Block-diagonal Research Articles

Quantum LDPC Codes Based on Cocyclic Block Matrices.

Motivated by a family of binary cocyclic block matrices over GF(2), we proposed a construction method to gain the stabilizer of long-length quantum error-correction codes (QECCs). Stabilizer quantum codes (SQCs) can be obtained by the different rows of the yielded circulant permutation matrices; hence, the quantum codes have the virtue of a fast construction algorithm. The recursive relation of a block matrix is employed in the proposed approach, so that the generator matrix of quantum cocyclic codes with long length can be constructed easily. Furthermore, the obtained quantum codes have the low-density advantage of there being no 4-cycles in the Tanner graph.

Efficient Layered Parallel Architecture and Application for Large Matrix LDPC Decoder

For a 50G passive optical network (PON) low-density parity-check (LDPC) decoder, decoding performance and area efficiency must be balanced. This paper adopts a layered decoder method to improve the area efficiency of the decoder. By parallel processing of three submatrices and storage reuse of node information, optimizing the matrix partitioning and processing order of the 50G-PON standard, the throughput of 1235 bps was reached under 100 MHz circuit frequency in field-programmable gate array (FPGA) implementation, and 9.864 Gbps was achieved based on Taiwan semiconductor manufacturing company (TSMC) 65 nm synthesis with 800 MHz circuit frequency in an area of 2.61 mm2 by proposing a mechanism of spare decision storage to avoid errors caused by quantization overflow of the decoder and using full verification to terminate decoding in advance to improve performance. Finally, at an input bit error rate (BER) of 2.3×10−2 (signal-to-noise ratio (SNR) of about 3.72 dB), the output BER was lower than 10−12, and the throughput area rate (TAR) also increased by 2 to 4 times compared with other papers. In conclusion, an area-efficient LDPC decoder without sacrificing decoding performance is made.

Sensitivity analysis of a layered piezoelectric system using ZFEM

AbstractThe complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two‐dimensional linear first‐order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady‐state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT‐4 and PZT‐5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well‐known benchmark problem. Comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT‐5 specifically in , , and .

A Novel relaxation of the static output feedback problem for a class of plants

The static output feedback control problem is important, as it is concerned with the case when one cannot measure all state variables. It seeks to obtain a stabilising control under these conditions and is, often, difficult to solve. For a certain class of linear dynamical systems, we provide a novel approach to obtain a stabilising control gain matrix. The class of plants considered is of those, for which we can measure at least half of all state variables and where those measurements affect at least half of all state variables. Moreover, when we write the (linearly transformed) system matrix in block form, we require that either the two lower block matrices are nonsingular, or, if the inputs affect the measured state variables directly, at least the lower left one is nonsingular. We then show that we can determine the stabilising control gain matrix from the solution of a linear matrix inequality. Finally, we apply the approach to different benchmark problems, where it performs well, and confirm its good performance through additional numerical experiments.

The novel diagonal suprascapular canal block for shoulder surgery analgesia: a comprehensive technical report.

The novel diagonal suprascapular canal block for shoulder surgery analgesia: a comprehensive technical report.

Realizations of the generalized adaptive cross approximation in an acoustic time domain boundary element method

AbstractIn acoustics, the boundary element method (BEM) is much more common compared to elasticity. This is driven by the applications, which are in acoustics very often radiation problems causing trouble in finite element or finite volume methods. Nevertheless, for a time domain calculation, still an efficient BE formulations is lacking. We consider the time domain BEM for the homogeneous wave equation with vanishing initial conditions and given Dirichlet boundary conditions. The generalized convolution quadrature method (gCQ) developed by Lopez‐Fernandez and Sauter is used for the temporal discretisation. The spatial discretisation is done classically. Essentially, the gCQ requires to establish boundary element matrices of the corresponding elliptic problem in Laplace domain at several complex frequencies. Consequently, an array of system matrices is obtained. This array of system matrices can be interpreted as a three‐dimensional array of data, which should be approximated by a data‐sparse representation. The adaptive cross approximation (ACA) can be generalized to handle these three‐dimensional data arrays. Adaptively, the rank of the three‐dimensional data array is increased until a prescribed accuracy is obtained. On a pure algebraic level, it is decided whether a low‐rank approximation of the three‐dimensional data array is close enough to the original matrix. Hierarchical matrices are used in the two spatial dimensions and the third dimension are the complex frequencies. Hence, the algorithm makes not only a data sparse approximation in the two spatial dimensions but detects adaptively how much frequencies are necessary for which matrix block.

