In Streptococcus pneumoniae such transformation was first demonstrated. Perhaps our fascination with genetics derived from our ancestors observing their own progeny, with its retention and assortment of parental traits, but such interest must have been accelerated after the dawn of agriculture. It was in pea plants that Gregor Mendel in the late 1800s examined inherited traits and found them to be determined by physical elements, or genes, passed from parents to progeny. In our day, the material basis of these genetic determinants was revealed to be DNA by the lowly bacteria, in particular, the pneumococcus. For this species, transformation by free DNA is a sexual process that enables cells to sport new combinations of genes and traits. Genetic transformation of the type found in S. pneumoniae occurs naturally in many species of bacteria (70), but, initially only a few other transformable species were found, namely, Haemophilus influenzae, Neisseria meningitides, Neisseria gonorrheae, and Bacillus subtilis (96). Natural transformation, which requires a set of genes evolved for the purpose, contrasts with artificial transformation, which is accomplished by shocking cells either electrically, as in electroporation, or by ionic and temperature shifts. Although such artificial treatments can introduce very small amounts of DNA into virtually any type of cell, the amounts introduced by natural transformation are a million-fold greater, and S. pneumoniae can take up as much as 10% of its cellular DNA content (40).
Absolute Stability And Hyperstability In Hilbert Space
Wen, John Ting-Yung
1989-01-01
Theorems on stabilities of feedback control systems proved. Paper presents recent developments regarding theorems of absolute stability and hyperstability of feedforward-and-feedback control system. Theorems applied in analysis of nonlinear, adaptive, and robust control. Extended to provide sufficient conditions for stability in system including nonlinear feedback subsystem and linear time-invariant (LTI) feedforward subsystem, state space of which is Hilbert space, and input and output spaces having finite numbers of dimensions. (In case of absolute stability, feedback subsystem memoryless and possibly time varying. For hyperstability, feedback system dynamical system.)
On enumeration of Hilbert-like curves
Smrek, Jan; Y Grosberg, Alexander
2015-05-01
We present an analytical method to explicitly enumerate all self-similar space-filling curves similar to Hilbert curve, and find their number grows with length L as {{Z}L}∼ {{1.35699}L}. This presents a first step in the exact characterization of the crumpled globule ensemble relevant for dense topologically constrained polymer matter and DNA folding. Moreover, this result gives a stringent lower bound on the number of Hamiltonian walks on a simple cubic lattice. Additionally, we compute the exact number of crumpled curves with arbitrary endpoints, and the closed crumpled curves on a 4× 4× 4 cube.
Concerning the Hilbert 16th problem
Ilyashenko, Yu; Il'yashenko, Yu
1995-01-01
This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting important new developments in this area, this book contains an introductory paper which outlines the general context and describes connections between the papers in the volume. The book will appeal to researchers and graduate students working in the qualit
Baker, W.R.
1959-08-25
Transformers of a type adapted for use with extreme high power vacuum tubes where current requirements may be of the order of 2,000 to 200,000 amperes are described. The transformer casing has the form of a re-entrant section being extended through an opening in one end of the cylinder to form a coaxial terminal arrangement. A toroidal multi-turn primary winding is disposed within the casing in coaxial relationship therein. In a second embodiment, means are provided for forming the casing as a multi-turn secondary. The transformer is characterized by minimized resistance heating, minimized external magnetic flux, and an economical construction.
Sur la tour de Hilbert de certains corps
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Abdelmalek Azizi
2016-06-01
Full Text Available In this paper, we determine the first Hilbert $2$-class field for some quartic cyclic number fields ${\\mathrm k}$ and the Galois group of the second Hilbert $2$-class field of ${\\mathrm k}$ over ${\\mathrm k}$.
A note on tensor fields in Hilbert spaces
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LEONARDO BILIOTTI
2002-06-01
Full Text Available We discuss and extend to infinite dimensional Hilbert spaces a well-known tensoriality criterion for linear endomorphisms of the space of smooth vector fields in n.Discutimos e estendemos para espaços de Hilbert um critério de tensorialidade para endomorfismos do espaço dos campos vetoriais em Rpot(n.
HILBERT-SPACE REPRESENTATIONS OF M-DEPENDENT PROCESSES
DEVALK, [No Value
A representation of one-dependent processes is given in terms of Hilbert spaces, vectors and bounded linear operators on Hilbert spaces. This generalizes a construction of one-dependent processes that are not two-block-factors. We show that all one-dependent processes admit a representation. We
On closed sets with convex projections in Hilbert space
Barov, S.T.; Dijkstra, J.J.
2007-01-01
Let k be a fixed natural number. We show that if C is a closed and nonconvex set in Hilbert space such that the closures of the projections onto all k-hyperplanes (planes with codimension k) are convex and proper, then C must contain a closed copy of Hilbert space. In order to prove this result we
The rigged Hilbert space approach to the Gamow states
de la Madrid, Rafael
2012-01-01
We use the resonances of the spherical shell potential to present a thorough description of the Gamow (quasinormal) states within the rigged Hilbert space. It will be concluded that the natural setting for the Gamow states is a rigged Hilbert space whose test functions fall off at infinity faster than Gaussians.
DEFF Research Database (Denmark)
Peters, Terri
2011-01-01
Artiklen diskuterer ordet "transformation" med udgangspunkt i dels hvorledes ordet bruges i arkitektfaglig terminologi og dels med fokus på ordets potentielle indhold og egnethed i samme teminologi....
Coulomb branch Hilbert series and Hall-Littlewood polynomials
Cremonesi, Stefano; Mekareeya, Noppadol; Zaffaroni, Alberto
2014-01-01
There has been a recent progress in understanding the chiral ring of 3d $\\mathcal{N}=4$ superconformal gauge theories by explicitly constructing an exact generating function (Hilbert series) counting BPS operators on the Coulomb branch. In this paper we introduce Coulomb branch Hilbert series in the presence of background magnetic charges for flavor symmetries, which are useful for computing the Hilbert series of more general theories through gluing techniques. We find a simple formula of the Hilbert series with background magnetic charges for $T_\\rho(G)$ theories in terms of Hall-Littlewood polynomials. Here $G$ is a classical group and $\\rho$ is a certain partition related to the dual group of $G$. The Hilbert series for vanishing background magnetic charges show that Coulomb branches of $T_\\rho(G)$ theories are complete intersections. We also demonstrate that mirror symmetry maps background magnetic charges to baryonic charges.
Applications of rigged Hilbert spaces in quantum mechanics and signal processing
Energy Technology Data Exchange (ETDEWEB)
Celeghini, E., E-mail: celeghini@fi.infn.it [Dipartimento di Fisica, Università di Firenze and INFN-Sezione di Firenze, 150019 Sesto Fiorentino, Firenze (Italy); Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, Paseo Belén 7, 47011 Valladolid (Spain); Gadella, M., E-mail: manuelgadella1@gmail.com; Olmo, M. A. del, E-mail: olmo@fta.uva.es [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, Paseo Belén 7, 47011 Valladolid (Spain)
2016-07-15
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 is 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.
Applications of rigged Hilbert spaces in quantum mechanics and signal processing
Celeghini, E.; Gadella, M.; del Olmo, M. A.
2016-07-01
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 is 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.
Hilbert Space Operators in Quantum Physics
Blank, Jiří; Havlíček, Miloslav
2008-01-01
The second edition of this course-tested book provides a detailed and in-depth discussion of the foundations of quantum theory as well as its applications to various systems. The exposition is self-contained; in the first part the reader finds the mathematical background in chapters about functional analysis, operators on Hilbert spaces and their spectral theory, as well as operator sets and algebras. This material is used in the second part to a systematic explanation of the foundations, in particular, states and observables, properties of canonical variables, time evolution, symmetries and various axiomatic approaches. In the third part, specific physical systems and situations are discussed. Two chapters analyze Schrödinger operators and scattering, two others added in the second edition are devoted to new important topics, quantum waveguides and quantum graphs. Some praise for the previous edition: "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands...
Quantum mechanics in an evolving Hilbert space
Artacho, Emilio; O'Regan, David D.
2017-03-01
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed.
A Riemann-Hilbert Approach for the Novikov Equation
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.
Partial Differential Equations A unified Hilbert Space Approach
Picard, Rainer
2011-01-01
This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. Thefocus on a Hilbert space setting is a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations.This global point of view is takenby focussing on the issues involved in determining the appropriate func
Multicomplementary operators via finite Fourier transform
Energy Technology Data Exchange (ETDEWEB)
Klimov, Andrei B [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico); Sanchez-Soto, Luis L [Department of Physics, Lakehead University, Thunder Bay, Ontario P7B 5E1 (Canada); Guise, Hubert de [Department of Physics, Lakehead University, Thunder Bay, Ontario P7B 5E1 (Canada)
2005-03-25
A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.
Coherent states on quaternion slices and a measurable field of Hilbert spaces
Muraleetharan, B.; Thirulogasanthar, K.
2016-12-01
A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral appears again as a reproducing kernel Hilbert space for a bigger Hilbert space over the whole quaternions. Hilbert spaces over quaternion slices are identified as representation spaces for a set of irreducible unitary group representations and their direct integral is shown to be a reducible representation for the Hilbert space over the whole quaternion field.
Distributional Watson transforms
Dijksma, A.; Snoo, H.S.V. de
1974-01-01
For all Watson transforms W in L2(R+) a triple of Hilbert space LG ⊂ L2(R+) ⊂ L'G is constructed such that W may be extended to L'G. These results allow the construction of a triple L ⊂ L2(R+) ⊂ L', where L is a Gelfand-Fréchet space. This leads to a theory of distributional Watson transforms.
Quantitative coarse embeddings of quasi-Banach spaces into a Hilbert space
Kraus, Michal
2015-01-01
We study how well a quasi-Banach space can be coarsely embedded into a Hilbert space. Given any quasi-Banach space X which coarsely embeds into a Hilbert space, we compute its Hilbert space compression exponent. We also show that the Hilbert space compression exponent of X is equal to the supremum of the amounts of snowflakings of X which admit a bi-Lipschitz embedding into a Hilbert space.
Covariance differences of linealy representable sequences in hilbert ...
African Journals Online (AJOL)
TThe paper introduces the concepts of covariance differences of a sequence and establishes its relationship with the covariance function. One of the main results of this paper is the criteria of linear representability of sequences in Hilbert spaces.
HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
Directory of Open Access Journals (Sweden)
GIORGIO VENTURI
Full Text Available Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.
Introduction to Hilbert space and the theory of spectral multiplicity
Halmos, Paul R
2017-01-01
Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.
Isometric Reflection Vectors and Characterizations of Hilbert Spaces
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Donghai Ji
2014-01-01
Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.
On equivariant embedding of Hilbert C C C modules
Indian Academy of Sciences (India)
equivariant unitary map T ∈ L(E1,E2). We call a (G − A) module of the form (A ⊗ H,αg ⊗ γg). (where H is a Hilbert space) a trivial G − A module. We say that (E,β) is embeddable if there is an equivariant isometry from E to A⊗H for some Hilbert space H ...
Uncertainty relations as Hilbert space geometry
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.
Physics of the Hilbert Book Model
Energy Technology Data Exchange (ETDEWEB)
Leunen, Hans van
2014-07-01
The Hilbert Book Model is the name of a personal project of the author. The model is deduced from a foundation that is based on quantum logic and that is subsequently extended with trustworthy mathematical methods. What is known from conventional physics is used as a guideline, but the model is not based on the methodology of contemporary physics. In this way the model can reach deeper into the basement of physics. The ambition of the model is rather modest. It limits its scope to the lowest levels of the physical hierarchy. Thus fields and elementary particles are treated in fair detail, but composites are treated marginally and only some aspects of cosmology are touched. Still the model dives into the origins of gravitation and inertia and explains the diversity of the elementary particles. It explains what photons are and introduces a lower level of physical objects and a new kind of ultra-high frequency waves that carry information about their emitters. It explains entanglement and the Pauli principle. Above all the HBM introduces a new way of looking at space and time. Where contemporary physics applies the spacetime model, the HBM treats space and progression as a paginated model.
Molecular Energy Decompositions in the Hilbert-Space of Atomic Orbitals at Correlated Level
Alcoba, Diego R.; Bochicchio, Roberto C.; Lain, Luis; Torre, Alicia
This work describes a new model to partition the molecular energy into one- and two-center contributions in the Hilbert-space of atomic orbitals at correlated level. Our proposal makes explicit use of the pairing nature of chemical bonding phenomena to accommodate appropriately the correlation effects within these contributions. The model is based on the treatment of the kinetic energy as contributing to both one- and two-atom terms, according to the pairing or unpairing character of the electron cloud, and on the appropriate assignment of the density cumulant dependent contributions. Numerical results for selected systems are reported and compared with those arising from other models, showing the reliability of our predictions.
Causal discovery via reproducing kernel Hilbert space embeddings.
Chen, Zhitang; Zhang, Kun; Chan, Laiwan; Schölkopf, Bernhard
2014-07-01
Causal discovery via the asymmetry between the cause and the effect has proved to be a promising way to infer the causal direction from observations. The basic idea is to assume that the mechanism generating the cause distribution p(x) and that generating the conditional distribution p(y|x) correspond to two independent natural processes and thus p(x) and p(y|x) fulfill some sort of independence condition. However, in many situations, the independence condition does not hold for the anticausal direction; if we consider p(x, y) as generated via p(y)p(x|y), then there are usually some contrived mutual adjustments between p(y) and p(x|y). This kind of asymmetry can be exploited to identify the causal direction. Based on this postulate, in this letter, we define an uncorrelatedness criterion between p(x) and p(y|x) and, based on this uncorrelatedness, show asymmetry between the cause and the effect in terms that a certain complexity metric on p(x) and p(y|x) is less than the complexity metric on p(y) and p(x|y). We propose a Hilbert space embedding-based method EMD (an abbreviation for EMbeDding) to calculate the complexity metric and show that this method preserves the relative magnitude of the complexity metric. Based on the complexity metric, we propose an efficient kernel-based algorithm for causal discovery. The contribution of this letter is threefold. It allows a general transformation from the cause to the effect involving the noise effect and is applicable to both one-dimensional and high-dimensional data. Furthermore it can be used to infer the causal ordering for multiple variables. Extensive experiments on simulated and real-world data are conducted to show the effectiveness of the proposed method.
A New Method for Non-linear and Non-stationary Time Series Analysis:
The Hilbert Spectral Analysis
CERN. Geneva
2000-01-01
A new method for analysing non-linear and non-stationary 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 extreme, and also having symmetric envelopes defined by the local maximal 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 non-linear and non-stationary 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. Classical non-l...
Hyperellipsoidal statistical classifications in a reproducing kernel Hilbert space.
Liang, Xun; Ni, Zhihao
2011-06-01
Standard support vector machines (SVMs) have kernels based on the Euclidean distance. This brief extends standard SVMs to SVMs with kernels based on the Mahalanobis distance. The extended SVMs become a special case of the Euclidean distance when the covariance matrix in a reproducing kernel Hilbert space is degenerated to an identity. The Mahalanobis distance leads to hyperellipsoidal kernels and the Euclidean distance results in hyperspherical ones. In this brief, the Mahalanobis distance-based kernel in a reproducing kernel Hilbert space is developed systematically. Extensive experiments demonstrate that the hyperellipsoidal kernels slightly outperform the hyperspherical ones, with fewer SVs.
Four-dimensional hilbert curves for R-trees
DEFF Research Database (Denmark)
Haverkort, Herman; Walderveen, Freek van
2011-01-01
Two-dimensional R-trees are a class of spatial index structures in which objects are arranged to enable fast window queries: report all objects that intersect a given query window. One of the most successful methods of arranging the objects in the index structure is based on sorting the objects...... according to the positions of their centers along a two-dimensional Hilbert space-filling curve. Alternatively, one may use the coordinates of the objects' bounding boxes to represent each object by a four-dimensional point, and sort these points along a four-dimensional Hilbert-type curve. In experiments...
Electromagnetic characteristics of Hilbert curve-based metamaterials
Chen, Ruirui; Li, Sucheng; Gu, Chendong; Anwar, Shahzad; Hou, Bo; Lai, Yun
2014-08-01
As the typical building blocks of metamaterials, the cut wire and the split ring resonator have been extensively studied in recent years. Besides them, the space-filling curve-based metamaterials are receiving great attentions because of their intrinsic subwavelength and multi-bands characteristics. In this work, we have investigated experimentally and numerically the electromagnetic characteristics of such Hilbert curve metamaterial in the microwave frequency regime and found a deeply subwavelength magnetic resonance supported by the fractal pattern and featuring the wavelength-to-size ratio more than 20. The subwavelength electromagnetic properties of the Hilbert curve will be beneficial to realize high-performance metamaterials.
On the 5d instanton index as a Hilbert series
Energy Technology Data Exchange (ETDEWEB)
Rodríguez-Gómez, Diego, E-mail: d.rodriguez.gomez@uniovi.es [Department of Physics, Universidad de Oviedo, Avda. Calvo Sotelo 18, 33007 Oviedo (Spain); Zafrir, Gabi, E-mail: gabizaf@techunix.technion.ac.il [Department of Physics, Technion, Israel Institute of Technology, Haifa 32000 (Israel)
2014-01-15
The superconformal index for N=2 5d theories contains a non-perturbative part arising from 5d instantonic operators which coincides with the Nekrasov instanton partition function. In this article, for pure gauge theories, we elaborate on the relation between such instanton index and the Hilbert series of the instanton moduli space. We propose a non-trivial identification of fugacities allowing the computation of the instanton index through the Hilbert series. We show the agreement of our proposal with existing results in the literature, as well as use it to compute the exact index for a pure U(1) gauge theory.
Generalized noncommutative Hardy and Hardy-Hilbert type inequalities
DEFF Research Database (Denmark)
Hansen, Frank; Krulic, Kristina; Pecaric, Josip
2010-01-01
We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it ......, it is typical that the operator versions hold only for 1 functions with values in 2 × 2 matrices.......We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1...
The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces
Ćurgus, Branko; Dijksma, Aad; Read, Tom
2001-01-01
The boundary eigenvalue problems for the adjoint of a symmetric relation S in a Hilbert space with finite, not necessarily equal, defect numbers, which are related to the selfadjoint Hilbert space extensions of S are characterized in terms of boundary coefficients and the reproducing kernel Hilbert
On Nyman, Beurling and Baez-Duarte's Hilbert space reformulation ...
Indian Academy of Sciences (India)
There has been a surge of interest of late in an old result of Nyman and Beurling giving a Hilbert space formulation of the Riemann hypothesis. Many authors have contributed to this circle of ideas, culminating in a beautiful refinement due to Baez-Duarte. The purpose of this little survey is to dis-entangle the resulting web of ...
Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces.
Piccione, Paolo; Tausk, Daniel V
2005-12-01
We prove that any countable family of Lagrangian subspaces of a symplectic Hilbert space admits a common complementary Lagrangian. The proof of this puzzling result, which is not totally elementary also in the finite dimensional case, is obtained as an application of the spectral theorem for unbounded self-adjoint operators.
Lectures on Hilbert modular varieties and modular forms
Goren, Eyal Z
2001-01-01
This book is devoted to certain aspects of the theory of p-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of p-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelian varieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of p-adic Hilbert modular forms and the geometry of moduli spaces of abelian varieties are related. This relation is used to study q-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-exper...
Precise asymptotics for complete moment convergence in Hilbert ...
Indian Academy of Sciences (India)
... Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 122; Issue 1. Precise Asymptotics for Complete Moment Convergence in Hilbert Spaces. Keang Fu Juan Chen. Volume 122 Issue 1 February 2012 ...
Hilbert space renormalization for the many-electron problem.
Li, Zhendong; Chan, Garnet Kin-Lic
2016-02-28
Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction Ansatz, namely, the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the "physical indices" or the coupling rules in the HS-MPS. Alternatively, simply truncating the "virtual dimension" of the HS-MPS leads to a family of size-extensive wave function Ansätze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.
On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space
Directory of Open Access Journals (Sweden)
Hamdy M. Ahmed
2009-01-01
Full Text Available We study a class of fractional stochastic integrodifferential equations considered in a real Hilbert space. The existence and uniqueness of the Mild solutions of the considered problem is also studied. We also give an application for stochastic integropartial differential equations of fractional order.
The 2-Hilbert space of a prequantum bundle gerbe
Bunk, Severin; Sämann, Christian; Szabo, Richard J.
We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf’s version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantization. We then extend the transgression functor to the full 2-category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant-Souriau prequantization in this setting, including its dimensional reduction to ordinary prequantization.
Perturbation for Frames for a Subspace of a Hilbert Space
DEFF Research Database (Denmark)
Christensen, Ole; deFlicht, C.; Lennard, C.
1997-01-01
We extend a classical result stating that a sufficiently small perturbation$\\{ g_i \\}$ of a Riesz sequence $\\{ f_i \\}$ in a Hilbert space $H$ is again a Riesz sequence. It turns out that the analog result for a frame does not holdunless the frame is complete. However, we are able to prove a very...
Large Scale 3D Scene Reconstruction with Hilbert Maps
2016-12-01
in which different dimensions in the projected Hilbert space operate within independent length- scale values. The proposed technique was tested... Vector Machines, Regularization, Optimization, and Beyond. The MIT Press, 2001. [21] D. Sculley. Web- scale k-means clustering. In Proceedings of the...
Precise asymptotics for complete moment convergence in Hilbert ...
Indian Academy of Sciences (India)
(Math. Sci.) Vol. 122, No. 1, February 2012, pp. 87–97. c Indian Academy of Sciences. Precise asymptotics for complete moment convergence in Hilbert spaces ... School of Statistics and Mathematics, Zhejiang Gongshang University, .... Now we start to introduce some Propositions, and the proof of our main result is based.
Space filling modular optics: expanded Peano and collapsed Hilbert curves
Schamschula, Marius P.; Caulfield, H. John
1994-10-01
Recently we introduced space filling curves such as the Peano and Hilbert curves as a method of realizing compact modular optics. In this paper we modify the primitives of these curves to construct novel compact two-dimensional modular optical systems.
A reproducing kernel hilbert space approach for q-ball imaging.
Kaden, Enrico; Kruggel, Frithjof
2011-11-01
Diffusion magnetic resonance (MR) imaging has enabled us to reveal the white matter geometry in the living human brain. The Q-ball technique is widely used nowadays to recover the orientational heterogeneity of the intra-voxel fiber architecture. This article proposes to employ the Funk-Radon transform in a Hilbert space with a reproducing kernel derived from the spherical Laplace-Beltrami operator, thus generalizing previous approaches that assume a bandlimited diffusion signal. The function estimation problem is solved within a Tikhonov regularization framework, while a Gaussian process model allows for the selection of the smoothing parameter and the specification of confidence bands. Shortcomings of Q-ball imaging are discussed.
Riemann-Hilbert technique scattering analysis of metamaterial-based asymmetric 2D open resonators
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.
Using Peano-Hilbert space filling curves for fast bidimensional ensemble EMD realization
Costa, Paulo; Barroso, João; Fernandes, Hugo; Hadjileontiadis, Leontios J.
2012-12-01
Empirical mode decomposition (EMD) is a fully unsupervised and data-driven approach to the class of nonlinear and non-stationary signals. A new approach is proposed, namely PHEEMD, to image analysis by using Peano-Hilbert space filling curves to transform 2D data (image) into 1D data, followed by ensemble EMD (EEMD) analysis, i.e., a more robust realization of EMD based on white noise excitation. Tests' results have shown that PHEEMD exhibits a substantially reduced computational cost compared to other 2D-EMD approaches, preserving, simultaneously, the information lying at the EMD domain; hence, new perspectives for its use in low computational power devices, like portable applications, are feasible.
Reproducing kernel Hilbert spaces with odd kernels in price prediction.
Krejník, Miloš; Tyutin, Anton
2012-10-01
For time series of futures contract prices, the expected price change is modeled conditional on past price changes. The proposed model takes the form of regression in a reproducing kernel Hilbert space with the constraint that the regression function must be odd. It is shown how the resulting constrained optimization problem can be reduced to an unconstrained one through appropriate modification of the kernel. In particular, it is shown how odd, even, and other similar kernels emerge naturally as the reproducing kernels of Hilbert subspaces induced by respective symmetry constraints. To test the validity and practical usefulness of the oddness assumption, experiments are run with large real-world datasets on four futures contracts, and it is demonstrated that using odd kernels results in a higher predictive accuracy and a reduced tendency to overfit.
Betti numbers of space curves bounded by Hilbert functions
Directory of Open Access Journals (Sweden)
Renato Maggioni
1997-05-01
Full Text Available We study relationships between Hilbert functions and graded Betti numbers of two space curves C and C_0 bilinked by a sequence of basic double linkages; precisely we obtain bounds for the graded Betti numbers of C by means of the Hilbert functions of the two curves and the graded Betti numbers of C_0 . On the other hand for every set of integers satisfying these bounds we can construct a curve with these integers as its graded Betti numbers. As a consequence we get a Dubreil-type theorem for a curve C which strongly dominates C_0 at height h which is exactly the Amasaki bound for Buchsbaum curves. Moreover we deduce for biliaison classes of Buchsbaum curves that a strong Lazarsfeld-Rao property holds.
The Hilbert Series of the One Instanton Moduli Space
Benvenuti, Sergio; Mekareeya, Noppadol; 10.1007
2010-01-01
The moduli space of k G-instantons on R^4 for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have N = 2 supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.
Some means inequalities for positive operators in Hilbert spaces.
Liang, Jin; Shi, Guanghua
2017-01-01
In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and show that the weighted multivariate operator geometric mean possess several attractive properties and means inequalities.
Explicit signal to noise ratio in reproducing kernel Hilbert spaces
DEFF Research Database (Denmark)
Gomez-Chova, Luis; Nielsen, Allan Aasbjerg; Camps-Valls, Gustavo
2011-01-01
an alternative kernel MNF (KMNF) in which the noise is explicitly estimated in the reproducing kernel Hilbert space. This enables KMNF dealing with non-linear relations between the noise and the signal features jointly. Results show that the proposed KMNF provides the most noise-free features when confronted...... with PCA, MNF, KPCA, and the previous version of KMNF. Extracted features with the explicit KMNF also improve hyperspectral image classification....
Improved Hilbert phase contrast for transmission electron microscopy.
