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A new method of obtaining a sequence of isolated complex Hadamard matrices (CHM) for dimensions N ⩾ 7, based on block-circulant structures, is presented. We discuss several analytic examples resulting from a modification of the Sinkhorn algorithm. In particular, we present new isolated matrices of orders 9, 10, and 11, which elements are not roots of unity, and also several new multiparametric families of order 10. We note novel connections between certain eight-dimensional matrices and provide new insights toward the classification of CHM for N ⩾ 7. These contributions can find real applications in quantum information theory and constructions of new families of mutually unbiased bases or unitary error bases. [ABSTRACT FROM AUTHOR]

Copyright of Journal of South China University of Technology (Natural Science Edition) is the property of South China University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we present a learning-based approach to speech compressive subsampling. Prior work in the field has mainly used random or deterministic matrices, which are unaffected by the structure and nature of the signal to be sampled. As a result, recovery algorithms require more computational and power resources to recover the original signal from a small number of samples. The framework presented in this paper aims to propose an efficient methodology for optimised speech sensing matrix design using standard speech datasets via offline training. The effectiveness of the suggested method is assessed using the signal-to-noise ratio that is obtained after reconstructing the original speech signal from samples supplied by the developed matrix. The baseline sensing matrices chosen for this work are widely used random and deterministic matrices, including the Gaussian random matrix, the Bernoulli random matrix, the Toeplitz matrix, and the Hadamard matrix. Convex relaxation and linear reconstruction algorithms were used to perform the signal reconstruction, and the key performance indicators for the relevant sensing matrix are chosen to be reconstruction accuracy and speed. In this work, we observe almost 4% on average improvement in reconstruction accuracy when the proposed method is compared with one of the efficient sensing matrices. [ABSTRACT FROM AUTHOR]

The μ -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 ∘ B) Δ (t) and ((A ∘ B) T Δ (t) + Δ (t) (A ∘ B)) . [ABSTRACT FROM AUTHOR]

We introduce a Generalized LU Factorization (GLU) for low-rank matrix approximation. We relate this to past approaches and extensively analyze its approximation properties. The established deterministic guarantees are combined with sketching ensembles satisfying Johnson--Lindenstrauss properties to present complete bounds. Particularly good performance is shown for the subsampled randomized Hadamard transform (SRHT) ensemble. Moreover, the factorization is shown to unify and generalize many past algorithms, sometimes providing strictly better approximations. It also helps to explain the effect of sketching on the growth factor during Gaussian elimination. [ABSTRACT FROM AUTHOR]

The error-correcting output codes(ECOC) is the ensemble method for the multi-class classification problem. In some applications of ECOC, Hadamard matrices are used because they have good properties to apply ECOC. However, due to the difficulties of the construction of Hadamard matrices of some specific orders, only Hadamard matrices of order a power of 2 constructed by Kronecker product were usually used. In this paper, we consider Hadamard matrices of various orders to the Hadamard ECOC to determine which orders of Hadamard matrices give a good performance compared to the number of classes. We apply the Hadamard ECOC to the image datasets including CIFAR-10, CIFAR-100, subsets of CIFAR-100, and EMNIST-Letters. We also compare the result of the Hybrid Hadamard ECOC with the Hadamard ECOC. For our experiment, a convolutional neural network(CNN) is chosen as a base learner, which is largely used in the image classification problems. [ABSTRACT FROM AUTHOR]

A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application (Solé et al. 2021). In this paper we introduce the analogous notion for complex Hadamard matrices, and we study the self-dual class in length at most 90. We use three competing methods of generation: Brute force, Linear Algebra and Groebner bases. Regular complex Hadamard matrices and Bush-type complex Hadamard matrices provide many examples. We introduce the strong automorphism group of complex Hadamard matrices, which acts on their associated self-dual bent sequences. We give an efficient algorithm to compute that group. We also answer the question which complex Hadamard matrices can be uniquely reconstructed from the off-diagonal elements, define a related concept of mixed-skew Hadamard matrix, and show the existence of mixed-skew Hadamard matrices of small orders. [ABSTRACT FROM AUTHOR]

The generalized resolution was introduced and justified as a criterion for selecting nonregular factorial designs. Although there has been extensive research conducted on other aspects of nonregular designs, few works have investigated the construction of nonregular designs with maximum generalized resolutions, as we do in this study. To date, our knowledge of nonregular designs with maximum generalized resolutions is predominantly computational, except for very few theoretical results. We derive lower bounds on relevant J-characteristics and present the construction results. With the assistance of the lower bounds, many of the constructed designs are shown to have maximum generalized resolutions. [ABSTRACT FROM AUTHOR]

