Showing papers on "Biorthogonal system published in 2018"
TL;DR: This work provides a comprehensive framework for generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.
Abstract: Non-Hermitian systems exhibit striking exceptions from the paradigmatic bulk-boundary correspondence, including the failure of bulk Bloch band invariants in predicting boundary states and the (dis)appearance of boundary states at parameter values far from those corresponding to gap closings in periodic systems without boundaries. Here, we provide a comprehensive framework to unravel this disparity based on the notion of biorthogonal quantum mechanics: While the properties of the left and right eigenstates corresponding to boundary modes are individually decoupled from the bulk physics in non-Hermitian systems, their combined biorthogonal density penetrates the bulk precisely when phase transitions occur. This leads to generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries. We illustrate our general insights by deriving the phase diagram for several microscopic open boundary models, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.
916 citations
TL;DR: It is found in this work that the usage of modified biorthogonal wavelet transform increases the detection accuracy and CR of the proposed design, and the Wi-Fi-based wireless protocol is used for compressed data transmission.
Abstract: The new age advancements in information technology due to materials and integrated circuit (IC) technologies and their applications in biomedical sciences have made the healthcare facilities more compact and affordable for the aging population. Market trends in healthcare and related devices indicate a sharp rise in their demand. Hence the researchers have converged the efforts on designing more smart and advanced medical devices using IC technology. Among these devices, cardiac pacemakers have become a recurrent biomedical device which is engrafted in the human body to detect and monitor a person's heart beating rate. The data thus generated is processed for various medical usages and devices via wireless methods. Cardiovascular diseases (CVDs) or diseases related to the heart are due to abnormalities or disorders of the heart and blood vessels. Till date, limited literature is available which focuses on a single technique that can perform all of the ECG signal denoising, ECG detection, lossless data compression and wireless transmission. In this work, a joint approach for denoising, detection, compression, and wireless transmission of ECG signal is proposed. The modified biorthogonal wavelet transform is used for denoising, detection and lossless compression of ECG signal. To reduce the circuit complexity, biorthogonal wavelet transform is realized using linear phase structure. Further, it is found in this work that the usage of modified biorthogonal wavelet transform increases the detection accuracy and CR of the proposed design. Also, in this work, the Wi-Fi-based wireless protocol is used for compressed data transmission. The proposed ECG detector achieves the highest sensitivity and positive predictivity of 99.95% and 99.92%, respectively, with the MIT-BIH arrhythmia database. The use of modified biorthogonal 3.1 wavelet transform and run-length encoding (RLE) for the compression of ECG data achieves a higher compression ratio (CR) of 6.271. To justify the effectiveness of the proposed algorithm, which uses modified biorthogonal wavelet 3.1transform, the results are compared with the existing methods, namely, Huffman coding/simple predictor, Huffman coding/adaptive, and slope predictor/fixed length packaging.
53 citations
TL;DR: In this paper, the authors study the fluctuations of certain biorthogonal ensembles for which the underlying family { P, Q } satisfies a finite-term recurrence relation of the form x P (x ) = J P(x ).
34 citations
TL;DR: The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed, and the usefulness of the circuit formalism in designing WTs, including various classes of symmetric wavelets and multiwavelets, boundary wavelets, and biorthogonal wavelets are demonstrated.
Abstract: The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multiscale representation of quantum many-body wave functions using unitary circuits, further cementing the relation established in the literature between classical and quantum multiscale methods. An algorithm for constructing the circuit representation of known orthogonal, dyadic, discrete WTs is presented, and the explicit representation for Daubechies wavelets, coiflets, and symlets is provided. Furthermore, we demonstrate the usefulness of the circuit formalism in designing WTs, including various classes of symmetric wavelets and multiwavelets, boundary wavelets, and biorthogonal wavelets.
32 citations
TL;DR: In this paper, the authors discuss some features of non-self-adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors, like the generalized Riesz systems, enjoying certain properties.
Abstract: Continuing the analysis undertaken in previous articles, we discuss some features of non-self-adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors, like the so-called generalized Riesz systems, enjoying certain properties. In particular, we discuss what happens when they forms two D-quasi-bases.
29 citations
TL;DR: A CAD system was designed for the classification of Protein Kinase B using ten different discrete wavelet transforms and SSVM and SVM classifier and the highest overall classification accuracy of 80% was obtained.
