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In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible. [ABSTRACT FROM AUTHOR]

This paper is concerned with an important matrix condition in compressed sensing known as the restricted isometry property (RIP). We demonstrate that testing whether a matrix satisfies RIP is \ssr NP-hard. As a consequence of our result, it is impossible to efficiently test for RIP provided \ssr P\ne\ssr NP. [ABSTRACT FROM PUBLISHER]

This paper proposes a new coupling matrix synthesis technique called the coupling matrix compression technique, which focuses on reducing the dimension of the $N+2$ coupling matrix. The presented coupling matrices can be compressed, and this technique can be used to design dual-mode resonators for high-isolation dual-band filters. One dual-mode resonator is represented as two closely coupled resonators when using this technique. The formulae for resonant frequencies and $\omega _{m}$ in dual-mode theory are also derived in this paper. A dual-mode embedded hairpin resonator is designed and analyzed using this technique, and a dual-band filter using the proposed resonators is designed and fabricated to validate the proposed technique. [ABSTRACT FROM AUTHOR]

The construction of a quasi-cyclic low density parity-check (QC-LDPC) matrix is usually carried out in two steps. In the first step, a prototype matrix is defined according to certain criteria (size, girth, check and variable node degrees, and so on). The second step involves the expansion of the prototype matrix. During this last phase, an integer value is assigned to each non-null position in the prototype matrix corresponding to the right-rotation of the identity matrix. The problem of determining these integer values is complex. The state-of-the-art solutions use either some mathematical constructions to guarantee a given girth of the final QC-LDPC code, or a random search of values until the target girth is satisfied. In this paper, we propose an alternative/complementary method that reduces the search space by defining large equivalence classes of topologically identical matrices through row and column permutations using additive, structural, and multiplicative transformations. Selecting only a single element per equivalence class can reduce the search space by a few orders of magnitude. Then, we use the formalism of constraint programming to list the exhaustive sets of solutions for a given girth and a given expansion factor. An example is presented in all sections of the paper to illustrate the methodology. [ABSTRACT FROM AUTHOR]

In the field of frontier research, information security has received a lot of interest, but in the field of information security algorithm, the introduction of decimals makes it impossible to bypass the topic of calculation accuracy. This article creatively proposes the definition and related proofs of double parameters fractal sorting matrix (DPFSM). As a new matrix classification with fractal properties, DPFSM contains self-similar structures in the ordering of both elements and sub-blocks in the matrix. These two self-similar structures are determined by two different parameters. To verify the theory, this paper presents a type of $2\times 2$ DPFSM iterative generation method, as well as the theory, steps, and examples of the iteration. DPFSM is a space position transformation matrix, which has a better periodic law than a single parameter fractal sorting matrix (FSM). The proposal of DPFSM expands the fractal theory and solves the limitation of calculation accuracy on information security. The image encryption algorithm based on DPFSM is proposed, and the security analysis demonstrates the security. DPFSM has good application value in the field of information security. [ABSTRACT FROM AUTHOR]

In 2010, Silva et al. studied certain classes of finite-field matrix channels in order to model random linear network coding where exactly $t$ random errors are introduced. In this paper, we consider a generalization of these matrix channels where the number of errors is not required to be constant, indeed the number of errors may follow any distribution. We show that a capacity-achieving input distribution can always be taken to have a very restricted form (the distribution should be uniform given the rank of the input matrix). This result complements, and is inspired by a paper of Nobrega et al., which establishes a similar result for a class of matrix channels that model network coding with link erasures. Our result shows that the capacity of our channels can be expressed as maximization over probability distributions on the set of possible ranks of input matrices: a set of linear rather than exponential size. [ABSTRACT FROM AUTHOR]

Data, which lie in the space \mathcal Pm\, , of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications, including medical imaging, computer vision, and radar signal processing. An open challenge, for these applications, is to find a class of probability distributions, which is able to capture the statistical properties of data in \mathcal Pm\, , as they arise in real-world situations. The present paper meets this challenge by introducing Riemannian Gaussian distributions on \mathcal Pm\, . Distributions of this kind were first considered by Pennec in 2006. However, the present paper gives an exact expression of their probability density function for the first time in existing literature. This leads to two original contributions. First, a detailed study of statistical inference for Riemannian Gaussian distributions, uncovering the connection between the maximum likelihood estimation and the concept of Riemannian centre of mass, widely used in applications. Second, the derivation and the implementation of an expectation-maximisation algorithm, for the estimation of mixtures of Riemannian Gaussian distributions. The paper applies this new algorithm, to the classification of data in \mathcal Pm\, , (concretely, to the problem of texture classification, in computer vision), showing that it yields significantly better performance, in comparison to recent approaches. [ABSTRACT FROM PUBLISHER]