In recent years, it has been evident that internet is the most effective means of transmitting information in the form of documents, photographs, or videos around the world. The purpose of an image compression method is to encode a picture with fewer bits while retaining the decompressed image's visual quality. During transmission, this massive data necessitates a lot of channel space. In order to overcome this problem, an effective visual compression approach is required to resize this large amount of data. This work is based on lossy image compression and is offered for static color images. The quantization procedure determines the compressed data quality characteristics. The images are converted from RGB to International Commission on Illumination CIE La*b*; and YCbCr color spaces before being used. In the transform domain, the color planes are encoded using the proposed quantization matrix. To improve the efficiency and quality of the compressed image, the standard quantization matrix is updated with the respective image block. We used seven discrete orthogonal transforms, including five variations of the Complex Hadamard Transform, Discrete Fourier Transform and Discrete Cosine Transform, as well as thresholding, quantization, de-quantization and inverse discrete orthogonal transforms with CIE La*b*; and YCbCr to RGB conversion. Peak to signal noise ratio, signal to noise ratio, picture similarity index and compression ratio are all used to assess the quality of compressed images. With the relevant transforms, the image size and bits per pixel are also explored. Using the (n, n) block of transform, adaptive scanning is used to acquire the best feasible compression ratio. Because of these characteristics, multimedia systems and services have a wide range of possible applications. [ABSTRACT FROM AUTHOR]

This paper contains the idea of inserting a watermark with the variance of color components of the image. The color image is converted into CIE color space. Chromatic components are transformed into a sequency domain by applying the complex Hadamard transform. The variance of the spatio-chromatic coefficients is calculated and the watermark is selected from the transformed image based on the variance by setting the threshold value. The watermark is only inserted in image blocks that have a smaller value of variance than the threshold value. Simulation results are presented and discussed using the two variants of complex Hadamard transform and discrete cosine transform. [ABSTRACT FROM AUTHOR]

A function ... with ... is called the Hadamard composition of the genus m ≥ 1 of functions ... where ... is a homogeneous polynomial of degree m ≥ 1. Let ... and functions α, β be positive continuous and increasing to +∞ on [x0,+∞). To characterize the growth of the function M(σ, F), we use generalized ... generalized type ... and membership in the converZgence class defined by the condition... Assuming the functions α, β and α-1(cβ(ln x)) are slowly increasing for each c ∈ (0,+∞) and ln n = O(λn) as n → ∞, it is proved, for example, that if the functions Fj have the same generalized order ϱα,β[Fj ] = ϱ ∈ (0,+∞) and the types Tα,β[Fj ] = Tj ∈ [0,+∞), cm0...0 = c ̸= 0, |an,1| > 0 and |an,j | = o(|an,1|) as n → ∞ for 2 ≤ j ≤ p, and F is the Hadamard composition of genus m ≥ 1 of the functions Fj then ϱα,β[F] = ϱ and ... It is proved also that F belongs to the generalized convergence class if and only if all functions Fj belong to the same convergence class. [ABSTRACT FROM AUTHOR]

A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application (Solé, et al., 2021). The authors study the self-dual class in length at most 196. The authors use three competing methods of generation: Exhaustion, Linear Algebra and Gröbner bases. Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples. The authors conjecture that if v is an even perfect square, a self-dual bent sequence of length v always exists. The authors introduce the strong automorphism group of Hadamard matrices, which acts on their associated self-dual bent sequences. The authors give an efficient algorithm to compute that group. [ABSTRACT FROM AUTHOR]

In this research a new approach is introduced for detecting and classifying faults in a Thyristor-Controlled Series Capacitor (TCSC) compensated power system. Our proposed scheme utilizes both the Fast Walsh Hadamard Transform (FWHT) and machine learning algorithms. The FWHT is employed to extract fault features from current data obtained from the TCSC compensated transmission line, while machine learning algorithms such as K-Nearest Neighbor (K-NN) and Support Vector Machine (SVM) are used to classify the extracted features for the purpose of fault detection and identification. To evaluate the performance of our proposed scheme, simulation studies were conducted on a test system under various fault conditions. The simulation results demonstrate that our approach is highly effective in accurately and quickly detecting and classifying faults, even when noise and TCSC compensation are present. This scheme has the potential to enhance the reliability and efficiency of power transmission systems. [ABSTRACT FROM AUTHOR]