Koeck, Philip J B
2015-07-01
Hilbert phase contrast has been recognized as a means of recording high resolution images with high contrast using a transmission electron microscope. This imaging mode could be used to image typical phase objects such as unstained biological molecules or cryo sections of biological tissue. According to the original proposal by (Danev et al., 2002) the Hilbert phase plate applies a phase shift of π to approximately half the focal plane (for example the right half excluding the central beam) and an image is recorded at Gaussian focus. After correction for the inbuilt asymmetry of differential phase contrast this image will have an almost perfect contrast transfer function (close to 1) from the lowest spatial frequency up to a maximum resolution determined by the wave length and spherical aberration of the microscope. In this paper I present theory and simulations showing that this maximum spatial frequency can be increased considerably almost without loss of contrast by using a Hilbert phase plate of half the thickness, leading to a phase shift of π/2, and recording images at Scherzer defocus. The maximum resolution can be improved even more by imaging at extended Scherzer defocus, though at the cost of contrast loss at lower spatial frequencies. Copyright © 2015 Elsevier B.V. All rights reserved.
Construction and coupling of frames in Hilbert spaces with W-metrics
Directory of Open Access Journals (Sweden)
German Escobar
2016-05-01
Full Text Available A definition of frames unitarily equivalent in Hilbert spaces with W-metric is stated, and a characterization is given in terms of their respective analysis operators. From a Hilbert space with a frame we construct a Hilbert space with W-metric and a frame unitarily equivalent to the given one. Finally, we prove that the coupling of two frames is a frame. Resumen. Se definen marcos unitariamente equivalentes en espacios de Hilbert con W-métricas, y se da una caracterización de ellos comparando sus respectivos operadores de análisis. A partir de un espacio de Hilbert con un marco se construye un espacio de Hilbert con W-métrica y un marco unitariamente equivalente al dado. Finalmente, se muestra que el acoplamiento de dos marcos es un marco.
Neuscamman, Eric
2013-11-21
The Jastrow-modified antisymmetric geminal power (JAGP) ansatz in Hilbert space successfully overcomes two key failings of other pairing theories, namely, a lack of inter-pair correlations and a lack of multiple resonance structures, while maintaining a polynomially scaling cost, variational energies, and size consistency. Here, we present efficient quantum Monte Carlo algorithms that evaluate and optimize the JAGP energy for a cost that scales as the fifth power of the system size. We demonstrate the JAGP's ability to describe both static and dynamic correlation by applying it to bond stretching in H2O, C2, and N2 as well as to a novel, multi-reference transition state of ethene. JAGP's accuracy in these systems outperforms even the most sophisticated single-reference methods and approaches that of exponentially scaling active space methods.
Neuscamman, Eric
2013-11-01
The Jastrow-modified antisymmetric geminal power (JAGP) ansatz in Hilbert space successfully overcomes two key failings of other pairing theories, namely, a lack of inter-pair correlations and a lack of multiple resonance structures, while maintaining a polynomially scaling cost, variational energies, and size consistency. Here, we present efficient quantum Monte Carlo algorithms that evaluate and optimize the JAGP energy for a cost that scales as the fifth power of the system size. We demonstrate the JAGP's ability to describe both static and dynamic correlation by applying it to bond stretching in H2O, C2, and N2 as well as to a novel, multi-reference transition state of ethene. JAGP's accuracy in these systems outperforms even the most sophisticated single-reference methods and approaches that of exponentially scaling active space methods.
Construction and coupling of frames in Hilbert spaces with W-metrics
Directory of Open Access Journals (Sweden)
German Escobar
2016-01-01
Full Text Available Se definen marcos unitariamente equivalentes en espacios de Hilbert con W-métricas, y se da una caracterización de ellos comparando sus respectivos operadores de análisis. A partir de un espacio de Hilbert con un marco se construye un espacio de Hilbert con W-métrica y un marco unitariamente equivalente al dado. Finalmente, se muestra que el acoplamiento de dos marcos es un marco.
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
Integral transformations applied to image encryption
Vilardy, Juan M.; Perez, Ronal; Torres, Cesar O.
2017-01-01
In this paper we consider the application of the integral transformations for image encryption through optical systems, a mathematical algorithm under Matlab platform using fractional Fourier transform (FrFT) and Random Phase Mask (RPM) for digital images encryption is implemented. The FrFT can be related to others integral transforms, such as: Fourier transform, Sine and Cosine transforms, Radial Hilbert transform, fractional Sine transform, fractional Cosine transform, fractional Hartley transform, fractional Wavelet transform and Gyrator transform, among other transforms. The encryption scheme is based on the use of the FrFT, the joint transform correlator and two RPMs, which provide security and robustness to the implemented security system. One of the RPMs used during encryption-decryption and the fractional order of the FrFT are the keys to improve security and make the system more resistant against security attacks.
LaZerte, Stefanie E; Reudink, Matthew W; Otter, Ken A; Kusack, Jackson; Bailey, Jacob M; Woolverton, Austin; Paetkau, Mark; de Jong, Adriaan; Hill, David J
2017-10-01
Radio frequency identification (RFID) provides a simple and inexpensive approach for examining the movements of tagged animals, which can provide information on species behavior and ecology, such as habitat/resource use and social interactions. In addition, tracking animal movements is appealing to naturalists, citizen scientists, and the general public and thus represents a tool for public engagement in science and science education. Although a useful tool, the large amount of data collected using RFID may quickly become overwhelming. Here, we present an R package (feedr) we have developed for loading, transforming, and visualizing time-stamped, georeferenced data, such as RFID data collected from static logger stations. Using our package, data can be transformed from raw RFID data to visits, presence (regular detections by a logger over time), movements between loggers, displacements, and activity patterns. In addition, we provide several conversion functions to allow users to format data for use in functions from other complementary R packages. Data can also be visualized through static or interactive maps or as animations over time. To increase accessibility, data can be transformed and visualized either through R directly, or through the companion site: http://animalnexus.ca, an online, user-friendly, R-based Shiny Web application. This system can be used by professional and citizen scientists alike to view and study animal movements. We have designed this package to be flexible and to be able to handle data collected from other stationary sources (e.g., hair traps, static very high frequency (VHF) telemetry loggers, observations of marked individuals in colonies or staging sites), and we hope this framework will become a meeting point for science, education, and community awareness of the movements of animals. We aim to inspire citizen engagement while simultaneously enabling robust scientific analysis.
Yan, Zhenya
2017-05-01
We extend the idea of the Fokas unified transform to investigate the initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line. The solution of this system can be expressed in terms of the solution of a 4 × 4 matrix Riemann-Hilbert (RH) problem formulated in the complex k-plane. The relevant jump matrices of the RH problem can be explicitly found using the two spectral functions s(k) and S(k), which can be defined by the initial data, the Dirichlet-Neumann boundary data at x = 0. The global relation is established between the two dependent spectral functions. The general mappings between Dirichlet and Neumann boundary values are analyzed in terms of the global relation. These results may be of the potential significance in both spinor Bose-Einstein condensates and the theory of multi-component integrable systems.
Dual pairs of gabor frames for trigonometric generators without the partition of unity property
DEFF Research Database (Denmark)
Christensen, Ole; Jakobsen, Mads Sielemann
2011-01-01
Frames is a strong tool to obtain series expansions in Hilbert spaces under less restrictive conditions than imposed by orthonormal bases. In order to apply frame theory it is necessary to construct a pair of so called dual frames. The goal of the article is to provide explicit constructions...
Real analysis measure theory, integration, and Hilbert spaces
Stein, Elias M
2005-01-01
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After
The ion pairs and superconducting bosons
Minasyan, V. N.
2008-01-01
First, it is shown that the creation of the spinless ion pairs in the lattice, which are hold by the binding with neighbor ion pairs together regarded as covalent. These ion pairs are created by the repulsive potential interaction of two ions which is bound as linear oscillator. The repulsive S-wave scattering between ion pairs and electrons is transformed to the attractive effective interaction between electrons which leads to a creation of electron pairs by a binding energy depending on the...
Mieck, Bernhard
2010-01-01
The standard model of the strong and electroweak interactions is transformed from the ordinary path integral with the Lagrangians of quarks and leptons and with the Abelian and non-Abelian gauge fields to corresponding self-energies. We apply the precise formulation in terms of massless Majorana Fermi fields with 'Nambu' doubling which naturally leads to the appropriate HST's of the self-energies and to the subsequent coset decomposition for the SSB. The total coset decomposition of the Fermi fields is given by the dimension N0=90 for the symmetry breaking SO(N0,N0)/U(N0)xU(N0) where the densities of fermions, related to the invariant subgroup U(N0), are contained in a background functional for the remaining SO(N0,N0)/U(N0) coset field degrees of freedom.
Homborg, A.M.; Tinga, Tiedo; Zhang, X; Westing, E.P.M.; Oonincx, P.J.; Ferrari, G.M.; de Wit, J.H.W.; Mol, J.M.C.
2013-01-01
Hilbert spectra allow identification of instantaneous frequencies that are attributed to specific corrosion mechanisms in electrochemical noise data. The present work proposes to identify and analyze areas of interest in Hilbert spectra, which enables to obtain valuable frequency information from
A Slice Algorithm for Corners and Hilbert-Poincaré Series of Monomial Ideals
DEFF Research Database (Denmark)
Roune, Bjarke Hammersholt
2010-01-01
We present an algorithm for computing the corners of a monomial ideal. The corners are a set of multidegrees that support the numerical information of a monomial ideal such as Betti numbers and Hilbert-Poincaré series. We show an experiment using corners to compute Hilbert-Poincaré series...... of monomial ideals with favorable results....
Intersection numbers on the relative Hilbert schemes of points on surfaces
DEFF Research Database (Denmark)
Gholampour, Amin; Sheshmani, Artan
2015-01-01
We study certain top intersection products on the Hilbert scheme of points on a nonsingular surface relative to an effective smooth divisor. We find a formula relating these numbers to the corresponding intersection numbers on the non-relative Hilbert schemes. In particular, we obtain a relative ...
Aveiro method in reproducing kernel Hilbert spaces under complete dictionary
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.
Three-Hilbert-Space Formulation of Quantum Mechanics
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Miloslav Znojil
2009-01-01
Full Text Available In paper [Znojil M., Phys. Rev. D 78 (2008, 085003, 5 pages, arXiv:0809.2874] the two-Hilbert-space (2HS, a.k.a. cryptohermitian formulation of Quantum Mechanics has been revisited. In the present continuation of this study (with the spaces in question denoted as H^{(auxiliary} and H^{(standard} we spot a weak point of the 2HS formalism which lies in the double role played by H^{(auxiliary}. As long as this confluence of roles may (and did! lead to confusion in the literature, we propose an amended, three-Hilbert-space (3HS reformulation of the same theory. As a byproduct of our analysis of the formalism we offer an amendment of the Dirac's bra-ket notation and we also show how its use clarifies the concept of covariance in time-dependent cases. Via an elementary example we finally explain why in certain quantum systems the generator H^{(gen} of the time-evolution of the wave functions may differ from their Hamiltonian H.
Theory and experiments on Peano and Hilbert curve RFID tags
McVay, John; Hoorfar, Ahmad; Engheta, Nader
2006-05-01
Recently, there has been considerable interest in the area of Radio Frequency Identification (RFID) and Radio Frequency Tagging (RFTAG). This emerging area of interest can be applied for inventory control (commercial) as well as friend/foe identification (military) to name but a few. The current technology can be broken down into two main groups, namely passive and active RFID tags. Utilization of Space-Filling Curve (SFC) geometries, such as the Peano and Hilbert curves, has been recently investigated for use in completely passive RFID applications [1, 2]. In this work, we give an overview of our work on the space-filling curves and the potential for utilizing the electrically small, resonant characteristics of these curves for use in RFID technologies with an emphasis on the challenging issues involved when attempting to tag conductive objects. In particular, we investigate the possible use of these tags in conjunction with high impedance ground-planes made of Hilbert or Peano curve inclusions [3, 4] to develop electrically small RFID tags that may also radiate efficiently, within close proximity of large conductive objects [5].
Hilbert-Schmidt quantum coherence in multi-qudit systems
Maziero, Jonas
2017-11-01
Using Bloch's parametrization for qudits ( d-level quantum systems), we write the Hilbert-Schmidt distance (HSD) between two generic n-qudit states as an Euclidean distance between two vectors of observables mean values in R^{Π_{s=1}nds2-1}, where ds is the dimension for qudit s. Then, applying the generalized Gell-Mann's matrices to generate SU(ds), we use that result to obtain the Hilbert-Schmidt quantum coherence (HSC) of n-qudit systems. As examples, we consider in detail one-qubit, one-qutrit, two-qubit, and two copies of one-qubit states. In this last case, the possibility for controlling local and non-local coherences by tuning local populations is studied, and the contrasting behaviors of HSC, l1-norm coherence, and relative entropy of coherence in this regard are noticed. We also investigate the decoherent dynamics of these coherence functions under the action of qutrit dephasing and dissipation channels. At last, we analyze the non-monotonicity of HSD under tensor products and report the first instance of a consequence (for coherence quantification) of this kind of property of a quantum distance measure.
Energy Technology Data Exchange (ETDEWEB)
Allan, Phoebe K. [University of Cambridge, University Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW, U.K.; Gonville and Caius College, Trinity; Griffin, John M. [University of Cambridge, University Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW, U.K.; Darwiche, Ali [Institut; Réseau sur le Stockage Electrochimique de l’Energie (RS2E), FR CNRS 3459, 80039 Amiens Cedex, France; Borkiewicz, Olaf J. [X-ray; Wiaderek, Kamila M. [X-ray; Chapman, Karena W. [X-ray; Morris, Andrew J. [Theory of; Chupas, Peter J. [X-ray; Monconduit, Laure [Institut; Réseau sur le Stockage Electrochimique de l’Energie (RS2E), FR CNRS 3459, 80039 Amiens Cedex, France; Grey, Clare P. [University of Cambridge, University Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW, U.K.
2016-02-15
Operando pair distribution function (PDF) analysis and ex situ Na-23 magic-angle spinning solid-state nuclear magnetic resonance (MAS ssNMR) spectroscopy are used to gain insight into the alloying mechanism of high-capacity antimony anodes for sodium-ion batteries. Subtraction of the PDF of crystalline NaxSb phases from the total PDF, an approach constrained by chemical phase information gained from Na-23 ssNMR in reference to relevant model compounds, identifies two previously uncharacterized intermediate species formed electro-chemically; a-Na3-xSb (x approximate to 0.4-0.5), a structure locally similar to crystalline Na3Sb (c-Na3Sb) but with significant numbers of sodium vacancies and a limited correlation length, and a-Na1.7Sb, a highly amorphous structure featuring some Sb-Sb bonding. The first sodiation breaks down the crystalline antimony to form first a-Na3-xSb and, finally, crystalline Na3Sb. Desodiation results in the formation of an electrode formed of a composite of crystalline and amorphous antimony networks. We link the different reactivity of these networks to a series of sequential sodiation reactions manifesting as a cascade of processes observed in the electrochemical profile of subsequent cycles. The amorphofis network reacts at higher voltages reforming a-Na1.7Sb, then a-Na3-xSb, whereas lower potentials are required for the sodiation of crystalline antimony, which reacts to form a-Na3-xSb without the formation of a-Na3-xSb. a-Na3-xSb is converted to crystalline Na3Sb at the end of the second discharge. We find no evidence of formation of NaSb. Variable temperature Na-23 NMR experiments reveal significant sodium mobility within c-Na3Sb; this is a possible contributing factor to the excellent rate performance of Sb anodes.
Quantum weak and modular values in enlarged Hilbert spaces
Ho, Le Bin; Imoto, Nobuyuki
2018-01-01
We introduce an enlarged state, which combines both pre- and postselection states at a given time t in between the pre- and postselection. Based on this form, quantum weak and modular values can be completely interpreted as expectation values of a linear combination of given operators in the enlarged Hilbert space. This formalism thus enables us to describe and measure the weak and modular values at any time dynamically. A protocol for implementing an enlarged Hamiltonian has also been proposed and applied to a simple example of a single spin under an external magnetic field. In addition, the time-dependent weak and modular values for pre- and postselection density matrices mapping onto an enlarged density matrix are also discussed.
Invariance of Topological Indices Under Hilbert Space Truncation
Huang, Zhoushen; Zhu, W.; Arovas, Daniel P.; Zhu, Jian-Xin; Balatsky, Alexander V.
2018-01-01
We show that the topological index of a wave function, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, Z2 topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possible application, we propose a partial quantum tomography scheme from which the topological index of a generic multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.
Structured functional additive regression in reproducing kernel Hilbert spaces.
Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen
2014-06-01
Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.
Public channel cryptography: chaos synchronization and Hilbert's tenth problem.
Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang
2008-08-22
The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.
Convex analysis and monotone operator theory in Hilbert spaces
Bauschke, Heinz H
2017-01-01
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...
Fractal nanostructures with Hilbert curve geometry as a SERS substrate
Grigorenko, Ilya
2013-03-01
A new type of substrates for Surface Enhanced Raman Scattering measurements is proposed. The shape of the substrate is based on self-similar fractal space filling curves, which possess properties of both one dimensional and two dimensional geometries. Here I present theoretical studies of the dielectric response of thin film doped semiconductor nanostructures, where conducting electrons are trapped in an effective potential having the geometry of the Hilbert curve. It is found that the system may exhibit the induced charge distributions specific for either two dimensional or one dimensional systems, depending on the excitation frequency. It is also shown that with the increase of the depth of the trapping potential the resonance of the system demonstrates a counter-intuitive shift to lower frequencies.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
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Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Simplified fractional Fourier transforms.
Pei, S C; Ding, J J
2000-12-01
The fractional Fourier transform (FRFT) has been used for many years, and it is useful in many applications. Most applications of the FRFT are based on the design of fractional filters (such as removal of chirp noise and the fractional Hilbert transform) or on fractional correlation (such as scaled space-variant pattern recognition). In this study we introduce several types of simplified fractional Fourier transform (SFRFT). Such transforms are all special cases of a linear canonical transform (an affine Fourier transform or an ABCD transform). They have the same capabilities as the original FRFT for design of fractional filters or for fractional correlation. But they are simpler than the original FRFT in terms of digital computation, optical implementation, implementation of gradient-index media, and implementation of radar systems. Our goal is to search for the simplest transform that has the same capabilities as the original FRFT. Thus we discuss not only the formulas and properties of the SFRFT's but also their implementation. Although these SFRFT's usually have no additivity properties, they are useful for the practical applications. They have great potential for replacing the original FRFT's in many applications.
Patient Specific Seizure Prediction System Using Hilbert Spectrum and Bayesian Networks Classifiers
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Nilufer Ozdemir
2014-01-01
Full Text Available The aim of this paper is to develop an automated system for epileptic seizure prediction from intracranial EEG signals based on Hilbert-Huang transform (HHT and Bayesian classifiers. Proposed system includes decomposition of the signals into intrinsic mode functions for obtaining features and use of Bayesian networks with correlation based feature selection for binary classification of preictal and interictal recordings. The system was trained and tested on Freiburg EEG database. 58 hours of preictal data, 40-minute data blocks prior to each of 87 seizures collected from 21 patients, and 503.1 hours of interictal data were examined resulting in 96.55% sensitivity with 0.21 false alarms per hour, 13.896% average proportion of time spent in warning, and 33.21 minutes of average detection latency using 30-second EEG segments with 50% overlap and a simple postprocessing technique resulting in a decision (a seizure is expected/not expected every 5 minutes. High sensitivity and low false positive rate with reasonable detection latency show that HHT based features are acceptable for patient specific seizure prediction from intracranial EEG data. Time spent for testing an EEG segment was 4.1451 seconds on average, which makes the system viable for use in real-time seizure control systems.
Directory of Open Access Journals (Sweden)
Banan Maayah
2014-01-01
Full Text Available A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.
Maximizing the Hilbert space for a finite number of distinguishable quantum states.
Greentree, Andrew D; Schirmer, S G; Green, F; Hollenberg, Lloyd C L; Hamilton, A R; Clark, R G
2004-03-05
Given a particular quantum computing architecture, how might one optimize its resources to maximize its computing power? We consider quantum computers with a number of distinguishable quantum states, and entangled particles shared between those states. Hilbert-space dimensionality is linked to nonclassicality and, hence, quantum computing power. We find that qutrit-based quantum computers optimize the Hilbert-space dimensionality and so are expected to be more powerful than other qudit implementations. In going beyond qudits, we identify structures with much higher Hilbert-space dimensionalities.
Application of Arbitrary-Order Hilbert Spectral Analysis to Passive Scalar Turbulence
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Huang, Y X; Lu, Z M; Liu, Y L [Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072 (China); Schmitt, F G [CNRS, Laboratory of Oceanology and Geosciences, UMR 8187, F-62930 Wimereux (France); Gagne, Y, E-mail: yongxianghuang@gmail.com [LEGI, CNRS/UJF/INPG, UMR 5519, 38041 Grenoble (France)
2011-12-22
In previous work [Huang et al., PRE 82, 26319, 2010], we found that the passive scalar turbulence field maybe less intermittent than what we believed before. Here we apply the same method, namely arbitrary-order Hilbert spectral analysis, to a passive scalar (temperature) time series with a Taylor's microscale Reynolds number Re{sub {lambda}} {approx_equal} 3000. We find that with increasing Reynolds number, the discrepancy of scaling exponents between Hilbert {xi}{sub {theta}}(q) and Kolmogorov-Obukhov-Corrsin (KOC) theory is increasing, and consequently the discrepancy between Hilbert and structure function could disappear at infinite Reynolds number.
Reconstruction from free-breathing cardiac MRI data using reproducing kernel Hilbert spaces.
Cîndea, Nicolae; Odille, Freddy; Bosser, Gilles; Felblinger, Jacques; Vuissoz, Pierre-André
2010-01-01
This paper describes a rigorous framework for reconstructing MR images of the heart, acquired continuously over the cardiac and respiratory cycle. The framework generalizes existing techniques, commonly referred to as retrospective gating, and is based on the properties of reproducing kernel Hilbert spaces. The reconstruction problem is formulated as a moment problem in a multidimensional reproducing kernel Hilbert spaces (a two-dimensional space for cardiac and respiratory resolved imaging). Several reproducing kernel Hilbert spaces were tested and compared, including those corresponding to commonly used interpolation techniques (sinc-based and splines kernels) and a more specific kernel allowed by the framework (based on a first-order Sobolev RKHS). The Sobolev reproducing kernel Hilbert spaces was shown to allow improved reconstructions in both simulated and real data from healthy volunteers, acquired in free breathing. Copyright (c) 2009 Wiley-Liss, Inc.
3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries
DEFF Research Database (Denmark)
Ujang, Uznir; Antón Castro, Francesc/François; Azri, Suhaibah
2014-01-01
objects. In this research, the authors 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, they extend the Hilbert space-filling curve to one higher dimension for 3D city model data implementations. The query performance was tested for single object, nearest neighbor and range search queries 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 sub-interval of the ([0,1]) interval to the corresponding...
Stable sheaves on a smooth quadric surface with linear Hilbert bipolynomials.
Ballico, Edoardo; Huh, Sukmoon
2014-01-01
We investigate the moduli spaces of stable sheaves on a smooth quadric surface with linear Hilbert bipolynomial in some special cases and describe their geometry in terms of the locally free resolution of the sheaves.
Homborg, A.M.; Westing, E.P.M. van; Tinga, T.; Ferrari, G.M.; Zhang, X.; Wit, J.H.W. de; Mol, J.M.C.
2014-01-01
This study validates the ability of Hilbert spectra to investigate transients in an electrochemical noise signal for an aqueous corrosion inhibition process. The proposed analysis procedure involves the identification and analysis of transients in the electrochemical current noise signal. Their
On the minimizers of calculus of variations problems in Hilbert spaces
Gomes, Diogo A.
2014-01-19
The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert spaces. © 2014 Springer-Verlag Berlin Heidelberg.
Homborg, A.M.; Westing, E.P.M.; Tinga, Tiedo; Ferrari, G.M.; Zhang, X; de Wit, J.H.W.; Mol, J.M.C.
2013-01-01
This study validates the ability of Hilbert spectra to investigate transients in an electrochemical noise signal for an aqueous corrosion inhibition process. The proposed analysis procedure involves the identification and analysis of transients in the electrochemical current noise signal. Their
Hilbert space inverse wave imaging in a planar multilayer environment.
Lehman, Sean K
2005-05-01
Most diffraction tomography (DT) algorithms use a homogeneous Green function (GF) regardless of the medium being imaged. This choice is usually motivated by practical considerations: analytic inversions in standard geometries (Cartesian, spherical, etc.) are significantly simplified by the use of a homogeneous GF, estimating a nonhomogeneous GF can be very difficult, as can incorporating a nonhomogeneous GF into standard DT algorithms. Devaney has circumvented these issues by developing a purely numerical DT inversion algorithm [A. J. Devaney and M. Dennison, Inverse Probl. 19, 855-870 (2003)] that is independent of measurement system geometry, number of frequencies used in the reconstruction, and GF. A planar multilayer GF has been developed for use in Devaney's "Hilbert space" algorithm and used in a proof-of-principle nondestructive evaluation (NDE) experiment to image noninvasively a flaw in an aluminum/copper planar multilayer medium using data collected from an ultrasonic measurement system. The data were collected in a multistatic method with no beamforming: all focusing through the multilayer was performed mathematically "after-the-fact," that is, after the data were collected.
Clustering in Hilbert space of a quantum optimization problem
Morampudi, S. C.; Hsu, B.; Sondhi, S. L.; Moessner, R.; Laumann, C. R.
2017-10-01
The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground-state subspace of a certain quantum optimization problem. This involves extending the notion of clustering to Hilbert space, where the classical Hamming distance is not immediately useful. Quantum clusters correspond to macroscopically distinct subspaces of the full quantum ground-state space which grow with the system size. We explicitly demonstrate that such clusters arise in the solution space of random quantum satisfiability (3-QSAT) at its satisfiability transition. We estimate both the number of these clusters and their internal entropy. The former are given by the number of hard-core dimer coverings of the core of the interaction graph, while the latter is related to the underconstrained degrees of freedom not touched by the dimers. We additionally provide numerical evidence suggesting that the 3-QSAT satisfiability transition may coincide with the product satisfiability transition, which would imply the absence of an intermediate entangled satisfiable phase.
Alabiso, Carlo
2015-01-01
This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all sub...
Z-related pairs in microtonal systems
Althuis, T.A.; Gobel, F.
2000-01-01
Various infinite families of Z-related pairs in microtonal systems are presented. Soderberg's dual inversion is compared to a more special transformation, the one-pitch shift. The material is illustrated by several examples.
2014-11-19
The Generalized Empirical Interpolation Method: stability theory on Hilbert spaces with an application to the Stokes equation Maday, Y.a,b,c,e, Mula...interpolant (the Lebesgue constant) by relating it to an inf-sup problem in the case of Hilbert spaces . In the second part of the paper, it will be explained...SUBTITLE The Generalized Empirical Interpolation Method: stability theory on Hilbert spaces with an application to the Stokes equation 5a. CONTRACT
Soft and hard classification by reproducing kernel Hilbert space methods.
