Constraint Matrix Research Articles

Capacity optimization using augmented lagrange method in intelligent reflecting surface-based MIMO communication systems

In this paper, we present an algorithm for capacity optimization in intelligent reflecting surface (IRS)-based multiple-input multiple-output (MIMO) communication systems. To maximize the capacity of elements in IRS, we use augmented Lagrange method with the equivalent transformations on the covariance matrix and reflection matrix constraints. This results an adjustable phase shift on the incident signal. Furthermore, we reshape the complex-valued covariance matrix and reflection matrix to a vector for the ease of calculating partial derivatives to find the search direction. Then, the quasi-Newton updates and modified Broyden-Fletcher-Goldfarb-Shano (BFGS) method in the complex domain form are used to find the local minimum. Finally, numerical simulation results demonstrate that our proposed IRS-aided system using the algorithm performs better than the state-of-the-art and the conventional communication systems.

Submatrix constrained left and right inverse eigenvalue problem for centrosymmetric matrices

ABSTRACT In this article, we will find centrosymmetric matrix solutions A of the left and right inverse eigenvalue problem under a submatrix constraint, where is also a centrosymmetric matrix. In other words, expand the system (matrix) A from the centre subsystem (submatrix) satisfying the matrix constraint, where A and are both centrosymmetric matrices. Using the similar structure of A and , we discuss the sufficient and necessary conditions for the left and right inverse eigenvalue problem having solutions, and give the expression for its general solution. Then, we discuss its optimal approximation problem and gain the expression of its solution. Last, we provide a feasible algorithm for computing the unique solution to its optimal approximation problem, which is proved by some numerical examples.

Single-Antenna-Based GPS Antijamming Method Exploiting Polarization Diversity

The vulnerability of Global Positioning System (GPS) receivers to jammers is a major concern owing to the extremely weak received signal power of GPS. Researches have been conducted on a variety of antenna array techniques to be used as countermeasures to GPS jammers, and their antijamming performance is known to be greater than that of single antenna methods. However, the application of antenna arrays remains limited because of their size, cost, and computational complexity. This study proposes and experimentally validates a novel space-time-polarization domain adaptive processing for a single-element dual-polarized antenna (STPAPS) by focusing on the polarization diversity of a dual-polarized antenna. The mathematical models of arbitrarily polarized signals received by dual-polarized antenna are derived, and an appropriate constraint matrix for dual-polarized-antenna-based GPS antijam is suggested. To reduce the computational complexity of the constraint matrix approach, the eigenvector constraint design scheme is adopted. The performance of STPAPS is quantitively and qualitatively evaluated through experiments as follows. 1) The carrier-to-noise-density ratio (C/N0) of STPAPS under synthetic jamming is demonstrated to be higher than that of the previous minimum mean squared error (MMSE) or minimum variance distortionless response (MVDR) based dual-polarized antenna methods. 2) The strengths and weaknesses of STPAPS are qualitatively compared with those of the previous single-element dual-polarized antenna methods that are not based on the MMSE or MVDR algorithms. 3) The characteristics of STPAPS (in terms of the directions and polarizations of the GPS and jamming signals) are compared with those of the conventional two-element single-polarized antenna array method, which has the same degree of freedom as that of STPAPS.

Generalized Embedding Regression: A Framework for Supervised Feature Extraction.

Sparse discriminative projection learning has attracted much attention due to its good performance in recognition tasks. In this article, a framework called generalized embedding regression (GER) is proposed, which can simultaneously perform low-dimensional embedding and sparse projection learning in a joint objective function with a generalized orthogonal constraint. Moreover, the label information is integrated into the model to preserve the global structure of data, and a rank constraint is imposed on the regression matrix to explore the underlying correlation structure of classes. Theoretical analysis shows that GER can obtain the same or approximate solution as some related methods with special settings. By utilizing this framework as a general platform, we design a novel supervised feature extraction approach called jointly sparse embedding regression (JSER). In JSER, we construct an intrinsic graph to characterize the intraclass similarity and a penalty graph to indicate the interclass separability. Then, the penalty graph Laplacian is used as the constraint matrix in the generalized orthogonal constraint to deal with interclass marginal points. Moreover, the L2,1 -norm is imposed on the regression terms for robustness to outliers and data's variations and the regularization term for jointly sparse projection learning, leading to interesting semantic interpretability. An effective iterative algorithm is elaborately designed to solve the optimization problem of JSER. Theoretically, we prove that the subproblem of JSER is essentially an unbalanced Procrustes problem and can be solved iteratively. The convergence of the designed algorithm is also proved. Experimental results on six well-known data sets indicate the competitive performance and latent properties of JSER.