Inverses and Determinants of n × n Block Matrices

Block matrices play an important role in all branches of pure and applied mathematics. In this paper, we study the two fundamental concepts: inverses and determinants of general n×n block matrices. In the first part, the inverses of 2×2 block matrices are given, where one of the blocks is a non-singular matrix, a result which can be generalised to a block matrix of any size, by splitting it into four blocks. The second part focuses on the determinants, which is covered in two different methods. In the first approach, we revise a formula for the determinant of a block matrix A, with blocks elements of R; a commutative subring of Mn×n(F). The determinants of tensor products of two matrices are also given in this part. In the second method for computing the determinant, we give the general formula, which would work for any block matrix, regardless of the ring or the field under consideration. The individual formulas for determinants of 2×2 and 3×3 block matrices are also produced here.

In-Memory Transposable Multibit Multiplication Based on Diagonal Symmetry Weight Block

A possible approach to overcome the von Neumann bottleneck and meet the increasing demand for better computing performance is to computing in-memory (CIM). The results of the in-memory calculations are primarily reflected in the vertical bitline (BL) analog voltage. However, the nonlinearity of the BL discharge deteriorates with the increase in discharge voltage. In this study, we propose a diagonal symmetry weight block (DSWB) based on an eight-transistor (8T) static random access memory (SRAM) that can achieve multibit transposable operations. In addition, to guarantee linearity and complete multibit multiplication operations, we propose a cascode current mirror (CCM)-based multiplier. To achieve low-overhead and more efficient quantification, our proposed CIM macro uses a counter-type quantization circuit to read out the analog calculation results. We simulated the performance of the proposed 8T SRAM in a 28-nm complementary metal–oxide–semiconductor process. The integral nonlinearity (INL) of the proposed CCM-based CIM decreased by approximately 54.4% compared with the traditional CIM. Furthermore, the proposed in-memory multibit multiplication throughput density was 6.74 GOPS/kb; this throughput density improvement is approximately 3.3–10.5 times higher than the existing CIM works.

Matrix splitting preconditioning based on sine transform for solving two-dimensional space-fractional diffusion equations

Finite difference discretization of the two-dimensional space-fractional diffusion equations derives a complicated linear system consisting of identity matrix and four scaled block-Toeplitz with Toeplitz block (BTTB) matrices resulted from the left and right Riemann–Liouville fractional derivatives in different directions. Incorporating with the diffusion coefficients and the symmetric parts of the BTTB matrices, we construct a diagonal and symmetric splitting (DSS) iteration method, which is demonstrated to be convergent conditionally when the considered space-fractional diffusion equations have sufficiently close diffusion coefficients. By further replacing the symmetric Toeplitz matrices involved in the BTTB matrices with τ matrices, an approximated DSS (ADSS) preconditioner based on two-dimensional fast sine transform is designed to accelerate the convergence rates of the Krylov subspace iteration methods. In this way, the total computational complexity of the ADSS-preconditioned GMRES method will be of O(n2logn), where n2 represents the dimension of the corresponding discrete linear system. In addition, theoretical analysis demonstrates that the eigenvalues of the ADSS-preconditioned matrix are weakly clustered around a complex disk centered at 1 with the radius less than 1. Numerical experiments show that the ADSS-preconditioned GMRES method is much more efficient than the other existing methods, and can show h-independent convergence behavior.

Privacy-Preserving Parallel Computation of Matrix Determinant With Edge Computing

With the widespread deployment of secure outsourcing computation, the resource-constrained client can delegate intensive computation tasks to powerful servers. Matrix determinant computation is a fundamental mathematical operation that has been widely used in IoT applications. This operation is computationally expensive. Nevertheless, the existing secure outsourcing protocols for matrix determinant are all designed based on one cloud server, which cannot well meet the low-latency and real-time computing requirements for the client. To address this issue, we explore accelerating the computation of matrix determinant by parallel outsourcing based on two nearby edge servers and propose the first practical protocol. We use the matrix blocking technique to split the computation task into multiple subtasks, which are parallel outsourced to edge servers for accelerating the computation. Moreover, we propose a privacy-preserving matrix transformation technique for data privacy protection. This technique only involves the operations of matrix-vector multiplication and matrix-matrix addition. It achieves the lightweight computation for the client and supports computational indistinguishability for the blinded input and a uniform distribution. The correctness, privacy and verifiability of the proposed protocol are analyzed. Finally, the performance advantage of the proposed protocol is demonstrated through simulation experiments.