In the multiple-response dynamic graph regression problem, given a n × d matrix embedding M of a graph G and a n × d ′ response matrix B , we want to update the solution of a r g m i n X | | M · X - B | | F 2 , after update operations in the graph. In this paper, we present new theoretical results for the update time of this problem. More precisely, we show that using an affine embedding defined as subsampled randomized Hadamard transform and after an edge insertion or an edge deletion, a 1 ± ϵ approximation to the optimal solution can be updated in O d ′ ϵ - 2 log 2 n time. Moreover, using an affine embedding defined as CountSketch and after a node insertion or a node deletion or an edge insertion or an edge deletion, an approximate solution can be updated in O d ′ ϵ - 2 log 6 ϵ - 1 time. To the best of our knowledge, these are the best theoretical results obtained for the update time of approximate multiple-response dynamic graph regression. [ABSTRACT FROM AUTHOR]

On an n-dimensional (n ≥ 2) compact connected manifold without boundary, we obtain the sharp range of p to ensure the Lp convergence of the wave operator. We are not able to show the optimum result at the end point ∣ 1 p − 1 2 ∣ = 1 n − 1 if n ≠ 3, but an interesting result for n = 3 is given. The main result is an extension of a result on n-dimensional Euclidean space ℝn. [ABSTRACT FROM AUTHOR]

This paper considers the orthogonal observation matrix design of deterministic compressive sampling (CS). An observation matrix called the weighted truncated Hadamard-modulated wideband converter (WITH-MWC) is deterministically designed based on the truncated Hadamard matrix. This matrix can meet the restricted isometry property (RIP) condition with overwhelming probability by randomly or strategically extracting from a standard Hadamard matrix. Most compressed sampling systems are highly sensitive to noise. To reduce the adverse effects of noise interference, partial specific matrix elements are weighted according to the sparse characteristics of multiband signals, and the recovery probability is provably better than that of the original system and other deterministic observation matrices, especially in the low signal-to-noise ratio scenario. Compared to the random Gaussian and random Bernoulli matrices, WITH-MWC is much easier to implement in hardware. The simulations verify the above analysis. [ABSTRACT FROM AUTHOR]

In 2013, Nebe and Villar gave a series of ternary self-dual codes of length 2 (p + 1) for a prime p congruent to 5 modulo 8. As a consequence, the third ternary extremal self-dual code of length 60 was found. We show that these ternary self-dual codes contain codewords which form a Hadamard matrix of order 2 (p + 1) when p is congruent to 5 modulo 24. In addition, we show that the ternary self-dual codes found by Nebe and Villar are generated by the rows of the Hadamard matrices. We also demonstrate that the third ternary extremal self-dual code of length 60 contains at least two inequivalent Hadamard matrices. [ABSTRACT FROM AUTHOR]

Embedding the watermark is still a challenge in image watermarking. The watermark should not reduce the visual quality of the image being watermarked and hard to distinguish from its original. Embedding a watermark of a small size might be a good solution. However, the watermark might be easy to lose if there is any tampering with the watermarked image. This research proposes to increase the visual quality of the watermarked image using the Walsh Hadamard transform, which is applied to the singular value decomposition-based image watermarking. Technically, the watermark image is converted into a low bit-rate signal before being embedded in the host image. Using various watermark sizes, experimental results show that the proposed method could produce a good imperceptibility with 47.10 dB on average and also gives robustness close to the original watermark with a normalized correlation close to 1 on average. The proposed method can also recognize the original watermark from the tampered watermarked image at different levels of robustness. [ABSTRACT FROM AUTHOR]

The purpose of this study is to give some findings on the existence, uniqueness, and Hyers-Ulam stability of the solution of an implicit coupled system of impulsive fractional differential equations possessing a fractional derivative of the Hadamard type. The existence and uniqueness findings are obtained using a fixed point theorem of the type of Kransnoselskii. In keeping with this, many forms of Hyers-Ulam stability are examined. Ultimately, to support main results, an example is provided. [ABSTRACT FROM AUTHOR]

As an interesting generalization involving the interval-valued convex functions, the interval-valued exponential trigonometric convex function is firstly introduced, and their meaningful properties are then investigated. Meanwhile, certain Hermite-Hadamard- and Pachpattetype integral inclusion relations are also developed via the newly proposed functions in intervalvalued fractional calculus. In particular, an improved version of the Hermite-Hadamard's integral inclusions pertaining to the interval-valued exponential trigonometric convex functions is proposed as well. To identify the correctness of the derived inclusion relations in the study, the graphical representations for the outcomes are provided in terms of the change of the parameter α. [ABSTRACT FROM AUTHOR]