Finite‐time functional interval observer for linear systems with uncertainties

This study investigates the problem of designing a finite-time functional interval observer (FTFIO) for linear systems with uncertainties. A novel structure is proposed to design an FTFIO for uncertain systems. Based on the proposed structure, the sufficient conditions for the existence of such a finite-time observer are established as a set of coefficient matrix equations with a constraint matrix. Meanwhile, using the obtained existence conditions, the parametric expression of an FTFIO is developed by adopting the solutions to a type of first-order Sylvester equations, which provides extra degrees of freedom. Finally, the FTFIO design method is efficiently applied to the estimation problem in two examples, including the simple numerical system and chaotic system.

Sequence optimization of machining elements for process model based on the genetic algorithm of matrix constrained

Process sequence planning is the permutation and combination orienting to product manufacturing process, which plays an important role in improving the manufacturing produce efficiency and reducing the manufacturing cost. In this paper, an improved constraint matrix method is proposed to transform the relation between manufacturing features into the constraint relation between machining elements, and to determine the sequence coefficient of machining elements according to the correlation relation of manufacturing features. Through constructing the interactive associative relationship of sequence constraint matrix and combined constraint matrix, the initial population with high adaptability is selected out, and can improves the adaptability of initial population of genetic algorithm by using the process sequencing algorithm of improved constraint matrix. In order to improve the convergence speed, the accuracy and efficiency of process sequencing, the genetic algorithm of elite preserving is used.

Relaxed multi-view clustering in latent embedding space

Although many multi-view clustering approaches have been developed recently, one common shortcoming of most of them is that they generally rely on the original feature space or consider the two components of the similarity-based clustering separately (i.e., similarity matrix construction and cluster indicator matrix calculation), which may negatively affect the clustering performance. To tackle this shortcoming, in this paper, we propose a new method termed Multi-view Clustering in Latent Embedding Space (MCLES), which jointly recovers a comprehensive latent embedding space, a robust global similarity matrix and an accurate cluster indicator matrix in a unified optimization framework. In this framework, each variable boosts each other in an interplay manner to achieve the optimal solution. To avoid the optimization problem of quadratic programming, we further propose to relax the constraint of the global similarity matrix, based on which an improved version termed Relaxed Multi-view Clustering in Latent Embedding Space (R-MCLES) is proposed. Compared with MCLES, R-MCLES achieves lower computational complexity with more correlations between pairs of data points. Extensive experiments conducted on both image and document datasets have demonstrated the superiority of the proposed methods when compared with the state-of-the-art.

Newton projection method as applied to assembly simulation

In this paper, we consider Newton projection method for solving the quadratic programming problem that emerges in simulation of joining process for assembly with compliant parts. This particular class of problems has specific features such as an ill-conditioned Hessian and a sparse matrix of constraints as well as a requirement for the large-scale computations. We use the projected Newton method with a quadratic rate of convergence and suggest some improvements to reduce the solving time: a method for solving the system of linear equations, so-called constraint recalculation method, and compare different approaches for step-size selection. We use the duality principle to formulate alternative forms of the minimization problem that, as a rule, can be solved faster. We describe how to solve the considered nonlinear minimization problem with the nonsmooth objective function by modifying Newton projection method and employing subgradients. In addition, we prove the convergence of the suggested algorithm. Finally, we compare Newton projection method with the other quadratic programming techniques on a number of assembly simulation problems.