Multiview Regularized Discriminant Canonical Correlation Analysis: Sequential Extraction of Relevant Features From Multiblock Data.

One of the important issues associated with real-life high-dimensional data analysis is how to extract significant and relevant features from multiview data. The multiset canonical correlation analysis (MCCA) is a well-known statistical method for multiview data integration. It finds a linear subspace that maximizes the correlations among different views. However, the existing methods to find the multiset canonical variables are computationally very expensive, which restricts the application of the MCCA in real-life big data analysis. The covariance matrix of each high-dimensional view may also suffer from the singularity problem due to the limited number of samples. Moreover, the MCCA-based existing feature extraction algorithms are, in general, unsupervised in nature. In this regard, a new supervised feature extraction algorithm is proposed, which integrates multimodal multidimensional data sets by solving maximal correlation problem of the MCCA. A new block matrix representation is introduced to reduce the computational complexity for computing the canonical variables of the MCCA. The analytical formulation enables efficient computation of the multiset canonical variables under supervised ridge regression optimization technique. It deals with the "curse of dimensionality" problem associated with high-dimensional data and facilitates the sequential generation of relevant features with significantly lower computational cost. The effectiveness of the proposed multiblock data integration algorithm, along with a comparison with other existing methods, is demonstrated on several benchmark and real-life cancer data.

NOT ENTIRELY ICHTHYOSAUR: A MYSTERIOUS LAMNIFORM AND ICHTHYOPTERYGIAN-FALL ASSOCIATION FROM THE ABYSSAL UPPER CRETACEOUS OF THE NORTHERN APENNINES (ITALY)

ABSTRACT Axial remains of a large ichthyosaur and a medium-sized anacoracid shark from the deep-water sediments of the Cenomanian of the Northern Apennines (Northern Italy) are described in detail. The specimens were found closely associated (less than 0.3 m apart), and offer an invaluable window into the taphonomy and dead-fall stages of pelagic vertebrates in a Mesozoic abyssal plain. The anacoracid shark remains, initially misinterpreted as an ichthyosaur, consist of eight articulated vertebrae embedded in a block of dark arenaceous matrix, and represent the first occurrence of an articulated shark from the Northern Apennines. The ichthyosaur remains consist of seven discoidal vertebrae and several unidentified fragments. Due to the absence of diagnostic skeletal elements, both specimens are assigned only at higher taxonomic levels. The two fossils, which come from the same outcrop and possibly from the same stratigraphic horizon, share a common taphonomic history, in terms of both their preservation and diagenesis. Mineralogy of the matrices of both is dominated by manganese micro-nodules, consistent with the deposition of polymetallic nodules in bathyal-abyssal settings. Biostratinomic processes that impacted the two specimens also provide insight on the development of Mesozoic marine vertebrate-falls in the deep-sea. Localized pyrite framboids inside the bone spongiosa are possible evidence of the sulfophilic stage (microbially mediated sulfur mobilization during lipid decay) in the ichthyosaur fall. Burrows assigned to Taenidium on the surface of the shark block, interpreted as worm-like feeding burrows or arthropod locomotion and feeding trails, might represent evidence of the enrichment opportunistic stage. Although intriguing, we have no evidence to support the hypothesis that this peculiar association of two pelagic predators is due to ecological interaction between the two animals.