The main objective of this paper is to study and validate the effectiveness of the tensor-product (TP)-model transformation in a state-dependent nonlinear controller design for a prototypical aeroelastic system that exhibits a variety of control phenomena such as limit cycle oscillation, flutter, and even chaotic vibrations. In this paper, the TP-model transformation is applied to transform the identified analytic model of the prototypical aeroelastic system to TP-model form whereupon linear matrix inequality-based controller-design theorems, within the parallel- distributed-compensation (PDC) frameworks, can be immediately executed. Numerical simulations are used to provide empirical validation of the control results. The effectiveness of the controller design is compared to the former approaches. [ABSTRACT FROM AUTHOR]

In this paper, a direct coupling matrix technique is presented for narrowband mixed topology filters that possess a series of extracted-pole sections. With respect to previous works, this technique exhibits distinct benefits due to its simplicity as all the coupling elements, of both cross-coupled and extracted-pole structures, can be obtained as an entity at one time. As the basis, a unique process is introduced to rebuild the couplings and admittance functions for an N th-order cross-coupled low-pass prototype, from which a series of extracted-pole sections can be naturally generated with no more operations, thus deriving a mixed topology transversal array directly. To show the flexibility of this paper, a couple of examples, including fully canonical cases and fully extracted-pole cases (considered as a particular kind of mixed topology filters here), are demonstrated. Moreover, a miniaturized coupled line structure is proposed to properly construct filters of fully extracted poles, which provides a reasonable possibility to design compact planar mixed topology filters, in comparison with others in the literature. The simulated and measured results are in good agreement. [ABSTRACT FROM PUBLISHER]

This paper focuses on the behavior similarity of workflow nets (WF-nets). The similarity of two WF-nets reflects their consistent degree in behaviors. It explores the behavioral relations of subsets of transitions based on the interleaving semantics, and more accurate relations are defined than the existing work. Therefore, a more accurate similarity of two WF-nets (in their behaviors) can be obtained than that in the existing work that usually do not consider the loop and complex correspondence. By refining the interleaving relation in a behavioral profile into six types, this paper proposes the notion of a relation profile based on behavioral profile. Based on the relation profile of a WF-net, behavioral relation matrix can be constructed. Additionally, we refine the complex correspondence and generate a group of behavioral relation submatrices from the behavioral relation matrix. By using them we present a new formula to measure the behavior similarity of two WF-nets. Finally, examples illustrate that our method can measure the similarity degree more accurately. [ABSTRACT FROM AUTHOR]

This paper evaluates a design structure matrix (DSM) as a new approach for assessing the system readiness level (SRL) of complex systems. A framework to demonstrate how a current SRL calculation method can be incorporated into the DSM tool is presented to demonstrate the benefits of DSMs for improved confidence in system readiness assessments. A cross-comparison of the modeled system readiness results obtained with a current SRL approach with nesting assumptions and the proposed DSM approach suggests that the DSM approach provides more accurate results and may be more practical for complex system analysis. The application of the DSM approach to a real-world example is also presented to demonstrate how a DSM framework facilitates the decision-making process for system readiness assessment by providing a more evidence-based maturity assessment for complex systems. The DSM approach discussed in this research can be easily adopted by program managers and practitioners for a wide range of complex systems and system architectures with multiple subsystem components. [ABSTRACT FROM AUTHOR]

Sampling plays a critical role in remote sensing and signal analysis. In conventional sampling theory, the signal is sampled at a uniform rate at a minimum of twice the signal bandwidth. Sampling with an aperture function requires a fixed-aperture function, which can be removed by deconvolution after signal reconstruction. However, in some cases, the signal samples are available only at irregular positions, and different samples use different aperture functions. In this paper, the theory of finite-length signal reconstruction with irregular samples and variable apertures in one and two dimensions is considered. In the 1-D case, a band-limited discrete signal can be exactly reconstructed from a finite number of arbitrarily spaced samples with few restrictions on the aperture functions. Exact reconstruction in the 2-D case requires the sampling matrix be invertable, and is not always possible. Variable aperture functions, while complicating the process, can enable reconstruction for a broader range of sample locations. Practical issues are discussed, and numerical examples are provided. Variable aperture reconstruction has application in a variety of remote sensing problems. In this paper, reconstruction from 2-D irregular sampling with variable apertures is illustrated using Special Sensor Microwave/Imager radiometer observations. [ABSTRACT FROM PUBLISHER]

