Block-diagonal Research Articles

One-way reflection waveform inversion with depth-dependent gradient preconditioning

Summary Reflection Waveform Inversion (RWI) is a technique that uses pure reflection data to estimate subsurface background velocity, relying on evolving seismic images. Conventional RWI operates in a cyclic workflow, with two key components in each cycle—migration and reflection tomography. Conventional RWI may result in suboptimal background velocity estimation, partly due to limited or unresolved resolution within each component in each cycle. While gradient preconditioning with the reciprocal of Hessian information helps resolve this issue in both components of RWI, it becomes impractical for a large number of model parameters. One-way reflection waveform inversion (ORWI) is a reflection waveform inversion technique in which the forward modeling scheme operates in one direction (downward and then upward) via virtual parallel depth levels within the medium. Leveraging the ORWI framework, we decompose and reduce the linear Hessian operator (also known as the approximate Hessian or Gauss-Newton Hessian) into multiple smaller sub-operators. In particular, the diagonal blocks of the mono-frequency approximate Hessian operators, each corresponding to a single depth level within the medium, are extracted and inverted to precondition the corresponding mono-frequency gradients in both the migration and reflection tomography components of ORWI. This depth-dependent gradient preconditioning transforms standard ORWI into a high-resolution, yet computationally feasible version aimed at addressing suboptimal velocity estimation, referred to as high-resolution ORWI (HR-ORWI). The effectiveness of the proposed approach is demonstrated through successful applications to synthetic data examples.

The $$2 \times 2$$ block matrices associated with an annulus

The $$2 \times 2$$ block matrices associated with an annulus

Rogue wave patterns in the nonlocal nonlinear Schrödinger equation

This paper investigates rogue wave patterns in the nonlocal nonlinear Schrödinger (NLS) equation. Initially, employing the Kadomtsev–Petviashvili reduction method, rogue wave solutions of the nonlocal NLS equation, whose τ function is a 2×2 block matrix, are simplified. Afterward, utilizing the asymptotic analysis approach, we investigate the rogue wave patterns when two free parameters a2m1+1 and b2m2+1 are considerably large and fulfill the condition |a2m1+1|2/(2m1+1)=O(|b2m2+1|1/(2m2+1)). Our findings reveal that under these conditions, rogue wave solutions of the nonlocal NLS equation exhibit novel patterns, which consist of three regions, which are the outer region, the middle region and the inner region. In the outer and middle regions, only single rogue waves with singularities may occur, and their locations are characterized by roots of two polynomials from the Yablonskii–Vorob'ev polynomial hierarchies. In the inner region, a possible lower order rogue wave may appear, which can be singular or regular, depending on the values of m1,m2, the sizes of τ function, and certain free parameters. Finally, the numerical results indicate that the predicted outcomes are in close alignment with real rogue waves.

Algorithms for solving the inverse scattering problem for the Manakov model

The paper considers algorithms for solving inverse scattering problems based on the discretization of the Gelfand–Levitan–Marchenko integral equations, associated with the system of nonlinear Schrödinger equations of the Manakov model. The numerical algorithm of the first order approximation for solving the scattering problem is reduced to the inversion of a series of nested block Toeplitz matrices using the Levinson-type bordering method. Increasing the approximation accuracy violates the Toeplitz structure of block matrices. Two algorithms are described that solve this problem for second order accuracy. One algorithm uses a block version of the Levinson bordering algorithm, which recovers the Toeplitz structure of the matrix by moving some terms of the systems of equations to the right-hand side. Another algorithm is based on the Toeplitz decomposition of an almost block-Toeplitz matrix and the Tyrtyshnikov bordering algorithm. The speed and accuracy of calculations using the presented algorithms are compared on an exact solution (the Manakov vector soliton).

A Novel k-Means Framework via Constrained Relaxation and Spectral Rotation.