Generalized efficient robust predictive control for networked interval type-2 T–S fuzzy system with adaptive event-triggered scheme

This article studies the generalized efficient robust predictive control (GERPC) for the nonlinear systems denoted by interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model over networks with consideration of packet dropout, bounded disturbance and adaptive event-triggered scheme (AETS). First, the packet dropout is described by a Bernoulli process, and an AETS with thresholds that can be self-regulated according to different situations is employed to decide whether to release data into the communication network, so as to reduce the data transmission frequency and the network burden; Second, taking into consideration of packet dropout and AETS, a unified IT2 T–S fuzzy control model based on GERPC is established, and the stability of closed-loop system with bounded disturbance is guaranteed by quadratic boundedness (QB) technique; Third, generalized efficient robust predictive controller is designed to obtain a larger initial feasible region, smaller online computation and acceptable control performance. The unconstrained control law is designed offline, and a new variable will be optimized online to achieve good control performance, which is introduced to adjust the control quantity. Then, the convex LMI reformulation method is utilized to handle non-convex terms in optimization problem, and the effectiveness of the GERPC algorithm is proved by the matrix partition technique. At last, the effectiveness of the designed controller based on the GERPC strategy is verified by a given simulation experiment.

Covariance-Matrix-Based Criteria for Network Entanglement.

Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful tools in entanglement theory, have been also applied to the network scenario. We present simple proofs for the decomposition of such matrices into the sum of positive semi-definite block matrices and, based on that, develop analytical and computable necessary criteria for preparing states in quantum networks. These criteria can be applied to networks where nodes share at most one source, such as all bipartite networks.

A Representation of the Drazin Inverse for the Sum of Two Matrices and the Anti-Triangular Block Matrices

In this paper, a new formula for the Drazin inverse for the Sum of Two Matrices is given under conditions weaker than those used in some current literature. Further, we apply our results to obtain new representations for the Drazin inverse of an anti-triangular block matrix under some conditions, which also extend some existing results.

Rosenbrock-W methods for stochastic Galerkin systems

The stochastic Galerkin approach is a widely used method for quantifying uncertainty in dynamical systems. A polynomial chaos expansion of physical variables is used to represent uncertainty. Thus the evolution equations for the dynamics of physical quantities are replaced by evolution equations for the polynomial chaos coefficients. The dimension of the stochastic Galerkin system is m times larger than the dimension of the original physical system, where m is the number of polynomial chaos coefficients. The cost of implicit time integration methods, required for stiff dynamical systems, increases considerably, for example, by a factor m3 when direct linear solvers are used.This work studies efficient implicit methods for the time integration of stiff stochastic Galerkin systems consisting of ordinary differential equations. Linearly-implicit Rosenbrock–Wanner schemes are considered. A block-diagonal approximation of the Jacobian of the stochastic Galerkin system is employed, where the diagonal blocks are the Jacobian of the physical system, evaluated at the mean solution value. We perform a theoretical study of numerical stability for this approximation, using a stochastic extension of the Dahlquist test equation, and propose a concept of linear stochastic Galerkin stability. A rigorous analysis is done for methods of order one and two. A third-order scheme is designed to investigate the stability properties by numerical experiments. Numerical results confirm the theoretical findings.

Cross-sectional evaluation of the association between greenness and cognitive performance in Mexican pre-pubertal boys

BackgroundEvidence shows that greenspace exposure benefits children's health and cognitive development. However, evidence assessing this association in young children in low- and middle-income economies is scarce. ObjectiveTo assess the association between exposure to greenness and cognitive performance in pre-pubertal boys living in Mexico City. MethodsCross-sectional study using data from 144 boys aged 6–11 years living in Mexico City in 2017 and enrolled in the “MetCog” study. Cognitive performance was evaluated through selected Wechsler Scale for Intelligence in Children Fourth Edition (WISC-IV) and Neuropsychological Assessment of Children (Evaluación Neuropsicológica Infantil, ENI) tests. Exposure to greenness was assessed through Normalised Difference Vegetation Index (NDVI) at 300, 500, 1500, 2000, and 3000 m buffer zones from children's residences. Multiple linear regression analysis was undertaken to assess associations between cognitive performance and greenness (aβ) with 95% confidence intervals (CI) and adjusted for potential confounding variables. Significance was set at q < 0.05 after False Discovery Rate (FDR) correction. ResultsA positive association was found between the NDVI Interquartile Range (IQR) at 2000 m and the WISC-IV block design test score (aβ 2000 = 1.18, 95% CI = 0.31, 2.06; q < 0.05), which assesses perceptual reasoning. Positive associations were found with NDVI IQR at 1500 m and WISC-IV block design (aβ1500 = 1.00, 95% CI = 0.14, 1.86) and matrix reasoning (aβ1500 = 0.83, 95% CI = 0.06, 1.61) scores, but neither survived FDR correction. No significant associations were found between NDVI IQR at any buffer size with other WISC-IV and ENI task scores. ConclusionsGreater exposure to greenness was associated with higher perceptual reasoning skills in 144 pre-pubertal boys living in Mexico City. Thus, urban planning should consider increasing vegetation in megacities, especially in neighbourhoods with high percentages of young children.