Wahba, Grace
2002-12-24
Reproducing kernel Hilbert space (RKHS) methods provide a unified context for solving a wide variety of statistical modelling and function estimation problems. We consider two such problems: We are given a training set [yi, ti, i = 1, em leader, n], where yi is the response for the ith subject, and ti is a vector of attributes for this subject. The value of y(i) is a label that indicates which category it came from. For the first problem, we wish to build a model from the training set that assigns to each t in an attribute domain of interest an estimate of the probability pj(t) that a (future) subject with attribute vector t is in category j. The second problem is in some sense less ambitious; it is to build a model that assigns to each t a label, which classifies a future subject with that t into one of the categories or possibly "none of the above." The approach to the first of these two problems discussed here is a special case of what is known as penalized likelihood estimation. The approach to the second problem is known as the support vector machine. We also note some alternate but closely related approaches to the second problem. These approaches are all obtained as solutions to optimization problems in RKHS. Many other problems, in particular the solution of ill-posed inverse problems, can be obtained as solutions to optimization problems in RKHS and are mentioned in passing. We caution the reader that although a large literature exists in all of these topics, in this inaugural article we are selectively highlighting work of the author, former students, and other collaborators.
Fractional Transforms in Optical Information Processing
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Maria Luisa Calvo
2005-06-01
Full Text Available We review the progress achieved in optical information processing during the last decade by applying fractional linear integral transforms. The fractional Fourier transform and its applications for phase retrieval, beam characterization, space-variant pattern recognition, adaptive filter design, encryption, watermarking, and so forth is discussed in detail. A general algorithm for the fractionalization of linear cyclic integral transforms is introduced and it is shown that they can be fractionalized in an infinite number of ways. Basic properties of fractional cyclic transforms are considered. The implementation of some fractional transforms in optics, such as fractional Hankel, sine, cosine, Hartley, and Hilbert transforms, is discussed. New horizons of the application of fractional transforms for optical information processing are underlined.
Lossless compression of medical images using Hilbert space-filling curves.
Liang, Jan-Yie; Chen, Chih-Sheng; Huang, Chua-Huang; Liu, Li
2008-04-01
A Hilbert space-filling curve is a curve traversing the 2(n) x 2(n)two-dimensional space and it visits neighboring points consecutively without crossing itself. The application of Hilbert space-filling curves in image processing is to rearrange image pixels in order to enhance pixel locality. A computer program of the Hilbert space-filling curve ordering generated from a tensor product formula is used to rearrange pixels of medical images. We implement four lossless encoding schemes, run-length encoding, LZ77 coding, LZW coding, and Huffman coding, along with the Hilbert space-filling curve ordering. Combination of these encoding schemes are also implemented to study the effectiveness of various compression methods. In addition, differential encoding is employed to medical images to study different format of image representation to the above encoding schemes. In the paper, we report the testing results of compression ratio and performance evaluation. The experiments show that the pre-processing operation of differential encoding followed by the Hilbert space-filling curve ordering and the compression method of LZW coding followed by Huffman coding will give the best compression result.
Applying Hilbert spatial ordering code to partition massive spatial data in PC cluster system
Wang, Yongjie; Hong, Xinlan; Meng, Lingkui; Zhao, Chunyu
2006-10-01
In order to handle massive spatial data quickly and efficiently, a superior solution is to store and handle them in parallel spatial database management systems under the environment of PC cluster at present, and thus its spatial partitioning strategy of data needs solving first. Hilbert spatial ordering code based on Hilbert space-filling curve is an excellent linear mapping method, and gets wider and wider applications in processing spatial data. After studying Hilbert curve, this paper proposes a new and efficient algorithm for the generation of Hilbert code, and it has overcome drawbacks of the traditional algorithm. Then Hilbert code is applied to spatial partitioning with the method of cluster analysis, and a concrete method is given, which fully considers characteristics of spatial data, such as the aggregation of spatial data, reduces the time of disks accesses, and achieves better performance by experiments than the compulsory partitioning of ORACLE Spatial based on X coordinate values and (or) Y coordinate values in subsequent parallel processing of spatial data.
Silva, Ralph; Manzano, Gonzalo; Skrzypczyk, Paul; Brunner, Nicolas
2016-09-01
Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.
Bounds for the Hilbert function of polynomial ideals and for the degrees in the Nullstellensatz
Sombra, M
1996-01-01
We present a new effective Nullstellensatz with bounds for the degrees which depend not only on the number of variables and on the degrees of the input polynomials but also on an additional parameter called the {\\it geometric degree of the system of equations}. The obtained bound is polynomial in these parameters. It is essentially optimal in the general case, and it substantially improves the existent bounds in some special cases. The proof of this result is combinatorial, and it relies on global estimations for the Hilbert function of homogeneous polynomial ideals. In this direction, we obtain a lower bound for the Hilbert function of an arbitrary homogeneous polynomial ideal, and an upper bound for the Hilbert function of a generic hypersurface section of an unmixed radical polynomial ideal.
Experimental Investigation of a Direct Methanol Fuel Cell with Hilbert Fractal Current Collectors
Directory of Open Access Journals (Sweden)
Jing-Yi Chang
2014-01-01
Full Text Available The Hilbert curve is a continuous type of fractal space-filling curve. This fractal curve visits every point in a square grid with a size of 2×2, 4×4, or any other power of two. This paper presents Hilbert fractal curve application to direct methanol fuel cell (DMFC current collectors. The current collectors are carved following first, second, and third order Hilbert fractal curves. These curves give the current collectors different free open ratios and opening perimeters. We conducted an experimental investigation into DMFC performance as a function of the free open ratio and opening perimeter on the bipolar plates. Nyquist plots of the bipolar plates are made and compared using electrochemical impedance spectroscopy (EIS experiments to understand the phenomena in depth. The results obtained in this paper could be a good reference for future current collector design.
Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications
Directory of Open Access Journals (Sweden)
Lokenath Debnath
2012-01-01
Full Text Available This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in inequalities are the best possible. Many particular cases of Hilbert-type inequalities are presented with numerous applications. A large number of major books and recent research papers published during 2009–2012 are included to stimulate new interest in future study and research.
Asymmetric Ion-Pairing Catalysis
Brak, Katrien
2014-01-01
Charged intermediates and reagents are ubiquitous in organic transformations. The interaction of these ionic species with chiral neutral, anionic, or cationic small molecules has emerged as a powerful strategy for catalytic, enantioselective synthesis. This review describes developments in the burgeoning field of asymmetric ion-pairing catalysis with an emphasis on the insights that have been gleaned into the structural and mechanistic features that contribute to high asymmetric induction. PMID:23192886
Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces
Zhou, Haiyun
2008-07-01
Let C be a closed convex subset of a real Hilbert space H and assume that T is a [kappa]-strict pseudo-contraction on C. Consider Mann's iteration algorithm given by It is proved that if the control sequence {[alpha]n} is chosen so that [kappa]Rhoades [B.E. Rhoades, Fixed point iterations using infinite matrices, Trans. Amer. Math. Soc. 196 (1974) 162-176] and of Marino and Xu [G. Marino, H.-K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (1) (2007) 336-346].
Nanostructures with the Hilbert curve geometry as surface enhanced Raman scattering substrates
Grigorenko, Ilya
2013-07-01
In this work, we consider fractal substrates for Surface Enhanced Raman Scattering measurements. The shape of the substrates is based on self-similar space filling Hilbert curves, which possess properties of both one dimensional and two dimensional geometries. The dielectric response of a doped semiconductor nanostructure, where conducting electrons are trapped in an effective potential having the geometry of the Hilbert curve is calculated and analysed. It is found that the system may exhibit electronic collective excitations specific for either a two dimensional or one dimensional system, depending on the excitation frequency.
Sampling in the Linear Canonical Transform Domain
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Bing-Zhao Li
2012-01-01
Full Text Available This paper investigates the interpolation formulae and the sampling theorem for bandpass signals in the linear canonical transform (LCT domain. Firstly, one of the important relationships between the bandpass signals in the Fourier domain and the bandpass signals in the LCT domain is derived. Secondly, two interpolation formulae from uniformly sampled points at half of the sampling rate associated with the bandpass signals and their generalized Hilbert transform or the derivatives in the LCT domain are obtained. Thirdly, the interpolation formulae from nonuniform samples are investigated. The simulation results are also proposed to verify the correctness of the derived results.
Energy Technology Data Exchange (ETDEWEB)
Szu, H.; Hsu, C. [Univ. of Southwestern Louisiana, Lafayette, LA (United States)
1996-12-31
Human sensors systems (HSS) may be approximately described as an adaptive or self-learning version of the Wavelet Transforms (WT) that are capable to learn from several input-output associative pairs of suitable transform mother wavelets. Such an Adaptive WT (AWT) is a redundant combination of mother wavelets to either represent or classify inputs.
Stochastic control of infinite dimensional systems in Hilbert space: A factorization perspective
Milman, Mark M.; Schumitzky, Alan
1987-01-01
A factorization perspective on problems of optimal causal estimation and optimal causal control of linear stochastic systems defined on an infinite-dimensional Hilbert space is presented. A separation principle is derived for the case in which the system input/output map is generated by an abstract evolution operator. The factorization formalism allows for an essentially algebraic approach to these problems.
Growth estimates for $\\exp(A^{-1}t)$ on a Hilbert space
Zwart, Heiko J.
2007-01-01
Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space $H$. Since $A^{-1}$ is a bounded operator, it is the infinitesimal generator of a strongly continuous semigroup. In this paper we show that the growth of this semigroup is bounded by
Approximately dual frames in Hilbert spaces and applications to Gabor frames
DEFF Research Database (Denmark)
Christensen, Ole; Laugesen, Richard S.
2011-01-01
Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames...
The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space.
Censor, Y; Gibali, A; Reich, S
2011-02-01
We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.
New Hybrid Iterative Schemes for an Infinite Family of Nonexpansive Mappings in Hilbert Spaces
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Guo Baohua
2010-01-01
Full Text Available We propose some new iterative schemes for finding common fixed point of an infinite family of nonexpansive mappings in a Hilbert space and prove the strong convergence of the proposed schemes. Our results extend and improve ones of Nakajo and Takahashi (2003.
Scattering analysis of asymmetric metamaterial resonators by the Riemann-Hilbert approach
DEFF Research Database (Denmark)
Kaminski, Piotr Marek; Ziolkowski, Richard W.; Arslanagic, Samel
2016-01-01
with an aperture. Exact analytical solution of the problem is derived; it is based on the n-series approach which is casted into the equivalent Riemann-Hilbert problem. The examined configuration leads to large enhancements of the radiated field and to steerable Huygens-like directivity patterns. Particularly...
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Shahnam Javadi
2014-10-01
Full Text Available In this paper, we apply the new implementation of reproducing kernel Hilbert space method to give the approximate solution to some functional integral equations of the second kind. To show its effectiveness and convenience, some examples are given.
The basis of the physical Hilbert space of lattice gauge theories
Energy Technology Data Exchange (ETDEWEB)
Burgio, G. E-mail: burgio@parma.infn.it; De Pietri, R.; Morales-Tecotl, H.A.; Urrutia, L.F.; Vergara, J.D
2000-02-07
Non-linear Fourier analysis on compact groups is used to construct an orthonormal basis of the physical (gauge invariant) Hilbert space of Hamiltonian lattice gauge theories. In particular, the matrix elements of the Hamiltonian operator involved are explicitly computed. Finally, some applications and possible developments of the formalism are discussed.
A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces
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Singthong Urailuk
2010-01-01
Full Text Available We introduce a new general iterative method by using the -mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert spaces. A strong convergence theorem of the purposed iterative method is established under some certain control conditions. Our results improve and extend the results announced by many others.
The classes of the quasihomogeneous Hilbert schemes of points on the plane
Buryak, A.
2012-01-01
Abstract: In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of -quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric interpretation of the -Catalan numbers. Finally, we
A Canonical Analysis of the Einstein-Hilbert Action in First Order Form
Kiriushcheva, N.; Kuzmin, S. V.; McKeon, D. G. C.
2006-01-01
Using the Dirac constraint formalism, we examine the canonical structure of the Einstein-Hilbert action $S_d = \\frac{1}{16\\pi G} \\int d^dx \\sqrt{-g} R$, treating the metric $g_{\\alpha\\beta}$ and the symmetric affine connection $\\Gamma_{\\mu\
Noncommutative Grobner basis, Hilbert series, Anick's resolution and BERGMAN under MS-DOS
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S. Cojocaru
1995-06-01
Full Text Available The definition and main results connected with Grцbner basis, Hilbert series and Anick's resolution are formulated. The method of the infinity behavior prediction of Grцbner basis in noncommutative case is presented. The extensions of BERGMAN package for IBM PC compatible computers are described.
Hilbert space method for the numerical solution of reactor physics problems
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T. (UKAEA Risley Nuclear Power Development Labs.)
1983-01-01
A Hilbert space approach is used to give a unified treatment of neutron transport by finite element methods. Global solutions can be found by least squares, variational and weighted residual methods stemming from an identity. Bounds for local characteristics of solutions are found by a bi-variational method.
Energy Technology Data Exchange (ETDEWEB)
Degroote, M. [Rice Univ., Houston, TX (United States); Henderson, T. M. [Rice Univ., Houston, TX (United States); Zhao, J. [Rice Univ., Houston, TX (United States); Dukelsky, J. [Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia; Scuseria, G. E. [Rice Univ., Houston, TX (United States)
2018-01-03
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. 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.
DEFF Research Database (Denmark)
Wang, Wei; Zhang, Shun; Ma, Ning
2015-01-01
In this paper, a high-dimensional statistical signal processing is revisited with the aim of introducing the concept of vector signal representation derived from the Riesz transforms, which are the natural extension and generalization of the one-dimensional Hilbert transform. Under the new concep...... of vector correlations proposed recently, the statistical properties of the vector signal representation for random signal are presented and some applications to speckle metrology developed recently are reviewed to demonstrate the unique capability of Riesz transforms....
The unified transform method for the Sasa-Satsuma equation on the half-line.
Xu, Jian; Fan, Engui
2013-11-08
We implement the unified transform method to the initial-boundary value (IBV) problem of the Sasa-Satsuma equation on the half line. In addition to presenting the basic Riemann-Hilbert formalism, which linearizes this IBV problem, we also analyse the associated general Dirichlet to Neumann map using the so-called global relation.
Endocrine factors of pair bonding.
Stárka, L
2007-01-01
Throughout literature--fiction and poetry, fine arts and music--falling in love and enjoying romantic love plays a central role. While several psychosocial conceptions of pair attachment consider the participation of hormones, human endocrinology has dealt with this theme only marginally. According to some authors in addictology, falling in love shows some signs of hormonal response to stressors with changes in dopamine and serotonin signalling and neurotrophin (transforming growth factor b) concentration. Endorphins, oxytocin and vasopressin may play a role during the later phases of love. However, proof of hormonal events associated with love in humans has, until recently, been lacking.
Effective realistic interactions for low momentum Hilbert spaces
Energy Technology Data Exchange (ETDEWEB)
Weber, Dennis
2012-12-13
described method to calculate the operator representation is applied to different effective realistic potentials. In a first application the Argonne V18 potential, transformed by means of the Unitary Correlation Operator Method (UCOM), is considered. As second application an operator representation of the Similarity Renormalization Group (SRG) transformed Argonne potential is obtained. Finally an operator representation of the JISP16 interaction, which is specifically designed for the harmonic oscillator basis, is derived by using the same ansatz as for the SRG transformed Argonne potential.Summing up, there is no general set of operators which can be used to describe all the different effective interactions by just adjusting the particular radial functions. However, it is possible to find a suitable operator representation, even for effective operators that are specifically designed for numerical feasibility and are treating each partial wave separately.
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George Isac
2004-01-01
Full Text Available In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators.
Slices to sums of adjoint orbits, the Atiyah-Hitchin manifold, and Hilbert schemes of points
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Bielawski Roger
2017-02-01
Full Text Available We show that the regular Slodowy slice to the sum of two semisimple adjoint orbits of GL(n, ℂ is isomorphic to the deformation of the D2-singularity if n = 2, the Dancer deformation of the double cover of the Atiyah-Hitchin manifold if n = 3, and to the Atiyah-Hitchin manifold itself if n = 4. For higher n, such slices to the sum of two orbits, each having only two distinct eigenvalues, are either empty or biholomorphic to open subsets of the Hilbert scheme of points on one of the above surfaces. In particular, these open subsets of Hilbert schemes of points carry complete hyperkähler metrics. In the case of the double cover of the Atiyah-Hitchin manifold this metric turns out to be the natural L2-metric on a hyperkähler submanifold of the monopole moduli space.
The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping
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Jarosław Górnicki
2009-01-01
Full Text Available The purpose of this paper is to prove, by asymptotic center techniques and the methods of Hilbert spaces, the following theorem. Let H be a Hilbert space, let C be a nonempty bounded closed convex subset of H, and let M=[an,k]n,k≥1 be a strongly ergodic matrix. If T:C→C is a lipschitzian mapping such that liminfn→∞infm=0,1,...∑k=1∞an,k·‖Tk+m‖2<2, then the set of fixed points Fix T={x∈C:Tx=x} is a retract of C. This result extends and improves the corresponding results of [7, Corollary 9] and [8, Corollary 1].
Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space.
Poulin, David; Qarry, Angie; Somma, Rolando; Verstraete, Frank
2011-04-29
We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a well-known counting argument. This also demonstrates that a computational model based on arbitrarily rapidly changing Hamiltonians is no more powerful than the standard quantum circuit model.
A novel autofocusing method using the angle of Hilbert space for microscopy.
Tan, Zuojun; Sun, Dehui; Xie, Jing; Chen, Lu; Li, Liang
2014-04-01
Autofocusing technology is indispensable for routine use of microscopes on a large scale in biological field. The autofocusing method using the angle of Hilbert space is brought forward to measure whether the image is focused or not. The angle of Hillbert space can be used to evaluate accurately the similarity degree of two images. The experiment results show that the autofocusing method can decrease the computational cost and get accuracy for real-time biological and biomedical images with noise robustness. The focus curves are smooth and possess the unimodality, the monotonicity and the symmetry. Compared with other classic and optimum focus method, the Hilbert method demonstrates its robustness to noise and can improve the focus speed. The experiments showed that the proposed method can increase the overall performance of an autofocus system and has strong applicability in various autofocusing algorithms. Copyright © 2014 Wiley Periodicals, Inc.
Hilbert Series and Mixed Branches of T[SU(N)] theories
Energy Technology Data Exchange (ETDEWEB)
Carta, Federico [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Hayashi, Hirotaka [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Tokai University,4-1-1 Kitakaname, Hiratsuka, Kanagawa 259-1292 (Japan)
2017-02-07
We consider mixed branches of 3dN=4T[SU(N)] theory. We compute the Hilbert series of the Coulomb branch part of the mixed branch from a restriction rule acting on the Hilbert series of the full Coulomb branch that will truncate the magnetic charge summation only to the subset of BPS dressed monopole operators that arise in the Coulomb branch sublocus where the mixed branch stems. This restriction can be understood directly from the type IIB brane picture by a relation between the magnetic charges of the monopoles and brane position moduli. We also apply the restriction rule to the Higgs branch part of a given mixed branch by exploiting 3d mirror symmetry. Both cases show complete agreement with the results calculated by different methods.
Free probability induced by electric resistance networks on energy Hilbert spaces
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Ilwoo Cho
2011-01-01
Full Text Available We show that a class of countable weighted graphs arising in the study of electric resistance networks (ERNs are naturally associated with groupoids. Starting with a fixed ERN, it is known that there is a canonical energy form and a derived energy Hilbert space \\(H_{\\mathcal{E}}\\. From \\(H_{\\mathcal{E}}\\, one then studies resistance metrics and boundaries of the ERNs. But in earlier research, there does not appear to be a natural algebra of bounded operators acting on \\(H_{\\mathcal{E}}\\. With the use of our ERN-groupoid, we show that \\(H_{\\mathcal{E}}\\ may be derived as a representation Hilbert space of a universal representation of a groupoid algebra \\(\\mathfrak{A}_G\\, and we display other representations. Among our applications, we identify a free structure of \\(\\mathfrak{A}_G\\ in terms of the energy form.
On the duality of c-fusion frames in Hilbert spaces
Rahimi, A.; Darvishi, Z.; Daraby, B.
2017-12-01
Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may not be defined. To overcome this problem, the new concept namely Q-dual for c-fusion frames will be defined and some of its properties will be investigated.
First-order selfadjoint singular differential operators in a Hilbert space of vector functions
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Pembe Ipek
2017-06-01
Full Text Available In this article, we give a representation of all selfadjoint extensions of the minimal operator generated by first-order linear symmetric multipoint singular differential expression, with operator coefficient in the direct sum of Hilbert spaces of vector-functions defined at the semi-infinite intervals. To this end we use the Calkin-Gorbachuk method. Finally, the geometry of spectrum set of such extensions is researched.
On synchronal algorithm for fixed point and variational inequality problems in hilbert spaces.
Bulama, L M; Kılıçman, A
2016-01-01
The aim of this article is to expand and generalize some approximation methods proposed by Tian and Di (J Fixed Point Appl, 2011. doi:10.1186/1687-1812-21) to the class of [Formula: see text]-total asymptotically strict pseudocontraction to solve the fixed point problem as well as variational inequality problem in the frame work of Hilbert space. Further, the results presented in this paper extend, improve and also generalize several known results in the literature .
Hilbert spaces contractively included in the Hardy space of the bidisk
Alpay, D.; Bolotnikov, V.; Dijksma, A.; Sadosky, C.
We study the reproducing kernel Hilbert spaces h(D-2,S) with kernels of the form I-S(z(1),z(2)>)S(w(1),w(2))*/(1-z(1)w(1)*) (1-z(2)w(2)*) where S(z(1),z(2)) is a Schur function of two variables z(1),z(2)is an element of D. They are analogs of the spaces h(D,S) with reproducing kernel
Haiyun Zhou; Shin Min Kang; Yeol Je Cho
2008-01-01
Abstract Let be a real Hilbert space, a nonempty closed convex subset of , and a maximal monotone operator with . Let be the metric projection of onto . Suppose that, for any given , , and , there exists satisfying the following set-valued mapping equation: for all , where with as and is regarded as an error sequence such that . Let be a real sequence such that as and . For any fixed , define a sequence iteratively as for all . Then converges stron...
Hilbert series and operator basis for NRQED and NRQCD/HQET
Kobach, Andrew; Pal, Sridip
2017-09-01
We use a Hilbert series to construct an operator basis in the 1 / m expansion of a theory with a nonrelativistic heavy fermion in an electromagnetic (NRQED) or color gauge field (NRQCD/HQET). We present a list of effective operators with mass dimension d ≤ 8. Comparing to the current literature, our results for NRQED agree for d ≤ 8, but there are some discrepancies in NRQCD/HQET at d = 7 and 8.
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
W. Luo and P. Sarnak have proved quantum unique ergodicity for Eisenstein series on $PSL(2,Z) \\backslash H$. We extend their result to Eisenstein series on $PSL(2,O) \\backslash H^n$, where $O$ is the ring of integers in a totally real field of degree $n$ over $Q$ with narrow class number one, usi...... the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms....
Energy Technology Data Exchange (ETDEWEB)
Theiler, James P [Los Alamos National Laboratory
2009-01-01
Following an analogous distinction in statistical hypothesis testing, we investigate variants of machine learning where the training set comes in matched pairs. We demonstrate that even conventional classifiers can exhibit improved performance when the input data has a matched-pair structure. Online algorithms, in particular, converge quicker when the data is presented in pairs. In some scenarios (such as the weak signal detection problem), matched pairs can be generated from independent samples, with the effect not only doubling the nominal size of the training set, but of providing the structure that leads to better learning. A family of 'dipole' algorithms is introduced that explicitly takes advantage of matched-pair structure in the input data and leads to further performance gains. Finally, we illustrate the application of matched-pair learning to chemical plume detection in hyperspectral imagery.
Strong Convergence Theorems for a Pair of Strictly Pseudononspreading Mappings
Directory of Open Access Journals (Sweden)
Bin-Chao Deng
2013-01-01
Full Text Available Let H be a real Hilbert space. Let T1,T2:H→H be k1-, k2-strictly pseudononspreading mappings; let αn and βn be two real sequences in (0,1. For given x0∈H, the sequence xn is generated iteratively by xn+1=βnxn+1-βnTw1αnγfxn+I-μαnBTw2xn, ∀n∈N, where Twi=1−wiI+wiTi with i=1,2 and B:H→H is strongly monotone and Lipschitzian. Under some mild conditions on parameters αn and βn, we prove that the sequence xn converges strongly to the set FixT1∩FixT2 of fixed points of a pair of strictly pseudononspreading mappings T1 and T2.
Facts about the Fourier-Stieltjes Transform of Vector Measures on Compact Groups
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Yaogan MENSAH
2013-07-01
Full Text Available This paper gives an interpretation of the Fourier-Stieltjes transform of vector measures by means of the tensor product of Hilbert spaces. It also extends the Kronecker product to some operators arising from the Fourier-Stieltjes transformation and associated with the equivalence classes of unitary representations of a compact group. We obtain among other results the effect of this product on convolution of vector measures.
Signal transforms in dynamic measurements
Layer, Edward
2015-01-01
This book is devoted to the analysis of measurement signals which requires specific mathematical operations like Convolution, Deconvolution, Laplace, Fourier, Hilbert, Wavelet or Z transform which are all presented in the present book. The different problems refer to the modulation of signals, filtration of disturbance as well as to the orthogonal signals and their use in digital form for the measurement of current, voltage, power and frequency are also widely discussed. All the topics covered in this book are presented in detail and illustrated by means of examples in MathCad and LabVIEW. This book provides a useful source for researchers, scientists and engineers who in their daily work are required to deal with problems of measurement and signal processing and can also be helpful to undergraduate students of electrical engineering.
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Huibo Meng
2012-03-01
Full Text Available The turbulent flow in a Kenics Static Mixer (KSM was intensified under the mutual-coupling effect between the twisted leaves and the tube-wall. In order to understand the intrinsic features of turbulent flow in KSM, the Hilbert-Huang Transform based on Empirical Mode Decomposition were first introduced to describe the time-frequency features of the pressure fluctuation. The Hilbert spectra of pressure fluctuation time series were quantitatively evaluated under different Reynolds numbers, and different radial and axial positions, respectively. The experimental results showed that: the fluctuation frequencies of pressure signals in a KSM were mainly distributed below 40 Hz, and more than 68% of the energy of signals is concentrated within 10 Hz. Compared with the other IMFs, the pressure component of C6 in the range of 7.82~15.63 Hz has the maximum fluctuation energy ratio. As the flow rate increases, the energy of fluctuation of fluid micelles and the proportion of low-frequency energy increases. The pressure fluctuation with higher energy ratio of low frequency (0~10 Hz had lower amplitudes at r/R=0.3 because of the core of forced vortex. Nevertheless, the effect of the free vortex was that the pressure fluctuation with lower energy ratio of low frequency had higher amplitudes at r/R=0.8. The higher amplitudes of pressure fluctuation at cross sections of CS3 (z=420 mm and CS5 (z=620 mm proved that the transitions between the adjacent mixing element had better mixing performance.