Owing to its simplicity, the traditional k - means (Lloyd heuristic) clustering method plays a vital role in a variety of machine-learning applications. Disappointingly, the Lloyd heuristic is prone to local minima. In this article, we propose k - mRSR, which converts the sum-of-squared error (SSE) (Lloyd) into a combinatorial optimization problem and incorporates a relaxed trace maximization term and an improved spectral rotation term. The main advantage of k - mRSR is that it only needs to solve the membership matrix instead of computing the cluster centers in each iteration. Furthermore, we present a nonredundant coordinate descent method that brings the discrete solution infinitely close to the scaled partition matrix. Two novel findings from the experiments are that k - mRSR can further decrease (increase) the objective function values of the k - means obtained by Lloyd (CD), while Lloyd (CD) cannot decrease (increase) the objective function obtained by k - mRSR. In addition, the results of extensive experiments on 15 datasets indicate that k - mRSR outperforms both Lloyd and CD in terms of the objective function value and outperforms other state-of-the-art methods in terms of clustering performance.

Solving an internal problem for finite regular two-dimensional lattice spiral elements, excitable plate electromagnetic wave

Background. The work is aimed at developing and researching rigorous methods for solving internal problem of electrodynamics for multi-element structures (metastructures) consisting from the final number of elements, as well as to study the physical processes occurring in them. A special case of such structures are two-dimensional lattices with a fixed interelement distance, consisting of identical elements having the same spatial orientation (regular lattices). Aim. In this work, based on an iterative approach, the internal solution is solved. problems of electrodynamics for a finite regular two-dimensional lattice of spiral elements. In order to obtain a priori information about the electrodynamic characteristics of elements lattice and justification for the choice of projection function systems are analyzed spectral characteristics of the integral operator of the internal problem for a single spiral element. Then the currents on the structure elements are calculated, their spectral characteristics are determined. The results of spectral analysis allow increase the efficiency of solving an internal problem. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). The solution of the internal problem within the framework of the method of moments is reduced to solving a SLAE with a block matrix. Results. A mathematical model of a finite two-dimensional lattice of spiral elements is proposed radiating structure. For the specified structure, in the case of its excitation by a flat electromagnetic wave, based on the iterative approach, the internal problem of electrodynamics was solved. The following were carried out in a wide frequency range: analysis of the convergence of the iterative process, spectral analysis of the integral operator of the internal problem for a single spiral element, as well as spectral analysis of external field and current functions functions on lattice elements. Conclusion. The feasibility of determining the spectral characteristics of integral operators is shown internal task for the elements forming the metastructure. A relationship has been identified between the frequency dependence eigenvalues of the integral operator of the internal problem of single elements, forming a metastructure, with resonance phenomena arising in the metastructure, the influence of resonances on the convergence of the iterative process was confirmed. The feasibility of considering averaged amplitude current spectra is shown. It was revealed that the averaged spectrum of current functions is close to degenerate, especially near resonant frequencies. This allows for use as projection functions a compact set of eigenfunctions that have significant amplitudes in the vicinity of the frequency under study, which significantly simplifies the solution of the internal problem.

A user selection algorithm for downlink MU-MIMO systems using product of singular values of effective channels

User selection plays a crucial role when aiming to improve channel throughput in multiuser multiple- input multiple-output downlink systems with block diagonalization linear precoding. While an optimal group of users can be found by exhaustively searching all possible combinations of users, the process becomes prohibitively complex when there is a large number of users. In this paper, we propose a greedy suboptimal user selection algorithm, which iteratively selects a user to maximize the product of the singular values of the effective channels from a set of unselected users. The proposed algorithm is based on the iterative precoder design method, whereby interuser interference is perfectly cancelled with lower complexity than with the singular value decomposition-based precoding technique. Moreover, to avoid frequent use of singular value decomposition, the proposed algorithm applies QR decomposition to the selected channel matrices in order to obtain singular values, which are equivalent to the product of diagonal elements in the upper triangular matrix. Simulation results show that, under a high SNR regime, the proposed algorithm outperforms several other greedy algorithms and can provide the same performance as a capacity-based algorithm for both correlated and uncorrelated channels with significantly reduced complexity.

Japanese Performance Profile on the WAIS-IV and Purported Cultural Influences.