Structural brain correlates of non-verbal cognitive ability in 5-year-old children: Findings from the FinnBrain birth cohort study.

Non-verbal cognitive ability predicts multiple important life outcomes, for example, school and job performance. It has been associated with parieto-frontal cortical anatomy in prior studies in adult and adolescent populations, while young children have received relatively little attention. We explored the associations between cortical anatomy and non-verbal cognitive ability in 165 5-year-old participants (mean scan age 5.40 years, SD 0.13; 90 males) from the FinnBrain Birth Cohort study. T1-weighted brain magnetic resonance images were processed using FreeSurfer. Non-verbal cognitive ability was measured using the Performance Intelligence Quotient (PIQ) estimated from the Block Design and Matrix Reasoning subtests from the Wechsler Preschool and Primary Scale of Intelligence (WPPSI-III). In vertex-wise general linear models, PIQ scores associated positively with volumes in the left caudal middle frontal and right pericalcarine regions, as well as surface area in left the caudal middle frontal, left inferior temporal, and right lingual regions. There were no associations between PIQ and cortical thickness. To the best of our knowledge, this is the first study to examine structural correlates of non-verbal cognitive ability in a large sample of typically developing 5-year-olds. The findings are generally in line with prior findings from older age groups, with the important addition of the positive association between volume / surface area in the right medial occipital region and non-verbal cognitive ability. This finding adds to the literature by discovering a new brain region that should be considered in future studies exploring the role of cortical structure for cognitive development in young children.

The Complexity of the Super Subdivision of Cycle-Related Graphs Using Block Matrices

The complexity (number of spanning trees) in a finite graph Γ (network) is crucial. The quantity of spanning trees is a fundamental indicator for assessing the dependability of a network. The best and most dependable network is the one with the most spanning trees. In graph theory, one constantly strives to create novel structures from existing ones. The super subdivision operation produces more complicated networks, and the matrices of these networks can be divided into block matrices. Using methods from linear algebra and the characteristics of block matrices, we derive explicit formulas for determining the complexity of the super subdivision of a certain family of graphs, including the cycle Cn, where n=3,4,5,6; the dumbbell graph Dbm,n; the dragon graph Pm(Cn); the prism graph Πn, where n=3,4; the cycle Cn with a Pn2-chord, where n=4,6; and the complete graph K4. Additionally, 3D plots that were created using our results serve as illustrations.

THERMAL CONDUCTIVITY OF PARTITION BOARD BY POLYMER COMPOSITE WITH FILLER EMPTY FRIUT BUNCHES FIBRES

Utilization and management of Empty Fruit Bunches (EFB) fibre continue to develop as the main ingredient and additional material used in various industrial products. The technological breakthrough targeted in this study is the developed EFB fibre as a filler in polymer composite partition boards which are used as heat retainers in the interior construction of buildings. The partition board is a heat insulator, and its thermal conductivity is affected by mass density and porosity. The purpose of this study was to determine the heat resistance of partition board products to reduce the heat entering the room from outside by propagating through walls exposed to direct sunlight. The test method used is adopted from ASTM C177-13, namely the measurement of heat propagation with a modification of the heat source of 40 watts. In addition, mass density tests (referring to SNI 03-2105-2006) and water absorption (referring to ASTM D5229M-12) were also carried out on the product. The specimens were based on the formation of Singapore Highpolymer Chemical Product (SHCP) 2667 WNC polyester resin matrix partition board with weight fractions of 25%, 30%, and 35% chop strand mat (CSM). The test results show that the highest thermal conductivity value is found on the board with a weight fraction of 25%, namely 0.153 W/m.°C with a mass density of 1.16 g/cm3 and a water absorption capacity of 3.38%. However, the lowest thermal conductivity value was found in the fibre with weight fraction of 35%, namely 0.147 W/m. °C at a mass density of 1.24 g/cm3 and a water absorption capacity of 3.75%.