In this paper, field projection methods are used to couple finite-element analysis carried out on different meshes and different temporal discretization bases. The prior-art mesh-to-mesh spatial field projection is extended to the time domain in this paper. We first define a space-time error norm between a given field distribution and the target field to be determined, and then minimize it using the Galerkin method. Biorthogonal test functions are also introduced into the projection process to replace inner product matrices with diagonal matrices and reduce the computation cost in terms of memory as well as the calculation time required. [ABSTRACT FROM AUTHOR]

This paper develops a simplified phasor model for predicting harmonics present at the point of common coupling between a voltage-source power converter and the utility network. It employs the frequency coupling matrix (FCM) modeling technique. The FCM is experimentally determined without requiring access to converter internal details, such as control and output filter parameters, which are generally not available for converters used in distributed generation systems. Experimental measurements are conducted on a commercially available two-stage, three phase, grid-tied photovoltaic inverter to assess the accuracy of experimentally determined FCMs to predict the harmonic behavior of grid-connected converters. This paper considers two grid conditions for the experimental analysis: 1) when the grid is stiff and contains only background voltage harmonics and 2) when the grid contains harmonic grid impedances as well as background voltage harmonics. In all cases, a close match between the results predicted by the FCM approach and experimental measurements is achieved, thus demonstrating the practical viability of using experimentally determined FCM models for harmonic predictions. [ABSTRACT FROM PUBLISHER]

This paper is concerned with quasi-synchronization of delayed memristive neural networks (MNNs) with switching jumps mismatches via aperiodically intermittent control. The issue is presented for three reasons: 1) the existing controllers for synchronization may be too complicated and not economical; 2) under the influence of switching jumps mismatches, synchronization of MNNs may fail to achieve; and 3) matrix measure method is less conservative but cannot be applied directly to synchronization of MNNs. To overcome these difficulties, the concept of asynchronously switching time interval is proposed to describe the phenomenon when the drive-response MNNs switch their connection weights asynchronously. Then, aperiodically intermittent control is designed and quasi-synchronization analysis is carried out based on a combined method that compromises the merits of interval matrix method and matrix measure method. A quasi-synchronization criterion, expressed in terms of the mixture of ${p}$ -norm and matrix measure of the memristive connection weights, is established. Meanwhile, the fundamental reason for the failure of complete synchronization is revealed. Moreover, an explicit expression of the error level is obtained and the design of the controller under a predetermined error level is presented. The obtained results in this paper reduce the conservativeness and provide a novel insight into the research of synchronization of MNNs. [ABSTRACT FROM AUTHOR]

Compressive sensing (CS) has been widely used in vehicular technology including compressive spectrum sensing, sparse channel estimation, and vehicular communications. The complete procedure of CS consists of sparse representation, sparse measurement, and sparse recovery. In the CS, measurement matrix $\mathbf {\Phi }$ is utilized to sample a sparse signal, while sensing matrix $\mathbf {\Psi }$ is exploited for sparse recovery. It is important to properly design the sensing matrix that significantly affects the signal recovery performance. This paper addresses the issue of the sensing matrix design for the CS with multiple measurement vectors (MMV). We first study sufficient conditions for the MMV-CS and then develop three sensing matrix design approaches in different situations. The proposed methods have their roots in the principle of minimum variance distortionless response (MVDR) beamformer. This allows us to optimally determine the sensing matrix in the framework of the MVDR, which amounts to minimizing local cumulative cross-coherence between $\mathbf {\Phi }$ and $\mathbf {\Psi }$ while keeping the columns of $\mathbf {\Psi }$ highly correlated to their counterparts of $\mathbf {\Phi }$. Simulation results are presented to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector x observed through a linear transform A. In the case of large i.i.d. zero-mean Gaussian A, the methods exhibit fast convergence with precise analytic characterizations on the algorithm behavior. However, the convergence of AMP under general transforms A is not fully understood. In this paper, we provide sufficient conditions for the convergence of a damped version of the generalized AMP (GAMP) algorithm in the case of quadratic cost functions (i.e., Gaussian likelihood and prior). It is shown that, with sufficient damping, the algorithm is guaranteed to converge, although the amount of damping grows with peak-to-average ratio of the squared singular values of the transforms A. This result explains the good performance of AMP on i.i.d. Gaussian transforms A, but also their difficulties with ill-conditioned or non-zero-mean transforms A. A related sufficient condition is then derived for the local stability of the damped GAMP method under general cost functions, assuming certain strict convexity conditions. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has been successfully applied in several data mining tasks. Recently, there is an increasing interest in the acceleration of NMF, due to its high cost on large matrices. On the other hand, the privacy issue of NMF over federated data is worthy of attention, since NMF is prevalently applied in image and text analysis which may involve leveraging privacy data (e.g, medical image and record) across several parties (e.g., hospitals). In this paper, we study the acceleration and security problems of distributed NMF. First, we propose a distributed sketched alternating nonnegative least squares(DSANLS) framework for NMF, which utilizes a matrix sketching technique to reduce the size of nonnegative least squares subproblems with a convergence guarantee. For the second problem, we show that DSANLS with modification can be adapted to the security setting, but only for one or limited iterations. Consequently, we propose four efficient distributed NMF methods in both synchronous and asynchronous settings with a security guarantee. We conduct extensive experiments on several real datasets to show the superiority of our proposed methods. The implementation of our methods is available at https://github.com/qianyuqiu79/DSANLS. [ABSTRACT FROM AUTHOR]