Balanced Incomplete Block Designs (BIBD) are the designs obtained from the arrangement of symbols in blocks following established rules and satisfying relevant necessary conditions. BIBDs have broad applications in many fields.The entries in a Hadamard matrix H are all +1’s or -1’s, satisfying the property HHT = n In [2]. Rhotrix is a new concept in mathematics having applications in cryptography. In this paper, using SBIB designs the Hadamard Rhotrices are constructed. AMS Subject classification: 05B05, 05B20, 62K10.

Single-pixel cameras offer improved performance in non-visible imaging compared with modern digital cameras which capture images with an array of detector pixels. However, the quality of the images reconstructed by single-pixel imaging technology fails to match traditional cameras. Since it requires a sequence of measurements to retrieve a single image, the temporal fluctuation of illumination intensity during the measuring will cause inconsistence for consecutive measurements and thus noise in reconstructed images. In this paper, a normalization protocol utilizing the differential measurements in single-pixel imaging is proposed to reduce such inconsistence with no additional hardware required. Numerical and practical experiments are performed to investigate the influences of temporal fluctuation of different degrees on image quality and to demonstrate the feasibility of the proposed normalization protocol. Experimental results show that our normalization protocol can match the performance of the system with the reference arm. The proposed normalization protocol is straightforward with the potential to be easily applied in any temporal-sequence imaging strategy. [ABSTRACT FROM AUTHOR]

We obtain a large number of degree and distance-based topological indices, graph and Laplacian spectra and the corresponding polynomials, entropies and matching polynomials of n-dimensional hypercubes through the use of Hadamard symmetry and recursive dynamic computational techniques. Moreover, computations are used to provide independent numerical values for the topological indices of the 11- and 12-cubes. We invoke symmetry-based recursive Hadamard transforms to obtain the graph and Laplacian spectra of nD-hypercubes and the computed numerical results are constructed for up to 23-dimensional hypercubes. The symmetries of these hypercubes constitute the hyperoctahedral wreath product groups which also pave the way for the symmetry-based elegant computations. These results are used to independently validate the exact analytical expressions that we have obtained for the topological indices as well as graph, Laplacian spectra and their polynomials. We invoke a robust dynamic programming technique to handle the computationally intensive generation of matching polynomials of hypercubes and compute all matching polynomials up to the 6-cube. The distance degree sequence vectors have been obtained numerically for up to 108-dimensional cubes and their frequencies are found to be in binomial distributions akin to the spectra of n-cubes. [ABSTRACT FROM AUTHOR]

In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the matrices in logarithmic form, which is comparable to the morphism given in a recent note of Ó Catháin and Swartz. That is, we show how, if given a Butson Hadamard matrix over the k th roots of unity, we can construct a larger Butson matrix over the ℓ th roots of unity for any ℓ dividing k, provided that any prime p dividing k also divides ℓ . We prove that a Z p s -additive code with p a prime number is isomorphic as a group to a BH-code over Z p s and the image of this BH-code under the Gray map is a BH-code over Z p (binary Hadamard code for p = 2 ). Further, we investigate the inherent propelinear structure of these codes (and their images) when the Butson matrix is cocyclic. Some structural properties of these codes are studied and examples are provided. [ABSTRACT FROM AUTHOR]

In this paper, a new hybrid methodology that combines precoding transform and companding transforms is being proposed for next-generation heterogeneous wireless networks. This method will improve the performance of the orthogonal frequency division multiplexing (OFDM) system by reducing the Peak to average power ratio (PAPR). A hybrid methodology that combines exponential companding (EC), which is a non-linear companding technique with Discrete Hartley Transform (DHT), as well as Walsh Hadamard Transform (WHT), is proposed and investigated. When the three simulated results are compared with original OFDM signal, piecewise linear companding shows an improvement factor of 28.8% over the original OFDM signal. Exponential companding is having an improvement factor of 33.49% over the original OFDM signal. Walsh Hadamard transform combined with exponential companding shows an improvement factor of 34.99% over OFDM. Discrete Hartley Transform combined with Exponential Companding is having an improvement factor of 38.09% over OFDM. The two proposed methods do not introduce any In-band distortion as well as Out-of-band Radiation when compared to the existing technique PLC (Meixia et al. in IEEE Trans Broadcast 60(3):532-539, 2014) which can be observed from the PSD analysis. Among the two proposed methods, the DHT precoded OFDM with the EC system shows significant BER improvement over the remaining methods. In addition to AWGN Channel, this proposed method shows significant BER performance improvement under the SUI-1 to 6 (WiMAX Channels) channels making use of 256-QAM as the modulation technique. As we move to a higher-order constellation, it is possible to transmit more bits per symbol; in such cases, the proposed technique will achieve better improvement in the performance of BER over all the existing techniques. [ABSTRACT FROM AUTHOR]