Inferring linear feasible regions using inverse optimization

Consider a problem where a set of feasible observations are provided by an expert, and a cost function exists that characterizes which of the observations dominate the others and are hence, preferred. Assume the expert has an implicit optimization model in mind to identify the feasible observations, but the explicit constraints of this underlying model are unknown. Our goal is to infer the feasible region of such an optimization model that would render these observations feasible while making the best ones optimal for the cost (objective) function. Such feasible regions (i) build a baseline for a systematic categorization of future observations, and (ii) allow for using sensitivity analysis to discern changes in optimal solutions if the objective function changes in the future.In this paper, we propose a general inverse optimization methodology that recovers the complete constraint matrix of a linear model and then introduce a tractable equivalent reformulation. Furthermore, we provide and discuss several generalized loss functions to inform the desirable properties of the feasible region based on user preference and historical data. We demonstrate our approach using numerical examples and a realistic diet recommendation case study for imputing personalized diets. Our numerical examples verify the validity of our approach and emphasize the differences among the proposed loss functions. The diet recommendation case study shows that the proposed models can improve the palatability of the recommended diets for each user, and it provides further intuition for large-scale implementations of the proposed methodology.

On the existence of a short pivoting sequence for a linear program

We show that given a feasible primal–dual pair of linear programs in canonical form, there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, leading from the origin to the optimum. The sequence of pivots give a sequence of square and nonsingular submatrices of the constraint matrix. Solving two linear equations involving such a submatrix give primal–dual optimal solutions to the corresponding linear program in canonical form.

A Rotation-Based Method for Precoding in Gaussian MIMOME Channels

The problem of maximizing secrecy rate of multiple-input multiple-output multiple-eavesdropper (MIMOME) channels with arbitrary numbers of antennas at each node is studied in this paper. First, the optimization problem corresponding to the secrecy capacity of the MIMOME channel is converted to an equivalent optimization based on Givens rotations and eigenvalue decomposition of the covariance matrix. In this new formulation, precoder is a rotation matrix which results in a positive semi-definite (PSD) covariance matrix by construction. This removes the PSD matrix constraint and makes the problem easier to tackle. Next, a Broyden-Fletcher-Goldfarb-Shanno (BFGS)-based algorithm is developed to find the rotation and power allocation parameters. Further, the generalized singular value decomposition (GSVD)-based precoding is used to initialize this algorithm. The proposed rotation-BFGS method provides an efficient approach to find a near-optimal transmit strategy for the MIMOME channel and outperforms various state-of-the-art analytical and numerical methods. In particular, the rotation-BFGS precoding achieves higher secrecy rates than the celebrated GSVD precoding, with a reasonably higher computational complexity. Extensive numerical results elaborate on the effectiveness of the rotation-BFGS precoding. The new framework developed in this paper can be applied to a variety of similar problems in the context of multi-antenna channels with and without secrecy.

A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill

One of the main issues in a paper mill is the minimization of trim loss when cutting master reels and stocked reels into reels of smaller required widths. The losses produced in trimming at a paper mill are reprocessed by using different chemicals which contributes to significant discharge of effluent to surface water and causes environmental damage. This paper presents a real-world industrial problem of production planning and cutting optimization of reels at a paper mill and differs from other cutting stock problems by considering production and cutting of master reels of flexible widths and cutting already stocked over-produced and useable leftover reels of smaller widths. The cutting process of reels is performed with a limited number of cutting knives at the winder. The problem is formulated as a linear programming model where the generation of all feasible cutting patterns determines the columns of the constraint matrix. The model is solved optimally using simplex algorithm with the objective of trim loss minimization while satisfying a set of constraints. The solution obtained is rounded in a post-optimization procedure in order to satisfy integer constraints. When tested on data from the paper mill, the results of the proposed model showed a significant reduction in trim loss and outperformed traditional exact approaches. The cutting optimization resulted in minimum losses in paper trimming and a lesser amount of paper is reprocessed to make new reels which reduced the discharge of effluent to the environment.

Implementation of Presolving and Interior-Point Algorithm for Linear & Mixed Integer Programming: SOFTWARE

AbstractLinear and mixed integer programming are very popular and important methods to make efficient scientific management decision. With large size of real application data, the use of linear-mixed integer programming is facing problems with more complexity; therefore, preprocessing techniques become very important. Preprocessing aims to check and delete redundant information from the problem formulation. It is a collection of techniques that reduce the size of the problem and try to strengthen the formulation. Fast and effective preprocessing techniques are very important and essential for solving linear or mixed integer programming instances. In this paper, we demonstrate a set of techniques to presolve linear and mixed integer programming problems. Experiment results showed that when preprocessing is well done, then it becomes easier for the solver; we implemented interior-point algorithm for computational experiment. However, preprocessing is not enough to reduce the size and total nonzero elements from the constraints matrix. Moreover, we also demonstrate the impact of minimum degree reordering on the speed and storage requirements of a matrix operation. All techniques mentioned above are presented in a multifunctional software to facilitate users.