Abstract: In this paper a CAD system was designed for the classification of Protein Kinase B (PKB) using ten different discrete wavelet transforms and SSVM and SVM classifier. A set of different images has been collected from which data is divided into training and testing data set. The PKB is categorized into two classes called absent or present. The highest overall classification accuracy of 80% was obtained with biorthogonal: bior 4.4 wavelet transforms and daubechies: db6 wavelet transforms using SSVM classifier.
25 citations
TL;DR: A digital electrocardiogram (ECG) detector with low power consumption and high performance based on biorthogonal 2.2 wavelet transform and applicable for the modern implantable cardiac pacemakers is proposed in the present work.
Abstract: A digital electrocardiogram (ECG) detector with low power consumption and high performance based on biorthogonal 2.2 wavelet transform and applicable for the modern implantable cardiac pacemakers is proposed in the present work. Biorthogonal 2.2 wavelet transform is chosen due to its high SNR, less number of coefficients, resemblance of shape with ECG wave and ability to increase QRS complex detection performance. Architecture of the proposed ECG detector includes modified biorthogonal 2.2 wavelet filter bank and a modified soft threshold-based QRS complex detector. Three low-pass filters and one high-pass filter with pipelined architecture are used which are lesser than the earlier designed detectors. Various blocks of proposed detector are designed to denoise the input ECG signal and then to find the correct location of R-wave. Verilog hardware description language for design entry, Modelsim embedded in Xilinx ISE v.14.1 for simulation, Virtex-6 FPGAs for synthesis and Xilinx ISE tools are used to measure the performance, area and power of the proposed ECG detector and its constituent blocks. A low detection error rate of 0.13%, positive predictivity (
$$\hbox {P}^{+}$$
) of 99.94% and sensitivity (
$$\hbox {S}_{\mathrm{e}}$$
) of 99.92% are achieved for the proposed ECG detector which are better compared to the previous results. Also, it consumes only 20 mW of total power at 50 KHz and shows the overall delay of 18.924 ns which makes it useful for the low power and high-performance applications.
22 citations
TL;DR: In this article, the Deift-Zhou steepest descent method was used to obtain the matching condition of the local parametrix at the origin of the Biorthogonal Ensemble.
Abstract: The Muttalib-Borodin biorthogonal ensemble is a probability density function for $n$ particles on the positive real line that depends on a parameter $\theta$ and an external field $V$. For $\theta=\frac{1}{2}$ we find the large $n$ behavior of the associated correlation kernel with only few restrictions on $V$. The idea is to relate the ensemble to a type II multiple orthogonal polynomial ensemble that can in turn be related to a $3\times 3$ Riemann-Hilbert problem which we then solve with the Deift-Zhou steepest descent method. The main ingredient is the construction of the local parametrix at the origin, with the help of Meijer G-functions, and its matching condition with a global parametrix. We will present a new iterative technique to obtain the matching condition, which we expect to be applicable in more general situations as well.
22 citations
TL;DR: In this paper, the authors obtained Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces, and showed that these estimates are equivalent to embeddings between the given Banach space and certain discrete weighted Lorentz spaces.
Abstract: We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We also show that these estimates are equivalent to embeddings between the given Banach space and certain discrete weighted Lorentz spaces. Finally, the asymptotic optimality of these inequalities is illustrated in various examples of not necessarily quasi-greedy bases.
20 citations
TL;DR: In this article, the controllability of a Burgers equation with nonlocal viscosity was analyzed by using Fourier decomposition and biorthogonal techniques, and a fixed point method was used to deduce the result for the nonlinear initial problem.
19 citations
TL;DR: In this article, the singular values of certain triangular random matrices are studied and the squares of the singular value form a biorthogonal ensemble, and with an appropriate change in the distribution of the diagonal elements, they give the biorhogonal Laguerre ensemble.
TL;DR: A new numerical approach for finding the solution of linear time‐delay control systems with a quadratic performance index using new hybrid functions based on a hybrid of block‐pulse functions and biorthogonal multiwavelets that consist of cubic Hermite splines on the primal side.
TL;DR: In this article, the authors studied the problem of computing the normalisations and the biorthogonal polynomials of the Muttalib-Borodin ensembles with classical weights on the positive half-line.
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TL;DR: In this paper, the Heun-Hahn operator on uniform grids is defined and an extension of the Hahn algebra is described, including the generator of Biorthogonal rational functions.