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Juan Ospina
2006-12-01
Full Text Available Hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. An adaptation of Tien D. Kieu¿s quantum hypercomputational algorithm is carried out for the dynamical algebra su(1, 1 of the Poschl-Teller potentials. The classically incomputable problem that is resolved with this hypercomputational algorithm is Hilbert¿s tenth problem. We indicated that an essential mathematical condition of these algorithms is the existence of infinitedimensional unitary irreducible representations of low dimensional dynamical algebras that allow the construction of coherent states of the Barut-Girardello type. In addition, we presented as a particular case of our hypercomputational algorithm on Poschl-Teller potentials, the hypercomputational algorithm on an infinite square well presented previously by the authors.Los hipercomputadores computan funciones o números, o en general solucionan problemas que no pueden ser computados o solucionados por una máquina de Turing. Se presenta una adaptación del algoritmo cuántico hipercomputacional propuesto por Tien D. Kieu, al álgebra dinámica su(1, 1 realizada en los potenciales Pöschl-Teller. El problema clásicamente incomputable que se resuelve con este algoritmo hipercomputacional es el d´ecimo problema de Hilbert. Se señala que una condición matemática fundamental para estos algoritmos es la existencia de una representación unitaria infinito dimensional irreducible de álgebras de baja dimensión que admitan la construcción de estados coherentes del tipo Barut-Girardello. Adicionalmente se presenta como caso límite del algoritmo propuesto sobre los potenciales Pöschl-Teller, el algoritmo hipercomputacional sobre la caja de potencial infinita construido previamente por los autores.
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Ali Hadi Abdulwahid
2016-12-01
Full Text Available Nowadays, the use of distributed generation (DG has increased because of benefits such as increased reliability, reduced losses, improvement in the line capacity, and less environmental pollution. The protection of microgrids, which consist of generation sources, is one of the most crucial concerns of basic distribution operators. One of the key issues in this field is the protection of microgrids against permanent and temporary failures by improving the safety and reliability of the network. The traditional method has a number of disadvantages. The reliability and stability of a power system in a microgrid depend to a great extent on the efficiency of the protection scheme. The application of Artificial Intelligence approaches was introduced recently in the protection of distribution networks. The fault detection method depends on differential relay based on Hilbert Space-Based Power (HSBP theory to achieve fastest primary protection. It is backed up by a total harmonic distortion (THD detection method that takes over in case of a failure in the primary method. The backup protection would be completely independent of the main protection. This is rarely attained in practice. This paper proposes a new algorithm to improve protection performance by adaptive network-based fuzzy inference system (ANFIS. The protection can be obtained in a novel way based on this theory. An advantage of this algorithm is that the protection system operates in fewer than two cycles after the occurrence of the fault. Another advantage is that the error detection is not dependent on the selection of threshold values, and all types of internal fault can identify and show that the algorithm operates correctly for all types of faults while preventing unwanted tripping, even if the data were distorted by current transformer (CT saturation or by data mismatches. The simulation results show that the proposed circuit can identify the faulty phase in the microgrid quickly and
Directory of Open Access Journals (Sweden)
Xingmou Liu
2016-01-01
Full Text Available This paper presents a time–frequency analysis of the vibration of transformer under direct current (DC bias through Hilbert–Huang transform (HHT. First, the theory of DC bias for the transformer was analyzed. Next, the empirical mode decomposition (EMD process, which is the key in HHT, was introduced. The results of EMD, namely, intrinsic mode functions (IMFs, were calculated and summed by Hilbert transform(HT to obtain time-dependent series in a 2D time–frequency domain. Lastly, a test system of vibration measurement for the transformer was set up. Three direction (x, y, and z axes components of core vibration were measured. Decomposition of EMD and HHT spectra showed that vibration strength increased, and odd harmonics were produced with DC bias. Results indicated that HHT is a viable signal processing tool for transformer health monitoring.
Pairing in spherical nanograins
Energy Technology Data Exchange (ETDEWEB)
Kuzmenko, N.K., E-mail: kuzmenko@NK9433.spb.ed [V.G. Khlopin Radium Institute, 2-nd Murinsky avenue 28, 194021 St.-Petersburg (Russian Federation); Mikhajlov, V.M. [Institute of Physics, St.-Petersburg State University, Ul' yanovskaya 3, 198904 Petergof (Russian Federation)
2010-02-01
Conditions are ascertained when the pairing and other thermodynamic properties of spherical nanograins with numbers of delocalized electrons N<10{sup 5} can be investigated by using the Single Shell Model (SSM) that gives the eigenvalues of the pairing Hamiltonian for a solitary shell. In the frame of SSM the exact canonical and grand canonical descriptions are employed first to analyze the absence of the abrupt superconducting-normal phase transition in finite systems in which an increase of the pairing and BCS critical temperature can be observed and secondly to study such new phenomena as the temperature re-entrance of the pairing in postcritical magnetic fields and also low temperature oscillations of the magnetic susceptibility and electronic heat capacity in an increasing uniform magnetic field.
Diagonalization of a self-adjoint operator acting on a Hilbert module
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Parfeny P. Saworotnow
1985-01-01
Full Text Available For each bounded self-adjoint operator T on a Hilbert module H over an H*-algebra A there exists a locally compact space m and a certain A-valued measure μ such that H is isomorphic to L2(μ⊗A and T corresponds to a multiplication with a continuous function. There is a similar result for a commuting family of normal operators. A consequence for this result is a representation theorem for generalized stationary processes.
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Mourad Kerboua
2014-12-01
Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.
Application of the Hilbert space average method on heat conduction models.
Michel, Mathias; Gemmer, Jochen; Mahler, Günter
2006-01-01
We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy diffusion with respect to a coarse-grained description for almost all initial states. Close to the respective equilibrium, we investigate this behavior in terms of heat transport and derive the heat conduction coefficient. Thus, we are able to show that both heat (energy) diffusive behavior as well as Fourier's law follows from and is compatible with a reversible Schrödinger dynamics on the complete level of description.
Role of the effective Hilbert-space size of the reservoir for the decoherence process.
Oliveira, Adélcio C; de Magalhães, A R Bosco
2009-08-01
We show that an environment composed by N bosons coupled through cross-Kerr interaction to an oscillator of interest can be effective at destroying quantum coherences at short times and around the revival times even if N=1 . It is analytically shown for this model that the effective Hilbert-space size is a relevant parameter for decoherence process. Based on numerical results, we investigate the long time dynamics and the classical limit. Since we are dealing with a phase reservoir, the model does not describe dissipation.
Noisy bases in Hilbert space: A new class of thermal coherent states and their properties
Vourdas, A.; Bishop, R. F.
1995-01-01
Coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, are introduced as a 'random' (or 'thermal' or 'noisy') basis in Hilbert space. A resolution of the identity for these states is proved and used to generalize the usual coherent state formalism for the finite temperature case. The Bargmann representation of an operator is introduced and its relation to the P and Q representations is studied. Generalized P and Q representations for the finite temperature case are also considered and several interesting relations among them are derived.
Energy-like Liapunov functionals for linear elastic systems on a Hilbert space.
Walker, J. A.
1973-01-01
An approach is presented for generating energy-like functionals for linear elastic dynamic systems on a Hilbert space. The objective is to obtain a family of functionals which may be used for stability analysis of the equilibrium, i.e., Liapunov functionals. Although the energy functional, when one exists, is always a member of this family, the family is shown to exist even when an energy functional does not. Several discrete and distributed-parameter examples are presented, as are certain specific techniques for utilizing this approach.
Components of the Hilbert scheme of space curves on low-degree smooth surfaces
Kleppe, Jan Oddvar; Ottem, John Christian
2015-01-01
We study maximal families W of the Hilbert scheme, H(d, g)sc, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. We give conditions on C under which W is a generically smooth component of H(d, g)sc and we determine dim W. If s = 4 and W is an irreducible component of H(d, g)sc, then the Picard number of S is at most 2 and we explicitly describe, also for s ≥ 5, non-reduced and generically smooth components in the case Pic(S) is generated by the clas...
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Sedigheh Farzaneh Javan
2017-01-01
Full Text Available A new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second-kind nonlinear integral equations. In this case, the Gram-Schmidt process is substituted by another process so that a satisfactory result is obtained. In this method, the solution is expressed in the form of a series. Furthermore, the convergence of the proposed technique is proved. In order to illustrate the effectiveness and efficiency of the method, four sample integral equations arising in electromagnetics are solved via the given algorithm.
Hilbert-diagnostics of vortex rings induced in air by a pressure pulse on a hole
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VA Arbuzov
2016-09-01
Full Text Available Formation and evolution of complementary vortical rings induced in air by a pressure pulse on a hole under various boundary conditions are investigated by Hilbert-optics methods and computer modeling. It is experimentally demonstrated that reverse ring-shaped vortices inside the chamber after its depressurization are formed not only in the case with a reduced initial pressure in the chamber as compared with the ambient atmospheric pressure but also in the case with a higher gas pressure in the chamber than the atmospheric pressure. The complementary vortex rings propagating in forward and reverse directions might significantly affect the combustion process in the jets.
Quadratic optimization of fixed points for a family of nonexpansive mappings in Hilbert space
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B. E. Rhoades
2004-06-01
Full Text Available Given a finite family of nonexpansive self-mappings of a Hilbert space, a particular quadratic functional, and a strongly positive selfadjoint bounded linear operator, Yamada et al. defined an iteration scheme which converges to the unique minimizer of the quadratic functional over the common fixed point set of the mappings. In order to obtain their result, they needed to assume that the maps satisfy a commutative type condition. In this paper, we establish their conclusion without the assumption of any type of commutativity.
Quadratic optimization of fixed points for a family of nonexpansive mappings in Hilbert space
Directory of Open Access Journals (Sweden)
Rhoades BE
2004-01-01
Full Text Available Given a finite family of nonexpansive self-mappings of a Hilbert space, a particular quadratic functional, and a strongly positive selfadjoint bounded linear operator, Yamada et al. defined an iteration scheme which converges to the unique minimizer of the quadratic functional over the common fixed point set of the mappings. In order to obtain their result, they needed to assume that the maps satisfy a commutative type condition. In this paper, we establish their conclusion without the assumption of any type of commutativity.
Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales
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Monnanda Erappa Shobha
2014-01-01
Full Text Available Recently, Vasin and George (2013 considered an iterative scheme for approximately solving an ill-posed operator equation F(x=y. In order to improve the error estimate available by Vasin and George (2013, in the present paper we extend the iterative method considered by Vasin and George (2013, in the setting of Hilbert scales. The error estimates obtained under a general source condition on x0-x^ (x0 is the initial guess and x^ is the actual solution, using the adaptive scheme proposed by Pereverzev and Schock (2005, are of optimal order. The algorithm is applied to numerical solution of an integral equation in Numerical Example section.
Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces
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Juguo Su
2012-01-01
Full Text Available The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.
Minimal sufficient positive-operator valued measure on a separable Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Kuramochi, Yui, E-mail: kuramochi.yui.22c@st.kyoto-u.ac.jp [Department of Nuclear Engineering, Kyoto University, 6158540 Kyoto (Japan)
2015-10-15
We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.
Riemann-Hilbert approach to the time-dependent generalized sine kernel
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2010-12-15
We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann-Hilbert based analysis. (orig.)
Some New Characterizations and g-Minimality and Stability of g-Bases in the Hilbert Spaces
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Xunxiang Guo
2013-01-01
Full Text Available The concept of g-basis in the Hilbert spaces is introduced by Guo (2012 who generalizes the Schauder basis in the Hilbert spaces. g-basis plays the similar role in g-frame theory to that the Schauder basis plays in frame theory. In this paper, we establish some important properties of g-bases in the Hilbert spaces. In particular, we obtain a simple condition under which some important properties established in Guo (2012 are still true. With these conditions, we also establish some new interesting properties of g-bases which are related to g-minimality. Finally, we obtain a perturbation result about g-bases.
HILBERT-PÓLYA Conjecture, Zeta Functions and Bosonic Quantum Field Theories
Andrade, Julio C.
2013-07-01
The original Hilbert and Pólya conjecture is the assertion that the nontrivial zeros of the Riemann zeta function can be the spectrum of a self-adjoint operator. So far no such operator was found. However, the suggestion of Hilbert and Pólya, in the context of spectral theory, can be extended to approach other problems and so it is natural to ask if there is a quantum mechanical system related to other sequences of numbers which are originated and motivated by Number Theory. In this paper, we show that the functional integrals associated with a hypothetical class of physical systems described by self-adjoint operators associated with bosonic fields whose spectra is given by three different sequence of numbers cannot be constructed. The common feature of the sequence of numbers considered here, which causes the impossibility of zeta regularizations, is that the various Dirichlet series attached to such sequences — such as those which are sums over "primes" of (norm P)-s have a natural boundary, i.e. they cannot be continued beyond the line Re(s) = 0. The main argument is that once the regularized determinant of a Laplacian is meromorphic in s, it follows that the series considered above cannot be a regularized determinant. In other words, we show that the generating functional of connected Schwinger functions of the associated quantum field theories cannot be constructed.
From Kant to Hilbert a source book in the foundations of mathematics
Ewald, William Bragg
1996-01-01
This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume. - ;Immanuel Kant''s Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics--algebra, geometry, number. theory, analysis, logic and set theory--with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are repro...
Junctionless Cooper pair transistor
Energy Technology Data Exchange (ETDEWEB)
Arutyunov, K. Yu., E-mail: konstantin.yu.arutyunov@jyu.fi [National Research University Higher School of Economics , Moscow Institute of Electronics and Mathematics, 101000 Moscow (Russian Federation); P.L. Kapitza Institute for Physical Problems RAS , Moscow 119334 (Russian Federation); Lehtinen, J.S. [VTT Technical Research Centre of Finland Ltd., Centre for Metrology MIKES, P.O. Box 1000, FI-02044 VTT (Finland)
2017-02-15
Highlights: • Junctionless Cooper pair box. • Quantum phase slips. • Coulomb blockade and gate modulation of the Coulomb gap. - Abstract: Quantum phase slip (QPS) is the topological singularity of the complex order parameter of a quasi-one-dimensional superconductor: momentary zeroing of the modulus and simultaneous 'slip' of the phase by ±2π. The QPS event(s) are the dynamic equivalent of tunneling through a conventional Josephson junction containing static in space and time weak link(s). Here we demonstrate the operation of a superconducting single electron transistor (Cooper pair transistor) without any tunnel junctions. Instead a pair of thin superconducting titanium wires in QPS regime was used. The current–voltage characteristics demonstrate the clear Coulomb blockade with magnitude of the Coulomb gap modulated by the gate potential. The Coulomb blockade disappears above the critical temperature, and at low temperatures can be suppressed by strong magnetic field.
Some spherical analysis related to the pairs (U (n), Hn)
Indian Academy of Sciences (India)
In this paper, we define the normalized spherical transform associated with the generalized Gelfand pair ( U ( p , q ) , H n ) , where H n is the Heisenberg group 2 + 1-dimensional and + = . We show that the normalized spherical transform F ( f ) of a Schwartz function on H n restricted to the spectrum of the Gelfand ...
DEFF Research Database (Denmark)
Dalgas, Karina Märcher
2015-01-01
Since 2000, thousands of young Filipino migrants have come to Denmark as au pairs. Officially, they are there to “broaden their cultural horizons” by living temporarily with a Danish host family, but they also conduct domestic labor in exchange for food and money, which allows them to send...
DEFF Research Database (Denmark)
Rodríguez, J. Tinguaro; Franco de los Ríos, Camilo; Gómez, Daniel
2015-01-01
In this paper we want to stress the relevance of paired fuzzy sets, as already proposed in previous works of the authors, as a family of fuzzy sets that offers a unifying view for different models based upon the opposition of two fuzzy sets, simply allowing the existence of different types of neu...
Młynarczyk, A.K.
2004-01-01
The received view on Slavic aspect is that it is intrinsically complex, and that there is little hope of discerning any substantial regularity. We argue that this view is mistaken. We argue that the vast majority of Polish verbs really do come in aspectual pairs and that far from being a mysterious
Energy Technology Data Exchange (ETDEWEB)
Lopez-Arrietea, M. G.; Solis, M. A.; De Llano, M. [Universidad Nacional Autonoma de Mexico, Mexico, D.F (Mexico)
2001-02-01
Excited cooper pairs formed in a many-fermion system are those with nonzero total center-of mass momentum (CMM). They are normally neglected in the standard Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity for being too few compared with zero CMM pairs. However, a Bose-Einstein condensation picture requires both zero and nonzero CMM pairs. Assuming a BCS model interaction between fermions we determine the populations for all CMM values of Cooper pairs by actually calculating the number of nonzero-CMM pairs relative to that of zero-CMM ones in both 2D and 3D. Although this ratio decreases rapidly with CMM, the number of Cooper pairs for any specific CMM less than the maximum (or breakup of the pair) momentum turns out to be typically larger than about 95% of those with zero-CMM at zero temperature T. Even at T {approx}100 K this fraction en 2D is still as large as about 70% for typical quasi-2D cuprate superconductor parameters. [Spanish] Los pares de cooper excitados formados en un sistema de muchos electrones, son aquellos con momentos de centro de masa (CMM) diferente de cero. Normalmente estos no son tomados en cuenta en la teoria estandar de la superconductividad de Bardeen-Cooper-Schrieffer (BCS) al suponer que su numero es muy pequeno comparados con los pares de centro de masa igual a cero. Sin embargo, un esquema de condensacion Bose-Einstein requiere de ambos pares, con CMM cero y diferente de cero. Asumiendo una interaccion modelo BCS entre los fermiones, determinamos la poblacion de pares cooper con cada uno de todos los posibles valores del CMM calculando el numero de pares con momentos de centro de masa diferente de cero relativo a los pares de CMM igual a cero, en 2D y 3D. Aunque esta razon decrece rapidamente con el CMM, el numero de pares de cooper para cualquier CMM especifico menor que el momento maximo (o rompimiento de par) es tipicamente mas grande que el 95% de aquellos con CMM cero. Aun a T {approx}100 K esta fraccion en 2D es
Nakahira, Kenji; Usuda, Tsuyoshi Sasaki
2015-01-01
We study the discrimination of multipartite quantum states by local operations and classical communication. We derive that any optimal discrimination of quantum states spanning a two-dimensional Hilbert space in which each party's space is finite dimensional is possible by local operations and one-way classical communication, regardless of the optimality criterion used and how entangled the states are.
Application of Hilbert-Huang Transform in Structural Health Monitoring: A State-of-the-Art Review
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Bo Chen
2014-01-01
Full Text Available This paper reviews the development and application of HHT in the field of SHM in the last two decades. The challenges and future trends in the development of HHT based techniques for the SHM of civil engineering structures are also put forward. It also reviews the basic principle of the HHT method, which contains the extraction of the intrinsic mode function (IMF, mechanism of the EMD, and the features of HT; shows the application of HHT in the system identification, which contains the introduction of theoretical method, the identification of modal parameters, and the system identification on real structures; and discusses the structural damage detection using HHT based approaches, which includes the detection of common damage events, sudden damage events, and cracks and flaws.
Appell Transformation and Canonical Transforms
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Amalia Torre
2011-07-01
Full Text Available The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell transformation, well known in the theory of heat equation, is shown to be amenable for a similar interpretation involving the Laplace transform rather than the Fourier transform, when dealing with the 1D heat equation. Accordingly, when considering the radial heat equation, suitably defined Hankel-type transforms come to be involved in the inherent Appell transformation. The analysis is aimed at outlining the link between the Appell transformation and the canonical transforms.
Exploring Function Transformations Using the Common Core
Hall, Becky; Giacin, Rich
2013-01-01
When examining transformations of the plane in geometry, teachers typically have students experiment with transformations of polygons. Students are usually quick to notice patterns with ordered pairs. The Common Core State Standard, Geometry, Congruence 2 (G-CO.2), requires students to describe transformations as functions that take points in the…
On the surface nature of the nuclear pairing
Baldo, M.; Lombardo, U.; Saperstein, E. E.; Zverev, M. V.
2004-03-01
The surface nature of nuclear pairing is confirmed microscopically. A two-step approach is used in which the full Hilbert space S is split into the model subspace S0 and the complementary one, S‧. The gap equation is solved in the model space in terms of the effective interaction Veffp which obeys the Bethe-Goldstone-type equation in the complementary subspace. The simplest nuclear systems with one-dimensional inhomogeneity are considered, i.e. semi-infinite nuclear matter and the nuclear slab. Numerical solution is carried out for the separable representation of the Paris NN-potential. The equation for the effective pairing interaction is solved directly, without use of any form of local approximation. A version of the local approximation, the local potential approximation, is suggested which works sufficiently well even in the surface region. The effective pairing interaction obtained in our calculations reveals a strong variation in the surface region changing from a strong attraction outside the nuclear matter to almost zero value inside. The effective interaction is found to be dependent on the chemical potential μ. At μ=-8 MeV, it reproduces qualitatively the phenomenological density-dependent effective pairing interaction, with the surface dominance, which was found previously in the self-consistent finite Fermi systems theory and in the new version of the energy functional method by Fayans et al. As | μ| decreases, the surface attraction becomes stronger. The gap equation was solved in semi-infinite matter and in the slab system with the help of the method by Khodel, Khodel and Clark which was suggested recently for nuclear matter. This method extended to non-homogeneous systems turned out to be very efficient in this case. The gap Δ found for both the systems exhibits a strong variation in the surface region with a pronounced maximum near the surface. The surface effect in Δ turned out to be μ-dependent being enhanced at small | μ|.
Martín-Merino, Manuel; Blanco, Angela; De Las Rivas, Javier
2009-01-01
DNA microarrays provide rich profiles that are used in cancer prediction considering the gene expression levels across a collection of related samples. Support Vector Machines (SVM) have been applied to the classification of cancer samples with encouraging results. However, they rely on Euclidean distances that fail to reflect accurately the proximities among sample profiles. Then, non-Euclidean dissimilarities provide additional information that should be considered to reduce the misclassification errors. In this paper, we incorporate in the nu-SVM algorithm a linear combination of non-Euclidean dissimilarities. The weights of the combination are learnt in a (Hyper Reproducing Kernel Hilbert Space) HRKHS using a Semidefinite Programming algorithm. This approach allows us to incorporate a smoothing term that penalizes the complexity of the family of distances and avoids overfitting. The experimental results suggest that the method proposed helps to reduce the misclassification errors in several human cancer problems.
Cheng, Ching-An; Huang, Han-Pang; Hsu, Huan-Kun; Lai, Wei-Zh; Cheng, Chih-Chun
2016-07-01
We investigate the modeling of inverse dynamics without prior kinematic information for holonomic rigid-body robots. Despite success in compensating robot dynamics and friction, general inverse dynamics models are nontrivial. Rigid-body models are restrictive or inefficient; learning-based models are generalizable yet require large training data. The structured kernels address the dilemma by embedding the robot dynamics in reproducing kernel Hilbert space. The proposed kernels autonomously converge to rigid-body models but require fewer samples; with a semi-parametric framework that incorporates additional parametric basis for friction, the structured kernels can efficiently model general rigid-body robots. We tested the proposed scheme in simulations and experiments; the models that consider the structure of function space are more accurate.
Zhou, Shaohua Kevin; Chellappa, Rama
2006-06-01
This paper addresses the problem of characterizing ensemble similarity from sample similarity in a principled manner. Using reproducing kernel as a characterization of sample similarity, we suggest a probabilistic distance measure in the reproducing kernel Hilbert space (RKHS) as the ensemble similarity. Assuming normality in the RKHS, we derive analytic expressions for probabilistic distance measures that are commonly used in many applications, such as Chernoff distance (or the Bhattacharyya distance as its special case), Kullback-Leibler divergence, etc. Since the reproducing kernel implicitly embeds a nonlinear mapping, our approach presents a new way to study these distances whose feasibility and efficiency is demonstrated using experiments with synthetic and real examples. Further, we extend the ensemble similarity to the reproducing kernel for ensemble and study the ensemble similarity for more general data representations.
Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method
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Ghaleb Gumah
2016-01-01
Full Text Available We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space W21a,b in order to formulate the analytical solutions in a rapidly convergent series form in terms of their α-cut representation. The approximation solution is expressed by n-term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations.
de Andrade, Paulo C P; Freire, José A
2004-04-22
We develop nonorthogonal projectors, called Löwdin projectors, to construct an effective donor-acceptor system composed of localized donor (D) and acceptor (A) states of a long-distance electron transfer problem. When these states have a nonvanishing overlap with the bridge states these projectors are non-Hermitian and there are various possible effective two-level systems that can be built. We show how these can be constructed directly from the Schrödinger or Dyson equation projected onto the D-A subspace of the Hilbert space and explore these equations to determine the connection between Hamiltonian and Green function partitioning. We illustrate the use of these effective two-level systems in estimating the electron transfer rate in the context of a simple electron transfer model. (c) 2004 American Institute of Physics
Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation.
Sikora, Jamie; Varvitsiotis, Antonios; Wei, Zhaohui
2016-08-05
Consider a two-party correlation that can be generated by performing local measurements on a bipartite quantum system. A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlation. In this Letter, we identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a given two-party quantum correlation. We show that our bound is tight on many well-known correlations and discuss how it can rule out correlations of having a finite-dimensional quantum representation. We show that our bound is multiplicative under product correlations and also that it can witness the nonconvexity of certain restricted-dimensional quantum correlations.
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Energy Technology Data Exchange (ETDEWEB)
Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)
2017-06-15
We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
Numerical optimization in Hilbert space using inexact function and gradient evaluations
Carter, Richard G.
1989-01-01
Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.
Single image super-resolution via an iterative reproducing kernel Hilbert space method.
Deng, Liang-Jian; Guo, Weihong; Huang, Ting-Zhu
2016-11-01
Image super-resolution, a process to enhance image resolution, has important applications in satellite imaging, high definition television, medical imaging, etc. Many existing approaches use multiple low-resolution images to recover one high-resolution image. In this paper, we present an iterative scheme to solve single image super-resolution problems. It recovers a high quality high-resolution image from solely one low-resolution image without using a training data set. We solve the problem from image intensity function estimation perspective and assume the image contains smooth and edge components. We model the smooth components of an image using a thin-plate reproducing kernel Hilbert space (RKHS) and the edges using approximated Heaviside functions. The proposed method is applied to image patches, aiming to reduce computation and storage. Visual and quantitative comparisons with some competitive approaches show the effectiveness of the proposed method.