Copy number evolution with weighted aberrations in cancer.

MotivationCopy number aberrations (CNAs), which delete or amplify large contiguous segments of the genome, are a common type of somatic mutation in cancer. Copy number profiles, representing the number of copies of each region of a genome, are readily obtained from whole-genome sequencing or microarrays. However, modeling copy number evolution is a substantial challenge, because different CNAs may overlap with one another on the genome. A recent popular model for copy number evolution is the copy number distance (CND), defined as the length of a shortest sequence of deletions and amplifications of contiguous segments that transforms one profile into the other. In the CND, all events contribute equally; however, it is well known that rates of CNAs vary by length, genomic position and type (amplification versus deletion).ResultsWe introduce a weighted CND that allows events to have varying weights, or probabilities, based on their length, position and type. We derive an efficient algorithm to compute the weighted CND as well as the associated transformation. This algorithm is based on the observation that the constraint matrix of the underlying optimization problem is totally unimodular. We show that the weighted CND improves phylogenetic reconstruction on simulated data where CNAs occur with varying probabilities, aids in the derivation of phylogenies from ultra-low-coverage single-cell DNA sequencing data and helps estimate CNA rates in a large pan-cancer dataset.Availability and implementationCode is available at https://github.com/raphael-group/WCND.Supplementary information Supplementary data are available at Bioinformatics online.

A Fast Blocking Matrix Generating Algorithm for Generalized Sidelobe Canceller Beamformer in High Speed Rail Like Scenario

A fast algorithm to generate the Blocking Matrix for Generalized Sidelobe Canceller (GSC) beamforming is proposed in this paper. The proposed algorithm uses a Simplified Zero Placement Algorithm (SZPA) to directly generate the column vectors of the Blocking Matrix using the polynomial method. The constrained signal incoming angles are converted to spatial frequency and designated as zero locations in the <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</b> domain. Independent vectors that span the whole left null space of the constraint matrix is then built using a simple shift operation. The algorithm also supports the derivative constraints used for robust beamforming. Compared to the conventional methods based on Singular Value Decomposition (SVD), the SZPA algorithm can generate Blocking Matrix more than 9 times faster for scenarios with 15 constraints and will be even more advantageous for more constraints. The Blocking Matrix generated by the SZPA and SVD methods is then implemented in the same GSC architecture for performance evaluation. The numerical simulation confirms that the same overall optimum state performance and learning speed can be achieved. By reducing the calculation time of blocking matrix from 1.541ms of SVD method to 0.168ms, the proposed SZPA algorithm is fast and insensitive to the number of constraints as the required calculation time incremental for each additional constraint with SZPA is only around 1/16 of SVD method. This makes it suitable for scenarios like train to infrastructure communication in High Speed Rail (HSR) where there are multiple constraints and frequent constraints update is required.

Robust estimation for the correlation matrix of multivariate longitudinal data

Modelling the covariance structure of multivariate longitudinal data is more challenging than its univariate counterpart, owing to the complex correlated structure among multiple responses. Furthermore, there are little methods focusing on the robustness of estimating the corresponding correlation matrix. In this paper, we propose an alternative Cholesky block decomposition (ACBD) for the covariance matrix of multivariate longitudinal data. The new unconstrained parameterization is capable to automatically eliminate the positive definiteness constraint of the covariance matrix and robustly estimate the correlation matrix with respect to the model misspecifications of the nested prediction error covariance matrices. The entries of the new decomposition are modelled by regression models, and the maximum likelihood estimators of the regression parameters in joint mean–covariance models are computed by a quasi-Fisher iterative algorithm. The resulting estimators are shown to be consistent and asymptotically normal. Simulations and real data analysis illustrate that the new method performs well.