In this paper, a novel fractional-order no-equilibrium chaotic system with hidden attractor is presented. The dynamical characteristics of the fractional-order system are analyzed by the phase diagram, Lyapunov exponents, bifurcation diagram, complexity, and attractor basin. Based on the above analysis, an image encryption scheme performs discrete cosine transform on the R, G, and B channels of the original color image to get the corresponding sparse coefficient matrices. Then, the measurement matrix generated by the Hadamard matrix and the chaotic pseudo-random sequence is used to compress and perceive the sparse coefficient matrices. In addition, the row and column scrambling and GF (257) domain diffusion algorithm are performed on the compressed pixel matrix to obtain the final cipher image. Experimental results and performance analysis display that the scheme has high compressibility and security. Even if the compression rate is 0.25, the calculated PSNR values are around 30. In addition, the χ2-value of the encrypted Lena image is 248.2824, and the algorithm has passed the UACI and NPCR tests and can resist differential attacks. Therefore, the proposed algorithm is effectively. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the explicit solution of a class of singular impulsive fractional differential equation of order α ∈ (n − 1 , n) involving the Hadamard fractional derivatives. In particular, the result is given in the form of necessary and sufficient conditions about the explicit solution. The proof of the main theorem is obtained by converting boundary value problems into integral equations and applying analytical techniques. Finally, some examples explain the application of the main theorem in this paper. [ABSTRACT FROM AUTHOR]

We provide conditions that guarantee local rates of convergence in distribution of iterated random functions that are not nonexpansive mappings in locally compact Hadamard spaces. Our results are applied to stochastic instances of common algorithms in optimization, stochastic tomography for X-FEL imaging and a stochastic algorithm for the computation of Fréchet means in model spaces for phylogenetic trees. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we study the classes of approximate Minty and Stampacchia type vector variational inequalities along with their local and weak versions on a Hadamard manifold, and a class of nonsmooth interval-valued multiobjective optimization problems, respectively. We obtain the equivalence between the solutions of considered approximate vector variational inequalities and LU-efficient solutions of nonsmooth interval-valued multiobjective optimization problems in which the cost function is assumed to be geodesic approximately LU-convex or geodesic LU-α-convex. [ABSTRACT FROM AUTHOR]

We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that these are actually special cases of some more general identity (or class of identities) connecting permanents and determinants. The proof combines some basic facts from the theory of symmetric functions with an application of a famous theorem of Binet and Cauchy in linear algebra. [ABSTRACT FROM AUTHOR]

Regular two-level designs are useful and popular screening designs, but if they need to be run in blocks, their projection properties can dramatically deteriorate. Interactions may be fully confounded with block defining contrast(s), causing uncertainty in the identification of active factors. In this paper, we demonstrate alternative ways of blocking two-level regular designs such that their projective properties can be preserved or just weakly affected at the expense of just a small decrease in efficiency. Thereby, we can estimate effects we are normally interested in even if the design is blocked. Common regular two-level designs with 16, 32 and 64 runs are considered. • Projection properties may be preserved when regular two-level designs are blocked. • Several blocking strategies can be used depending on the design's alias structure. • The blocked designs also have good estimation capacities. [ABSTRACT FROM AUTHOR]

We give explicit constructions of square (1 , − 1) -matrices of order congruent to 2 modulo 4 with large determinants. In particular, we construct nine families of near-Hadamard matrices based on almost supplementary difference sets with two blocks, and compute their determinants. As consequences, we obtain many (1 , − 1) -matrices which are almost D -optimal or have at least 80% D -efficiency. [ABSTRACT FROM AUTHOR]