Vanfleteren, Diederik; Van Neck, Dimitri; Bultinck, Patrick; Ayers, Paul W; Waroquier, Michel
2010-12-21
A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.
Ito, Kazufumi
1987-01-01
The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
Divide and conquer the Hilbert space of translation-symmetric spin systems.
Weisse, Alexander
2013-04-01
Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of frustration. To reach sensible system sizes such numerical calculations heavily depend on the use of symmetries. We describe a divide-and-conquer strategy for implementing translation symmetries of finite spin clusters, which efficiently uses and extends the "sublattice coding" of H. Q. Lin [Phys. Rev. B 42, 6561 (1990)]. With our method, the Hamiltonian matrix can be generated on-the-fly in each matrix vector multiplication, and problem dimensions beyond 10^{11} become accessible.
Live Cell Refractometry Using Hilbert Phase Microscopy and Confocal Reflectance Microscopy†
Lue, Niyom; Choi, Wonshik; Popescu, Gabriel; Yaqoob, Zahid; Badizadegan, Kamran; Dasari, Ramachandra R.; Feld, Michael S.
2010-01-01
Quantitative chemical analysis has served as a useful tool for understanding cellular metabolisms in biology. Among many physical properties used in chemical analysis, refractive index in particular has provided molecular concentration that is an important indicator for biological activities. In this report, we present a method of extracting full-field refractive index maps of live cells in their native states. We first record full-field optical thickness maps of living cells by Hilbert phase microscopy and then acquire physical thickness maps of the same cells using a custom-built confocal reflectance microscope. Full-field and axially averaged refractive index maps are acquired from the ratio of optical thickness to physical thickness. The accuracy of the axially averaged index measurement is 0.002. This approach can provide novel biological assays of label-free living cells in situ. PMID:19803506
Live cell refractometry using Hilbert phase microscopy and confocal reflectance microscopy.
Lue, Niyom; Choi, Wonshik; Popescu, Gabriel; Yaqoob, Zahid; Badizadegan, Kamran; Dasari, Ramachandra R; Feld, Michael S
2009-11-26
Quantitative chemical analysis has served as a useful tool for understanding cellular metabolisms in biology. Among many physical properties used in chemical analysis, refractive index in particular has provided molecular concentration that is an important indicator for biological activities. In this report, we present a method of extracting full-field refractive index maps of live cells in their native states. We first record full-field optical thickness maps of living cells by Hilbert phase microscopy and then acquire physical thickness maps of the same cells using a custom-built confocal reflectance microscope. Full-field and axially averaged refractive index maps are acquired from the ratio of optical thickness to physical thickness. The accuracy of the axially averaged index measurement is 0.002. This approach can provide novel biological assays of label-free living cells in situ.
A Riemann-Hilbert problem for the shape of a body dissolving in flow
Moore, Nick; Huang, Jinzi Mac; Ristroph, Leif; Applied Math Lab, Courant Institute Team
2014-11-01
As is familiar to anyone who has stirred sugar into coffee, fluid flow can enhance the dissolution of solid material. This effect plays an important role in contexts as varied as landscape formation and drug delivery within the body, but such processes are not well understood due to the interaction between evolving surfaces and flow. By performing experiments with hard-candy bodies dissolving in fast flowing water, we find that different initial geometries converge to the same final shape as they vanish. By modeling both the separated flow around the body and the molecular diffusion of material within the boundary layer, we obtain a Riemann-Hilbert problem for the terminal shape. The solution predicts a front surface of nearly constant curvature, in agreement with experimental measurements. Once formed, this geometry dissolves self-similarly in time and vanishes with a power-law predicted by the model.
Differential Galois theory through Riemann-Hilbert correspondence an elementary introduction
Sauloy, Jacques
2017-01-01
Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equat...
A nanocrystalline Hilbert phase-plate for phase-contrast transmission electron microscopy.
Dries, M; Hettler, S; Gamm, B; Müller, E; Send, W; Müller, K; Rosenauer, A; Gerthsen, D
2014-04-01
Thin-film-based phase-plates are applied to enhance the contrast of weak-phase objects in transmission electron microscopy. In this work, metal-film-based phase-plates are considered to reduce contamination and electrostatic charging, which up to now limit the application of phase-plates fabricated from amorphous C-films. Their crystalline structure requires a model for the simulation of the effect of crystallinity on the phase-plate properties and the image formation process. The model established in this work is verified by experimental results obtained by the application of a textured nanocrystalline Au-film-based Hilbert phase-plate. Based on the model, it is shown that monocrystalline and textured nanocrystalline phase-plate microstructures of appropriate thickness and crystalline orientation can be a promising approach for phase-contrast transmission electron microscopy. Copyright © 2014 Elsevier B.V. All rights reserved.
Hilbert Modules and Stochastic Dilation of a Quantum Dynamical Semigroup on a von Neumann Algebra
Goswami, Debashish; Sinha, Kalyan B.
A general theory for constructing a weak Markov dilation of a uniformly continuous quantum dynamical semigroup Tt on a von Neumann algebra ? with respect to the Fock filtration is developed with the aid of a coordinate-free quantum stochastic calculus. Starting with the structure of the generator of Tt, existence of canonical structure maps (in the sense of Evans and Hudson) is deduced and a quantum stochastic dilation of Tt is obtained through solving a canonical flow equation for maps on the right Fock module ?⊗Γ(L2(+,k0)), where k0 is some Hilbert space arising from a representation of ?'. This gives rise to a *-homomorphism jt of ?. Moreover, it is shown that every such flow is implemented by a partial isometry-valued process. This leads to a natural construction of a weak Markov process (in the sense of [B-P]) with respect to Fock filtration.
SRB measures for a class of partially hyperbolic attractors in Hilbert spaces
Lian, Zeng; Liu, Peidong; Lu, Kening
2016-07-01
In this paper, we study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic and the system is topological mixing and the splitting is Hölder continuous, then there exists a unique SRB measure which is mixing; (iii) if the attractor is uniformly hyperbolic and the system is non-wondering and the splitting is Hölder continuous, then there exist at most finitely many SRB measures; (iv) for a given hyperbolic measure, there exist at most countably many ergodic components whose basin contains an observable set.
Weakly Ordered A-Commutative Partial Groups of Linear Operators Densely Defined on Hilbert Space
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Jirí Janda
2013-01-01
Full Text Available The notion of a generalized effect algebra is presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on a Hilbert space with the usual sum of operators. The structure of the set of not only positive linear operators can be described with the notion of a weakly ordered partial commutative group (wop-group.Due to the non-constructive algebraic nature of the wop-group we introduce its stronger version called a weakly ordered partial a-commutative group (woa-group. We show that it also describes the structure of not only positive linear operators.
Blanchard, Philippe
2015-01-01
The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
2011-01-01
W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on PSL(2, )\\. Their result is quantitative in the sense that they find the precise asymptotics of the measure considered. We extend their result to Eisenstein series on , where is the ring of integers in...... in a totally real field of degree n over with narrow class number one, using the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms.......W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on PSL(2, )\\. Their result is quantitative in the sense that they find the precise asymptotics of the measure considered. We extend their result to Eisenstein series on , where is the ring of integers...
Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy
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Bibhas Ranjan Majhi
2013-01-01
Full Text Available A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument: diffeomorphisms keep the horizon structure invariant. This complements similar earlier results (Majhi and Padmanabhan (2012 (arXiv:1204.1422 obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.
Strong Metrizability for Closed Operators and the Semi-Fredholm Operators between Two Hilbert Spaces
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Mohammed Benharrat
2015-08-01
Full Text Available To be able to refine the completion of C(H1, H2, the of set all closed densely defined linear operators between two Hilbert spaces H1 and H2, we define in this paper some new strictly stronger metrics than the gap metric g and we characterize the closure with respect to theses metrics of the subset L(H1, H2 of bounded elements of C(H1, H2. In addition, several operator norm inequalities concerning the equivalence of some metrics on L(H1, H2 are presented. We also establish the semi-Fredholmness and Fredholmness of unbounded in terms of bounded pure contractions.
Fano, Guido
2017-01-01
This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result...
Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces
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Cho Yeol
2011-01-01
Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.
Zhang, Ray Ruichong; King, Robert; Olson, Larry; Xu, You-Lin
2005-08-01
This paper presents the implementation of a method for nonlinear, nonstationary data processing, namely the Hilbert-Huang transform (HHT) in traditional vibration-based approaches to characterizing structural damage and shows the frequency signature of local structural damage in nonstationary vibration recordings. In particular, following the review of traditional approaches to characterizing structural damage from nonstationary vibration recordings, this study first offers the justifications of the HHT as an alternative and complementary data process in addressing the nonstationarity of the vibration. With the use of recordings from controlled field vibration tests of substructures in the Trinity River Relief Bridge in Texas in its intact, minor- and severe-damage pile states, this study then shows that the HHT-based approach can single out some natural frequencies of the structure from a mixed frequency content in recordings that also contain the time-dependent excitation and noise frequencies. Subsequently, this study exposes that the frequency downshift for the damaged pile relative to the undamaged one is an indicative index for the damage extent. The above results are also validated by an ANSYS model-based analysis. Finally, a comprehensive HHT-based characterization of structural damage is discussed, and the potential use for cost-effective, efficient structural damage diagnosis procedures and health-monitoring systems is provided.
A Possible Solution for Hilbert's Unsolved 8th Problem: Twin Prime Conjecture
Chen, Yuhsin; Ni, Yensen; Chen, Muyi
2017-01-01
We measure whether there are numerous pairs of twin primes (hereafter referred to as twin prime pairs) according to the prime number inferred by sieve of Eratosthenes. In this study, we reveal at least three additional twin prime pairs increased as n is increased by 1, while setting (6n+5)**2 as the range for estimating twin prime pairs. As a result, we prove the Twin Prime Conjecture proposed by de Polignac in 1849. That is, there are numerous twin prime pairs, indicating that there are nume...
He, Wangpeng; Zi, Yanyang; Chen, Binqiang; Wu, Feng; He, Zhengjia
2015-03-01
Mechanical anomaly is a major failure type of induction motor. It is of great value to detect the resulting fault feature automatically. In this paper, an ensemble super-wavelet transform (ESW) is proposed for investigating vibration features of motor bearing faults. The ESW is put forward based on the combination of tunable Q-factor wavelet transform (TQWT) and Hilbert transform such that fault feature adaptability is enabled. Within ESW, a parametric optimization is performed on the measured signal to obtain a quality TQWT basis that best demonstrate the hidden fault feature. TQWT is introduced as it provides a vast wavelet dictionary with time-frequency localization ability. The parametric optimization is guided according to the maximization of fault feature ratio, which is a new quantitative measure of periodic fault signatures. The fault feature ratio is derived from the digital Hilbert demodulation analysis with an insightful quantitative interpretation. The output of ESW on the measured signal is a selected wavelet scale with indicated fault features. It is verified via numerical simulations that ESW can match the oscillatory behavior of signals without artificially specified. The proposed method is applied to two engineering cases, signals of which were collected from wind turbine and steel temper mill, to verify its effectiveness. The processed results demonstrate that the proposed method is more effective in extracting weak fault features of induction motor bearings compared with Fourier transform, direct Hilbert envelope spectrum, different wavelet transforms and spectral kurtosis.
DEFF Research Database (Denmark)
Dalgas, Karina Märcher
2016-01-01
Ethnographers are increasingly making use of Facebook to acquire access and general acquaintance with their field of study. However, little has been written on how Facebook is used methodologically in research that does not have social media sites as the main focus of interest. This article argues...... that engagement with Facebook as a methodological tool can be useful in research among migrants in highly politicised fields. Pointing to a discursive construction of Filipina au pairs as victims of labour exploitation, the article shows how fieldwork on Facebook enables the exploration of the ways in which...... and on Facebook....
Canonical transformations and loop formulation of SU(N) lattice gauge theories
Mathur, Manu; Sreeraj, T. P.
2015-12-01
We construct canonical transformations to reformulate SU(N) Kogut-Susskind lattice gauge theory in terms of a set of fundamental loop and string flux operators along with their canonically conjugate loop and string electric fields. The canonical relations between the initial SU(N) link operators and the final SU(N) loop and string operators, consistent with SU(N) gauge transformations, are explicitly constructed over the entire lattice. We show that as a consequence of SU(N) Gauss laws all SU(N) string degrees of freedom become cyclic and decouple from the physical Hilbert space Hp. The Kogut-Susskind Hamiltonian rewritten in terms of the fundamental physical loop operators has global SU(N) invariance. There are no gauge fields. We further show that the (1 /g2 ) magnetic field terms on plaquettes create and annihilate the fundamental plaquette loop fluxes while the (g2 ) electric field terms describe all their interactions. In the weak coupling (g2→0 ) continuum limit the SU(N) loop dynamics is described by SU(N) spin Hamiltonian with nearest neighbor interactions. In the simplest SU(2) case, where the canonical transformations map the SU(2) loop Hilbert space into the Hilbert spaces of hydrogen atoms, we analyze the special role of the hydrogen atom dynamical symmetry group S O (4 ,2 ) in the loop dynamics and the spectrum. A simple tensor network ansatz in the SU(2) gauge invariant hydrogen atom loop basis is discussed.
On the continuity of the map square root of nonnegative isomorphisms in Hilbert spaces
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Jeovanny de Jesus Muentes Acevedo
2015-06-01
Full Text Available Let H be a real (or complex Hilbert space. Every nonnegative operator L ∈ L(H admits a unique nonnegative square root R ∈ L(H, i.e., a nonnegative operator R ∈ L(H such that R2 = L. Let GL+ S (H be the set of nonnegative isomorphisms in L(H. First we will show that GL+ S (H is a convex (real Banach manifold. Denoting by L1/2 the nonnegative square root of L. In [3], Richard Bouldin proves that L1/2 depends continuously on L (this proof is non-trivial. This result has several applications. For example, it is used to find the polar decomposition of a bounded operator. This polar decomposition allows us to determine the positive and negative spectral subespaces of any self-adjoint operator, and moreover, allows us to define the Maslov index. The autor of the paper under review provides an alternative proof (and a little more simplified that L1/2 depends continuously on L, and moreover, he shows that the map is a homeomorphism. Resumen. Sea H un espacio de Hilbert real (o complejo. Todo operador no negativo L ∈ L(H admite una única raíz cuadrada no negativa R ∈ L(H, esto es, un operador no negativo R ∈ L(H tal que R2 = L. Sea GL+ S (H el conjunto de los isomorfismos no negativos en L(H. Primero probaremos que GL+ S (H es una variedad de Banach (real. Denotando como L1/2 la raíz cuadrada no negativa de L, en [3] Richard Bouldin prueba que L1/2 depende continuamente de L (esta prueba es no trivial. Este resultado tiene varias aplicaciones. Por ejemplo, es usado para encontrar la descomposición polar de un operador limitado. Esta descomposición polar nos lleva a determinar los subespacios espectrales positivos y negativos de cualquier operador autoadjunto, y además, lleva a definir el índice de Máslov. El autor de este artículo da una prueba alternativa (y un poco más simplificada de que L1/2 depende continuamente de L, y además, prueba que la aplicación es un homeomorfismo
Interior tomography with radial Hilbert filtering and a priori information in a small circular area
Tang, Shaojie; Yang, Yi; Tang, Xiangyang
2012-03-01
Interior tomography problem can be solved using the so-called differentiated backprojection-projection onto convex sets (DBP-POCS) method, which requires a priori information within a small area interior to the region of interest (ROI) to be imaged. In theory, the small area wherein the a priori information is required can be in any shape, but most of the existing implementations carry out the Hilbert filtering either horizontally or vertically, leading to a vertical or horizontal strip that may be across a large area in the object. In this work, we specifically re-derive the reconstruction formula in the DBP-POCS fashion with radial Hilbert filtering (namely radial DBP-POCS method henceforth). We implement the radial DBP-POCS method, and thus the small area with the a priori information can be roughly circular (e.g., a sinus or ventricles among other anatomic cavities in human or animal body). We also conduct an experimental evaluation to verify the performance of this practical implementation. The performance of the radial DBP-POCS method with the a priori information in a small circular area is evaluated with projection data of the standard Shepp-Logan phantom simulated by computer. The preliminary performance study shows that, if the a priori information in a small circular area is available, the radial DBP-POCS method can solve the interior tomography problem in a much more practical way at high accuracy. In comparison to the implementations of DBP-POCS method demanding the a priori information in horizontal or vertical strip, the radial DBP-POCS method requires the a priori information within a small circular area only. Such a relaxed requirement on the availability of a priori information can be readily met in practice, because a variety of small circular areas (e.g., air-filled sinuses or fluid-filled ventricles among other anatomic cavities) exist in human or animal body. Therefore, the radial DBP-POCS method with a priori information in a small circular
Laplace transforms and the American straddle
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G. Alobaidi
2002-01-01
partial Laplace transform techniques due to Evans et al. (1950 to derive a pair of integral equations giving the locations of the optimal exercise boundaries for an American straddle option with a constant dividend yield.
SUR UNE CERTAINE CLASSE D’OPERATEURS A SPECTRE CONCENTRE EN UN POINT DANS UN ESPACE DE HILBERT
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B BENDOUKHA
2000-12-01
Full Text Available Le présent travail est consacré à l'étude de certaines classes d’opérateurs qui sont parfaitement définis par leur spectre. Pour ces opérateurs (définis dans des espaces de Hilbert abstraits, on donnera une représentation explicite et uniquement à l’aide du spectre dans l’espace des fonctions à carrés intégrables.
Multi-pair states in electron–positron pair creation
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Anton Wöllert
2016-09-01
Full Text Available Ultra strong electromagnetic fields can lead to spontaneous creation of single or multiple electron–positron pairs. A quantum field theoretical treatment of the pair creation process combined with numerical methods provides a description of the fermionic quantum field state, from which all observables of the multiple electron–positron pairs can be inferred. This allows to study the complex multi-particle dynamics of electron–positron pair creation in-depth, including multi-pair statistics as well as momentum distributions and spin. To illustrate the potential benefit of this approach, it is applied to the intermediate regime of pair creation between nonperturbative Schwinger pair creation and perturbative multiphoton pair creation where the creation of multi-pair states becomes nonnegligible but cascades do not yet set in. Furthermore, it is demonstrated how spin and helicity of the created electrons and positrons are affected by the polarization of the counterpropagating laser fields, which induce the creation of electron–positron pairs.
On Quantile Regression in Reproducing Kernel Hilbert Spaces with Data Sparsity Constraint.
Zhang, Chong; Liu, Yufeng; Wu, Yichao
2016-04-01
For spline regressions, it is well known that the choice of knots is crucial for the performance of the estimator. As a general learning framework covering the smoothing splines, learning in a Reproducing Kernel Hilbert Space (RKHS) has a similar issue. However, the selection of training data points for kernel functions in the RKHS representation has not been carefully studied in the literature. In this paper we study quantile regression as an example of learning in a RKHS. In this case, the regular squared norm penalty does not perform training data selection. We propose a data sparsity constraint that imposes thresholding on the kernel function coefficients to achieve a sparse kernel function representation. We demonstrate that the proposed data sparsity method can have competitive prediction performance for certain situations, and have comparable performance in other cases compared to that of the traditional squared norm penalty. Therefore, the data sparsity method can serve as a competitive alternative to the squared norm penalty method. Some theoretical properties of our proposed method using the data sparsity constraint are obtained. Both simulated and real data sets are used to demonstrate the usefulness of our data sparsity constraint.
Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space.
Athalye, Vivek; Lustig, Michael; Uecker, Martin
2015-04-01
In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. To understand and design k-space sampling patterns, a theoretical framework is needed to analyze how well arbitrary sampling patterns reconstruct unsampled k-space using receive coil information. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional image-domain g-factor noise analysis to both noise amplification and approximation errors in k-space. This is demonstrated with numerical examples.
Non-Markovian quantum dynamics: correlated projection superoperators and Hilbert space averaging.
Breuer, Heinz-Peter; Gemmer, Jochen; Michel, Mathias
2006-01-01
The time-convolutionless (TCL) projection operator technique allows a systematic analysis of the non-Markovian quantum dynamics of open systems. We present a class of projection superoperators that project the states of the total system onto certain correlated system-environment states. It is shown that the application of the TCL technique to this class of correlated superoperators enables the nonperturbative treatment of the dynamics of system-environment models for which the standard approach fails in any finite order of the coupling strength. We demonstrate further that the correlated superoperators correspond to the idea of a best guess of conditional quantum expectations, which is determined by a suitable Hilbert-space average. The general approach is illustrated by means of the model of a spin that interacts through randomly distributed couplings with a finite reservoir consisting of two energy bands. Extensive numerical simulations of the full Schrödinger equation of the model reveal the power and efficiency of the method.
Adaptive learning in complex reproducing kernel Hilbert spaces employing Wirtinger's subgradients.
Bouboulis, Pantelis; Slavakis, Konstantinos; Theodoridis, Sergios
2012-03-01
This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources.
A reproducing kernel Hilbert space framework for spike train signal processing.
Paiva, António R C; Park, Il; Príncipe, José C
2009-02-01
This letter presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical description as point processes. Moreover, because many inner products can be formulated, a particular definition can be crafted to best fit an application. These ideas are illustrated by the definition of a number of spike train inner products. To further elicit the advantages of the RKHS framework, a family of these inner products, the cross-intensity (CI) kernels, is analyzed in detail. This inner product family encapsulates the statistical description from the conditional intensity functions of spike trains. The problem of their estimation is also addressed. The simplest of the spike train kernels in this family provide an interesting perspective to others' work, as will be demonstrated in terms of spike train distance measures. Finally, as an application example, the RKHS framework is used to derive a clustering algorithm for spike trains from simple principles.
Ghiloni, Riccardo; Moretti, Valter; Perotti, Alessandro
The possibility of formulating quantum mechanics over quaternionic Hilbert spaces can be traced back to von Neumann’s foundational works in the thirties. The absence of a suitable quaternionic version of spectrum prevented the full development of the theory. The first rigorous quaternionic formulation has started only in 2007 with the definition of the spherical spectrum of a quaternionic operator based on a quadratic version of resolvent operator. The relevance of this notion is proved by the existence of a quaternionic continuous functional calculus and a theory of quaternionic semigroups relying upon it. A problem of the quaternionic formulation is the description of composite quantum systems in the absence of a natural tensor product due to non-commutativity of quaternions. A promising tool towards a solution is a quaternionic projection-valued measure (PVM), making possible a tensor product of quaternionic operators with physical relevance. A notion with this property, called intertwining quaternionic PVM, is presented here. This foundational paper aims to investigate the interplay of this new mathematical object and the spherical spectral features of quaternionic generally unbounded normal operators. We discover, in particular, the existence of other spectral notions equivalent to the spherical ones, but based on a standard non-quadratic notion of resolvent operator.
Huang, Yongxiang; Schmitt, François G.; Lu, Zhiming.; Liu, Yulu
2009-06-01
SummaryIn this paper we presented the analysis of two long time series of daily river flow data, 32 years recorded in the Seine river (France), and 25 years recorded in the Wimereux river (Wimereux, France). We applied a scale based decomposition method, namely Empirical Mode Decomposition (EMD), on these time series. The data were decomposed into several Intrinsic Mode Functions (IMF). The mean frequency of each IMF mode indicated that the EMD method acts as a filter bank. Furthermore, the cross-correlation between these IMF modes from the Seine river and Wimereux river demonstrated correlation among the large scale IMF modes, which indicates that both rivers are likely to be influenced by the same maritime climate event of Northern France. As a confirmation we found that the large scale parts have the same evolution trend. We finally applied arbitrary order Hilbert spectral analysis, a new technique coming from turbulence studies and time series analysis, on the flow discharge of the Seine river. This new method provides an amplitude-frequency representation of the original time series, giving a joint pdf p(ω,A). When marginal moments of the amplitude are computed, one obtains an intermittency study in the frequency space. Applied to river flow discharge data from the Seine river, this shows the scaling range and characterizes the intermittent fluctuations over the range of scales from 4.5 to 60 days, between synoptic and intraseasonal scales.
Hilbert series for moduli spaces of instantons on ℂ{sup 2}/ℤ{sub n}
Energy Technology Data Exchange (ETDEWEB)
Dey, Anindya [Theory Group and Texas Cosmology Center, Department of Physics,University of Texas at Austin, Austin, TX 78712 (United States); Hanany, Amihay [Theoretical Physics Group, The Blackett Laboratory, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom); Mekareeya, Noppadol [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, 80805 München (Germany); Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland); Rodríguez-Gómez, Diego [Department of Physics, Universidad de Oviedo,Avda. Calvo Sotelo 18, 33007, Oviedo (Spain); Seong, Rak-Kyeong [Theoretical Physics Group, The Blackett Laboratory, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom); School of Physics, Korea Institute for Advanced Study,85 Hoegi-ro, Seoul 130-722 (Korea, Republic of)
2014-01-31
We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A{sub n−1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected.
Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
Dey, Anindya; Mekareeya, Noppadol; Rodríguez-Gómez, Diego; Seong, Rak-Kyeong
2014-01-01
We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A_{n-1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiv...
SOLUTION TO A PARABOLIC DIFFERENTIAL EQUATION IN HILBERT SPACE VIA FEYNMAN FORMULA I
Directory of Open Access Journals (Sweden)
I. D. Remizov
2015-01-01
Full Text Available A parabolic partial differential equation u′t (t, x = Lu(t, x is considered, where L is a linear second-order differential operator with time-independent coefficients, which may depend on x. We assume that the spatial coordinate x belongs to a finiteor infinite-dimensional real separable Hilbert space H.Assuming the existence of a strongly continuous resolving semigroup for this equation, we construct a representation of this semigroup by a Feynman formula, i.e. we write it in the form of the limit of a multiple integral over H as the multiplicity of the integral tends to infinity. This representation gives a unique solution to the Cauchy problem in the uniform closure of the set of smooth cylindrical functions on H. Moreover, this solution depends continuously on the initial condition. In the case where the coefficient of the first-derivative term in L vanishes we prove that the strongly continuous resolving semigroup exists (this implies the existence of the unique solution to the Cauchy problem in the class mentioned above and that the solution to the Cauchy problem depends continuously on the coefficients of the equation.The article is published in the author’s wording.