Bayes-Raking: Bayesian Finite Population Inference with Known Margins

Abstract Raking is widely used for categorical data modeling and calibration in survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution via two main strategies: (1) constructing solution subspaces via basis functions or the projection matrix and (2) modeling soft constraints. The proposed Bayes-raking estimation integrates the models for the margins, the sample selection and response mechanism, and the outcome as a systematic framework to propagate all sources of uncertainty. Computation is done via Stan, and codes are ready for public use. Simulation studies show that Bayes-raking can perform as well as raking with large samples and outperform in terms of validity and efficiency gains, especially with a sparse contingency table or dependent raking factors. We apply the new method to the longitudinal study of well-being study and demonstrate that model-based approaches significantly improve inferential reliability and substantive findings as a unified survey inference framework.

Hamilton–Jacobi analysis of the Freidel–Starodubtsev BF (A)dS gravity action

In this work, we perform the Hamilton–Jacobi analysis of a modified gravity action, the so-called Freidel–Starodubtsev model. The complete set of involutive Hamiltonians that guarantee the system’s integrability is obtained. The generalized Poisson brackets are calculated in the metric phase by means of a suitable constraint matrix inversion. We also present a discussion about the metric and non-metric degrees of freedom. From the fundamental differential we recover the equations of motion and explicitly obtain the generators of local Lorentz transformations and also diffeomorphisms for the tetrad and the spin connection fields.

Optimization Methods of Compressively Sensed Image Reconstruction Based on Single-Pixel Imaging

According to the theory of compressive sensing, a single-pixel imaging system was built in our laboratory, and imaging scenes are successfully reconstructed by single-pixel imaging, but the quality of reconstructed images in traditional methods cannot meet the demands of further engineering applications. In order to improve the imaging accuracy of our single-pixel camera, some optimization methods of key technologies in compressive sensing are proposed in this paper. First, in terms of sparse signal decomposition, based on traditional discrete wavelet transform and the characteristics of coefficients distribution in wavelet domain, a constraint condition of the exponential decay is proposed and a corresponding constraint matrix is designed to optimize the original wavelet decomposition basis. Second, for the construction of deterministic binary sensing matrices in the single-pixel camera, on the basis of a Gram matrix, a new algorithm model and a new method of initializing a compressed sensing measurement matrix are proposed to optimize the traditional binary sensing matrices via mutual coherence minimization. The gradient projection-based algorithm is used to solve the new mathematical model and train deterministic binary sensing measurement matrices with better performance. Third, the proposed optimization methods are applied to our single-pixel imaging system for optimizing the existing imaging methods. Compared with the conventional methods of single-pixel imaging, the accuracy of image reconstruction and the quality of single-pixel imaging have been significantly improved by our methods. The superior performance of our proposed methods has been fully tested and the effectiveness has also been demonstrated by numerical simulation experiments and practical imaging experiments.

Fibroblast rejuvenation by mechanical reprogramming and redifferentiation

Over the course of the aging process, fibroblasts lose contractility, leading to reduced connective-tissue stiffness. A promising therapeutic avenue for functional rejuvenation of connective tissue is reprogrammed fibroblast replacement, although major hurdles still remain. Toward this, we recently demonstrated that the laterally confined growth of fibroblasts on micropatterned substrates induces stem-cell-like spheroids. In this study, we embedded these partially reprogrammed spheroids in collagen-I matrices of varying densities, mimicking different three-dimensional (3D) tissue constraints. In response to such matrix constraints, these spheroids regained their fibroblastic properties and sprouted to form 3D connective-tissue networks. Interestingly, we found that these differentiated fibroblasts exhibit reduced DNA damage, enhanced cytoskeletal gene expression, and actomyosin contractility. In addition, the rejuvenated fibroblasts show increased matrix protein (fibronectin and laminin) deposition and collagen remodeling compared to the parental fibroblast tissue network. Furthermore, we show that the partially reprogrammed cells have comparatively open chromatin compaction states and may be more poised to redifferentiate into contractile fibroblasts in 3D-collagen matrix. Collectively, our results highlight efficient fibroblast rejuvenation through laterally confined reprogramming, which has important implications in regenerative medicine.