Matrix Form Research Articles

The Smith normal form of the walk matrix of the Dynkin graph An

In this paper, we give the rank of the walk matrix of the Dynkin graph An, and prove that its Smith normal form isdiag(1,…,1︸⌈n2⌉,0,…,0).

Explainable graph clustering via expanders in the massively parallel computation model

Explainable clustering provides human-understandable reasons for decisions in black-box learning models. In a previous work, a decision tree built on the set of dimensions was used to define ranges of values for k-means clusters. For explainable graph clustering, we use expander graphs instead of dense subgraphs since powering an expander graph is guaranteed to result in a clique after at most a logarithmic number of steps.Consider a set of multi-dimensional points labeled with k labels. We introduce the heat map sorting problem as reordering the rows and columns of an input matrix (each point is a column and each row is a dimension) such that the labels of the entries of the matrix form connected components (clusters). A cluster is preserved if it remains connected, i.e., if it is not split into several clusters and no two clusters are merged. In the massively parallel computation model (MPC), each machine has a sublinear memory and the total memory of the machines is linear.We prove the problem is NP-hard. We give a fixed-parameter algorithm in MPC and an approximation algorithm based on expander decomposition. We empirically compare our algorithm with explainable k-means on several graphs of email and computer networks.

Cross-spectrum method for acoustic source identification and visualization of airfoil noise

The identification and visualization of airfoil noise sources are critical for comprehending the interplay between flow and acoustics, and for understanding the generation and propagation of sound. In this paper, we introduce an innovative method, specifically designed to identify and visualize flow-induced noise sources associated with airfoil noise. This approach employs cross power spectral density analysis to distinctly identify flow-induced noise sources. The data for our study comes from large-eddy simulations of a NACA 0012 airfoil, characterized by a Reynolds number of 4×105, a Mach number of 0.058, and an angle of attack of 6.25∘. Different cross-spectrum formulations are examined and evaluated. The analysis includes a comparison of the cross-spectrum method's strengths and limitations relative to established data-driven approaches like dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD). We find that the cross-spectrum method provides both spectral magnitudes and phase topologies, allowing it to effectively compare sound intensities among various sources at specific frequencies, while retaining high-resolution spatiotemporal coherent flow and acoustic dynamics. One of the notable advantages of the cross-spectrum method over DMD or SPOD modes is its lesser reliance on extensive data manipulation in the form of large-size data matrix, making it a more efficient and user-friendly approach for practitioners, particularly when dealing with complex systems or high-dimensional datasets. This characteristic enhances its practicality and accessibility in the field of flow and acoustic visualization. Finally, the newly developed method is applied to three distinct flow transition scenarios to evaluate its proficiency in distinguishing acoustic generation and propagation mechanisms, depending on the specific transition case.

Speculative Cannibalism: Derrida and Viveiros de Castro on Eating-the-Other

ABSTRACT “Speculative cannibalism” names here some kind of transcendental logic that only works through figuration, in the specific form of an analogical matrix. This article tracks these configurations in the philosophical works of Jacques Derrida and in the anthropological foundations of Eduardo Viveiros de Castro. This article states that as transcendental, this analogical matrix is the condition of possibility of the meaning of alterity and difference—but as analogical works as a transcategorial function that is neither beyond nor before experience, only irreducible to a given explanatory category of judgment or being. This function is figurative, that is, constitutes meaning by an operation of comparison in Viveiros de Castro’s nomenclature, and of supplementation, in Derrida’s terminology. In both cases this function posits difference or equivocation as the main operator. Finally, this article argues that even though they are very similar speculative proposals, analogy works a bit differently for deconstruction and for post-structural anthropology: for the first, analogy is based on a supplementary logic that is only taken to be a formal operation, while for the former, analogy it is treated not only as a formal operation, but also as fixed within the material categories of Amerindian thought.

Multiscale reweighted smoothing regularization in curvelet domain for hyperspectral image denoising

ABSTRACT Hyperspectral images are easily contaminated by multi-modal noise in the process of data acquisition. Generally, hyperspectral signatures and noise appear unexpectedly scattered in the spatial-spectral domain. Conversely, in the transform domain, the principle components of an image are gathered in the low-frequency bands, while the details and noise often occur in high-frequency parts. The existing denoising methods usually divide the whole frequency domain into two parts, that is, high frequency and low frequency, which can not make the most of the knowledge contained at different frequencies or scales, especially in the multiscale transform domain. Furthermore, aiming to restore a clean image from the noise-corrupted data, hyperspectral image denoising often amounts to an ill-posed problem, in which reshaping cubic data into matrix form results in the loss of structure information. To address the aforementioned issues, this paper incorporates the reweighted smoothing regularization in the transform domain into the noise-perturbed degradation model to reformulate a novel optimization problem. First, the multiscale curvelet is leveraged to transform the spatial matrix into frequency domain, where the coefficients are carefully designed to weight the components at different scales and orientations. Second, l 1 -norm is imposed on the abundance term to promote sparsity in the transform domain for performance enhancement. Finally, using proximal alternating optimization, an efficient algorithm is well developed to obtain the closed-form solutions to the proposed denoising problem. The experimental results on several synthetic and real datasets, illustrate that the proposed method improves PSNR by at least 1.5 dB and reduces ERGAS error by more than 35% than the state-of-the-art approaches under the multi-modal noise mixed environments, which verifies the validity of regularization terms in hyperspectral images denoising.