Hashing plays an important role in information retrieval, due to its low storage and high speed of processing. As an effective multi-modal representation learning method, multi-modal hashing has received particular attention. Most of the existing multi-modal hashing methods adopt the fixed weighting factors to fuse multiple modalities for any query data, which cannot capture the variation among different queries. Besides, there are too much hyper-parameters in their models while it is time-consuming and labor-intensive to determine the proper parameters. The limitations may significantly hinder their promotion in practical applications. In this paper, we propose a simple, yet effective method that is inspired by the Hadamard matrix. On the one hand, our proposed method that involves a very few hyper-parameters is flexible. On the other hand, the complementary information between multi-modal data and the semantic discrimination information are preserved well in the hash codes. Extensive experimental results on four benchmark datasets show that the proposed framework is effective and achieves superior performance compared to state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Independent human living systems require smart, intelligent, and sustainable online monitoring so that an individual can be assisted timely. Apart from ambient assisted living, the task of monitoring human activities plays an important role in different fields including virtual reality, surveillance security, and human interaction with robots. Such systems have been developed in the past with the use of various wearable inertial sensors and depth cameras to capture the human actions. In this paper, we propose multiple methods such as random occupancy pattern, spatio temporal cloud, waypoint trajectory, Hilbert transform, Walsh Hadamard transform and bone pair descriptors to extract optimal features corresponding to different human actions. These features sets are then normalized using min-max normalization and optimized using the Fuzzy optimization method. Finally, the Masi entropy classifier is applied for action recognition and classification. Experiments have been performed on three challenging datasets, namely, UTDMHAD, 50 Salad, and CMU-MMAC. During experimental evaluation, the proposed novel approach of recognizing human actions has achieved an accuracy rate of 90.1% with UTD-MHAD dataset, 90.6% with 50 Salad dataset, and 89.5% with CMU-MMAC dataset. Hence experimental results validated the proposed system. [ABSTRACT FROM AUTHOR]

In this work using k -fractional Caputo derivatives we obtain some versions of the Hadamard inequality for the function f such that f(n) is (h,m)-convex modified of the second type. Throughout the work, we show that some known results from the literature can be obtained as particular cases of the results presented here. [ABSTRACT FROM AUTHOR]

• The spectral symmetry of sea clutter is validated in numerous measured data. • A specific matrix structure constraint is proposed based on the spectral symmetry. • Alternating optimization is adopted to solve the constrained ML estimation. Speckle covariance matrix estimation plays an important role in adaptive target detection of maritime radars. Spatial heterogeneity of sea clutter incurs insufficient secondary data in estimation, which degrades detection performance. It is an effective way of estimation improvement to exploit the Doppler spectrum knowledge of sea clutter for structural dimension reduction of the speckle covariance matrix. This paper proposes a speckle covariance matrix estimation method based on the spectral symmetry knowledge of sea clutter, indicating that the spectrum of sea clutter is symmetric with respect to the Doppler offset. First of all, the spectral symmetry of sea clutter is analyzed by using the measured data from several opened databases and the results show that most of the data excluding sea spikes have symmetric Doppler spectra. Secondly, the spectral symmetry constrains the speckle covariance matrix into the Hadamard product of a special rank-one Toeplitz matrix and a real positive definite symmetric matrix. The degrees of freedom are reduced to almost half of that of a Hermitian matrix and thus fewer secondary data are required. Thirdly, a robust iterative maximum likelihood estimator is proposed to estimate the speckle covariance matrix with structural constraint and is free of the clutter texture distribution. The performance of the estimator is verified by the measured data and the results show that it is superior to traditional estimators, particularly in fewer secondary data. [ABSTRACT FROM AUTHOR]

A complete complementary code (CCC) consists of M sequence sets with size M. The sum of the auto-correlation functions of each sequence set is an impulse function, and the sum of cross-correlation functions of the different sequence sets is equal to zero. Thanks to their excellent correlation, CCCs received extensive use in engineering. In addition, they are strongly connected to orthogonal matrices. In some application scenarios, additional requirements are made for CCCs, such as recently proposed for concatenative CCC (CCCC) division multiple access (CCC-CDMA) technologies. In fact, CCCCs are a special kind of CCCs which requires that each sequence set in CCC be concatenated to form a zero-correlation-zone (ZCZ) sequence set. However, this requirement is challenging, and the literature is thin since there is only one construction in this context. We propose to go beyond the literature through this contribution to reduce the gap between their interest and our limited knowledge of CCCCs. This paper will employ novel methods for designing CCCCs and precisely derive two constructions of these objects. The first is based on perfect cross Z-complementary pair and Hadamard matrices, and the second relies on extended Boolean functions. Specifically, we highlight that optimal and asymptotic optimal CCCCs could be obtained through the proposed constructions. Besides, we shall present a comparison analysis with former structures in the literature and examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