The present exploratory study aimed to examine the potential impact of culture on cognitive skills and intelligence by comparing the Japanese Wechsler Adult Intelligence Scale-IV (WAIS-IV) (JW) subtests, IQs, and index scores to those of the U.S. WAIS-IV (USW). JW raw scores corresponding to a scaled score of 10 for each subtest were scored with USW norms. Subtest, index, and IQ scores were then calculated for each age range. The impact of education on scores was evaluated through ratio of educational attainment for each cohort of the Japanese and US samples. Japanese and US data were compared using one-sample t-tests. Correlations between subtest, index, and IQ scores and education were calculated. The USW sample performed higher than the JW sample on verbal comprehension subtests, while the JW sample demonstrated stronger performances in processing speed and perceptual reasoning subtests. However, all scores with the exception of Block Design, Matrix Reasoning, and Figure Weights were significantly associated with differential educational attainment between the two countries. Educational differences were linearly associated with age with the higher educational attainment for younger Japanese age groups and higher attainment for the older US cohorts. The present study demonstrates cognitive differences between Japan and the USA. Performance on the WAIS-IV subtest and composite measures are highly correlated with education. Cultural factors impacting the cognitive profile of the Japanese sample such as differences in worldview, customs, educational systems, and writing system, were proposed. Clinical neuropsychologists should take these aspects into account when administering and interpreting test results.

Population-aware permutation-based significance thresholds for genome-wide association studies

Abstract Motivation Permutation-based significance thresholds have been shown to be a robust alternative to classical Bonferroni significance thresholds in genome-wide association studies for skewed phenotype distributions. The recently published method permGWAS introduced a batch-wise approach to efficiently compute permutation-based genome-wide association studies. However, running multiple univariate tests in parallel leads to many repetitive computations and increased computational resources. More importantly, traditional permutation methods that permute only the phenotype break the underlying population structure. Results We propose permGWAS2, an improved method that does not break the population structure during permutations and uses an elegant block matrix decomposition to optimize computations, thereby reducing redundancies. We show on synthetic data that this improved approach yields a lower false discovery rate for skewed phenotype distributions compared to the previous version and the commonly used Bonferroni correction. In addition, we re-analyze a dataset covering phenotypic variation in 86 traits in a population of 615 wild sunflowers (Helianthus annuus L.). This led to the identification of dozens of novel associations with putatively adaptive traits, and removed several likely false-positive associations with limited biological support. Availability permGWAS2 is open-source and publicly available on GitHub for download: https://github.com/grimmlab/permGWAS. Supplementary information Supplementary data are available at Bioinformatics Advances online.

Sensitivity analysis of a dual-continuum model system for integrated CO2 sequestration and geothermal extraction in a fractured reservoir

Depleted hydrocarbon reservoirs are considered as the most feasible option for CO2 geological sequestration and utilization. Most of the hydrocarbon reservoirs are naturally fractured. Simulation of fluid flow and heat transfer in these fractured formations remains a significant challenge in reservoir engineering. In this study, a dual-continuum model is developed to simulate integrated CO2 sequestration and CO2-circulated geothermal extraction in a fractured reservoir block in North Oman. The high-dimensional sensitivity of key parameters controlling CO2-brine flow and heat transfer in this matrix-fracture system is quantitatively evaluated by an efficient surrogate modeling approach. The surrogate models are constructed and validated based on a suite of physics-based model simulations. It is found that fracture permeability dominates the CO2 injectivity, storage, circulation and associated geothermal extraction. Response surface analysis shows that the flow area density between matrix-fracture and matrix block length controls the flux interaction between matrix and fracture formations. In contrast, the fracture aperture shows negligible influence in the dual-continuum modeling system. Particularly, sensitivity varying with locations on the response surface is analyzed for defined performance indicators.

An improved generalized flexibility matrix-based damage identification technique for derrick steel structures

An improved generalized flexibility matrix-based method using matrix partitioning technique for structure damage identification is proposed. As an effective damage identification method, the generalized flexibility matrix requires fewer vibration frequencies and corresponding modal shapes compared with the traditional flexibility matrix method. By introducing a new partitioning technique of the matrices involved in the constructive process of the governing equation, the improved method simplifies the process of calculation with a dramatic reduction in computational cost while maintaining accuracy of identification results. In the case of incomplete measured modal data, an improved matrix partitioning technique based on the model expansion method is applied and the damaged indicators can be identified using partial measured modal data. A K-type derrick steel structure in service is considered as a numerical example for inspection the validity and feasibility of the proposed method. Numerical results show better accuracy and efficiency of this method for various damage scenarios, and can be used for damage diagnosis or health monitoring of other large structures.