Risk management is considered as a vital process contributing to the successful outcome of a complex construction project in terms of achieving the associated project objectives. The widely used industrial practice in managing construction project risks is to assign probability and impact values to each risk and to map risks on a risk matrix. The main criticism of this practice relates to ignoring complex interdependencies between risks and using point estimates for probability and impact values. Furthermore, risks mapped on a matrix are deemed to influence a specific objective and there is a challenge involved in aggregating the impact of risks across multiple (conflicting) project objectives. Utilizing a data-driven Bayesian Belief Network methodology, in this paper we introduce a new process where the risks mapped on a risk matrix corresponding to each project objective are aggregated and modeled as a risk network, and a holistic impact of each risk is captured across the network by means of new risk metrics. The proposed methodology is demonstrated through a real application. The results specific to the two ranking schemes (assuming independence/interdependence of risks) are found to be negatively correlated, which substantiates the importance of utilizing an interdependency-based risk management process. [ABSTRACT FROM AUTHOR]

Motivated by applications in molecular biology and genotyping, this paper proposes a novel model of group testing for identifying items with real-valued status using nonbinary pooling designs under standard arithmetic observation. The purpose is to learn more information of each item to be tested rather than identify only which ones are defectives as was done in conventional group testing. This paper provides several efficiently decodable nonadaptive strategies for the considered problem. The major tool is a new structure called $q$ -ary additive $(w,d)$ -disjunct matrix, which is related to known structures: 1) the conventional disjunct matrix by Kautz and Singleton 1964 and 2) the SQ-disjunct matrix by Emad and Milenkovic 2012. [ABSTRACT FROM AUTHOR]

This paper first introduces a simplified construction of the constitutive matrices for general polyhedral meshes. These constitutive matrices are geometrically defined by means of simple closed-form expressions involving the geometric elements of the primal and dual meshes. Then, we solve for the first time the Maxwell’s eigenvalue problem on general polyhedral meshes. In particular, we analyze the convergence of the eigenvalues when the mesh is adaptively refined by using the subgridding technique together with the constitutive inconsistency as error indicator. [ABSTRACT FROM AUTHOR]

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization, even with huge size, can be solved very efficiently through the standard optimization algorithms in practice. However, due to the non-convexity caused by the factorization model, there is a limited theoretical understanding of whether these algorithms will generate a good solution. In this paper, we establish a theoretical guarantee for the factorization-based formulation to correctly recover the underlying low-rank matrix. In particular, we show that under similar conditions to those in previous works, many standard optimization algorithms converge to the global optima of a factorization-based formulation and recover the true low-rank matrix. We study the local geometry of a properly regularized objective and prove that any stationary point in a certain local region is globally optimal. A major difference of this paper from the existing results is that we do not need resampling (i.e., using independent samples at each iteration) in either the algorithm or its analysis. [ABSTRACT FROM PUBLISHER]

In this paper, we reinterpret the $(k+2,k)$ zigzag code in coding matrix and then propose an optimal exact repair strategy for its parity nodes, whose repair disk I/O approaches a lower bound derived in this paper. [ABSTRACT FROM PUBLISHER]