Hydrogel Derived from Decellularized Porcine Small Intestinal Submucosa as a Physical Shielding Repaired the Gut Epithelial Barrier of Murine Ulcerative Colitis

AbstractUlcerative colitis (UC) is associated with the shedding of the gut mucus. Decellularized porcine small intestinal submucosa (SIS‐ECM) contains numerous active forms of extracellular matrix as well as growth factors. Herein, a mucus‐mimetic hydrogel (MAG) is designed as a barrier therapy by integrating SIS‐ECM with hyaluronic acid and epigallocatechin‐3‐gallate. MAG not only presented the viscoelastic behaviors with G' of 4000 Pa but also good thixotropy. Moreover, MAG as a physical shielding is effective to hinder E. coli invasion. Besides, the good repairing effect on the injured Caco‐2 cells is presented by MAG. When MAG as a biomimetic mucus is rectally administrated to colitis mouse, it alleviated effectively the colitis symptoms and improved the colonic shorting. Moreover, expression of IL‐1β, IL‐6, and TNF‐α at the laminae propria is substantially inhibited by MAG. Besides, the colonic epitheliums are well rearranged, and the tight junction proteins (ZO‐1, Occludin‐1, Claudin‐5) between them are greatly upregulated after MAG treatment. Meanwhile, the mucus secretion of goblets cells is effectively repaired by MAG treatment. The repairing mechanism of intestinal mucosa barriers is associated with promoting the proliferation and differentiation of intestinal stem cells. Collectively, MAG might be a promising strategy of barrier therapy for UC.

Gradient-Based Optimization Method for Experimental Modal Parameter Estimation with Finite Element Model

This paper presents a novel gradient-based optimization algorithm for improving the accuracy of experimentally estimated modal parameters with the assistance of finite element models. Initially, we recast the discrete vibration response equation into a matrix form and formulate the parameter estimation problem in modal analysis as an optimization problem. Then the problem is solved with a gradient-based iterative algorithm, which explicitly exhibits the closed form of gradients used in optimization. Initial values for this iteration are parameters derived from finite element models, since every important engineering structure should be analyzed with a finite element model before it is constructed. Subsequently, the performance of this algorithm is validated by both pure numerical experiments, which simulate the physical world, and experiments using real measurement data gathered by sensors in the real physical world. The algorithm’s performance is further enhanced by incorporating gradient clipping and an adaptive iteration threshold. As a comparison, a discussion on classical least-squares time-domain method for the problem is provided. For practical applications, the Shi–Tomasi corner detection and Lucas–Kanade optical flow methods are deployed to detect corner points from videos taken during the vibration of a structure and track the motion of these points in the videos.

Distribution of benefits and adverse effects and their role in industrial symbiosis decision-making – A Swedish case study

Industrial symbiosis (IS) has been recognized as an important approach to succeed in the transition towards increased circularity in industry and society. IS involves collaboration between different actors sharing resources, aiming to minimize waste, improve resource and/or energy efficiency, resulting in reduced emissions and environmental impact. This study conducts an embedded single case study at an IS network in Sotenäs, Sweden, where both private and public actors collaborate by exchanging resources. The study identifies benefits and adverse effects of the IS network and explores how these are considered in the actors' decision-making regarding participation. The results indicate that different actors perceive different types and degrees of benefits and adverse effects. To add further value, this study develops an analytical framework for mapping benefits and adverse effects in the form of an impact assessment matrix. The framework maps at what level in society effects accrue and at what point in time they are expected to occur. The results of this study can help understand the role of specific benefits and adverse effects in actors’ decision-making, and show the distribution of effects across societal levels. This knowledge can help understand the complexity of IS networks and thereby facilitate the implementation of IS.