• Hybrid transforms are integrated in computational ghost imaging to simplify image reconstruction. • In experiments, hybridizations of Hadamard, discrete cosine, and Haar transform matrices are exploited. • With hybrid transforms, computational ghost imaging makes image encoding and image compression conveniently. • Computational ghost imaging with hybrid transforms may find flexible applications in image processing. A scenario of ghost imaging with hybrid transform approach is proposed by integrating Hadamard, discrete cosine, and Haar matrices. The measurement matrix is formed by the Kronecker product of the two different transform matrices. The image information can be conveniently reconstructed with the corresponding inverse matrices. In experiment, six sets of transform hybridizations are performed in computational ghost imaging. For an object of staggered stripes, only one bucket signal survives in the Hadamard-cosine, Haar-Hadamard, and Haar-cosine hybridization sets, showing flexible image compression. For a handmade windmill object, the quality factors of the reconstructed images vary with the hybridization sets. Sub-Nyquist sampling can be applied to either or both of the different transform matrices in each hybridization set in experiment. The hybridization method can be extended to apply more transforms in one experiment. Ghost imaging with hybrid transforms may find flexible applications in image processing, such as image compression and image encryption. [ABSTRACT FROM AUTHOR]

The fifth-generation wireless telecommunication technology (5G) with high speed, wide coverage and large amount of data have posed new requirements for the running time, security, and watermark capacity of digital watermark algorithms. For realizing the copyright protection of color image in 5G environment, a spatial digital watermarking scheme for dual color image fusing Hadamard transform is proposed in this paper. In this scheme, the protected color cover image is firstly channeled and then divided into 4 × 4 non-overlapping image blocks. Then, the maximum energy coefficient of image block in the Hadamard domain is acquired directly in the spatial domain, and the watermark information is hidden by quantizing this coefficient. Finally, the changed quantization variation of the special coefficient are evenly distributed to each coefficient of the original spatial image block, so as to realize the complete process of hiding the watermark. In the extraction stage, only the special coefficient of the watermarked image in the Hadamard domain is obtained in the spatial domain, and the coefficient threshold is analyzed to determine the coding of watermark information. This scheme combines the characteristics of spatial domain algorithm and frequency domain algorithm, and designs a set of high security encryption method, at the same time, considers the human vision system to color sensitivity and the correlation of color image channel. Compared with other schemes, it can be found that this scheme has excellent security and real-time performance, strong robustness to common attacks, and high image quality. [ABSTRACT FROM AUTHOR]

In the classical probability model, let f (n) be the maximum number of pairwise independent events for the sample space with n sample points. The determination of f (n) is equivalent to the problem of determining the maximum cardinality of specific intersecting families on the set { 1 , 2 , ... , n }. We show that f (n) ≤ n + 1 , and f (n) = n + 1 if there exists a Hadamard matrix of order n. [ABSTRACT FROM AUTHOR]

Frame memory compression (FMC) saves power by reducing the data bandwidth for accessing reference frames of video coding standards in the external memory. However, since the continuously accumulated data loss degrades the performance of video coding standards, the quality of the reconstructed reference frame must be improved. Previous lossy frame memory compression methods focused on processing speed or simplicity, but their performance remains limited in terms of the quality of the reconstructed frame. In this study, a Huffman coding with a fixed codebook designed to considerably reduce the latency caused by arithmetic coding in lossless compression schemes is proposed. A novel lossy frame memory compression technique based on the Hadamard transform that does not require additional memory access using a lookup table is also proposed. The result of experiments on several reconstructed videos preprocessed with HEVC show that the proposed method improves BDPSNR by 10.7 dB and BDBR by 40.4% compared with the DWT+SPIHT‐based compression technique which is widely used for lossy frame memory compression. [ABSTRACT FROM AUTHOR]

