The SK model proposed by Sherrington and Kirkpatrick is an important mean field model for spin glasses. The dependence structure of Hamiltonians of the SK model is considered in this paper. We have investigated the covariance matrix of Hamiltonians of the SK model, and establish a relationship between the rank of the corresponding covariance matrix and the dimension of the space spanned by the Hamiltonians. Finally, we also give an upper bound for the rank of the covariance matrix, which might be the best.

Osteoclasts (OCs) are the multinucleated, bone-resorbing giant cells originally differentiated from a monocyte/macrophage lineage. OC differentiation and maturation, also called osteoclastogenesis, are strictly regulated by a variety of signaling pathways primarily induced by the interactions of two prerequisite cytokines, macrophage colony-stimulating factor (M-CSF) and the receptor activator of nuclear factor-κB ligand (RANKL) to their respective surface receptors, c-fms and RANK, in OC precursors (pre-OCs). Rab11 has emerged as the spatiotemporal regulators of intracellular vesicular transport in the endosomal recycling system; however, how it regulates osteoclastogenesis is incompletely understood. OC-triggered bone resorption is best characterized to be immensely dependent upon lysosomal function, the intracellular acidic organelles containing more than 50 acid hydrolases secreted into bone matrix microenvironment (BME). On the contrary, it is little known about the lysosomal function on modulating the turnover of c-fms and RANK surface receptors via Rab GTPase-mediated vesicular transport, thereby dictating osteoclastogenesis. In this review, I briefly describe the mechanism underlying lysosome-induced osteoclastogenesis via the Rab11-mediated modulation of the surface receptors in OCs.

Kronecker products of matrices have some striking operation properties, one of which is called the mixed-product property $(A \!\otimes\! B)(C \!\otimes\! D) = AC \!\otimes\! BD$. In view of this property, the two-term Kronecker product $A_1 \otimes A_2$ can be rewritten as $A_1 \otimes A_2 = (A_1 \otimes I_{m_2})(I_{m_1} \otimes A_2)$ of dilation forms of $A_1$ and $A_2$, and three-term Kronecker product $A_1 \otimes A_2 \otimes A_3$ can be rewritten as the products $A_1 \otimes A_2 \otimes A_3 = (A_1\otimes I_{m_2} \otimes I_{m_3})(I_{m_1} \otimes A_2 \otimes I_{m_3})(I_{m_1} \otimes I_{m_2} \otimes A_3)$ of the dilation forms of $A_1$, $A_2$, and $A_3$, respectively, where the matrices on the right-hand sides of the two factorizations are commutative. In this note, we approach the commutative Kronecker products on the right-hand sides of the two factorization equalities, and present a variety of new and useful analytical formulas for calculating the ranks, dimensions, orthogonal projectors, and ranges of matrices composed of these Kronecker products.

Camera malfunctions or loss of storage elements in imaging devices may lead to loss of important image information or random impulse noise interference. Low rank is one of the important prior information in image optimization processing. This paper uses different low-rank constraint models of the image matrices to recover the impulse interference satellite images. Firstly, an overview of image inpainting models based on nuclear norm, truncated nuclear norm, weighted nuclear norm, and matrix-factorization-based F-norm is presented, and corresponding optimiza-tion iterative algorithms are provided. Then, we conducted experiments under three types of pulse interference and provided visual and numerical results. Finally, it is concluded that the WSVT_ADMM method based on the weighted nuclear norm can obtain the best image inpainting results; The UV_ADMM method based on F norm of matrix factorization has the least computa-tion time and can be used for large-scale low-rank matrix computation; The WSVT_ADMM method based on weighted nuclear norm and the TSVT_ ADMM method based on truncated nuclear norms can significantly improve the repair effect compared to the nuclear norm-based methods such as SVT, SVP, and n_ADMM.

This article investigates the information matching efficiency of the sponsored auction mechanism of search engine platform by implementing consumer purchase strategy. Then we examine the incentive mechanism for sellers to report product quality truthfully under information asymmetry and the reason how product quality signal could improve information matching efficiency of the sponsored auction mechanism. Using the data collected from Baidu search engine, we empirically test the theoretical research results. Our main research finding: under information asymmetry and without product quality signal mechanism, the equilibrium of bidding rank cannot match the consumer purchase strategy at all, causing the consumer welfare to suffer double losses due to the adverse selection of sellers. In the contrast, the search engine could improve partially the information matching efficiency of the sponsored search auction mechanism by identifying the product quality signal brought by the sellers with the highest product quality. However, the search engine has no incentive to design product quality signal for sellers.