Recommender systems (RSs) commonly adopt a user-item rating matrix to describe users’ preferences on items. With users and items exploding, such a matrix is usually high-dimensional and sparse (HiDS). Recently, the idea of deep learning has been applied to RSs. However, current deep-structured RSs suffer from high computational complexity. Enlightened by the idea of deep forest, this paper proposes a deep latent factor model (DLFM) for building a deep-structured RS on an HiDS matrix efficiently. Its main idea is to construct a deep-structured model by sequentially connecting multiple latent factor (LF) models instead of multilayered neural networks through a nonlinear activation function. Thus, the computational complexity grows linearly with its layer count, which is easy to resolve in practice. The experimental results on four HiDS matrices from industrial RSs demonstrate that when compared with state-of-the-art LF models and deep-structured RSs, DLFM can well balance the prediction accuracy and computational efficiency, which well fits the desire of industrial RSs for fast and right recommendations. [ABSTRACT FROM AUTHOR]

White-box block cipher (WBC) has been proposed by Chow et al. to prevent the secret key to be extracted from its implementation in an untrusted context. A pivotal technique behind WBC is to convert the iterated round functions into a series of look-up tables (LUTs) with encodings. The construction of encoded LUTs consists of matrix operations, such as multiplication and inversion. The widely-used matrix libraries in applications, such as open-source NTL and M4RI, are primarily designed for large dimensional matrix operations. Therefore, they might not be suitable for WBC implementations which are mainly based on small-scale matrices and vectors. In this paper, we propose a new matrix library named WBMatrix for the optimization of WBC implementations. WBMatrix reduces the operating steps of multiplication and simultaneously generates pairwise invertible matrices as encodings. The performance comparison supports that WBMatrix improves the table construction and encryption phases on Intel x86 and ARMv8 platforms. Moreover, WBMatrix also boosts the initialization and encryption phases of LowMC/LowMC-M block ciphers and enhances the performance for the generation of key-dependent Sbox. [ABSTRACT FROM AUTHOR]

We consider a distributed resource allocation problem in networks where each transmitter–receiver pair aims at maximizing its local utility function by adjusting its action matrix, which belongs to a given feasible set. This problem has been addressed recently by applying a matrix exponential learning (MXL) algorithm, which has a very appealing convergence rate. In this learning algorithm, however, each transmitter must know an estimate of the gradient matrix of the local utility. The knowledge of the gradient matrix at the transmitters incurs a high signaling overhead, especially that the matrix size increases with the dimension of the action matrix. In this paper, we therefore, investigate two strategies in order to decrease the informational exchange per iteration of the algorithm. In the first strategy, each receiver sends at each iteration part of the elements of the gradient matrix with respect to a certain probability. In the second strategy, each receiver feeds back “sporadically” the whole gradient matrix. We focus on the analysis of the convergence of the MXL algorithm to optimum under these two strategies. We prove that the algorithm can still converge to optimum almost surely. Upper bounds of the average convergence rate are also derived in both situations with general step-size setting, from which we can clearly see the impact of the incompleteness of the feedback information. The proposed algorithms are applied to solve the energy efficiency maximization problem in a multicarrier multiuser multiple-input and multiple-output (MIMO) network. Simulation results further corroborate our claim. [ABSTRACT FROM AUTHOR]

This contribution introduces a novel method for constructing mass matrices for general tetrahedral elements. By considering the construction of the reluctivity mass matrix as an example, a new derivation of a recipe to geometrically construct a symmetric positive semi-definite and consistent mass matrix is provided. It is shown why such a matrix can be used inside formulations where the mass matrix is right multiplied by the appropriate incidence matrix. Then, a second recipe is introduced to produce a consistent and symmetric positive definite matrix. The proposed method is based on an original algebraic technique that differs fundamentally from what is available in the literature. The proposed recipe opens also the possibility to improve the conditioning of the resulting elementary mass matrices. [ABSTRACT FROM AUTHOR]

The problem of partitioning dense matrices into sets of sub-matrices has received increased attention recently and is crucial when considering dense linear algebra and kernels with similar communication patterns on heterogeneous platforms. The problem of load balancing and minimizing communication is traditionally reducible to an optimization problem that involves partitioning a square into rectangles. This problem has been proven to be NP-Complete for an arbitrary number of partitions. In this paper, we present recent approaches that relax the restriction that all partitions be rectangles. The first approach uses an original mathematical technique to find the exact optimal partitioning. Due to the complexity of the technique, it has been developed for a small number of partitions only. However, even at a small scale, the optimal partitions found by this approach are often non-rectangular and sometimes non-intuitive. The second approach is the study of approximate partitioning methods utilizing recursive partitioning algorithms. In particular we use the work on optimal partitioning to improve pre-existing algorithms. In this paper we discuss the different perspectives this approach opens and present two algorithms, SNRPP which is a $\sqrt{\frac{3}{2}}$ approximation, and NRPP which is a $\frac{2}{\sqrt{3}}$ approximation. While sub-optimal, the NRRP approach works for an arbitrary number of partitions. We use the first exact approach to analyse how close to the known optimal solutions the NRRP algorithm is for small numbers of partitions. [ABSTRACT FROM AUTHOR]

