Search Results (40)

Secure compressive sensing (SCS) mostly benefits scenes such as IoT with finite computer resources, the fields of spaceflight and medicine, etc. Recently, research on SCS has aroused widespread interest. Nevertheless, existing work on embedding security of CS usually requires an extra cryptographic routine applied to the measurement vectors. In this paper, we proposed an SCS scheme boosted by the hyper-chaotic system, which outperforms state-of-the-art methods and endows the SCS with a high level of inherent security. Encryption and sampling processing are accomplished simultaneously in our scheme, i.e., security is achieved when sampling with a measurement matrix, which is generated by an initial-value (secret key)-driven discrete hyper-chaotic (HC) system. Moreover, the application of the HC matrix decreases both the computing and bandwidth consumption costs of secret key streams transmission compared with traditional CS-based encryption methods. Experimentally, the HC-based matrix demonstrates excellent reconstruction performance, achieving an average SSIM of 0.91 and PSNR of 29.09 dB on the Set5 dataset at a sampling ratio of 0.5, outperforming conventional matrices such as Bernoulli and Hadamard. Security analysis confirms that the system exhibits asymptotic spherical secrecy and high key sensitivity—a deviation of ${10}^{-16}$ in the initial value results in complete decryption failure. Furthermore, the scheme shows strong robustness against additive Gaussian white noise and cropping attacks, maintaining a PSNR above 15 dB even under 50% cropping. Compared to existing methods, the proposed approach reduces bandwidth consumption by transmitting only the HC initial parameters rather than the entire measurement matrix. These results demonstrate that the HC-driven SCS framework provides inherent security, high reconstruction fidelity, and practical efficiency, making it suitable for secure sensing in constrained environments. Full article

The primary objective of robust parameter design (RPD) is to determine the optimal settings of control factors in a system to minimize response variance while achieving a desirable mean response. This article investigates fractional factorial designs constructed from Hadamard matrices of orders 12, 16, and 20 to meet RPD requirements with minimal runs. For various combinations of control and noise factors, rather than recommending a single “best” design, up to the top ten good candidate designs are identified. All listed designs permit the estimation of all control-by-noise interactions and the main effects of both control and noise factors. Additionally, some nonregular RPDs allow for the estimation of one or two control-by-control interactions, which may be critical for achieving optimal mean response. These results provide practical options for efficient, resource-constrained experiments with economical run sizes. Full article

In this paper, we show that even-order Pascal tensors are positive-definite, and odd-order Pascal tensors are strongly completely positive. The significance of these is that our induction proof method also holds for some other families of completely positive tensors, whose construction satisfies certain rules, such that the inherence property holds. We show that for all tensors in such a family, even-order tensors would be positive-definite, and odd-order tensors would be strongly completely positive, as long as the matrices in this family are positive-definite. In particular, we show that even-order generalized Pascal tensors would be positive-definite, and odd-order generalized Pascal tensors would be strongly completely positive, as long as generalized Pascal matrices are positive-definite. We also investigate even-order positive-definiteness and odd-order strong complete positivity for fractional Hadamard power tensors. Furthermore, we study determinants of Pascal tensors. We prove that the determinant of the mth-order two-dimensional symmetric Pascal tensor is equal to the mth power of the factorial of $m-1$. Full article

By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models. Full article

Knowledge graph embedding (KGE) has been identified as an effective method for link prediction, which involves predicting missing relations or entities based on existing entities or relations. KGE is an important method for implementing knowledge representation and, as such, has been widely used in driving intelligent applications w.r.t. question-answering systems, recommendation systems, and relationship extraction. Models based on convolutional neural networks (CNNs) have achieved good results in link prediction. However, as the coverage areas of knowledge graphs expand, the increasing volume of information significantly limits the performance of these models. This article introduces a triple-attention-based multi-channel CNN model, named ConvAMC, for the KGE task. In the embedding representation module, entities and relations are embedded into a complex space and the embeddings are performed in an alternating pattern. This approach helps in capturing richer semantic information and enhances the expressive power of the model. In the encoding module, a multi-channel approach is employed to extract more comprehensive interaction features. A triple attention mechanism and max pooling layers are used to ensure that interactions between spatial dimensions and output tensors are captured during the subsequent tensor concatenation and reshaping process, which allows preserving local and detailed information. Finally, feature vectors are transformed into prediction targets for embedding through the Hadamard product of feature mapping and reshaping matrices. Extensive experiments were conducted to evaluate the performance of ConvAMC on three benchmark datasets compared with state-of-the-art (SOTA) models, demonstrating that the proposed model outperforms all compared models across all evaluation metrics on two of the datasets, and achieves advanced link prediction results on most evaluation metrics on the third dataset. Full article