Gangeh, Mehrdad J; Zarkoob, Hadi; Ghodsi, Ali
2017-01-01
In computational biology, selecting a small subset of informative genes from microarray data continues to be a challenge due to the presence of thousands of genes. This paper aims at quantifying the dependence between gene expression data and the response variables and to identifying a subset of the most informative genes using a fast and scalable multivariate algorithm. A novel algorithm for feature selection from gene expression data was developed. The algorithm was based on the Hilbert-Schmidt independence criterion (HSIC), and was partly motivated by singular value decomposition (SVD). The algorithm is computationally fast and scalable to large datasets. Moreover, it can be applied to problems with any type of response variables including, biclass, multiclass, and continuous response variables. The performance of the proposed algorithm in terms of accuracy, stability of the selected genes, speed, and scalability was evaluated using both synthetic and real-world datasets. The simulation results demonstrated that the proposed algorithm effectively and efficiently extracted stable genes with high predictive capability, in particular for datasets with multiclass response variables. The proposed method does not require the whole microarray dataset to be stored in memory, and thus can easily be scaled to large datasets. This capability is an important attribute in big data analytics, where data can be large and massively distributed.
DEFF Research Database (Denmark)
Pedersen, Pia
2012-01-01
the finished charts as a starting point and then going back to the beginning; furthermore, this inquiry presents a novel approach to clarifying the process by designing symbols and diagrams. It will be demonstrated that transformation offers an improved approach to data visualization. The message in the chart...... is not preformed, but formed through the process of transformation; this means that the purpose of transformation is not the styling of charts with pictograms, but rather creating a meaningful message. The contribution of this paper is an elaborated understanding of the process of transformation...... design. Recently transformation has attracted renewed interest because of the book The Transformer written by Robin Kinross and Marie Neurath. My on-going research project, summarized in this paper, identifies and depicts the essential principles of data visualization underlying the process...
Agaian, Sos; Egiazarian, Karen; Astola, Jaakko
2011-01-01
The Hadamard matrix and Hadamard transform are fundamental problem-solving tools in a wide spectrum of scientific disciplines and technologies, such as communication systems, signal and image processing (signal representation, coding, filtering, recognition, and watermarking), digital logic (Boolean function analysis and synthesis), and fault-tolerant system design. Hadamard Transforms intends to bring together different topics concerning current developments in Hadamard matrices, transforms, and their applications. Each chapter begins with the basics of the theory, progresses to more advanced
de Pondeca, M. S.; Park, S.; Purser, R.; Dimego, G.
2006-12-01
Cross-validation techniques provide robust methods for estimating the optimal parameters defining the covariance models employed by statistical variational assimilation schemes based on the given observational data. Provided the effective errors of the measurement data are statistically independent, the mean-square difference between a subset of these measurements and the collocated values of the analysis performed with these selected data withheld, which is the cross-validation statistic associated with this subset, can be used as an objective criterion for the tuning of covariance parameters. The use of multiple disjoint validation subsets to produce an aggregate validation statistic improves the reliability and robustness of the cross-validation method by reducing the random scatter that comes from the inevitable sampling effects. It is desirable that each validation subset contains representative data from all the geographical regions observed, but without the redundancy implied by selections that lead to close pairs or tight clusters in the validation subset, even if such clustering exists in the complete data set. We show that an application of a continuous space-filling Hilbert curve, to which all the data are mapped and sorted in the order of the curve's single real parameter, offers simple strategies for simultaneously constructing multiple disjoint validation subsets tending to possess the desired properties of representativeness and non-redundancy. We further show that a variant of this construction very naturally leads to an efficient partition of the data into subsets suitable for combination into super-observations that enable an effective reduction of the size of the measurement data sets with only minimal loss of actual information. The application of these ideas is illustrated in the context of NCEP's Real-Time Mesoscale Analysis (RTMA) system for North American surface data.
Energy Technology Data Exchange (ETDEWEB)
Pittel, S. [Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, 19716 Delaware (United States); Dussel, G. G. [Departamento de Fisica J.J. Giambiagi, Universidad de Buenos Aires, 1428 Buenos Aires (Argentina); Dukelsky, J.; Sarriguren, P. [Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid (Spain)
2008-12-15
We describe recent efforts to study Cooper pairs in atomic nuclei. We consider a self-consistent Hartree Fock mean field for the even Sm isotopes and compare results based on three treatments of pairing correlations: a BCS treatment, a number-projected BCS treatment and an exact treatment using the Richardson Ansatz. Significant differences are seen in the pairing correlation energies. Furthermore, because it does not average over the properties of the fermion pairs, the Richardson solution permits a more meaningful definition of the Cooper wave function and of the fraction of pairs that are collective. Our results confirm that only a few pairs near the Fermi surface in realistic atomic nuclei are collective. (Author)
The Pegg-Barnett phase operator and the discrete Fourier transform
Perez-Leija, Armando; Andrade-Morales, Luis A.; Soto-Eguibar, Francisco; Szameit, Alexander; Moya-Cessa, Héctor M.
2016-04-01
In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg-Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London-Susskind-Glogower phase operator, whose natural logarithm gives rise to the Pegg-Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties.
Lone pairs: an electrostatic viewpoint.
Kumar, Anmol; Gadre, Shridhar R; Mohan, Neetha; Suresh, Cherumuttathu H
2014-01-16
A clear-cut definition of lone pairs has been offered in terms of characteristics of minima in molecular electrostatic potential (MESP). The largest eigenvalue and corresponding eigenvector of the Hessian at the minima are shown to distinguish lone pair regions from the other types of electron localization (such as π bonds). A comparative study of lone pairs as depicted by various other scalar fields such as the Laplacian of electron density and electron localization function is made. Further, an attempt has been made to generalize the definition of lone pairs to the case of cations.
Image Matching Using Generalized Hough Transforms
Davis, L. S.; Hu, F. P.; Hwang, V.; Kitchen, L.
1983-01-01
An image matching system specifically designed to match dissimilar images is described. A set of blobs and ribbons is first extracted from each image, and then generalized Hough transform techniques are used to match these sets and compute the transformation that best registers the image. An example of the application of the approach to one pair of remotely sensed images is presented.
Cardinality of the metric projection on typical compact sets in Hilbert spaces
de Blasi, F. S.; Zamfirescu, T. I.
1999-01-01
The metric projection mapping [pi]X plays an important role in nonlinear approximation theory. Usually X is a closed subset of a Banach space [open face E] and, for each e[set membership][open face E], [pi]X(e) is the set, perhaps empty, of all points in X which are nearest to e. From a classical theorem due to Steckin [7] it is known that, when [open face E] is uniformly convex, the metric projection [pi]X(e) is single valued at each typical point e of [open face E] (in the sense of the Baire categories), i.e. at each point e of a residual subset of [open face E]. More recently Zamfirescu [8] has proven that, if X is a typical compact set in [open face R]n (in the sense of Baire categories) and n[gt-or-equal, slanted]2, then the metric projection [pi]X(e) has cardinality at least 2 at each point e of a dense subset of [open face R]n. This result has been extended in several directions by Zhivkov [9, 10], who has also considered the case of the metric antiprojection mapping [nu]X (which associates with each e[set membership][open face E] the set [nu]X(e), perhaps empty, of all [set membership]X which are farthest from e). For this mapping De Blasi [2] has shown that, if [open face E] is a real separable Hilbert space with dim[open face E]=+[infty infinity] and n is an arbitrary natural number not less than 2, then, for a typical compact convex set X[subset or is implied by][open face E], the metric antiprojection [nu]X(e) has cardinality at least n at each point e of a dense subset of [open face E]. A systematic discussion of the properties of the maps [pi]X and [nu]X, and additional bibliography, can be found in Singer [5, 6] and Dontchev and Zolezzi [3].In the present paper we consider some further properties of the metric projection mapping [pi]X, with X a compact set in a real separable Hilbert space [open face E]. If dim[open face E]=n and 2[gt-or-equal, slanted]n<+[infty infinity], it is proven that for a typical compact set X[subset or is implied by
Adaptive multiregression in reproducing kernel Hilbert spaces: the multiaccess MIMO channel case.
Slavakis, Konstantinos; Bouboulis, Pantelis; Theodoridis, Sergios
2012-02-01
This paper introduces a wide framework for online, i.e., time-adaptive, supervised multiregression tasks. The problem is formulated in a general infinite-dimensional reproducing kernel Hilbert space (RKHS). In this context, a fairly large number of nonlinear multiregression models fall as special cases, including the linear case. Any convex, continuous, and not necessarily differentiable function can be used as a loss function in order to quantify the disagreement between the output of the system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. To this end, we demonstrate a way to calculate the subgradients of robust loss functions, suitable for the multiregression task. As it is by now well documented, when dealing with online schemes in RKHS, the memory keeps increasing with each iteration step. To attack this problem, a simple sparsification strategy is utilized, which leads to an algorithmic scheme of linear complexity with respect to the number of unknown parameters. A convergence analysis of the technique, based on arguments of convex analysis, is also provided. To demonstrate the capacity of the proposed method, the multiregressor is applied to the multiaccess multiple-input multiple-output channel equalization task for a setting with poor resources and nonavailable channel information. Numerical results verify the potential of the method, when its performance is compared with those of the state-of-the-art linear techniques, which, in contrast, use space-time coding, more antenna elements, as well as full channel information.
Stereo Pair: Patagonia, Argentina
2000-01-01
This view of northern Patagonia, near El Cain, Argentina shows complexly eroded volcanic terrain, with basalt mesas, sinkholes, landslide debris, playas, and relatively few integrated drainage channels. Surrounding this site (but also extending far to the east) is a broad plateau capped by basalt, the Meseta de Somuncura. Here, near the western edge of the plateau, erosion has broken through the basalt cap in a variety of ways. On the mesas, water-filled sinkholes (lower left) are most likely the result of the collapse of old lava tubes. Along the edges of the mesas (several locations) the basalt seems to be sliding away from the plateau in a series of slices. Water erosion by overland flow is also evident, particularly in canyons where vegetation blankets the drainage channels (green patterns, bottom of image). However, overland water flow does not extend very far at any location. This entire site drains to local playas, some of which are seen here (blue). While the water can reach the playas and then evaporate, what becomes of the eroded rock debris? Wind might excavate some of the finer eroded debris, but the fate of much of the missing bedrock remains mysterious.This cross-eyed stereoscopic image pair was generated using topographic data from the Shuttle Radar Topography Mission, combined with an enhanced Landsat 7 satellite color image. The topography data are used to create two differing perspectives of a single image, one perspective for each eye. In doing so, each point in the image is shifted slightly, depending on its elevation. When stereoscopically merged, the result is a vertically exaggerated view of the Earth's surface in its full three dimensions.Landsat satellites have provided visible light and infrared images of the Earth continuously since 1972. SRTM topographic data match the 30-meter (99-foot) spatial resolution of most Landsat images and provide a valuable complement for studying the historic and growing Landsat data archive. The Landsat 7
On the surface nature of the nuclear pairing
Energy Technology Data Exchange (ETDEWEB)
Baldo, M.; Lombardo, U.; Saperstein, E.E.; Zverev, M.V
2004-03-01
The surface nature of nuclear pairing is confirmed microscopically. A two-step approach is used in which the full Hilbert space S is split into the model subspace S{sub 0} and the complementary one, S'. The gap equation is solved in the model space in terms of the effective interaction V{sub eff}{sup p} which obeys the Bethe-Goldstone-type equation in the complementary subspace. The simplest nuclear systems with one-dimensional inhomogeneity are considered, i.e. semi-infinite nuclear matter and the nuclear slab. Numerical solution is carried out for the separable representation of the Paris NN-potential. The equation for the effective pairing interaction is solved directly, without use of any form of local approximation. A version of the local approximation, the local potential approximation, is suggested which works sufficiently well even in the surface region. The effective pairing interaction obtained in our calculations reveals a strong variation in the surface region changing from a strong attraction outside the nuclear matter to almost zero value inside. The effective interaction is found to be dependent on the chemical potential {mu}. At {mu}=-8 MeV, it reproduces qualitatively the phenomenological density-dependent effective pairing interaction, with the surface dominance, which was found previously in the self-consistent finite Fermi systems theory and in the new version of the energy functional method by Fayans et al. As vertical bar {mu} vertical bar decreases, the surface attraction becomes stronger. The gap equation was solved in semi-infinite matter and in the slab system with the help of the method by Khodel, Khodel and Clark which was suggested recently for nuclear matter. This method extended to non-homogeneous systems turned out to be very efficient in this case. The gap {delta} found for both the systems exhibits a strong variation in the surface region with a pronounced maximum near the surface. The surface effect in {delta} turned out to
On transforms between Gabor frames and wavelet frames
DEFF Research Database (Denmark)
Christensen, Ole; Goh, Say Song
2013-01-01
We describe a procedure that enables us to construct dual pairs of wavelet frames from certain dual pairs of Gabor frames. Applying the construction to Gabor frames generated by appropriate exponential Bsplines gives wavelet frames generated by functions whose Fourier transforms are compactly...... supported splines with geometrically distributed knot sequences. There is also a reverse transform, which yields pairs of dual Gabor frames when applied to certain wavelet frames....
Characterization of Oblique Dual Frame Pairs
DEFF Research Database (Denmark)
Christensen, Ole; Eldar, Yonina
2006-01-01
Given a frame for a subspace W of a Hilbert space H, we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace V. In place of the standard description, which involves computing the pseudoinverse of the frame operator, we develop an alternative...... characterization which in some cases can be computationally more efficient. We first treat the case of a general frame on an arbitrary Hilbert space, and then specialize the results to shift-invariant frames with multiple generators. In particular, we present explicit versions of our general conditions...... for the case of shift-invariant spaces with a single generator. The theory is also adapted to the standard frame setting in which the original and dual frames are defined on the same space. Copyright (C) 2006 Hindawi Publishing Corporation. All rights reserved....
Instability of vortex pair leapfrogging
DEFF Research Database (Denmark)
Tophøj, Laust; Aref, Hassan
2013-01-01
Leapfrogging is a periodic solution of the four-vortex problem with two positive and two negative point vortices all of the same absolute circulation arranged as co-axial vortex pairs. The set of co-axial motions can be parameterized by the ratio 0 vortex pair sizes at the time when one...... pair passes through the other. Leapfrogging occurs for α > σ2, where is the silver ratio. The motion is known in full analytical detail since the 1877 thesis of Gröbli and a well known 1894 paper by Love. Acheson ["Instability of vortex leapfrogging," Eur. J. Phys.21, 269-273 (2000...... pairs fly off to infinity, and a "walkabout" mode, where the vortices depart from leapfrogging but still remain within a finite distance of one another. We show numerically that this transition is more gradual, a result that we relate to earlier investigations of chaotic scattering of vortex pairs [L...
Hall, Anndee
2017-01-01
Abstract: Transforming Anatomy Studying historic books allows people to witness the transformation of the world right before their very eyes. The Bruxellensis Icones Anatomicae[1] by Andreas Vesalius is a vital piece of evidence in the movement from a more rudimentary understanding of the human body into the more complex and accurate development of modern anatomy. Vesalius’ research worked to both refute and confirm findings of his predecessor, the great historical Greek philosopher, Galen...
Luzinski, Craig
2011-12-01
This month, the director of the Magnet Recognition Program® takes an in-depth look at the Magnet® model component transformational leadership. The author examines the expectations for Magnet organizations around this component. What are the qualities that make a nursing leader truly transformational, and what is the best approach to successfully lead a healthcare organization through today's volatile healthcare environment?
DEFF Research Database (Denmark)
Munck Petersen, Rikke
2005-01-01
Seminaroplæg fra forskere. Faglige seminarer på KA, forår 2005. Belyser transformation af det danske landskab fysisk som holdningsmæssigt, samt hvordan phd-arbejdets egen proces håndterer den.......Seminaroplæg fra forskere. Faglige seminarer på KA, forår 2005. Belyser transformation af det danske landskab fysisk som holdningsmæssigt, samt hvordan phd-arbejdets egen proces håndterer den....
Chang, Weng-Long; Ren, Ting-Ting; Feng, Mang
2015-01-01
In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNA-based algorithm solving the vertex-cover problem of any graph G with m edges and n vertices is the optimal quantum algorithm. Next, it is also demonstrated that mathematical solutions of the same biomolecular solutions are represented in terms of a unit vector in the finite-dimensional Hilbert space. Furthermore, for testing our theory, a nuclear magnetic resonance (NMR) experiment of three quantum bits to solve the simplest vertex-cover problem is completed.
Directory of Open Access Journals (Sweden)
Hua-Cheng Zhou
2016-02-01
Full Text Available This article is devoted to investigating the existence of solutions to fractional multi-point boundary-value problems at resonance in a Hilbert space. More precisely, the dimension of the kernel of the fractional differential operator with the boundary conditions be any positive integer. We point out that the problem is new even when the system under consideration is reduced to a second-order ordinary differential system with resonant boundary conditions. We show that the considered system admits at least a solution by applying coincidence degree theory first introduced by Mawhin. An example is presented to illustrate our results.
Li, Lin; Park, Il Memming; Brockmeier, Austin; Chen, Badong; Seth, Sohan; Francis, Joseph T; Sanchez, Justin C; Príncipe, José C
2013-07-01
The precise control of spiking in a population of neurons via applied electrical stimulation is a challenge due to the sparseness of spiking responses and neural system plasticity. We pose neural stimulation as a system control problem where the system input is a multidimensional time-varying signal representing the stimulation, and the output is a set of spike trains; the goal is to drive the output such that the elicited population spiking activity is as close as possible to some desired activity, where closeness is defined by a cost function. If the neural system can be described by a time-invariant (homogeneous) model, then offline procedures can be used to derive the control procedure; however, for arbitrary neural systems this is not tractable. Furthermore, standard control methodologies are not suited to directly operate on spike trains that represent both the target and elicited system response. In this paper, we propose a multiple-input multiple-output (MIMO) adaptive inverse control scheme that operates on spike trains in a reproducing kernel Hilbert space (RKHS). The control scheme uses an inverse controller to approximate the inverse of the neural circuit. The proposed control system takes advantage of the precise timing of the neural events by using a Schoenberg kernel defined directly in the space of spike trains. The Schoenberg kernel maps the spike train to an RKHS and allows linear algorithm to control the nonlinear neural system without the danger of converging to local minima. During operation, the adaptation of the controller minimizes a difference defined in the spike train RKHS between the system and the target response and keeps the inverse controller close to the inverse of the current neural circuit, which enables adapting to neural perturbations. The results on a realistic synthetic neural circuit show that the inverse controller based on the Schoenberg kernel outperforms the decoding accuracy of other models based on the conventional rate
Photonic Counterparts of Cooper Pairs
Saraiva, André; Júnior, Filomeno S. de Aguiar; de Melo e Souza, Reinaldo; Pena, Arthur Patrocínio; Monken, Carlos H.; Santos, Marcelo F.; Koiller, Belita; Jorio, Ado
2017-11-01
The microscopic theory of superconductivity raised the disruptive idea that electrons couple through the elusive exchange of virtual phonons, overcoming the strong Coulomb repulsion to form Cooper pairs. Light is also known to interact with atomic vibrations, as, for example, in the Raman effect. We show that photon pairs exchange virtual vibrations in transparent media, leading to an effective photon-photon interaction identical to that for electrons in the BCS theory of superconductivity, in spite of the fact that photons are bosons. In this scenario, photons may exchange energy without matching a quantum of vibration of the medium. As a result, pair correlations for photons scattered away from the Raman resonances are expected to be enhanced. An experimental demonstration of this effect is provided here by time-correlated Raman measurements in different media. The experimental data confirm our theoretical interpretation of a photonic Cooper pairing, without the need for any fitting parameters.
Exact solution for generalized pairing
Pan, Feng; Draayer, J. P.
1997-01-01
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with some numerical examples.
On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of Ã¢ÂˆÂ’1-Order and Applications
Directory of Open Access Journals (Sweden)
Bicheng Yang
2007-10-01
Full Text Available Some character of the symmetric homogenous kernel of Ã¢ÂˆÂ’1-order in Hilbert-type operator T:lrÃ¢Â†Â’lrÃ‚Â (r>1 is obtained. Two equivalent inequalities with the symmetric homogenous kernel of Ã¢ÂˆÂ’ÃŽÂ»-order are given. As applications, some new Hilbert-type inequalities with the best constant factors and the equivalent forms as the particular cases are established.
Power transformation for enhancing responsiveness of quality of life questionnaire
Zhou, YanYan Ange
2015-01-01
We investigate the effect of power transformation of raw scores on the responsiveness of quality of life survey. The procedure maximizes the paired t-test value on the power transformed data to obtain an optimal power range. The parallel between the Box–Cox transformation is also investigated for the quality of life data.
DEFF Research Database (Denmark)
Andersen, Nicolai Bo
This paper is about sustainable transformation with a particular focus on listed buildings. It is based on the notion that sustainability is not just a question of energy conditions, but also about the building being robust. Robust architecture means that the building can be maintained and rebuilt...... theoretical lenses. It is proposed that three parameters concerning the ꞌtransformabilityꞌ of the building can contribute to a more nuanced understanding of sustainable transformation: technical aspects, programmatic requirements and narrative value. It is proposed that the concept of ꞌsustainable...
Mehendale, A.; Hagedoorn, Wouter; Lötters, Joost Conrad
2008-01-01
A transformer core includes a stack of a plurality of planar core plates of a magnetically permeable material, which plates each consist of a first and a second sub-part that together enclose at least one opening. The sub-parts can be fitted together via contact faces that are located on either side
Mehendale, A.; Hagedoorn, Wouter; Lötters, Joost Conrad
2010-01-01
A transformer core includes a stack of a plurality of planar core plates of a magnetically permeable material, which plates each consist of a first and a second sub-part that together enclose at least one opening. The sub-parts can be fitted together via contact faces that are located on either side
DEFF Research Database (Denmark)
Neergaard, Helle; Robinson, Sarah; Jones, Sally
This paper develops the concept of ‘pedagogical nudging’ and examines four interventions in an entrepreneurship classroom and the potential it has for student identity transformation. Pedagogical nudging is positioned as a tool, which in the hands of a reflective, professional, with an understand......This paper develops the concept of ‘pedagogical nudging’ and examines four interventions in an entrepreneurship classroom and the potential it has for student identity transformation. Pedagogical nudging is positioned as a tool, which in the hands of a reflective, professional......, as well as the resources they have when they come to the classroom. It also incorporates perspectives from (ii) transformational learning and explores the concept of (iii) nudging from a pedagogical viewpoint, proposing it as an important tool in entrepreneurship education. The study incorporates......) assists students in straddling the divide between identities, the emotions and tensions this elicits, and (iv) transform student understanding. We extend nudging theory into a new territory. Pedagogical nudging techniques may be able to unlock doors and bring our students beyond the unacknowledged...
Termeer, Katrien; Dewulf, Art; Biesbroek, Robbert
2017-01-01
Although transformational change is a rather new topic in climate change adaptation literature, it has been studied in organisational theory for over 30 years. This paper argues that governance scholars can learn much from organisation theory, more specifically regarding the conceptualisation of
Majorana representation, qutrit Hilbert space and NMR implementation of qutrit gates
Dogra, Shruti; Dorai, Kavita; Arvind
2018-02-01
We report a study of the Majorana geometrical representation of a qutrit, where a pair of points on a unit sphere represents its quantum states. A canonical form for qutrit states is presented, where every state can be obtained from a one-parameter family of states via SO(3) action. The notion of spin-1 magnetization which is invariant under SO(3) is geometrically interpreted on the Majorana sphere. Furthermore, we describe the action of several quantum gates in the Majorana picture and experimentally implement these gates on a spin-1 system (an NMR qutrit) oriented in a liquid crystalline environment. We study the dynamics of the pair of points representing a qutrit state under various useful quantum operations and connect them to different NMR operations. Finally, using the Gell Mann matrix picture we experimentally implement a scheme for complete qutrit state tomography.
Hardy's paradox tested in the spin-orbit Hilbert space of single photons
Karimi, Ebrahim; Cardano, Filippo; Maffei, Maria; de Lisio, Corrado; Marrucci, Lorenzo; Boyd, Robert W.; Santamato, Enrico
2014-01-01
We test experimentally the quantum ``paradox'' proposed by Lucien Hardy in 1993 [Phys. Rev. Lett. 71, 1665 (1993)] by using single photons instead of photon pairs. This is achieved by addressing two compatible degrees of freedom of the same particle, namely its spin angular momentum, determined by the photon polarization, and its orbital angular momentum, a property related to the optical transverse mode. Because our experiment involves a single particle, we cannot use locality to logically e...
Organometallic frustrated Lewis pair chemistry.
Erker, Gerhard
2011-08-07
Frustrated Lewis pairs are playing an increasingly important role in organometallic chemistry. Examples are presented and discussed where organometallic systems themselves serve as the Lewis base or Lewis acid components in frustrated Lewis pair chemistry, mostly through their attached functional groups. Activation of dihydrogen takes place easily in many of these systems. This may lead to the generation of novel catalyst systems but also in many cases to the occurrence of specific reactions at the periphery of the organometallic frameworks. Increasingly, FLP reactions are used to carry out functional group conversions in organometallic systems under mild reaction conditions. The limits of typical FLP reactivity are explored with selected organometallic examples, a discussion that points toward new developments, such as the discovery of facile new 1,1-carboboration reactions. Learning more and more about the broad spectrum of frustrated Lewis pair chemistry helps us to find novel reactions and applications.
Some spherical analysis related to the pairs (U (n), Hn) and (U (p, q ...
Indian Academy of Sciences (India)
Abstract. In this paper, we define the normalized spherical transform associated with the generalized Gelfand pair (U (p, q), Hn), where Hn is the Heisenberg group 2n +. 1-dimensional and p+q = n. We show that the normalized spherical transform F(f ) of a Schwartz function f on Hn restricted to the spectrum of the Gelfand ...
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
Berg, Mark A
2010-04-14
Time-resolved spectroscopy that uses more than one incoherent excitation, and thus has multiple periods of time evolution, is becoming more common. A recent example is multiple population-period transient spectroscopy (MUPPETS), which is implemented as a high-order transient grating. In this paper, a formalism is developed to treat these types of incoherent spectroscopy in a manner that parallels the Liouville-pathway formalism used to treat multidimensional coherent spectroscopy. A Hilbert space of incoherent (population) states is defined and general expressions for transition and time-evolution operators acting on these states are derived from the corresponding quantum operators. This formalism describes incoherent experiments that involve an arbitrary number of temporal dimensions in terms of pathways through the Hilbert space. Each pathway is associated with a multiple-time rate-correlation function. Previous work has shown that these multiple-time correlation functions can measure heterogeneity in electronic-relaxation rates. Thus, they are an analog of coherent "echo" experiments, which measure heterogeneity in frequencies. We show that similar "MUPPETS echo" experiments can be done on any incoherent variable. For a dilute molecular solute, the Hilbert-space method leads to a systematic treatment of multidimensional transient gratings. The extension of irreducible-tensor methods to the incoherent Hilbert space results in a classification of orientational gratings of arbitrary order. The general methods developed in this paper are applied more specifically to single-photon, dipole transitions in the following paper.