Abstract: The Heun-Hahn operator on the uniform grid is defined. This operator is shown to map polynomials of degree $n$ to polynomials of degree $n+1$, to be tridiagonal in bases made out of either Pochhammer or Hahn polynomials and to be bilinear in the operators of the Hahn algebra. The extension of this algebra that includes the Heun-Hahn operator as generator is described. Biorthogonal rational functions on uniform grids are shown to be related to this framework.
TL;DR: In this paper, the authors discuss notions of convolutions generated by biorthogonal systems of elements of a Hilbert space and discuss properties of convolution and give a number of examples.
Abstract: In this note we discuss notions of convolutions generated by biorthogonal systems of elements of a Hilbert space. We develop the associated biorthogonal Fourier analysis and the theory of distributions, discuss properties of convolutions and give a number of examples.
TL;DR: In this article, the Fourier-like Sobolev polynomials and the corresponding Legendre spectral method are proposed in parallel for Dirichlet boundary value problems, which are not only efficient for solving elliptic problems but also equally applicable to indefinite Helmholtz equations and singular perturbation problems.
01 Nov 2018
TL;DR: A medical image compression algorithm that combines geometric active contour model and biorthogonal wavelet transform is proposed that is superior to traditional methods for MRI images.
Abstract: image compression optimizes the performance of any digital system by reducing time and cost. interested parties In medical diagnostics field provide more information about the image with a precision and completeness of diagnosis which related to a good quality, so the main objective of compression is to research an optimal reduction of image size without losing the quality. In this article, we proposed a medical image compression algorithm that combines geometric active contour model and biorthogonal wavelet transform. In this method it is necessary to localize the region of interest, using the level set for an optimal reduction, then we use the lifting scheme biorthogonal CDF (biorthogonal lifting scheme CDF9/7, Gall 5/3 and FB), coupled with the set partitioning in hierarchical trees algorithm., the proposed algorithm is superior to traditional methods for MRI images. The level set and CDF9/7 LIFTING scheme algorithm coupled with SPIHT provides very important PSNR (Peak Signal to Noise Ration) and MSSIM (Mean Structural Similarity) values
TL;DR: In this article, the spectral properties of an essentially nonself-adjoint problem generated by nonlocal multipoint conditions for the operator of differentiation of order 2n were studied and a system of root functions of the problem and elements of biorthogonal systems were constructed.
Abstract: We study spectral properties of an essentially nonself-adjoint problem generated by nonlocal multipoint conditions for the operator of differentiation of order 2n and analyze the cases of regular and irregular Birkhoff two-point boundary conditions. A system of root functions of the problem and elements of biorthogonal systems are constructed. We also establish sufficient conditions under which these systems are complete and conditions under which they form a Riesz basis (under certain additional assumptions).
TL;DR: In this letter, a technique to construct biorthogonal filters with rational coefficients is presented and the perfect reconstruction and the no-dc-leakage properties are preserved.
Abstract: Wavelet filters with rational coefficients can be implemented efficiently in digital hardware using simple register shifts and adders. In this letter, a technique to construct biorthogonal filters with rational coefficients is presented. The filters have linear phase and also have very similar characteristics to orthogonal filters, while the latter cannot have linear phase. The frame bound ratio of the filters is very close to unity, i.e., almost tight. The filters are constructed via the lifting scheme with four lifting steps. The perfect reconstruction and the no-dc-leakage properties are preserved with these rational coefficients filters.
TL;DR: The analysis and comparison of computational complexity of related algorithms have indicated that the proposed algorithm provided a faster computational approach for computing analysis/dual windows as compared with that of the existing algorithms, which can save amount of computation and memory.
Abstract: By using the biorthogonal analysis approach, an effective algorithm based on factorization for solving the analysis/dual windows in multiwindow discrete Gabor transform (M-DGT) is presented for arbitrary given synthesis windows. The constraint condition matrix of the M-DGT between analysis/dual windows and synthesis windows is proved to be equivalent to a fixed number of independent orthogonal relationship matrixes of discrete Gabor transform (DGT), which can be quickly and efficiently solved by using sub-equation sets. The analysis and comparison of computational complexity of related algorithms have indicated that the proposed algorithm provided a faster computational approach for computing analysis/dual windows as compared with that of the existing algorithms, which can save amount of computation and memory.
01 Jan 2018
TL;DR: In this paper, the authors extend some of the general results by Fattorini-Russell [ 12, 13 ] concerning biorthogonal families, using complex analysis techniques that were developed by Seidman [ 36 ], Guichal [ 20 ], Tenenbaum-Tucsnak [ 37 ] and Lissy [ 27, 28 ].