The aim of this survey is to review some recent developements in devising efficient preconditioners for sequences of linear systems A x = b. Such a problem arise in many scientific applications, such as discretization of transient PDEs, solution of eigenvalue problems, (Inexact) Newton method applied to nonlinear systems, rational Krylov methods for computing a function of a matrix. Full purpose preconditioners such as the Incomplete Cholesky (IC) factorization or approximate inverses are aimed at clustering eigenvalues of the preconditioned matrices around one. In this paper we will analyze a number of techniques of updating a given IC preconditioner (which we denote as P0 in the sequel) by a low-rank matrix with the aim of further improving this clustering. The most popular low-rank strategies are aimed at removing the smallest eigenvalues (deflation) or at shifting them towards the middle of the spectrum. The low-rank correction is based on a (small) number of linearly independent vectors whose choice is crucial for the effectiveness of the approach. In many cases these vectors are approximations of eigenvectors corresponding to the smallest eigenvalues of the preconditioned matrix P0 A. We will also review some techniques to efficiently approximate these vectors when incorporated within a sequence of linear systems all possibly having constant (or slightly changing) coefficient matrices. Numerical results concerning sequences arising from discretization of linear/nonlinear PDEs and iterative solution of eigenvalue problems show that the performance of a given iterative solver can be very much enhanced by the use of low-rank updates.

Bangladeshi construction industry suffers a lot of safety and accidental issues than other developing countries in the world. Among many of these, accident of construction project goes far beyond and shape a horrific figure of death for every year. The aims of this study is that analysis and discussion of causes of accident at construction project in Bangladesh. A widespread statistical data collection and data analysis take place to identify the causes and design the questionnaire. The questionnaire-based survey was used to elicit the attitude of four stakeholders as workers, owners, consultants, and contractors towards passive causes of fatal accident at construction site. These study also identify 77 passive causes under 14 major groups and ranked them based on Relative Importance Index (RII). The top 5 major group of causes are (1) Management related, (2) Consultant related, (3) Technology related, (4) Labour related and (5) Contractor related. The top 5 passive causes are: (1) Unaware of safety-related issue, (2) Lack of personal protective equipment, (3) Lack of safety eliminating/ avoiding design, (4) Unfit equipment, (5) Lack of knowledge and training on equipment.

Inositol is a natural carbocyclic sugar that plays an essential role in regulating the vital cellular functions of plants and animals. Current research has explored methyl derivatives of inositol, reporting on their various biological activities, including antitumor, anti-inflammatory, and anti-osteoporosis activities. Our previous study demonstrated that L-quebrachitol, a methyl derivative of inositol, enhances osteoblastogenesis and bone formation; however, its effect on osteoclastogenesis remains unclear. Consequently, we aimed to investigate the effect of L-quebrachitol on the receptor activator of nuclear factor-κB ligand-induced osteoclastogenesis in pre-osteoclastic RAW 264.7 cells. The results revealed that L-quebrachitol suppressed RANK-mediated signalling, including nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB) and Fos proto-oncogene (cFOS) pathways, at both gene and protein levels. Moreover, the critical transcription factor for osteoclastogenesis, nuclear factor of activated T cells c1 (NFATc1), was downregulated. Inhibition of osteoclast-associated marker genes encoding proteolytic enzymes, such as tartrate-resistant acid phosphatase (TRAP), matrix metallopeptidase 9 (MMP-9), and cathepsin K, led to reduced formation of TRAP-positive multinucleated cells and resorption pits. These findings demonstrate the dose-dependent inhibitory effect of L-quebrachitol on osteoclastogenesis through the modulation of receptor activator of nuclear factor κB (RANK)-mediated signalling pathways. However, further exploration of L-quebrachitol's potential as a therapeutic approach for osteoporosis is warranted.

This article shows how to establish expansion formulas for calculating the mixed operations $(A^{\dag})^{\#}$, $(A^{\#})^{\dag}$, $((A^{\dag})^{\#})^{\dag}$, $((A^{\#})^{\dag})^{\#}$, $\ldots$ of generalized inverses, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of a matrix and $(\cdot)^{\#}$ denotes the group inverse of a square matrix. As applications of the formulas obtained, the author constructs and classifies some groups of matrix equalities involving the above mixed operations, and derives necessary and sufficient conditions for them to hold.