In this paper, three discrete transforms related to vector spaces over finite fields are studied. For our purposes, and according to the properties of the finite fields, the most suitable transforms are as follows: for binary fields, this is the Walsh–Hadamard transform; for odd prime fields, the Vilenkin–Chrestenson transform; and for composite fields, the trace transform. A factorization of the transform matrices using Kronecker power is given so that the considered discrete transforms are reduced to the fast discrete transforms. Examples and applications are also presented of the considered transforms in coding theory for calculating the weight distribution of a linear code. Full article

Single-pixel imaging (SPI) is an alternative method for obtaining images using a single photodetector, which has numerous advantages over the traditional matrix-based approach. However, most experimental SPI realizations provide relatively low resolution compared to matrix-based imaging systems. Here, we show a simple yet effective experimental method to scale up the resolution of SPI. Our imaging system utilizes patterns based on Hadamard matrices, which, when reshaped to a variable aspect ratio, allow us to improve resolution along one of the axes, while sweeping of patterns improves resolution along the second axis. This work paves the way towards novel imaging systems that retain the advantages of SPI and obtain resolution comparable to matrix-based systems. Full article

Hypercomplex numbers, which are multi-dimensional extensions of complex numbers, have been proven beneficial in the development of advanced signal processing algorithms, including multi-dimensional filter design, linear regression and classification. We focus on multicomplex numbers, sets of hypercomplex numbers with commutative products, and introduce a vector representation allowing one to isolate the hyperbolic real and imaginary parts of a multicomplex number. The orthogonal decomposition of a multicomplex number is also discussed, and its connection with Hadamard matrices is highlighted. Finally, a multicomplex polar representation is provided. These properties are used to extend the standard complex baseband signal representation to the multi-dimensional case. It is shown that a set of $2^n$ Radio Frequency (RF) signals can be represented as the real part of a single multicomplex signal modulated by several frequencies. The signal RFs are related through a Hadamard matrix to the modulating frequencies adopted in the multicomplex baseband representation. Moreover, an orthogonal decomposition is provided for the obtained multicomplex baseband signal as a function of the complex baseband representations of the input RF signals. Full article

New possibilities of Gramian computation, by means of canonical transformations into diagonal, controllable, and observable canonical forms, are shown. Using such a technique, the Gramian matrices can be represented as products of the Hadamard matrices of multipliers and the matrices of the transformed right-hand sides of Lyapunov equations. It is shown that these multiplier matrices are invariant under various canonical transformations of linear continuous systems. The modal Lyapunov equations for continuous SISO LTI systems in diagonal form are obtained, and their new solutions based on Hadamard decomposition are proposed. New algorithms for the element-by-element computation of Gramian matrices for stable, continuous MIMO LTI systems are developed. New algorithms for the computation of controllability Gramians in the form of Xiao matrices are developed for continuous SISO LTI systems, given by the equations of state in the controllable and observable canonical forms. The application of transformations to the canonical forms of controllability and observability allowed us to simplify the formulas of the spectral decompositions of the Gramians. In this paper, new spectral expansions in the form of Hadamard products for solutions to the algebraic and differential Sylvester equations of MIMO LTI systems are obtained, including spectral expansions of the finite and infinite cross - Gramians of continuous MIMO LTI systems. Recommendations on the use of the obtained results are given. Full article