Existing electrical–thermal cosimulation methods require solving a system matrix when handling inhomogeneous materials and irregular geometries discretized into unstructured meshes. In this paper, a matrix-free method is developed for cosimulating full-wave Maxwell’s equations and the thermal diffusion equation in the time domain. The method is free of matrix solutions regardless of the shape of the element used for space discretization. A theoretical stability analysis is also developed for the coupled electrical and thermal analysis, which is nonlinear in nature. Numerical experiments on both unstructured tetrahedral and triangular prism element meshes have validated the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Fully polarimetric model-based decompositions are developed by accounting for the physical scattering model and experimental polarimetric SAR data acquisition processes. These decompositions offer the promising straightforward interpretation and highly improved inversion models for visualizing images of scattering scenarios optimally. However, the attempts in existing decompositions to implement the split real and imaginary components of the $T_{13}$ element of the coherency matrix have been hampered by the absence of physical models to fit the coherency matrix. In this paper, two additional physical scattering submodels are derived. The real and imaginary parts of $T_{13}$ are accounted for by implementing two newly developed physical scattering models. (One is for oriented dipole scattering and the other is for oriented quarter-wave reflection.) Furthermore, this paper is extended by implementing these physical models into a six-component scattering power model-based decomposition. To this date, the developed novel decompositions account for the maximum elements of the coherency matrix in a physical manner compared to the existing model-based decompositions. The proposed novel decomposition is tested on L-band and X-band fully polarimetric SAR data sets of the Advanced Land Observing Satellite-2/Phased Array L-band Synthetic Aperture Radar-2 and the X-band TerraSAR-X, respectively. This new decomposition produces additional two scattering submatrix components. Such scattering components are prevalent in vegetation and urban areas and even dominant over highly oriented urban scenarios. The new method enhances the truly existing double-bounce scattering contributions and reduces the overrated volume scattering from double-bounce scatterers. By comparing the results, it is found that the proposed decomposition considerably enhances the SAR image quality and its more correct visualizing presentation compared to existing decompositions. It is also found to be more robust over the oriented urban areas than the existing decompositions, resulting from the utilization of both the real and imaginary components of $T_{13}$ polarimetric information in a physical scattering manner. [ABSTRACT FROM AUTHOR]

This paper investigates the situation awareness issue of power system with massive measured data. To address this issue, first, a graph-theory-based network partitioning algorithm is proposed to realize decentralized detection in a faster response speed, while using power flow characteristics highlights the independency of different groups. Further, a hierarchical event detection method is proposed to judge voltage change and locate event position according to spectral distribution change of established multidimensional matrix. With the proposed method, the system situation can be assessed and the knowledge of the system model is not required. In addition, the accurate result of weak event happened in system could also be obtained. The simulation results are presented to illustrate the effectiveness of the proposed detection method. [ABSTRACT FROM AUTHOR]

Coded caching systems have been widely studied to reduce the data transmission during the peak traffic time. In practice, two important parameters of a coded caching system should be considered, i.e., the transmission rate which is the maximum amount of the data transmission during the peak traffic time, and the subpacketization level, the number of divided packets of each file when we implement a coded caching scheme. Although there exists a tradeoff between transmission rate and subpacketization, we prefer to design a scheme with transmission rate and subpacketization as small as possible since they reflect the transmission efficiency and complexity of the caching scheme, respectively. In this paper, we first characterize a coded caching scheme from the viewpoint of linear algebra and show that designing a linear coded caching scheme is equivalent to constructing three classes of matrices satisfying some rank conditions. Then based on the invariant subspaces in linear algebra and combinatorial design theory, a new class of coded caching schemes over $\mathbb {F}_{2}$ is obtained by constructing these three classes of matrices. It turns out that the transmission rate of our new scheme is the same as the scheme construct by Yan et al. (IEEE Trans. Inf. Theory 63, 5821-5833, 2017), but the subpacketization is significantly reduced. Finally by means of these matrices, we show that the minimum storage regenerating codes can also be used to construct coded caching schemes. [ABSTRACT FROM AUTHOR]

Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated heterogeneous variance structure. We propose a sequential test which utilizes the edge singular values (i.e., the largest few singular values) of the data matrix. It also naturally leads to a consistent sequential testing estimate of the number of signals. We describe the asymptotic distribution of the test statistic in terms of the Tracy-Widom distribution. The test is shown to be accurate and have full power against the alternative, both theoretically and numerically. The theoretical analysis relies on establishing the Tracy-Widom law for a large class of Gram type random matrices with non-zero means and completely arbitrary variance profiles, which can be of independent interest. [ABSTRACT FROM AUTHOR]

Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There exist several similarity measures for comparing SPD matrices with documented benefits. However, selecting an appropriate measure for a given problem remains a challenge and in most cases, is the result of a trial-and-error process. In this paper, we propose to learn similarity measures in a data-driven manner. To this end, we capitalize on the $\alpha \beta$ α β -log-det divergence, which is a meta-divergence parametrized by scalars $\alpha$ α and $\beta$ β , subsuming a wide family of popular information divergences on SPD matrices for distinct and discrete values of these parameters. Our key idea is to cast these parameters in a continuum and learn them from data. We systematically extend this idea to learn vector-valued parameters, thereby increasing the expressiveness of the underlying non-linear measure. We conjoin the divergence learning problem with several standard tasks in machine learning, including supervised discriminative dictionary learning and unsupervised SPD matrix clustering. We present Riemannian gradient descent schemes for optimizing our formulations efficiently, and show the usefulness of our method on eight standard computer vision tasks. [ABSTRACT FROM AUTHOR]

Shamir's secret sharing scheme is an effective way to distribute secret to a group of shareholders. The security of the unprotected sharing scheme, however, can be easily broken by cheaters or attackers who maliciously feed incorrect shares during the secret recovery stage or inject faults into hardware computing the secret. In this paper, we propose cheater detection and identification schemes based on robust and algebraic manipulation detection (AMD) codes and m-disjunct matrices (superimposed codes). We present the constructions of codes for cheater detection and identification and describe how the cheater identification problem can be related to the classic group testing algorithms based on m-disjunct matrices. Simulation and synthesis results show that the proposed architecture can improve the security level significantly even under strong cheating attack models with reasonable area and timing overheads. [ABSTRACT FROM PUBLISHER]

In this paper, we analyze the maximum likelihood decoding performance of Raptor codes with a systematic low-density generator-matrix code as the pre-code. By investigating the rank of the product of two random coefficient matrices, we derive upper and lower bounds on the decoding failure probability. The accuracy of our analysis is validated through simulations. Results of extensive Monte Carlo simulations demonstrate that for Raptor codes with different degree distributions and pre-codes, the bounds obtained in this paper are of high accuracy. The derived bounds can be used to design near-optimum Raptor codes with short and moderate lengths. [ABSTRACT FROM AUTHOR]

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well known that standard algorithms for matrix completion can return arbitrarily poor results, if even a single column is corrupted. One direct application comes from robust collaborative filtering. Here, some number of users are so-called manipulators who try to skew the predictions of the algorithm by calibrating their inputs to the system. In this paper, we develop an efficient algorithm for this problem based on a combination of a trimming procedure and a convex program that minimizes the nuclear norm and the \ell 1,2 norm. Our theoretical results show that given a vanishing fraction of observed entries, it is nevertheless possible to complete the underlying matrix even when the number of corrupted columns grows. Significantly, our results hold without any assumptions on the locations or values of the observed entries of the manipulated columns. Moreover, we show by an information-theoretic argument that our guarantees are nearly optimal in terms of the fraction of sampled entries on the authentic columns, the fraction of corrupted columns, and the rank of the underlying matrix. Our results therefore sharply characterize the tradeoffs between sample, robustness, and rank in matrix completion. [ABSTRACT FROM PUBLISHER]