We review a number of preconditioners for the advection-diffusion operator and for the Schur complement matrix which in turn constitute the building blocks for Constraint and Triangular Preconditioners to accelerate the iterative solution of the discretized and linearized Navier-Stokes equations. An intensive numerical testing is performed onto the driven cavity problem with low values of the viscosity coefficient. We devise an efficient multigrid preconditioner for the advection-diffusion matrix which, combined with the commuted BFBt Schur complement approximation, and inserted in a 2 x 2 block preconditioner, provides convergence of the GMRES method in a number of iteration independent of the meshsize for the lowest values of the viscosity parameter. The low-rank acceleration of such preconditioner is also investigated showing its great potential.

Model-based image reconstruction has brought improvements in terms of contrast and spatial resolution to imaging applications such as magnetic resonance imaging and emission computed tomography. However, their use for pulse-echo techniques like ultrasound imaging is limited by the fact that model-based algorithms assume a finite grid of possible locations of scatterers in a medium -- which does not reflect the continuous nature of real world objects and creates a problem known as off-grid deviation. To cope with this problem, we present a method of dictionary expansion and constrained reconstruction that approximates the continuous manifold of all possible scatterer locations within a region of interest. The expanded dictionary is created using a highly coherent sampling of the region of interest, followed by a rank reduction procedure based on a truncated singular value decomposition. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit (OMP), that uses a correlation-based non-convex constraint set that allows for the division of the region of interest into cells of any size. To evaluate the performance of the method, we present results of 2-dimensional ultrasound image reconstructions with simulated data in a nondestructive testing application. Our method succeeds in the reconstructions of sparse images from noisy measurements, providing higher accuracy than previous approaches based on regular discrete models.

This note addresses a fundamental problem in matrix theory on establishing and characterizing range equalities for matrix expressions that involve generalized inverses. We first establish a group of necessary and sufficient conditions for the matrix range equality ${\rm range}(D_1 - C_1A_1^{\dag}B_1) = {\rm range}(D_2 - C_2A_2^{\dag}B_2)$ to hold, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of matrix. We then give several groups of range equalities with extrusion properties for multiple matrix products associated with two matrices and their conjugate transposes and Moore--Penrose inverses.

Background Content marketing is increasingly important for online branding. Brand popularity can be more easily determined online than sales-based measures but is not yet well-explained from a content marketing perspective. Promising predictors are open data syndication policies, connectivity to e-commerce platforms, product reviews, data health, and the depth and width of a brands product portfolio. A predictive content marketing model can help brand owners to understand their e-commerce potential. Methods We used brand popularity (Brand Popularity Rank) and catalog data in combination with product reviews from an independent content aggregator. For all datasets, we selected the overlapping dataset for brand popularity and brand reviews based on a period of 90 days from June 10, 2022, till September 24, 2022 (n = 333 brands). Backward stepwise multiple linear regression was used to develop a predictive content marketing model of the Brand Popularity Rank. Results Through stepwise backward multiple linear regression five highly significant (p < 0.01) predictive factors for brand rank are selected in our content marketing model: the brand’s data syndication policy, the number of connected e-commerce platforms, a brand’s number of products, its number of products per category, and the number of product categories in which it is active. Our model explains 78% of the variance of Brand Popularity Rank and has a good and highly significant fit: F (5, 327) = 233.5, p < 0.00001. Conclusions We conclude that a content marketing model can adequately predict a Brand Popularity Rank based on online popularity. In this model an open content syndication policy, more connected e-commerce platforms, and catalog size, i.e., presence in more categories and more products per category are each related to a better (lower) Brand Popularity Rank score.

Given a square matrix $A$, we are able to construct numerous equalities that involve reasonable mixed operations of $A$ and its conjugate transpose $A^{\ast}$, Moore--Penrose inverse $A^{\dag}$, and group inverse $A^{\#}$. Such kind of equalities can be generally represented in the equation form $f(A, \, A^{\ast}, A^{\dag}, A^{\#}) =0$. In this article, the author constructs a series of simple or complicated matrix equalities, as well as matrix rank equalities involving the mixed operations of the four matrices. As applications, we give a sequence of necessary and sufficient conditions for a square matrix to be range-Hermitian.