An important problem in quantum computation is the generation of single-qubit quantum gates such as Hadamard (H) and $\pi /8$ (T) gates, which are components of a universal set of gates. Qubits in experimental realizations of quantum computing devices are interacting with their environment. While the environment is often considered as an obstacle leading to a decrease in the gate fidelity, in some cases, it can be used as a resource. Here, we consider the problem of the optimal generation of H and T gates using coherent control and the environment as a resource acting on the qubit via incoherent control. For this problem, we studied the quantum control landscape, which represents the behavior of the infidelity as a functional of the controls. We considered three landscapes, with infidelities defined by steering between two, three (via Goerz–Reich–Koch approach), and four matrices in the qubit Hilbert space. We observed that, for the H gate, which is a Clifford gate, for all three infidelities, the distributions of minimal values obtained with a gradient search have a simple form with just one peak. However, for the T gate, which is a non-Clifford gate, the situation is surprisingly different—this distribution for the infidelity defined by two matrices also has one peak, whereas distributions for the infidelities defined by three and four matrices have two peaks, which might indicate the possible existence of two isolated minima in the control landscape. It is important that, among these three infidelities, only those defined with three and four matrices guarantee the closeness of the generated gate to a target and can be used as a good measure of closeness. We studied sets of optimized solutions for the most general and previously unexplored case of coherent and incoherent controls acting together and discovered that they form sub-manifolds in the control space, and unexpectedly, in some cases, two isolated sub-manifolds. Full article

The selection of a demand forecasting method is critical for companies aiming to avoid manufacturing overproduction or shortages in pursuit of sustainable development. Various qualitative and quantitative criteria with different weights must be considered during the evaluation of a forecasting method. The qualitative criteria and criteria weights are usually assessed in linguistic terms. Aggregating these various criteria and linguistic weights for evaluating and selecting demand forecasting methods in sustainable manufacturing is a major challenge. This paper proposes an extension of fuzzy elimination and choice translating reality (ELECTRE) I to resolve this problem. In the proposed method, fuzzy weighted ratings are defuzzified with the signed distance to develop a crisp ELECTRE I model. Moreover, an extension to ELECTRE I is developed by suggesting an extended modified discordance matrix and a closeness coefficient for ranking alternatives. The proposed extension can overcome the problem of information loss, which can lead to incorrect ranking results when using the Hadamard product to combine concordance and modified discordance matrices. A comparison is conducted to show the advantage of the proposed extension. Finally, a numerical example is used to demonstrate the feasibility of the proposed method. Furthermore, a numerical comparison is made to display the advantage of the proposed method. Full article

Green matrices are interpreted as discrete version of Green functions and are used when working with inhomogeneous linear system of differential equations. This paper discusses accurate algebraic computations using a recent procedure to achieve an important factorization of these matrices with high relative accuracy and using alternative accurate methods. An algorithm to compute any minor of a Green matrix with high relative accuracy is also presented. The bidiagonal decomposition of the Hadamard product of Green matrices is obtained. Illustrative numerical examples are included. Full article

This paper presents a novel approach by introducing a set of operators known as the left and right generalized tempered fractional integral operators. These operators are utilized to establish new Hermite–Hadamard inequalities for convex functions as well as the multiplication of two convex functions. Additionally, this paper gives two useful identities involving the generalized tempered fractional integral operator for differentiable functions. By leveraging these identities, our results consist of integral inequalities of the Hermite–Hadamard type, which are specifically designed to accommodate convex functions. Furthermore, this study encompasses the identification of several special cases and the recovery of specific known results through comprehensive research. Lastly, this paper offers a range of applications in areas such as matrices, modified Bessel functions and $\mathsf{q}$-digamma functions. Full article

In this paper, we prove some Banach fixed point theorems in generalized metric space where the contractive conditions are endowed with the Hadamard product of real symmetric positive definite matrices. Since the condition that a matrix A converges to zero is not needed, this produces stronger results than those of Perov. As an application of our results, we study the existence and uniqueness of the solution for a system of matrix equations. Full article

The $\mu$-value or structured singular value is a prominent mathematical tool to analyze and synthesize both the robustness and performance of time-invariant systems. We establish and analyze new results concerning structured singular values for the Hadamard product of real square M-matrices. The new results are obtained for structured singular values while considering a set of block diagonal uncertainties. The targeted uncertainties are of two types, that is, pure real scalar block uncertainties and real full-block uncertainties. The eigenvalue perturbation result is utilized in order to determine the behavior of the spectrum of perturbed matrices $(A\circ B)\Delta \left(t\right)$ and $({(A\circ B)}^T\Delta \left(t\right)+\Delta \left(t\right)(A\circ B))$. Full article