DEFF Research Database (Denmark)
Majgaard, Klaus
The purpose of this paper is to enhance the conceptual understanding of the mediatory relationship between paradoxes on an organizational and an individual level. It presents a concept of agency that comprises and mediates between a structural and individual pole. The constitution of this agency...... is achieved through narrative activity that oscillates between the poles and transforms paradoxes through the configuration of plots and metaphors. Empirical cases are introduced in order to illustrate the implications of this understanding....
Directory of Open Access Journals (Sweden)
Felician ALECU
2012-04-01
Full Text Available XSLT style sheets are designed to transform the XML documents into something else. The two most popular parsers of the moment are the Document Object Model (DOM and the Simple API for XML (SAX. DOM is an official recommendation of the W3C (available at http://www.w3.org/TR/REC-DOM-Level-1, while SAX is a de facto standard. A good parser should be fast, space efficient, rich in functionality and easy to use.
Smith, James L.; Helenberg, Harold W.; Kilsdonk, Dennis J.
1979-01-01
There is provided an improved RF transformer having a single-turn secondary of cylindrical shape and a coiled encapsulated primary contained within the secondary. The coil is tapered so that the narrowest separation between the primary and the secondary is at one end of the coil. The encapsulated primary is removable from the secondary so that a variety of different capacity primaries can be utilized with one secondary.
The Peak Pairs algorithm for strain mapping from HRTEM images
Energy Technology Data Exchange (ETDEWEB)
Galindo, Pedro L. [Departamento de Lenguajes y Sistemas Informaticos, CASEM, Universidad de Cadiz, Pol. Rio San Pedro s/n. 11510, Puerto Real, Cadiz (Spain)], E-mail: pedro.galindo@uca.es; Kret, Slawomir [Institute of Physics, PAS, AL. Lotnikow 32/46, 02-668 Warsaw (Poland); Sanchez, Ana M. [Departamento de Ciencia de los Materiales e Ing. Metalurgica y Q. Inorganica, Facultad de Ciencias, Universidad de Cadiz, Pol. Rio San Pedro s/n. 11510, Puerto Real, Cadiz (Spain); Laval, Jean-Yves [Laboratoire de Physique du Solide, UPR5 CNRS-ESPCI, Paris (France); Yanez, Andres; Pizarro, Joaquin; Guerrero, Elisa [Departamento de Lenguajes y Sistemas Informaticos, CASEM, Universidad de Cadiz, Pol. Rio San Pedro s/n. 11510, Puerto Real, Cadiz (Spain); Ben, Teresa; Molina, Sergio I. [Departamento de Ciencia de los Materiales e Ing. Metalurgica y Q. Inorganica, Facultad de Ciencias, Universidad de Cadiz, Pol. Rio San Pedro s/n. 11510, Puerto Real, Cadiz (Spain)
2007-11-15
Strain mapping is defined as a numerical image-processing technique that measures the local shifts of image details around a crystal defect with respect to the ideal, defect-free, positions in the bulk. Algorithms to map elastic strains from high-resolution transmission electron microscopy (HRTEM) images may be classified into two categories: those based on the detection of peaks of intensity in real space and the Geometric Phase approach, calculated in Fourier space. In this paper, we discuss both categories and propose an alternative real space algorithm (Peak Pairs) based on the detection of pairs of intensity maxima in an affine transformed space dependent on the reference area. In spite of the fact that it is a real space approach, the Peak Pairs algorithm exhibits good behaviour at heavily distorted defect cores, e.g. interfaces and dislocations. Quantitative results are reported from experiments to determine local strain in different types of semiconductor heterostructures.
Atomic pair-state interferometer
DEFF Research Database (Denmark)
Nipper, J.; Balewski, Jonathan B.; Krupp, Alexander T.
2012-01-01
We present experiments measuring an interaction-induced phase shift of Rydberg atoms at Stark-tuned Förster resonances. The phase shift features a dispersive shape around the resonance, showing that the interaction strength and sign can be tuned coherently. We use a pair-state interferometer...
Electron pair creation by photons
Holtwijk, Theodoor
1960-01-01
In our experiment on the creation of electron pairs a 5 MeV betatron was used as radiation source and a cloud chamber (with magnetic field) was used as detection instrument. The experimental arrangement is described in section 2.1. The cloud chamber was of the overcompression type so that the
Instantons in lepton pair production
Brandenburg, A.; Ringwald, A.; Utermann, A.
2006-01-01
We consider QCD instanton-induced contributions to lepton pair production in hadron-hadron collisions. We relate these contributions to those known from deep inelastic scattering and demonstrate that they can be calculated reliably for sufficiently large momentum transfer. We observe that the
Conjugal Pairing in Escherichia Coli
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 8. Conjugal Pairing in Escherichia Coli. Joshua Lederberg. Classics Volume 13 Issue 8 August 2008 pp 793-794. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/013/08/0793-0794 ...
Pairing Linguistic and Music Intelligences
DiEdwardo, MaryAnn Pasda
2005-01-01
This article describes how music in the language classroom setting can be a catalyst for developing reading, writing, and understanding skills. Studies suggest that pairing music and linguistic intelligences in the college classroom improves students' grades and abilities to compose theses statements for research papers in courses that emphasize…
Kingravi, Hassan A; Chowdhary, Girish; Vela, Patricio A; Johnson, Eric N
2012-07-01
Classical work in model reference adaptive control for uncertain nonlinear dynamical systems with a radial basis function (RBF) neural network adaptive element does not guarantee that the network weights stay bounded in a compact neighborhood of the ideal weights when the system signals are not persistently exciting (PE). Recent work has shown, however, that an adaptive controller using specifically recorded data concurrently with instantaneous data guarantees boundedness without PE signals. However, the work assumes fixed RBF network centers, which requires domain knowledge of the uncertainty. Motivated by reproducing kernel Hilbert space theory, we propose an online algorithm for updating the RBF centers to remove the assumption. In addition to proving boundedness of the resulting neuro-adaptive controller, a connection is made between PE signals and kernel methods. Simulation results show improved performance.
Straeter, T. A.
1972-01-01
The Davidon-Broyden class of rank one, quasi-Newton minimization methods is extended from Euclidean spaces to infinite-dimensional, real Hilbert spaces. For several techniques of choosing the step size, conditions are found which assure convergence of the associated iterates to the location of the minimum of a positive definite quadratic functional. For those techniques, convergence is achieved without the problem of the computation of a one-dimensional minimum at each iteration. The application of this class of minimization methods for the direct computation of the solution of an optimal control problem is outlined. The performance of various members of the class are compared by solving a sample optimal control problem. Finally, the sample problem is solved by other known gradient methods, and the results are compared with those obtained with the rank one quasi-Newton methods.
Hermann, M. R.; Langhoff, P. W.
1983-01-01
Computational methods are reported for construction of discrete and continuum Schroedinger states in atoms and molecules employing explicit Hilbert space procedures familiar from bound state studies. As theoretical development, the Schroedinger problem of interest is described, the Cauchy-Lanczos bases and orthonormal polynomials used in constructing L-squared Stieltjes-Tchebycheff (ST) approximations to the discrete and continuum states are defined, and certain properties of these functions are indicated. Advantages and limitations of the ST approach to spectral studies relative to more conventional calculations are discussed, and aspects of the approach in single-channel approximations to larger molecules are described. Procedures are indicated for construction of photoejection anisotropies and for performing coupled-channel calculations employing the ST formalism. Finally, explicit descriptive intercomparisons are made of the nature and diagnostic value of ST functions with more conventional scattering functions.
Vanfleteren, Diederik; Van Neck, Dimitri; Bultinck, Patrick; Ayers, Paul W; Waroquier, Michel
2012-01-07
A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.
Pairing gaps in nucleonic superfluids
Energy Technology Data Exchange (ETDEWEB)
Chen, J.M.C. (McDonnell Center for the Space Sciences and Dept. of Physics, Washington Univ., St. Louis, MO (United States)); Clark, J.W. (McDonnell Center for the Space Sciences and Dept. of Physics, Washington Univ., St. Louis, MO (United States)); Dave, R.D. (McDonnell Center for the Space Sciences and Dept. of Physics, Washington Univ., St. Louis, MO (United States)); Khodel, V.V. (McDonnell Center for the Space Sciences and Dept. of Physics, Washington Univ., St. Louis, MO (United States))
1993-04-05
Singlet S-wave nucleonic superfluids are studied within a microscopic many-body theory that incorporates explicit spatial correlations due to strong short-range repulsive forces as well as the momentum-space pairing correlations of BCS theory. The theory is formulated within the method of correlated basis functions (CBF). Within this scheme, there results a nonlinear problem for the superfluid energy gap that is identical in form to the gap problem of conventional BCS theory. However, the input single-particle energies and pairing matrix elements are dressed by the short-range spatial correlations and accordingly incorporate an important class of medium corrections. The effective pairing force of the theory is finite even if the bare two-nucleon potential contains an infinitely hard core; both the pairing matrix elements and single-particle energies are to be constructed from normal-state CBF matrix elements and may be evaluated by cluster-expansion techniques. The theory is explicated and applied at a variational level that is equivalent to the leading order of a CBF superstate perturbation theory. New results are presented for the [sup 1]S[sub 0] pairing gap [Delta][sub kF] in pure neutron matter at densities relevant to the inner crust of a neutron star, based on a simplified version of the Reid soft-core interaction and spin-dependent spatial correlations optimized in the correlated normal state. Careful considering is given to the treatment of the gap equation at large intermediate-state momenta. The variational gap function evaluated at the Fermi surface, [Delta][sub F], is found to be larger than predicted in earlier work. Estimates of the suppression of the gap due to polarization processes (and other particle-particle and hole-irreducible medium effects of higher order within CBF superstate perturbation theory) yield values of [Delta][sub kF].
Sinha, Shriprakash
2017-12-04
Ever since the accidental discovery of Wingless [Sharma R.P., Drosophila information service, 1973, 50, p 134], research in the field of Wnt signaling pathway has taken significant strides in wet lab experiments and various cancer clinical trials, augmented by recent developments in advanced computational modeling of the pathway. Information rich gene expression profiles reveal various aspects of the signaling pathway and help in studying different issues simultaneously. Hitherto, not many computational studies exist which incorporate the simultaneous study of these issues. This manuscript ∙ explores the strength of contributing factors in the signaling pathway, ∙ analyzes the existing causal relations among the inter/extracellular factors effecting the pathway based on prior biological knowledge and ∙ investigates the deviations in fold changes in the recently found prevalence of psychophysical laws working in the pathway. To achieve this goal, local and global sensitivity analysis is conducted on the (non)linear responses between the factors obtained from static and time series expression profiles using the density (Hilbert-Schmidt Information Criterion) and variance (Sobol) based sensitivity indices. The results show the advantage of using density based indices over variance based indices mainly due to the former's employment of distance measures & the kernel trick via Reproducing kernel Hilbert space (RKHS) that capture nonlinear relations among various intra/extracellular factors of the pathway in a higher dimensional space. In time series data, using these indices it is now possible to observe where in time, which factors get influenced & contribute to the pathway, as changes in concentration of the other factors are made. This synergy of prior biological knowledge, sensitivity analysis & representations in higher dimensional spaces can facilitate in time based administration of target therapeutic drugs & reveal hidden biological information within
Usher, P. D.
1997-12-01
William Shakespeare's Hamlet has much evidence to suggest that the Bard was aware of the cosmological models of his time, specifically the geocentric bounded Ptolemaic and Tychonic models, and the infinite Diggesian. Moreover, Shakespeare describes how the Ptolemaic model is to be transformed to the Diggesian. Hamlet's "transformation" is the reason that Claudius, who personifies the Ptolemaic model, summons Rosencrantz and Guildenstern, who personify the Tychonic. Pantometria, written by Leonard Digges and his son Thomas in 1571, contains the first technical use of the word "transformation." At age thirty, Thomas Digges went on to propose his Perfit Description, as alluded to in Act Five where Hamlet's age is given as thirty. In Act Five as well, the words "bore" and "arms" refer to Thomas' vocation as muster-master and his scientific interest in ballistics. England's leading astronomer was also the father of the poet whose encomium introduced the First Folio of 1623. His oldest child Dudley became a member of the Virginia Company and facilitated the writing of The Tempest. Taken as a whole, such manifold connections to Thomas Digges support Hotson's contention that Shakespeare knew the Digges family. Rosencrantz and Guildenstern in Hamlet bear Danish names because they personify the Danish model, while the king's name is latinized like that of Claudius Ptolemaeus. The reason Shakespeare anglicized "Amleth" to "Hamlet" was because he saw a parallel between Book Three of Saxo Grammaticus and the eventual triumph of the Diggesian model. But Shakespeare eschewed Book Four, creating this particular ending from an infinity of other possibilities because it "suited his purpose," viz. to celebrate the concept of a boundless universe of stars like the Sun.
Wolfgang, F.; Nicol, J.
1962-11-01
Transformer apparatus is designed for measuring the amount of a paramagnetic substance dissolved or suspended in a diamagnetic liquid. The apparatus consists of a cluster of tubes, some of which are closed and have sealed within the diamagnetic substance without any of the paramagnetic material. The remaining tubes are open to flow of the mix- ture. Primary and secondary conductors are wrapped around the tubes in such a way as to cancel noise components and also to produce a differential signal on the secondaries based upon variations of the content of the paramagnetic material. (AEC)
McLyman, Colonel Wm. T.
1996-01-01
None given. From first Par: Many spacecraft (S/C) and surface rovers require the transfer of signals and power across rotating interfaces. Science instruments, antennas and solar arrays are elements needing rotary power transfer for certain (S/C) configurations. Delivery of signal and power has mainly been done by using the simplest means, the slip ring approach. This approach, although simple, leaves debris generating noise over a period of time...The rotary transformer is a good alternative to slip rings for signal and power transfer.
A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons
Energy Technology Data Exchange (ETDEWEB)
Hibberd, K.E. [Centre for Mathematical Physics, University of Queensland, 4072 (Australia); Dunning, C. [Institute of Mathematics, Statistics and Actuarial Science, University of Kent (United Kingdom); Links, J. [Centre for Mathematical Physics, University of Queensland, 4072 (Australia)]. E-mail: jrl@maths.uq.edu.au
2006-08-07
We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PT-symmetric wavefunctions defined on a contour in the complex plane.
A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons
Hibberd, K. E.; Dunning, C.; Links, J.
2006-08-01
We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrödinger operators. For the solution we derive here the potential of the Schrödinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PT-symmetric wavefunctions defined on a contour in the complex plane.
Marlow, D L
1996-01-01
In these uncertain times in the healthcare industry, administrators are asked to do more with less time and resources. Because of the extended roles they are playing in today's organizations, radiology administrators are looked upon as agents of change. What leadership skills do they need in this turbulent and uncertain healthcare environment? What are the trait's of tomorrow's leaders? The transformational leader is the one who will guide us through this changing healthcare environment. Several behavioral patterns emerge as important traits for tomorrow's leaders to have-individual consideration, intellectual stimulation and charisma. Tomorrow's leader must view each person as an individual, showing genuine concern and belief in each person's ability to perform. Transformational leaders stimulate others by encouraging them to be curious and try new ideas. The final characteristic, charisma, is the ability to inspire others. Luckily, leaders are made, not born: today's leaders can learn to be responsive, to draw out new ideas from employees, and to communicate self-esteem, energy and enthusiasm.
Hyponormal quantization of planar domains exponential transform in dimension two
Gustafsson, Björn
2017-01-01
This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.
Stern, Adrian
2008-03-01
The linear canonical transform (LCT) is the name of a parameterized continuum of transforms that include, as particular cases, many widely used transforms in optics such as the Fourier transform, fractional Fourier transform, and Fresnel transform. It provides a generalized mathematical tool for representing the response of any first-order optical system in a simple and insightful way. In this work we present four uncertainty relations between LCT pairs and discuss their implications in some common optical systems.
Rutherford, Ernest
2012-01-01
Radioactive Transformations describes Ernest Rutherford's Nobel Prize-winning investigations into the mysteries of radioactive matter. In this historic work, Rutherford outlines the scientific investigations that led to and coincided with his own research--including the work of Wilhelm Rӧntgen, J. J. Thomson, and Marie Curie--and explains in detail the experiments that provided a glimpse at special relativity, quantum mechanics, and other concepts that would shape modern physics. This new edition features a comprehensive introduction by Nobel Laureate Frank Wilczek which engagingly explains how Rutherford's early research led to a better understanding of topics as diverse as the workings of the atom's nucleus, the age of our planet, and the fusion in stars.
Modeling and testing of ethernet transformers
Bowen, David
2011-12-01
Twisted-pair Ethernet is now the standard home and office last-mile network technology. For decades, the IEEE standard that defines Ethernet has required electrical isolation between the twisted pair cable and the Ethernet device. So, for decades, every Ethernet interface has used magnetic core Ethernet transformers to isolate Ethernet devices and keep users safe in the event of a potentially dangerous fault on the network media. The current state-of-the-art Ethernet transformers are miniature (explored which are capable of exceptional miniaturization or on-chip fabrication. This dissertation thoroughly explores the performance of the current commercial Ethernet transformers to both increase understanding of the device's behavior and outline performance parameters for replacement devices. Lumped element and distributed circuit models are derived; testing schemes are developed and used to extract model parameters from commercial Ethernet devices. Transfer relation measurements of the commercial Ethernet transformers are compared against the model's behavior and it is found that the tuned, distributed models produce the best transfer relation match to the measured data. Process descriptions and testing results on fabricated thin-film dielectric-core toroid transformers are presented. The best results were found for a 32-turn transformer loaded with 100Ω, the impedance of twisted pair cable. This transformer gave a flat response from about 10MHz to 40MHz with a height of approximately 0.45. For the fabricated transformer structures, theoretical methods to determine resistance, capacitance and inductance are presented. A special analytical and numerical analysis of the fabricated transformer inductance is presented. Planar cuts of magnetic slope fields around the dielectric-core toroid are shown that describe the effect of core height and winding density on flux uniformity without a magnetic core.
A New Instantaneous Frequency Measure Based on The Stockwell Transform
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
Charge Aspects of Composite Pair Superconductivity
Flint, Rebecca
2014-03-01
Conventional Cooper pairs form from well-defined electronic quasiparticles, making the internal structure of the pair irrelevant. However, in the 115 family of superconductors, the heavy electrons are forming as they pair and the internal pair structure becomes as important as the pairing mechanism. Conventional spin fluctuation mediated pairing cannot capture the direct transition from incoherent local moments to heavy fermion superconductivity, but the formation of composite pairs favored by the two channel Kondo effect can. These composite pairs are local d-wave pairs formed by two conduction electrons in orthogonal Kondo channels screening the same local moment. Composite pairing shares the same symmetries as magnetically mediated pairing, however, only composite pairing necessarily involves a redistribution of charge within the unit cell originating from the internal pair structure, both as a monopole (valence change) and a quadrupole effect. This redistribution will onset sharply at the superconducting transition temperature. A smoking gun test for composite pairing is therefore a sharp signature at Tc - for example, a cusp in the Mossbauer isomer shift in NpPd5Al2 or in the NQR shift in (Ce,Pu)CoIn5.
EDITORIAL: Transformation optics Transformation optics
Shalaev, Vladimir M.; Pendry, John
2011-02-01
Metamaterials are artificial materials with versatile properties that can be tailored to fit almost any practical need and thus go well beyond what can be obtained with `natural' materials. Recent progress in developing optical metamaterials allows unprecedented extreme control over the flow of light at both the nano- and macroscopic scales. The innovative field of transformation optics, which is enabled by metamaterials, inspired researchers to take a fresh look at the very foundations of optics and helped to create a new paradigm for the science of light. Similar to general relativity, where time and space are curved, transformation optics shows that the space for light can also be bent in an almost arbitrary way. Most importantly, the optical space can be designed and engineered, opening up the fascinating possibility of controlling the flow of light with nanometer spatial precision. This new paradigm enables a number of novel optical devices guiding how, using metamaterials, the space for light can be curved in a pre-designed and well-controlled way. Metamaterials which incorporate the innovative theories of transformation optics are pertinent to the important areas of optical cloaking, optical black holes, super-resolution imaging, and other sci-fi-like devices. One such exciting device is an electromagnetic cloak that can bend light around itself, similar to the flow of water around a stone, making invisible both the cloak and the object hidden inside. Another important application is a flat hyperlens that can magnify the nanometer-scale features of an object that cannot be resolved with conventional optics. This could revolutionize the field of optical imaging, for instance, because such a meta-lens could become a standard add-on tool for microscopes. By enabling nanoscale resolution in optical microscopy, metamaterial-based transformation optics could allow one to literally see extremely small objects with the eye, including biological cells, viruses, and
Energy Technology Data Exchange (ETDEWEB)
Kraemer, Michael; Pellen, Mathieu [RWTH Aachen University, Institut fuer Theoretische Teilchenphysik und Kosmologie (Germany); Hangst, Christian; Muehlleitner, Margarete [KIT, Institut fuer Theoretische Physik (Germany); Popenda, Eva; Spira, Michael [PSI, Theory Group LTP (Switzerland)
2013-07-01
A lot of effort is and will be put in the search for supersymmetric particles at the LHC. For the interpretation of the experimental data precise theoretical predictions are crucial. The work presented in the talk contributes to this effort by providing NLO corrections to the pair production of squarks of the first two generations in a flexible partonic Monte Carlo program. In contrast to previous works no assumptions regarding the squark masses have been made and the different subchannels have been treated independently. The Monte Carlo framework allows investigating the impact of the supersymmetric QCD corrections at NLO on arbitrary distributions.
Lost Chevalier Pairs - A Followup
2012-01-01
correct, but the true 19 position angle was 180° minus the Chevalier value. The initial conclusion was that Chevalier had made a trigonometry error... trigonometry /plate errors, there was an additional 10’ error in Chevalier’s declination, due to an error in applying the y offset. Berk6 was unable to find...a match. After correcting for the plate center and trigonometry /plate errors, this pair was found to match 19498+2324 = J 496AB, as noted by Berko
Coisotropic Submanifolds and Dual Pairs
Cattaneo, Alberto S.
2014-03-01
The Poisson sigma model is a widely studied two-dimensional topological field theory. This note shows that boundary conditions for the Poisson sigma model are related to coisotropic submanifolds (a result announced in [math.QA/0309180]) and that the corresponding reduced phase space is a (possibly singular) dual pair between the reduced spaces of the given two coisotropic submanifolds. In addition the generalization to a more general tensor field is considered and it is shown that the theory produces Lagrangian evolution relations if and only if the tensor field is Poisson.
Kanter, Rosabeth Moss
2008-01-01
Large corporations have long been seen as lumbering, inflexible, bureaucratic--and clueless about global developments. But recently some multinationals seem to be transforming themselves: They're engaging employees, moving quickly, and introducing innovations that show true connection with the world. Harvard Business School's Kanter ventured with a research team inside a dozen global giants--including IBM, Procter & Gamble, Omron, CEMEX, Cisco, and Banco Real--to discover what has been driving the change. After conducting more than 350 interviews on five continents, she and her colleagues came away with a strong sense that we are witnessing the dawn of a new model of corporate power: The coordination of actions and decisions on the front lines now appears to stem from widely shared values and a sturdy platform of common processes and technology, not from top-down decrees. In particular, the values that engage the passions of far-flung workforces stress openness, inclusion, and making the world a better place. Through this shift in what might be called their guidance systems, the companies have become as creative and nimble as much smaller ones, even while taking on social and environmental challenges of a scale that only large enterprises could attempt. IBM, for instance, has created a nonprofit partnership, World Community Grid, through which any organization or individual can donate unused computing power to research projects and see what is being done with the donation in real time. IBM has gained an inspiring showcase for its new technology, helped business partners connect with the company in a positive way, and offered individuals all over the globe the chance to contribute to something big.
Random fractional Fourier transform.
Liu, Zhengjun; Liu, Shutian
2007-08-01
We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics. As a primary application the random fractional Fourier transform can be directly used in optical image encryption and decryption. The double phase encoding image encryption schemes can thus be modeled with cascaded random fractional Fourier transformers.
Hillenbrand, Benedikt
2017-01-01
Following the tile, this thesis seeks to find a methodology for detecting and interpreting instantaneous frequencies in stand-alone microgrids. This is not a novel exercise for scientists to do but it bears potential to be improved by making use of a new method - the Empirical Mode Decomposition (EMD). The EMD is a non-linear algorithm that separates any oscillating signal into mono-components, leaving space for time-varying amplitude and -frequency of the so called Intrinsic Mode Functions. ...
Lazar, Aurel A; Slutskiy, Yevgeniy B
2015-02-01
We present a multi-input multi-output neural circuit architecture for nonlinear processing and encoding of stimuli in the spike domain. In this architecture a bank of dendritic stimulus processors implements nonlinear transformations of multiple temporal or spatio-temporal signals such as spike trains or auditory and visual stimuli in the analog domain. Dendritic stimulus processors may act on both individual stimuli and on groups of stimuli, thereby executing complex computations that arise as a result of interactions between concurrently received signals. The results of the analog-domain computations are then encoded into a multi-dimensional spike train by a population of spiking neurons modeled as nonlinear dynamical systems. We investigate general conditions under which such circuits faithfully represent stimuli and demonstrate algorithms for (i) stimulus recovery, or decoding, and (ii) identification of dendritic stimulus processors from the observed spikes. Taken together, our results demonstrate a fundamental duality between the identification of the dendritic stimulus processor of a single neuron and the decoding of stimuli encoded by a population of neurons with a bank of dendritic stimulus processors. This duality result enabled us to derive lower bounds on the number of experiments to be performed and the total number of spikes that need to be recorded for identifying a neural circuit.
Directory of Open Access Journals (Sweden)
M. De la Sen
2017-01-01
Full Text Available This paper investigates some parallel relations between the operators I-G and G in Hilbert spaces in such a way that the pseudocontractivity, asymptotic pseudocontractivity, and asymptotic pseudocontractivity in the intermediate sense of one of them are equivalent to the accretivity, asymptotic accretivity, and asymptotic accretivity in the intermediate sense of the other operator. If the operators are self-adjoint then the obtained accretivity-type properties are also passivity-type properties. Such properties are very relevant in stability theory since they refer to global stability properties of passive feed-forward, in general, nonlinear, and time-varying controlled systems controlled via feedback by elements in a very general class of passive, in general, nonlinear, and time-varying controllers. These results allow the direct generalization of passivity results in controlled dynamic systems to wide classes of tandems of controlled systems and their controllers, described by G-operators, and their parallel interpretations as pseudocontractive properties of their counterpart I-G-operators. Some of the obtained results are also directly related to input-passivity, output-passivity, and hyperstability properties in controlled dynamic systems. Some illustrative examples are also given in the framework of dynamic systems described by extended square-integrable input and output signals.