It is a classic topic in algebras to construct and verify equalities that are composed of various algebraic operations of elements and their inverses or generalized inverses. In this note, the author constructs a matrix equality $(AB)^{\dag} = B^{\ast}(A^{\ast}ABB^{\ast})^{\#}A^{\ast}$ (called a mixed reverse-order law), where $A$ and $B$ are two matrices of appropriate sizes, $(\cdot)^{\ast}$, $(\cdot)^{\dag}$, and $(\cdot)^{\#}$ denote the conjugate transpose, the Moore--Penrose inverse, and the group inverse of a matrix, respectively, and shows that the mixed reverse-order law always holds. A list of variation forms of this matrix equality are also given, and necessary and sufficient conditions are obtained for them to hold. Especially, we show a remarkable fact that the two reverse-order laws $(AB)^{\dag} = B^{\dag}A^{\dag}$ and $(A^{\ast}ABB^{\ast})^{\#} = (BB^{\ast})^{\#}(A^{\ast}A)^{\#}$ are equivalent.

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is NP-hard. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.

One of matrix equalities composed of multiple products of matrices and their generalized inverses is given by $A_1B_1^{-}A_2B_2^{-} \cdots A_kB_k^{-}A_{k+1}= A$ where $A_1$, $B_1$, $A_2$, $B_2$, $\ldots$, $A_k$, $B_k$, $A_{k+1}$, and $A$ are given matrices of appropriate sizes, and $B_1^{-}$, $B_2^{-}$, $\cdots$, $B_k^{-}$ are generalized inverses of matrices. The cases for $k = 1, 2$ and their special forms were properly approached in the theory of generalized inverses of matrices. In this note, the author presents an algebraic procedure to derive explicit necessary and sufficient conditions for the equality with $k = 3$ to always hold using certain rank equalities for the block matrices constructed by the given matrices, and then mention a key step of extending the previous work to a general situation.

The rapid growth of the smart Internet of Things (IoT) and massive propagation of wireless technologies revealed the recent opportunities for development in various domains of real life such as smart cities and E-Health applications. A slight defense against different forms of attacks is offered for the current secure and lightweight Routing Protocol for Low Power and Lossy Networks (RPL) of IoT resource-constrained devices. Data packets are highly likely to be exposed while transmitting them during data packets routing. The RPL rank and version number attacks, which are two forms of RPL attacks, can have critical consequences for RPL networks. The studies conducted on these attacks have several security defects and performance shortcomings. The research proposes a Secure RPL Routing Protocol (SRPL-RP) for rank and version number attacks. It mainly detects, mitigates and isolates attacks in the RPL networks. The detection is based on a comparison of ranks strategy. The mitigation uses threshold and attacks status tables, and the isolation adds them to a blacklist table and alerts relevant nodes to skip them. SRPL-RP supports diverse types of network topologies and is comprehensively analyzed with multiple studies such as Standard RPL with Attacks, SBIDS and RPL+ Shield. The analysis results showed that the SRPL-RP achieves great improvements with Packet Delivery Ratio (PDR) of 98.48%, control message value of 991 packets/second, and average energy consumption of 1231.75 joules. It provides a better accuracy rate with 98.17% under the attacks.

COVID-19, caused by SARS-CoV-2, is responsible for widespread mortality and economic loss across almost 212 countries. The distribution of disease prevalence is, however, uneven and likely dependent on the range of human behavior and/or the pathogen and environmental variables. Here in this research we examined the correlation between daily and total COVID-19 case reports from Bangladesh and meteorological variables (average temperature, average humidity, and average wind speed) against one another using Spearman rank and Kendall correlation tests to highlight significant meteorological variables in relation to COVID-19. The tests revealed that both temperature and humidity had a non-significant correlation with COVID-19 transmission amid epicenter (EC) and non-epicenter (NEC) areas. However, a weak (KCC: 0.168, p < 0.05; SCC: 0.271, p < 0.05) correlation was found for temperature in ECs. Wind speed showed moderate to strong correlation in ECs with a very high statistical significance to both daily new cases [(KCC: 0.494, p < 0.01); (SCC: 0.689, p < 0.01)] and total cases [(KCC: 0.426, p < 0.01); (SCC: 0.617, p < 0.01)]. The COVID-19 transmission was found to have a weak (KCC: 0.354, p < 0.01) to moderate (SCC: 0.465, p < 0.01) correlation with daily new cases; however, a moderate (KCC: 0.497, p < 0.01) to strong (SCC: 0.712, p < 0.01) correlation with total cases was found in NECs. The results suggest that temperature and humidity have little influence on COVID-19 transmission, but wind speed may have some influence. Countries should prioritize social engineering to modify human behavior in order to combat the spread of COVID-19 and future pandemics.