Abstract: A classical and useful way to study controllability problems is the moment method developed by Fattorini-Russell [ 12 , 13 ], which is based on the construction of suitable biorthogonal families. Several recent problems exhibit the same behavior: the eigenvalues of the problem satisfy a uniform but rather 'bad' gap condition, and a rather 'good' but only asymptotic one. The goal of this work is to obtain general and precise upper and lower bounds for biorthogonal families under these two gap conditions, and thus to measure the influence of the 'bad' gap condition and the good influence of the 'good' asymptotic one. To achieve our goals, we extend some of the general results by Fattorini-Russell [ 12 , 13 ] concerning biorthogonal families, using complex analysis techniques that were developed by Seidman [ 36 ], Guichal [ 20 ], Tenenbaum-Tucsnak [ 37 ] and Lissy [ 27 , 28 ].
01 Oct 2018
TL;DR: Simulation and experimental results over an HF link reveals that biorthogonal signaling can improve the data rate by a factor of four to six times at a cost of only 4 to 5 dB loss in performance.
Abstract: Filter bank multi carrier spread spectrum (FB-MC-SS)has proven to be a robust and reliable waveform choice for communication over high frequency (HF)skywave links. In this paper, we study the use of biorthogonal signaling in order to improve on the spectral efficiency of FB-MC-SS. We develop a design strategy that improves on the spectral efficiency of FB-MC-SS while maintaining its low peak-to-average power ratio (PAPR). Moreover, our simulation and experimental results over an HF link reveals that biorthogonal signaling can improve the data rate by a factor of four to six times at a cost of only 4 to 5 dB loss in performance.
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TL;DR: The q-Heun operator of the big q-Jacobi type on the exponential grid is defined in this paper, which is the most general second order q-difference operator that maps polynomials of degree $n$ to polynomial of degree n+1$.
Abstract: The q-Heun operator of the big q-Jacobi type on the exponential grid is defined. This operator is the most general second order q-difference operator that maps polynomials of degree $n$ to polynomials of degree $n+1$. It is tridiagonal in bases made out of either q-Pochhammer or big q-Jacobi polynomials and is bilinear in the operators of the q-Hahn algebra. The extension of this algebra that includes the q-Heun operator as generator is described. Biorthogonal Pastro polynomials are shown to satisfy a generalized eigenvalue problem or equivalently to be in the kernel of a special linear pencil made out of two q-Heun operators. The special case of the q-Heun operator associated to the little q-Jacobi polynomials is also treated.
TL;DR: In this article, special classes of biorthogonal sets of vectors in Hilbert and in Krein spaces, and their relations with $\mathcal{G}$-quasi bases are analyzed.
Abstract: We analyse special classes of biorthogonal sets of vectors in Hilbert and in Krein spaces, and their relations with $\mathcal{G}$- quasi bases. We also discuss their relevance in some concrete quantum mechanical system driven by manifestly non self-adjoint Hamiltonians.
TL;DR: In this paper, it was shown that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight.
Abstract: We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight. This result generalizes a theorem by Young on reproducing kernels in the Paley-Wiener space and a recent result of Belov for the classical Bargmann-Segal-Fock space.
01 Nov 2018
TL;DR: A robust and easy to implement denoising algorithm has been proposed in the present paper, based on adaptive wavelet thresholding, the best mother wavelet of the reverse biorthogonal family being searched.
Abstract: Electrocardiography aids physicians to investigate the electrical activity of the heart. Fetal signals are difficult to record and usually affected by noise, making thus a clinical diagnosis difficult. A robust and easy to implement denoising algorithm has been proposed in the present paper. The method is based on adaptive wavelet thresholding, the best mother wavelet of the reverse biorthogonal family being searched. The results are competitive and the performance has been evaluated both graphically and with objective criteria.
TL;DR: In this article, the authors considered 6-fold linear equation in the class of analytic functions outside the equilateral triangle and vanishing at infinity, and proposed a method of equivalent regularization, using the theory of boundary value problem of Carleman.
Abstract: We considered 6-fold linear equation in the class of analytic functions outside the equilateral triangle and vanishing at infinity. We proposed a method of equivalent regularization, using the theory of boundary value problem of Carleman. Also, the paper is dedicated to applications to the problem of moments for entire functions of exponential type. In particular, we construct a system of functions biorthogonal whit piecewise-quasipolynomial weight to some power system on the three rays. The indicator of such functions is a piecewise-trigonometric function, with a period of 2π/3.