Pair distribution function computed tomography.
Jacques, Simon D M; Di Michiel, Marco; Kimber, Simon A J; Yang, Xiaohao; Cernik, Robert J; Beale, Andrew M; Billinge, Simon J L
2013-01-01
An emerging theme of modern composites and devices is the coupling of nanostructural properties of materials with their targeted arrangement at the microscale. Of the imaging techniques developed that provide insight into such designer materials and devices, those based on diffraction are particularly useful. However, to date, these have been heavily restrictive, providing information only on materials that exhibit high crystallographic ordering. Here we describe a method that uses a combination of X-ray atomic pair distribution function analysis and computed tomography to overcome this limitation. It allows the structure of nanocrystalline and amorphous materials to be identified, quantified and mapped. We demonstrate the method with a phantom object and subsequently apply it to resolving, in situ, the physicochemical states of a heterogeneous catalyst system. The method may have potential impact across a range of disciplines from materials science, biomaterials, geology, environmental science, palaeontology and cultural heritage to health.
Universalities of Triplet Pairing in Neutron Matter
Khodel, V. A.; Khodel, V. V.; Clark, J. W.
1998-01-01
The fundamental structure of the full set of solutions of the BCS $^3 P_2$ pairing problem in neutron matter is established. The relations between different spin-angle components in these solutions are shown to be practically independent of density, temperature, and the specific form of the pairing interaction. The spectrum of pairing energies is found to be highly degenerate.
Magnetic pair distribution function analysis of local magnetic correlations.
Frandsen, Benjamin A; Yang, Xiaohao; Billinge, Simon J L
2014-01-01
The analytical form of the magnetic pair distribution function (mPDF) is derived for the first time by computing the Fourier transform of the neutron scattering cross section from an arbitrary collection of magnetic moments. Similar to the atomic pair distribution function applied to the study of atomic structure, the mPDF reveals both short-range and long-range magnetic correlations directly in real space. This function is experimentally accessible and yields magnetic correlations even when they are only short-range ordered. The mPDF is evaluated for various example cases to build an intuitive understanding of how different patterns of magnetic correlations will appear in the mPDF.
Attenuated radon transform: theory and application in medicine and biology
Energy Technology Data Exchange (ETDEWEB)
Gullberg, G.T.
1979-06-01
A detailed analysis is given of the properties of the attenuated Radon transform and of how increases in photon attenuation influence the numerical accuracy and computation efficiency of iterative and convolution algorithms used to determine its inversion. The practical applications for this work involve quantitative assessment of the distribution of injected radiopharmaceuticals and radionuclides in man and animals for basic physiological and biochemical studies as well as clinical studies in nuclear medicine. A mathematical structure is developed using function theory and the theory of linear operators on Hilbert spaces which lends itself to better understanding the spectral properties of the attenuated Radon transform. The continuous attenuated Radon transform reduces to a matrix operator for discrete angular and lateral sampling, and the reconstruction problem reduces to a system of linear equations. For the situation of variable attenuation coefficient frequently found in nuclear medicine applications of imaging the heart and chest, the procedure developed in this thesis involves iterative techniques of performing the generalized inverse. For constant attenuation coefficient less than 0.15 cm/sup -1/, convolution methods can reliably reconstruct a 30 cm object with 0.5 cm resolution. However, for high attenuation coefficients or for the situation where there is variable attenuation such as reconstruction of distribution of isotopes in the heart, iterative techniques developed in this thesis give the best results. (ERB)
Inverse problem in archeological magnetic surveys using complex wavelet transform.
Saracco, G.; Moreau, F.; Mathe, P. E.; Hermitte, D.
2003-04-01
The wavelet transform applied to potential fields (electric, magnetic, or gravimetric, ...) has been now used from several years in geophysical applications, in particular to define the depth of potentiel sources verifying Poisson equation and responsible for potential anomalies measured at the ground surface. The complex continuous wavelet transform (CCWT) has been described, but the phase has not yet been exploited. (For these kinds of problem we construct a complex analyzing wavelet by Hilbert transforms of the Poisson or derivative of the Poisson wavelet which is real by definition). We show, here, that the phase of the CCWT provides useful information on the geometric and total magnetic inclination of the potential sources, as the modulus allows to characterize their depth and heterogenety degree. Regarding the properties of the phase compared to the modulus, it is more stable in presence of noise and we can defined it, independantly of the low level of energy of the signal. In this sense, information carried by the phase is more efficient to detect small objects or to separate close sources. We have applied a multi-scale analysis on magnetic measurements providing from a cesium magnetometer on the Fox-Amphoux site (France), to detect and localize buried structures like antik ovens. Conjointly, a rock magnetic study including susceptibility and magnetisations (induced or remanent) measurements give a better constrain on the magnetic parameters we want to extract.
Transformer Protection Using the Wavelet Transform
ÖZGÖNENEL, Okan; ÖNBİLGİN, Güven; KOCAMAN, Çağrı
2014-01-01
This paper introduces a novel approach for power transformer protection algorithm. Power system signals such as current and voltage have traditionally been analysed by the Fast Fourier Transform. This paper aims to prove that the Wavelet Transform is a reliable and computationally efficient tool for distinguishing between the inrush currents and fault currents. The simulated results presented clearly show that the proposed technique for power transformer protection facilitates the a...
Constructing pairs of dual bandlimited framelets with desired time localization
DEFF Research Database (Denmark)
Lemvig, Jakob
combination of dilations of ψ with explicitly given coefficients. The result allows a simple construction procedure for pairs of dual wavelet frames whose generators have compact support in the Fourier domain and desired time localization. The construction is based on characteriszing equations for dual......For sufficiently small translation parameters, we prove that any bandlimited function ψ, for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame with a dual frame also having the wavelet structure. This dual frame is generated by a finite linear...
Constructing pairs of dual bandlimited framelets with desired time localization
DEFF Research Database (Denmark)
Lemvig, Jakob
2009-01-01
combination of dilations of ψ with explicitly given coefficients. The result allows a simple construction procedure for pairs of dual wavelet frames whose generators have compact support in the Fourier domain and desired time localization. The construction is based on characteriszing equations for dual......For sufficiently small translation parameters, we prove that any bandlimited function ψ, for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame with a dual frame also having the wavelet structure. This dual frame is generated by a finite linear...
Composite order bilinear pairing on elliptic curve for dual system encryption
Latiff, Fatin Nabila Abd; Othman, Wan Ainun Mior
2015-10-01
In this paper, we explore the pairing-based cryptography on elliptic curve. The security of protocols using composite order bilinear pairing on elliptic curve depends on the difficulty of factoring the number N. Here, we show how to construct composite ordinary pairing-friendly elliptic curve having the subgroup of composite order N by using Cocks-Pinch Method. We also introduce dual system encryption to transform Identity-Based Encryption (IBE) scheme built over prime-order bilinear, to composite order bilinear groups. The new Identity-Based Encryption (IBE) is secured since it uses the Dual System Encryption methodology which guaranteed full security of the new IBE system.
An Improved Method of Training Overcomplete Dictionary Pair
Directory of Open Access Journals (Sweden)
Zhuozheng Wang
2014-01-01
Full Text Available Training overcomplete dictionary pair is a critical step of the mainstream superresolution methods. For the high time complexity and susceptible to corruption characteristics of training dictionary, an improved method based on lifting wavelet transform and robust principal component analysis is reported. The high-frequency components of example images are estimated through wavelet coefficients of 3-tier lifting wavelet transform decomposition. Sparse coefficients are similar in multiframe images. Accordingly, the inexact augmented Lagrange multiplier method is employed to achieve robust principal component analysis in the process of imposing global constraints. Experiments reveal that the new algorithm not only reduces the time complexity preserving the clarity but also improves the robustness for the corrupted example images.
Fascinating Organic Transformations
Indian Academy of Sciences (India)
RESONANCE │ December 2011. Fascinating Organic Transformations. 2. The Ubiquitous Hydrogen Bond. Subramania Ranganathan. Hydrogen bonds can transform simple molecules into beauti- ful architectures. This is well illustrated in this article. Organic transformations are generally assumed to involve reactions.
2D Prony-Huang Transform: A New Tool for 2D Spectral Analysis
Schmitt, Jeremy; Pustelnik, Nelly; Borgnat, Pierre; Flandrin, Patrick; Condat, Laurent
2014-12-01
This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.
Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.
Glasser, L.
1987-01-01
Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)
Heterospecific transformation among cyanobacteria.
Stevens, S E; Porter, R D
1986-01-01
Heterospecific transformation occurred between cyanobacteria currently classified in either the genus Synechococcus or Synechocystis. Cyanobacterial strains 73109 and 6906 were capable of physiological transformation.
Report on Pairing-based Cryptography.
Moody, Dustin; Peralta, Rene; Perlner, Ray; Regenscheid, Andrew; Roginsky, Allen; Chen, Lily
2015-01-01
This report summarizes study results on pairing-based cryptography. The main purpose of the study is to form NIST's position on standardizing and recommending pairing-based cryptography schemes currently published in research literature and standardized in other standard bodies. The report reviews the mathematical background of pairings. This includes topics such as pairing-friendly elliptic curves and how to compute various pairings. It includes a brief introduction to existing identity-based encryption (IBE) schemes and other cryptographic schemes using pairing technology. The report provides a complete study of the current status of standard activities on pairing-based cryptographic schemes. It explores different application scenarios for pairing-based cryptography schemes. As an important aspect of adopting pairing-based schemes, the report also considers the challenges inherent in validation testing of cryptographic algorithms and modules. Based on the study, the report suggests an approach for including pairing-based cryptography schemes in the NIST cryptographic toolkit. The report also outlines several questions that will require further study if this approach is followed.
Ordered pairing in liquid metallic hydrogen
Carlsson, A. E.; Ashcroft, N. W.
1983-01-01
We study two possible types of pairing involving the protons of a proposed low-temperature liquid phase metallic hydrogen. Electron-proton pairing, which can result in an insulating phase, is investigated by using an approximate solution of an Eliashberg-type equation for the anomalous self-energy. A very low estimate of the transition temperature is obtained by including proton correlations in the effective interaction. For proton-proton pairing, we derive a new proton pair potential based on the Abrikosov wave function. This potential includes the electron-proton interaction to all orders and has a much larger well depth than is obtained with linear screening methods. This suggests the possibility of either a superfluid paired phase analogous to that in He-3, or alternatively a phase with true molecular pairing.
Canonical transformation path to gauge theories of gravity
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.
An Entropic Approach for Pair Trading
Directory of Open Access Journals (Sweden)
Daisuke Yoshikawa
2017-06-01
Full Text Available In this paper, we derive the optimal boundary for pair trading. This boundary defines the points of entry into or exit from the market for a given stock pair. However, if the assumed model contains uncertainty, the resulting boundary could result in large losses. To avoid this, we develop a more robust strategy by accounting for the model uncertainty. To incorporate the model uncertainty, we use the relative entropy as a penalty function in the expected profit from pair trading.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
Dual origin of pairing in nuclei
Energy Technology Data Exchange (ETDEWEB)
Idini, A. [University of Jyvaskyla, Department of Physics (Finland); Potel, G. [Michigan State University, National Superconducting Cyclotron Laboratory (United States); Barranco, F. [Escuela Superior de Ingenieros, Universidad de Sevilla, Departamento de Fìsica Aplicada III (Spain); Vigezzi, E., E-mail: enrico.vigezzi@mi.infn.it [INFN Sezione di Milano (Italy); Broglia, R. A. [Università di Milano, Dipartimento di Fisica (Italy)
2016-11-15
The pairing correlations of the nucleus {sup 120}Sn are calculated by solving the Nambu–Gor’kov equations, including medium polarization effects resulting from the interweaving of quasiparticles, spin and density vibrations, taking into account, within the framework of nuclear field theory (NFT), processes leading to self-energy and vertex corrections and to the induced pairing interaction. From these results one can not only demonstrate the inevitability of the dual origin of pairing in nuclei, but also extract information which can be used at profit to quantitatively disentangle the contributions to the pairing gap Δ arising from the bare and from the induced pairing interaction. The first is the strong {sup 1}S{sub 0} short-range NN potential resulting from meson exchange between nucleons moving in time reversal states within an energy range of hundreds of MeV from the Fermi energy. The second results from the exchange of vibrational modes between nucleons moving within few MeV from the Fermi energy. Short- (v{sub p}{sup bare}) and long-range (v{sub p}{sup ind}) pairing interactions contribute essentially equally to nuclear Cooper pair stability. That is to the breaking of gauge invariance in open-shell superfluid nuclei and thus to the order parameter, namely to the ground state expectation value of the pair creation operator. In other words, to the emergent property of generalized rigidity in gauge space, and associated rotational bands and Cooper pair tunneling between members of these bands.
Castro, José; Georgiopoulos, Michael; Demara, Ronald; Gonzalez, Avelino
2005-09-01
The Fuzzy ARTMAP algorithm has been proven to be one of the premier neural network architectures for classification problems. One of the properties of Fuzzy ARTMAP, which can be both an asset and a liability, is its capacity to produce new nodes (templates) on demand to represent classification categories. This property allows Fuzzy ARTMAP to automatically adapt to the database without having to a priori specify its network size. On the other hand, it has the undesirable side effect that large databases might produce a large network size (node proliferation) that can dramatically slow down the training speed of the algorithm. To address the slow convergence speed of Fuzzy ARTMAP for large database problems, we propose the use of space-filling curves, specifically the Hilbert space-filling curves (HSFC). Hilbert space-filling curves allow us to divide the problem into smaller sub-problems, each focusing on a smaller than the original dataset. For learning each partition of data, a different Fuzzy ARTMAP network is used. Through this divide-and-conquer approach we are avoiding the node proliferation problem, and consequently we speedup Fuzzy ARTMAP's training. Results have been produced for a two-class, 16-dimensional Gaussian data, and on the Forest database, available at the UCI repository. Our results indicate that the Hilbert space-filling curve approach reduces the time that it takes to train Fuzzy ARTMAP without affecting the generalization performance attained by Fuzzy ARTMAP trained on the original large dataset. Given that the resulting smaller datasets that the HSFC approach produces can independently be learned by different Fuzzy ARTMAP networks, we have also implemented and tested a parallel implementation of this approach on a Beowulf cluster of workstations that further speeds up Fuzzy ARTMAP's convergence to a solution for large database problems.
Shepherd, James J; Scuseria, Gustavo E
2016-01-01
Over the past few years pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this, and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure.
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2013-09-03
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
Fourier series, Fourier transform and their applications to mathematical physics
Serov, Valery
2017-01-01
This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...
Space-Efficient Re-Pair Compression
DEFF Research Database (Denmark)
Bille, Philip; Gørtz, Inge Li; Prezza, Nicola
2017-01-01
Re-Pair [5] is an effective grammar-based compression scheme achieving strong compression rates in practice. Let n, σ, and d be the text length, alphabet size, and dictionary size of the final grammar, respectively. In their original paper, the authors show how to compute the Re-Pair grammar...
Exploring Pair Programming Benefits for MIS Majors
Dongo, Tendai; Reed, April H.; O'Hara, Margaret
2016-01-01
Pair programming is a collaborative programming practice that places participants in dyads, working in tandem at one computer to complete programming assignments. Pair programming studies with Computer Science (CS) and Software Engineering (SE) majors have identified benefits such as technical productivity, program/design quality, academic…
Enzymatic incorporation of a third nucleobase pair
National Research Council Canada - National Science Library
Yang, Zunyi; Sismour, A. Michael; Sheng, Pinpin; Puskar, Nyssa L; Benner, Steven A
2007-01-01
DNA polymerases are identified that copy a non-standard nucleotide pair joined by a hydrogen bonding pattern different from the patterns joining the dA:T and dG:dC pairs. 6-Amino-5-nitro-3-(1′-β-d-2′-deoxyribofuranosyl)-2(1H)-pyridone (dZ...
Indian Academy of Sciences (India)
ion plasma are discussed. It is shown that the temperature and/or mass difference of both species could produce drift wave in a pair-ion plasma. The results are discussed in the context of the fullerene pair-ion plasma experiment.
How to Analyze Paired Comparison Data
2011-05-01
How to Analyze Paired Comparison Data Kristi Tsukida and Maya R. Gupta Department of Electrical Engineering University of Washington Seattle, WA...REPORT TYPE 3. DATES COVERED 00-00-2011 to 00-00-2011 4. TITLE AND SUBTITLE How to Analyze Paired Comparison Data 5a. CONTRACT NUMBER 5b. GRANT
Electron pairing in nonlinear nanoelectromechanical systems
Droth, Matthias; Szechenyi, Gabor; Palyi, Andras
Despite the success of BCS-theory, the underlying mechanism for electron-pairing remains elusive for many superconducting materials. For SrTiO3, it has been shown that electron-pairing outside the superconducting regime can be explained with an effectively negative charging energy U graphene resonator.
Indian Academy of Sciences (India)
Xz; 52.27.Cm; 52.35.Kt. 1. Introduction. There has been an accrued interest in pair-ion plasmas, motivated by a recent experiment. [1] on particles with equal charge-to-mass ratio. Pair plasmas are also found in astro- physical environments [2].
Kinetic energy driven pairing in cuprate superconductors
Maier, TA; Jarrell, M; Macridin, A; Slezak, C
2004-01-01
Pairing occurs in conventional superconductors through a reduction of the electronic potential energy accompanied by an increase in kinetic energy. In the underdoped cuprates, optical experiments show that pairing is driven by a reduction of the electronic kinetic energy. Using the dynamical cluster
Transport de paires EPR dans des structures mesoscopiques
Dupont, Emilie
Dans cette these, nous nous sommes particulierement interesses a la propagation de paires EPR1 delocalisees et localisees, et a l'influence d'un supraconducteur sur le transport de ces paires. Apres une introduction de cette etude, ainsi que du cadre scientifique qu'est l'informatique quantique dans lequel elle s'inscrit, nous allons dans le chapitre 1 faire un rappel sur le systeme constitue de deux points quantiques normaux entoures de deux fils supraconducteurs. Cela nous permettra d'introduire une methode de calcul qui sera reutilisee par la suite, et de trouver egalement le courant Josephson produit par ce systeme transforme en SQUID-dc par l'ajout d'une jonction auxiliaire. Le SQUID permet de mesurer l'etat de spin (singulet ou triplet), et peut etre forme a partir d'autres systemes que nous etudierons ensuite. Dans le chapitre 2, nous rappellerons l'etude detaillee d'un intricateur d'Andreev faite par un groupe de Bale. La matrice T, permettant d'obtenir le courant dans les cas ou les electrons sont separes spatialement ou non, sera etudiee en detail afin d'en faire usage au chapitre suivant. Le chapitre 3 est consacre a l'etude de l'influence du bruit sur le fonctionnement de l'intricateur d'Andreev. Ce bruit modifie la forme du courant jusqu'a aboutir a d'autres conditions de fonctionnement de l'intricateur. En effet, le bruit present sur les points quantiques peut perturber le transport des paires EPR par l'intermediaire des degres de liberte. Nous montrerons que, du fait de l'"intrication" entre la charge de la paire et le bruit, la paire est detruite pour des temps longs. Cependant, le resultat le plus important sera que le bruit perturbe plus le transport des paires delocalisees, qui implique une resonance de Breit-Wigner a deux particules. Le transport parasite n'implique pour sa part qu'une resonance de Breit-Wigner a une particule. Dans le chapitre 4, nous reviendrons au systeme constitue de deux points quantiques entoures de deux fils
The information contained in multiple sibling pairs.
Hodge, S E
1984-01-01
In a sibship of size s, s(s-1)/2 sib pairs can be formed, but these pairs are statistically dependent when s greater than 2. This study examines how much independent information is obtained when all possible pairs are used to evaluate the sharing of genes identical by descent. A logarithmic measure of information, sigma pilog2pi [Shannon, 1948], is used. The basic unit of information is the binomial "bit," or the amount of information in the toss of a fair coin. It is shown that a single independent sib pair contains 1.5 bits. The complete sibship contains a total of 2s-3+(1/2)s-1 bits, or (2s-3+(1/2)s-1)/1.5 pair-equivalents of information. The information is reduced if all sib genotypes do not occur with equal probability.
PartialLy Shock-Transformed Olivine in Shocked Chondrites: Mechanisms of Solid-State Transformation
Sharp, T. G.; Xie, Z.
2007-12-01
High-pressure minerals, produced by shock meta-morphism, are common in and around melt veins in highly shocked chondrites. These minerals either crys-tallized from silicate melt in the shock-vein or formed by solid- state transformation of host-rock fragments entrained in the melt or along shock-vein margins. Olivine- ringwoodite transformation kinetics can be used to constrain shock duration if one knows P-T conditions and transformation mechanisms. Here we examine the solid-state transformation of olivine to ringwoodite and the formation of ringwoodite lamellae in Tenham. Partially transformed olivines show a variety of ringwoodite textures. Some have granular textures whereas others have straight or curved ringwoodite lamellae, made up of distinct (1 to 2 ?m) crystals. Many of these polycrystalline ringwoodite lamellae occur in pairs. Where these paired lamellae cross the are offset, suggesting that the lamellae are associated with shearing. Electron diffraction reveals that the ringwoodites in the polycrystalline lamellae, occur in roughly the same crystallographic orientation, defining a lattice-preferred orientation. TEM also shows that the remnant olivine is highly deformed, with high densities of complex dislocations. This olivine has a poorly organized sub-grain structure that grades into polycrystalline olivine. The nearby untransformed olivine is also highly de-formed, but less than the partially transformed olivine. TEM images of complex dislocation and sub-grain microstructures suggests that the transformation of olivine to ringwoodite involves extensive deformation. High densities of dislocations provide potential sites for heterogeneous nucleation of ringwoodite and may enhance Fe-Mg inter-diffusion. The differential stress at the initial stage of the shock results in high strains and local heating. The paired ringwoodite lamellae in olivine appear to result from shearing and possibly shear heating, where nucleation occurs on both sides of a shear
Error-correcting pairs for a public-key cryptosystem
Pellikaan, Ruud; Márquez-Corbella, Irene
2017-06-01
Code-based Cryptography (CBC) is a powerful and promising alternative for quantum resistant cryptography. Indeed, together with lattice-based cryptography, multivariate cryptography and hash-based cryptography are the principal available techniques for post-quantum cryptography. CBC was first introduced by McEliece where he designed one of the most efficient Public-Key encryption schemes with exceptionally strong security guarantees and other desirable properties that still resist to attacks based on Quantum Fourier Transform and Amplitude Amplification. The original proposal, which remains unbroken, was based on binary Goppa codes. Later, several families of codes have been proposed in order to reduce the key size. Some of these alternatives have already been broken. One of the main requirements of a code-based cryptosystem is having high performance t-bounded decoding algorithms which is achieved in the case the code has a t-error-correcting pair (ECP). Indeed, those McEliece schemes that use GRS codes, BCH, Goppa and algebraic geometry codes are in fact using an error-correcting pair as a secret key. That is, the security of these Public-Key Cryptosystems is not only based on the inherent intractability of bounded distance decoding but also on the assumption that it is difficult to retrieve efficiently an error-correcting pair. In this paper, the class of codes with a t-ECP is proposed for the McEliece cryptosystem. Moreover, we study the hardness of distinguishing arbitrary codes from those having a t-error correcting pair.
Particle dynamics and pair production in tightly focused standing wave
Jirka, M.; Klimo, O.; Vranić, M.; Weber, S.; Korn, G.
2017-05-01
With the advent of 10 PW laser facilities, new regimes of laser-matter interaction are opening since effects of quantum electrodynamics, such as electron-positron pair production and cascade development, start to be important. The dynamics of light charged particles, such as electrons and positrons, is affected by the radiation reaction force. This effect can strongly influence the interaction of intense laser pulses with matter since it lowers the energy of emitting particles and transforms their energy to the gamma radiation. Consequently, electron-positron pairs can be generated via Breit-Wheeler process. To study this new regime of interaction, numerical simulations are required. With their help it is possible to predict and study quantum effects which may occur in future experiments at modern laser facilities. In this work we present results of electron interaction with an intense standing wave formed by two colliding laser pulses. Due to the necessity to achieve ultra intense laser field, the laser beam has to be focused to a μm-diameter spot. Since the paraxial approximation is not valid for tight focusing, the appropriate model describing the tightly focused laser beam has to be employed. In tightly focused laser beam the longitudinal component of the electromagnetic field becomes significant and together with the ponderomotive force they affect the dynamics of interacting electrons and also newly generated Breit-Wheeler electron-positron pairs. Using the Particle-In-Cell code we study electron dynamics, gamma radiation and pair production in such a configuration for linear polarization and different types of targets.
Weird Stellar Pair Puzzles Scientists
2008-05-01
Astronomers have discovered a speedy spinning pulsar in an elongated orbit around an apparent Sun-like star, a combination never seen before, and one that has them puzzled about how the strange system developed. Orbital Comparison Comparing Orbits of Pulsar and Its Companion to our Solar System. CREDIT: Bill Saxton, NRAO/AUI/NSF Click on image for full caption information and available graphics. "Our ideas about how the fastest-spinning pulsars are produced do not predict either the kind of orbit or the type of companion star this one has," said David Champion of the Australia Telescope National Facility. "We have to come up with some new scenarios to explain this weird pair," he added. Astronomers first detected the pulsar, called J1903+0327, as part of a long-term survey using the National Science Foundation's Arecibo radio telescope in Puerto Rico. They made the discovery in 2006 doing data analysis at McGill University, where Champion worked at the time. They followed up the discovery with detailed studies using the Arecibo telescope, the NSF's Robert C. Byrd Green Bank Telescope (GBT) in West Virginia, the Westerbork radio telescope in the Netherlands, and the Gemini North optical telescope in Hawaii. The pulsar, a city-sized superdense stellar corpse left over after a massive star exploded as a supernova, is spinning on its axis 465 times every second. Nearly 21,000 light-years from Earth, it is in a highly-elongated orbit that takes it around its companion star once every 95 days. An infrared image made with the Gemini North telescope in Hawaii shows a Sun-like star at the pulsar's position. If this is an orbital companion to the pulsar, it is unlike any companions of other rapidly rotating pulsars. The pulsar, a neutron star, also is unusually massive for its type. "This combination of properties is unprecedented. Not only does it require us to figure out how this system was produced, but the large mass may help us understand how matter behaves at extremely