Scene classification plays an important role in the intelligent processing of high-resolution satellite (HRS) remotely sensed image. In HRS image classification, multiple features, e.g. shape, color, and texture features, are employed to represent scenes from different perspectives. Accordingly, effective integration of multiple features always results in better performance compared to methods based on a single feature in the interpretation of HRS image. In this paper, we introduce a multi-task joint sparse and low-rank representation model to combine the strength of multiple features for HRS image interpretation. Specifically, a multi-task learning formulation is applied to simultaneously consider sparse and low-rank structure across multiple tasks. The proposed model is optimized as a non-smooth convex optimization problem using an accelerated proximal gradient method. Experiments on two public scene classification datasets demonstrate that the proposed method achieves remarkable performance and improves upon the state-of-art methods in respective applications.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

Gradient based methods are popularly used in training neural networks and can be broadly categorized into first and second order methods. Second order methods have shown to have better convergence compared to first order methods, especially in solving highly nonlinear problems. The BFGS quasi-Newton method is the most commonly studied second order method for neural network training. Recent methods have shown to speed up the convergence of the BFGS method using the Nesterov’s acclerated gradient and momentum terms. The SR1 quasi-Newton method though less commonly used in training neural networks, are known to have interesting properties and provide good Hessian approximations when used with a trust-region approach. Thus, this paper aims to investigate accelerating the Symmetric Rank-1 (SR1) quasi-Newton method with the Nesterov’s gradient for training neural networks and briefly discuss its convergence. The performance of the proposed method is evaluated on a function approximation and image classification problem.

In this paper we perform numerous numerical studies for the problem of low-rank matrix completion. We compare the Bayesian approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optimal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesian estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. However, we also find that the length of the confidence intervals revealed by the de-biased estimator for an entry is absolutely shorter than the length of the considered credible interval. These suggest further theoretical studies on the estimation error and the concentration for Bayesian methods as they are being quite limited up to present.

In software development, developers received bug reports that describe the software bug. Developers find the cause of bug through reviewing the code and reproducing the abnormal behavior that can be considered as tedious and time-consuming processes. The developers need an automated system that incorporates large domain knowledge and recommends a solution for those bugs to ease on developers rather than spending more manual efforts to fixing the bugs or waiting on Q&A websites for other users to reply to them. Stack Overflow is a popular question-answer site that is focusing on programming issues, thus we can benefit knowledge available in this rich platform. This paper, presents a survey covering the methods in the field of mining software repositories. We propose an architecture to build a recommender System using the learning to rank approach. Deep learning is used to construct a model that solve the problem of learning to rank using stack overflow data. Text mining techniques were invested to extract, evaluate and recommend the answers that have the best relevance with the solution of this bug report.

Containing hundreds of spectral bands (features), hyperspectral images (HSIs) have high ability in discrimination of land cover classes. Traditional HSIs data processing methods consider the same importance for all bands in the original feature space (OFS), while different spectral bands play different roles in identification of samples of different classes. In order to explore the relative importance of each feature, we learn a weighting matrix and obtain the relative weighted feature space (RWFS) as an enriched feature space for HSIs data analysis in this paper. To overcome the difficulty of limited labeled samples which is common case in HSIs data analysis, we extend our method to semisupervised framework. To transfer available knowledge to unlabeled samples, we employ graph based clustering where low rank representation (LRR) is used to define the similarity function for graph. After construction the RWFS, any arbitrary dimension reduction method and classification algorithm can be employed in RWFS. The experimental results on two well-known HSIs data set show that some dimension reduction algorithms have better performance in the new weighted feature space.