In this article, a wavelet method is introduced for solving Caputo–Hadamard fractional differential equations on an arbitrary interval. The proposed method is the fractional‐order generalization of sine–cosine wavelets (FGSCWs). The operational matrices of fractional‐order integration are constructed for solving initial value problem as well as boundary value problem. Furthermore, numerical solution of nonlinear Caputo–Hadamard fractional differential equation is obtained with the conjunction of proposed method with quasilinearization technique. We have constructed the FGSCW operational matrix, FGSCW operational matrix of Hadamard fractional integration of arbitrary order, and FGSCW operational matrix of Hadamard fractional integration for Caputo–Hadamard fractional boundary value problems. Convergence analysis of the proposed method is investigated. Numerical procedure is given for both Caputo–Hadamard initial and boundary value problems. Illustrative examples show the reliability and efficiency of the proposed method and give solution with less error. [ABSTRACT FROM AUTHOR]

A novel permuted fast successive-cancellation list decoding algorithm with fast Hadamard transform (FHT-FSCL) is presented. The proposed decoder initializes $L$ $(L\geq 1)$ active decoding paths with $L$ random codeword permutations sampled from the full symmetry group of the codes. The path extension in the permutation domain is carried out until the first constituent RM code of order 1 is visited. Conventional path extension of the successive-cancellation list decoder is then utilized in the information bit domain. The simulation results show that for a RM code of length 512 with 46 information bits, by running 20 parallel permuted FHT-FSCL decoders with $L=4$ , we reduce 72% of the computational complexity, 22% of the decoding latency, and 84% of the memory consumption of the state-of-the-art simplified successive-cancellation decoder that uses 512 permutations sampled from the full symmetry group of the code, with similar error-correction performance at the target frame error rate of $10^{-4}$. [ABSTRACT FROM AUTHOR]

A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes based on successive permutations (SP) of the codeword is presented. A low-complexity SP scheme applied to a subset of the symmetry group of RM codes is first proposed to carefully select a good codeword permutation on the fly. Then, the proposed SP technique is integrated into an improved RLD algorithm that initializes different decoding paths with random codeword permutations, which are sampled from the full symmetry group of RM codes. Finally, efficient latency and complexity reduction schemes are introduced that virtually preserve the error-correction performance of the proposed decoder. Simulation results demonstrate that at the target frame error rate of 10−3 for the RM code of length 256 with 163 information bits, the proposed decoder reduces 6% of the computational complexity and 22% of the decoding latency of the state-of-the-art semi-parallel simplified successive-cancellation decoder with fast Hadamard transform (SSC-FHT) that uses 96 permutations from the full symmetry group of RM codes, while relatively maintaining the error-correction performance and memory consumption of the semi-parallel permuted SSC-FHT decoder. [ABSTRACT FROM AUTHOR]

Chaudhry et al. proposed perfect secret sharing schemes from combinatorial squares called Room squares based on certain balanced incomplete block designs. Their protocol is efficient and secure but it is based on a Room square of order r which exists if and only if r is odd and r ≠ 3, 5. Here, we have proposed the schemes from Room squares based on group divisible designs which are a broader class of designs. [ABSTRACT FROM AUTHOR]

It is proved that a code L(q) which is monomially equivalent to the Pless symmetry code C(q) of length 2 q + 2 contains the (0,1)-incidence matrix of a Hadamard 3- (2 q + 2 , q + 1 , (q - 1) / 2) design D(q) associated with a Paley–Hadamard matrix of type II. Similarly, any ternary extended quadratic residue code contains the incidence matrix of a Hadamard 3-design associated with a Paley–Hadamard matrix of type I. If q = 5 , 11 , 17 , 23 , then the full permutation automorphism group of L(q) coincides with the full automorphism group of D(q), and a similar result holds for the ternary extended quadratic residue codes of lengths 24 and 48. All Hadamard matrices of order 36 formed by codewords of the Pless symmetry code C(17) are enumerated and classified up to equivalence. There are two equivalence classes of such matrices: the Paley–Hadamard matrix H of type I with a full automorphism group of order 19584, and a second regular Hadamard matrix H ′ such that the symmetric 2-(36, 15, 6) design D associated with H ′ has trivial full automorphism group, and the incidence matrix of D spans a ternary code equivalent to C(17). [ABSTRACT FROM AUTHOR]

In this paper, we define refined (a, h-m)-convex function with respect to a strictly monotone function. This function provides refinements of various well-known classes of functions for specific strictly monotone functions. By applying definition of this new function we prove the Hadamard inequalities for Riemann-Liouville fractional integrals. These inequalities give the refinements of fractional Hadamard inequalities for convex, (a,m)-convex, (h - m)-convex, (s,m)-convex, h-convex and many other related well-known classes of functions implicitly. Also, Hadamard type inequalities for k-fractional integrals are given. [ABSTRACT FROM AUTHOR]