ON THE EVANS CHAIN COMPLEX

Abstract We elaborate on the construction of the Evans chain complex for higher-rank graph $C^*$ -algebras. Specifically, we introduce a block matrix presentation of the differential maps. These block matrices are then used to identify a wide family of higher-rank graph $C^*$ -algebras with trivial K-theory. Additionally, in the specialised case where the higher-rank graph consists of one vertex, we are able to use the Künneth theorem to explicitly compute the homology groups of the Evans chain complex.

A new matrix representation of the Maxwell equations based on the Riemann–Silberstein–Weber vector for a linear inhomogeneous medium

We derive a new eight dimensional matrix representation of the Maxwell equations for a linear homogeneous medium and extend it to the case of a linear inhomogneous medium. This derivation starts ab initio with the Maxwell equations and uses arguments based on the algebra of the Pauli matrices. This process leads automatically to the matrix representation based on the Riemann–Silberstein–Weber (RSW) vector. The new representation for the homogeneous medium is a direct sum of four Pauli matrix blocks. This aspect of the new representation should make it suitable for studying the propagation of electromagnetic waves in a linear inhomogeneous medium adopting the techniques of quantum mechanics treating the inhomogeneity as a perturbation. The new representation is used to rederive the Mukunda–Simon–Sudarshan matrix substitution rule for transition from the Helmholtz scalar wave optics to the Maxwell vector wave optics.

Transmit Precoding via Block Diagonalization with Approximately Optimized Distance Measures for Limited Feedback in Dense Cellular Networks with Multiantenna Base Stations

Transmit Precoding via Block Diagonalization with Approximately Optimized Distance Measures for Limited Feedback in Dense Cellular Networks with Multiantenna Base Stations

Segmenting hotspots from medical thermal images using Density-based modified FC-Pc FS with spatial information

ABSTRACT Thermal cameras complemented with robust and automated computational intelligence-aided diagnostic systems can be deployed at public gathering points and on smartphones to raise alarms about thriving diseases of their body due to inflammation in a timely manner, thereby strengthening human health systems. In this work, we have proposed two robust Density-based modified Picture Fuzzy Clustering methods with spatial information to segment hotspots from human’s abnormal thermal images. We formulated and solved the objective function by combining P c FS-based clustering method with modified Renyi’s Entropy. We demonstrated the robustness of our methods, DSIFC-Pc FS and DSIMFC-Pc FS, on three publicly available datasets and an artificially created noisy dataset of thermal images. We have obtained a ZC score of 0.933, 0.947 and 0.933 for DB-DMR-IR, DB-FOOT-IR and DB-THY-IR datasets, respectively. Also, our method converged to an optimal partition matrix in minimum iterations. The experimental performance shows that the proposed approaches, DSIFC- P c FS and DSIMFC- P c FS, outperformed other ten related approaches in segmenting the medical thermal images with and without noise, indicating their robustness and efficacy, in terms of various unsupervised evaluation metrics. Also, we statistically analysed their performance in contrast to other methods using the Friedman Test, which advocate their superiority.

Blind image authentication using singular value decomposition with enhanced robustness by augmenting hamming code

Singular value decomposition (SVD) based image authentication has widespread applications for digital media protection including forensic and medical domains due to the high stability and robustness of singular values under small perturbations. However, most of these techniques are non-blind and have high redundancies for the extraction of secret data. The proposed scheme employs a blind extraction strategy by utilizing the intrinsic relationship of coefficient pairs of the U matrix of the host image blocks. This relationship is utilized to hide a secret binary bit after computing a threshold value in constant time. The host image underwent block-wise decomposition and hash-based randomization of blocks, followed by block-wise SVD for embedding secret bits in the U matrix. Hamming coded watermark is embedded for high precision extraction under active attacks. High imperceptibility and strong robustness are observed under attacks when tested across general purpose as well as image datasets and the system outperforms many existing works. Experimental observation shows the average PSNR between the host and marked image and average NCC between embedded and extracted watermark to be 36.98 dB and 0.999 respectively for the SIPI dataset whereas 52.7 dB and 1 respectively for the X-Ray dataset. The system exhibited high robustness under Salt-and-pepper noise (SAPN), Gaussian Noise (GAUN), Cropping (CRP), Median Filtering (MF), Histogram Equalization (HEQ), and Jpeg Compression (JPC) with average NCC values of 0.998, 1, 0.932, 0.999 and 0.967 respectively for X-Ray dataset. The time complexity O (M × N) is observed for both embedding and extraction algorithms for a host image of size M × N.