Noisy data is always encountered in real applications, such as bioinformatics, neuroimage and remote sensing. Existing methods mainly consider linear or generalized linear errors-in-variables regression, while relatively little attention is paid for the multivariate response case, and how to evaluate the estimation performance under perturbed covariates is still an open question. In this paper, we consider the information-theoretic limitations of estimating a low-rank matrix in the multi-response errors-in-variables regression model. By application of the information theory and statistical techniques on concentration inequalities, the minimax lower bound is provided in terms of the squared Frobenius loss, which recaptures the rate provided under the clean covariate assumption in previous literatures. Hence our result further indicates that though under the more realistic errors-in-variables situation, no more samples are required so as to achieve a rate-optimal estimation.

In this paper, we use a machine learning method, known as Nonnegative Matrix Factorization, to extract from a given image some new information obtained from a number of color space representations. Such kind of information, termed ``metacolor'', can be considered as a particular color space representation of the image, which can be used to obtain a binary segmentation of the investigated image by distinguishing foreground and background pixels. Some numerical experiments prove that the proposed method shows improved results when compared with common simpler thresholding algorithms.

Wearable assistant devices play an important role in daily life for people with disabilities. Those who are hearing impaired may face dangers while walking or driving on the road. The major danger is their inability to hear warning sounds from cars or ambulances. Thus, the goal of this study is to develop a wearable assistant device for the hearing impaired to recognize emergency vehicle sirens on the road using edge computing. An EfficientNet-based fuzzy rank-based ensemble model was proposed to classify seven audio sounds, including human vocalizations and emergency vehicle sirens. This model was embedded in an Arduino Nano 33 BLE Sense development board. The audio files were respectively obtained from the CREMA-D dataset and Large Scale Audio dataset of emergency vehicle sirens on the road, with a total number of 8756 files. The seven audio sounds included neutral vocalization, anger vocalization, fear vocalization, happy vocalization, car horn sound, siren sound, and ambulance siren sound. The audio signal was converted into a spectrogram by the short-time Fourier transform as the feature. When one of the car horns, sirens, or ambulance sirens was detected, the wearable assistant device presented alarms through vibration and messages on the OLED panel. The performances of the EfficientNet-based fuzzy rank-based ensemble model in offline computing achieved an accuracy of 97.1%, precision of 97.79%, sensitivity of 96.8%, and specificity of 97.04%. In edge computing, the results were an accuracy of 95.2%, precision of 93.2%, sensitivity of 95.3%, and specificity of 95.1%. Thus, the proposed wearable assistant device has the potential benefit of helping the hearing impaired avoid traffic accidents.

For more than half a century, Manfred Deistler has been contributing to the construction of the rigorous theoretical foundations of the statistical analysis of time series and more general stochastic processes. Half a century of unremitting activity is not easily summarized in a few pages. In this short note, we chose to concentrate on a relatively little-known aspect of Manfred's contribution which nevertheless had quite an impact on the development of one of the most powerful tools of contemporary time series and econometrics: dynamic factor models.

In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n=4) of the sets of H-points of rank 2, which is indicated by P42.

A system of simultaneous multi-variable nonlinear equations can be solved by the Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superlinear convergence give solutions by approximating the Jacobian in some way. Unfortunately, the quasi-Newton condition (secant equation) doesn’t completely specify the Jacobian approximate in multi-dimensional case, so its full-rank update is not possible with classic variants of methods. The suggested new iteration strategy (“T-Secant”) allows full-rank update of the Jacobian approximate in each iteration by determining two independent approximates for the solution. They are used to generate a set of new independent trial approximates, then the Jacobian approximate can fully be updated. It is shown, that the T-Secant approximate is in the vicinity of the classic quasi-Newton approximate, providing that the solution is evenly surrounded by the new trial approximates. The suggested procedure increases the super-linear convergence of the secant method (φS = 1.618...) to super-quadratic (φT = φS + 1 = 2.618...) and the quadratic convergence of the Newton-method (φN = 2) to cubic (φT = φN + 1 = 3) in one dimensional case. The Broyden-type efficiency (mean convergence rate) of the suggested method in multi-dimensional case is an order higher than the efficiency of other classic low-rank update quasi-Newton methods as shown by numerical examples on a Rosenbrock-type test-function with up to 1000 variables. The geometrical representation (hyperbolic approximation) in single variable case helps explaining the basic operations and a vector-space description is also given in multi-variable case.