This paper studies the parameters for which binary Reed–Muller (RM) codes can be decoded successfully on the binary erasure channel and binary symmetry channel, and, in particular, when can they achieve capacity for these two classical channels. Necessarily, this paper also studies the properties of evaluations of multivariate $GF(2)$ polynomials on the random sets of inputs. For erasures, we prove that RM codes achieve capacity both for very high rate and very low rate regimes. For errors, we prove that RM codes achieve capacity for very low rate regimes, and for very high rates, we show that they can uniquely decode at about the square root of the number of errors at capacity. The proofs of these four results are based on different techniques, which we find interesting in their own right. In particular, we study the following questions about $E(m,r)$ , the matrix whose rows are the truth tables of all the monomials of degree $\leq r$ in $m$ variables. What is the most (resp. least) number of random columns in $E(m,r)$ that define a submatrix having full column rank (resp. full row rank) with high probability? We obtain tight bounds for very small (resp. very large) degrees $r$ , which we use to show that RM codes achieve capacity for erasures in these regimes. Our decoding from random errors follows from the following novel reduction. For every linear code $C$ of sufficiently high rate, we construct a new code $C'$ obtained by tensorizing $C$ , such that for every subset $S$ of coordinates, if $C$ can recover from erasures in $S$ , then $C'$ can recover from errors in $S$ . Specializing this to the RM codes and using our results for erasures imply our result on the unique decoding of the RM codes at high rate. Finally, two of our capacity achieving results require tight bounds on the weight distribution of RM codes. We obtain such bounds extending the recent bounds from constant degree to linear degree polynomials. [ABSTRACT FROM PUBLISHER]

Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori, which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of this kind of networks. By using integral matrices to deal with Cayley graphs over Abelian groups, we have been able to propose and analyze a family of high-dimensional mesh-based interconnection networks. As they are built over $n$-dimensional grids that induce a regular tiling of space, these topologies have been denoted lattice graphs. Higher dimensional networks can be composed over these graphs by means of a lift operation, which is also introduced in the paper. Easy network partitioning and minimal routing algorithm are also provided for these topologies based on this new network operation. Later we focus on cubic crystal lattices for modeling symmetric 3D networks and to show how lattice graphs can help in the design of twisted interconnection networks. In all cases, the networks obtained are better, in topological terms, than their standard tori counterparts. Finally, some practical issues such as implementability and preliminary performance evaluations have been addressed at the end of this work. [ABSTRACT FROM AUTHOR]

This paper presents a novel philosophy to compensate the load-reactive power demand through a three-phase unified power quality conditioner (UPQC). Most of the UPQC-based applications show the dependency on shunt inverter for load-reactive power compensation, whereas the series inverter is always looked as controlled voltage source to handle all voltage-related problems. This paper proposes a new functionality of UPQC in which both the shunt and series APFs supply the load-reactive power demand. This feature not only helps to share the load-reactive power demand, but also helps to reduce the shunt APF rating, and hence, the overall cost of UPQC. This results in better utilization of the existing series inverter. The theory and complete mathematical analysis termed as "power angle control (PAC)" is presented. The simulation results based on MATLAB/Simulink are discussed in detail to support the concept developed in the paper. The proposed approach is also validated through experimental study. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a numerical controller design methodology. This methodology is based on two steps. In the first step, the tensor product (TP) model transformation is applied, which is capable of transforming a given nonlinear state-space dynamic model into TP model form. Then, in the second step, the linear matrix inequality (LMI) theorems are used within the parallel distributed compensation (PDC) controller design frameworks. The main novelty of this paper is the TP model transformation of the first step. It is also capable of dealing with the tradeoff between complexity and accuracy of the resulting TP model. The TP model transformation is a numerical method that leads to the following advantages: it is capable of functioning with models given either by analytic explicit forms or by various soft-computing based identification techniques; it does not need problem dependent analytic derivations, but can be executed "automatically" by computers. Numerical simulations are used to provide empirical validation of the proposed control design methodology. In order to demonstrate the effectiveness of the TP model transformation a controller is derived for the prototypical aeroelastic wing section that exhibits limit cycle oscillation and chaotic behavior. [ABSTRACT FROM AUTHOR]

This paper proposes a new unsupervised spectral feature selection method to preserve both the local and global structure of the features as well as the samples. Specifically, our method uses the self-expressiveness of the features to represent each feature by other features for preserving the local structure of features, and a low-rank constraint on the weight matrix to preserve the global structure among samples as well as features. Our method also proposes to learn the graph matrix measuring the similarity of samples for preserving the local structure among samples. Furthermore, we propose a new optimization algorithm to the resulting objective function, which iteratively updates the graph matrix and the intrinsic space so that collaboratively improving each of them. Experimental analysis on 12 benchmark datasets showed that the proposed method outperformed the state-of-the-art feature selection methods in terms of classification performance. [ABSTRACT FROM AUTHOR]