Discrete-time distributed algorithms for solving linear equations via layered coordination

This paper is concerned with the problem of designing discrete-time distributed algorithms for solving large-scale linear equations via layered coordination. A row-column decomposition and a column-row decomposition are provided to partition the augmented matrix associated with the linear equations into several block matrices, respectively. By assigning an equation solver layer to computation and a data integration layer to data exchanges, a row-column decomposition-based discrete-time distributed algorithm and a column-row decomposition-based discrete-time distributed algorithm are proposed for solving large-scale linear equations, respectively. It is shown that the distributed algorithms proposed can reach a consensus exponentially on one of the solutions of linear equations. Finally, the effectiveness of the distributed algorithms proposed is validated via the numerical simulation of the power flow calculation of power systems and the problem of solving the large-scale linear equations.

Generalized sidelobe canceller based adaptive multiple-input multiple-output radar array beamforming under scenario mismatches

It is well known that the performance of an adaptive MIMO radar array fully depends on the precise steering control and is deteriorated by even a small scenario mismatch. This paper presents an advanced generalized sidelobe canceller (AGSC) based adaptive MIMO radar array beamformer with robustness against the effect due to scenario mismatches. A new signal blocking matrix is developed for effectively blocking the desired signal when the adaptive beamforming is performed under multiple scenario mismatches. The novelty of the new signal blocking matrix is that it contains two additional matrix components in addition to the conventional blocking matrix. The first one is a matrix made up of the basis orthogonal to some appropriately designed derivative constraint vector. It avoids the possible leakage of the desired signal due to scenario mismatches. The other one is a matrix made up of the dominant eigenvectors associated with the correlation matrix of the blocked data vector at the output of the first matrix component. It is employed to preserve all of the interference signals. As a result, the whole blocking operation can delete the desired signal and save the interference signals under multiple scenario mismatches. Hence, the AGSC based adaptive MIMO radar beamformer effectively deals with the performance degradation caused by scenario mismatches without resorting to any robust optimization algorithms. Performance analysis and complexity evaluation regarding the AGSC based adaptive MIMO radar beamformer are presented. Simulation results are also provided for confirmation and comparison.

On arbitrary matrix coefficient assignment for the characteristic matrix polynomial of block matrix linear control systems

For block matrix linear control systems, we study the property of arbitrary matrix coefficient assignability for the characteristic matrix polynomial. This property is a generalization of the property of eigenvalue spectrum assignability or arbitrary coefficient assignability for the characteristic polynomial from system with scalar $(s=1)$ block matrices to systems with block matrices of higher dimensions $(s>1)$. Compared to the scalar case $(s=1)$, new features appear in the block cases of higher dimensions $(s>1)$ that are absent in the scalar case. New properties of arbitrary (upper triangular, lower triangular, diagonal) matrix coefficient assignability for the characteristic matrix polynomial are introduced. In the scalar case, all the described properties are equivalent to each other, but in block matrix cases of higher dimensions this is not the case. Implications between these properties are established.

Some New Algebraic Method Developments in the Characterization of Matrix Equalities

Algebraic expressions and equalities can be constructed arbitrarily in a given algebraic framework according to the operational rules provided, and thus it is a prominent and necessary task in mathematics and applications to construct, classify, and characterize various simple general algebraic expressions and equalities. As an update to this prominent topic in matrix algebra, this article reviews and improves upon the well-known block matrix methodology and matrix rank methodology in the construction and characterization of matrix equalities. We present a collection of fundamental and useful formulas for calculating the ranks of a wide range of block matrices and then derive from these rank formulas various valuable consequences. In particular, we present several groups of equivalent conditions in the characterizations of the Hermitian matrix, the skew-Hermitian matrix, the normal matrix, etc.