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the reduced basis, i.e. the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of the PGD basis using a randomised SVD algorithm. Comparing to conventional approaches such as Gram-Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the reduced basis. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

Reverse-order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse-order laws for a matrix product AB is (AB)^(i,...,j) = B^(i,...,j)A^(i,...,j), where (·)^i,...,j denotes an {i,...,j}-generalized inverse of matrix. Because {i,...,j}-generalized inverse of a general matrix is not necessarily unique, the relationships between both sides of the reverse-order law can be divided into four situations for consideration. In this article, we first introduce a linear mixed model y = ABβ + Aγ + ε, present two least-squares methodologies to estimate the fixed parameter vector  in the model, and describe the connections between the two least-squares estimators and the reverse-order laws for generalized inverses of the matrix product AB. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of B^(i,...,j)A^(i,...,j), as well as necessary and sufficient conditions for B^(i,...,j)A^(i,...,j) to be invariant with respect to the choice of A^(i,...,j) and B^(i,...,j). We then present a unied approach to the 512 set inclusion problems {(AB)^(i,...,j) ⊇ {B^(i,...,j)A^(i,...,j)}for the eight commonly-used types of generalized inverses of A, B, and AB using the block matrix representation method (BMRM), matrix equation method (MEM), and matrix rank method (MRM), where {(·)^(i,...,j)} denotes the collection of all {i,...,j}-generalized inverse of a matrix.

This paper proposes two max-pooling engines, named the RTB-MAXP engine and the CMB-MAXP engine, with a scalable window size parameter for FPGA-based convolutional neural network (CNN) implementation. The max-pooling operation for the CNN can be decomposed into two stages, i.e., a horizontal axis max-pooling operation and a vertical axis max-pooling operation. These two one-dimensional max-pooling operations are performed by tracking the rank of the values within the window in the RTB-MAXP engine and cascading the maximum operations of the values in CMB-MAXP engine. Both the RBM-MAXP engine and the CMB-MAXP engine were implemented using VHSIC Hardware Description Language (VHDL) and verified by simulations. They have been employed for and tested in our CNN accelerator targeting at the CNN model YOLOv4-CSP-S-Leaky for object detection.

The Stochastic Optimisation Software (SOS) is a Java platform facilitating the algorithmic design process and the evaluation of metaheuristic optimisation algorithms. It reduces the burden of coding miscellaneous methods for dealing with several bothersome and time-demanding tasks such as parameter tuning, implementation of comparison algorithms and testbed problems, collecting and processing data to display results, measuring algorithmic overhead, etc. SOS provides numerous off-the-shelf methods including 1) customised implementations of statistical tests, such as the Wilcoxon Rank-Sum test and the Holm-Bonferroni procedure, for comparing performances of optimisation algorithms and automatically generate result tables in PDF and LaTeX formats; 2) the implementation of an original advanced statistical routine for accurately comparing couples of stochastic optimisation algorithms; 3) the implementation of a novel testbed suite for continuous optimisation, derived from the IEEE CEC 2014 benchmark, allowing for controlled activation of the rotation operator. each testbed function. Moreover, this article comments on the current state of the literature in stochastic optimisation and highlights similarities shared by modern metaheuristics inspired by nature. It is argued that the vast majority of these algorithms are simply a reformulation of the same methods and that metaheuristics for optimisation should be simply treated as stochastic processes with less emphasis on the inspiring metaphor behind them.

The Internet of Healthcare Things (IoHT) is an essential IoT domain that encompasses the necessary capabilities to transform the current healthcare system. IoHT generates, transfers, manages, stores, and processes highly confidential medical data and sensitive personal information. Thus, IoHT is a critical application from a security perspective and is most favorably targeted by attackers. Several security-breaching attempts can be carried out due to the vulnerabilities of the IoHT that put classified data at constant risk. Henceforth, this work aims to inspect the performance of 6LoWPAN-RPL-based `Patient-Centric IoHT’ in the presence of malicious intruders conducting blackhole, rank, and DoDAG attacks in both normal and emergency operational modes of the mentioned resource-constraint network. PC-IoHT is simulated on the Cooja simulator and Contiki-OS for each attack with two and four intruders (out of 10 motes) for both operation modes. Several performance evaluation parameters are used to assess the overall performance of the considered PC-IoHT. The attacks’ impact on PC-IoHT is analyzed by comparing blackhole, rank, and DoDAG attacks with the no-attack scenario.