Aerodynamic modeling and performance analysis of model predictive controller for fixed wing vertical takeoff and landing unmanned aerial vehicle

This research focuses mainly on the aerodynamic modelling and performance analysis of a model predictive controller for a hybrid fixed-wing vertical takeoff and landing of unmanned aerial vehicle. The aerodynamics, which comprises several aerodynamic characteristics including the lift, drag, and thrust coefficients, is modelled using Newton’s second law of motion. The force and moment equations were obtained, and they were then converted into matrix and state equation form, together with the transformation matrices. The essential equations with six degrees of freedom (6 DoF) and 12 state matrices including the control input and manipulating variables were obtained. The proposed model predictive controller (MPC) was designed using the optimal model predictive controller design parameters, such as a sampling time of 0.1, a prediction horizon of 15, a control horizon of 3 and additional controller settings. With a settling period of 3 s, an overshoot of 0.5865, and a steady state inaccuracy of 0.00785, the MATLAB simulation demonstrates that the system variables, including roll, pitch, and yaw, are stabilized. This MPC control is more effective in anticipating and optimizing the UAV than other control strategies. Eventually, the controller’s simulation on MATLAB Simulink demonstrates the controller’s ability to stabilize and control the system in a real-time application. Autonomous vertical takeoff and landing operations depend heavily on the mathematical model and architecture of the flight controller. Among the uses are inspection, monitoring, and rescue.

Cross-validation to select the optimum rank for a reduced-rank approximation to multivariate data

ABSTRACT In this paper we consider the Gabriel form of cross-validation (CV) and we investigate how to estimate the optimum rank for lower rank approximations of any dataset that can be written in matrix form, with particular application in multivariate analysis and in the analysis of multienvironment trials. The literature related to the method suggests that it can produce overfitting and poor-quality predictions, characteristics that result in overestimation of the rank. Because of this, it is proposed to change the rank selection criterion, testing thirteen statistics both in the original method and in four proposed extensions that seek to solve the above problems. A comparison is made with two gold standard methods for CV through a simulation study and through the analysis of seventeen real datasets, two of which are general multivariate and fifteen are from experiments with genotype-by-environment interaction. It is concluded that from a predictive point of view, the highest accuracy in estimating the rank is obtained by using a regularized singular value decomposition.

An overlooked source of uncertainty in the mass of the Milky Way

ABSTRACT In the conventional approach to decomposing a rotation curve into a set of contributions from mass model components, the measurements of the rotation curve at different radii are taken to be independent. It is clear, however, that radial correlations are present in such data, for instance (but not only) because the orbital speed depends on the mass distribution at all (or, minimally, inner) radii. We adopt a very simple parametric form for a covariance matrix and constrain its parameters using Gaussian process regression. Applied to the rotation curve of the Milky Way, this suggests the presence of correlations between neighbouring rotation curve points with amplitudes of $\lt 10\, \mathrm{km}\, \mathrm{s}^{-1}$ over length scales of 1.5–$2.5\, \mathrm{kpc}$ regardless of the assumed dark halo component. We show that accounting for such covariance can result in a ∼50 per cent lower total mass estimate for the Milky Way than when it is neglected, and that the uncertainty in model parameters increases such that it seems more representative of the uncertainty in the rotation curve measurement. The statistical uncertainty associated with the covariance is comparable to or exceeds the total systematic uncertainty budget. Our findings motivate including more detailed treatment of rotation curve covariance in future analyses.

Spectrum analysis for nonuniform sampling of bandlimited and multiband signals in the fractional Fourier domain

This paper explores fractional spectra of signals after two types of nonuniform samplings in the presence of timing offset. Both cases of bandlimited and multiband signals in the fractional Fourier domain are considered, based on which we provide conditions for reconstructing the spectrum and devise relevant methods for compensating the bias introduced by timing offset. To obtain these goals, we divide the nonuniformly sampled signal into uniformly sampled sub-sequences and establish the relationship between the discrete-time fractional Fourier transforms (DTFrFTs) of them and the FrFT of the original signal. It indicates that the obtained DTFrFTs consists of periodic replicas of the FrFT for the original signal with each replica being biased by a phase term introduced by timing offset. Based on the matrix form of the relationship, we implement spectral reconstruction of bandlimited signals under certain conditions by performing the inverse of a matrix determined by the phase terms. Different from bandlimited signals, the DTFrFTs of uniformly sampled sub-sequences for multiband signals are studied within disjoint fractional frequency sub-intervals separated by aliasing boundaries. Moreover, inverse of a matrix with fewer columns and rows is utilized to reconstruct the spectrum. Simulations verify the effectiveness of the proposed methods.

Magic in generalized Rokhsar-Kivelson wavefunctions

Magic is a property of a quantum state that characterizes its deviation from a stabilizer state, serving as a useful resource for achieving universal quantum computation e.g., within schemes that use Clifford operations. In this work, we study magic, as quantified by the stabilizer Renyi entropy, in a class of models known as generalized Rokhsar-Kivelson systems, i.e., Hamiltonians that allow a stochastic matrix form (SMF) decomposition. The ground state wavefunctions of these systems can be written explicitly throughout their phase diagram, and their properties can be related to associated classical statistical mechanics problems, thereby allowing powerful analytical and numerical approaches that are not usually available in conventional quantum many body settings. As a result, we are able to express the SRE in terms of wave function coefficients that can be understood as a free energy difference of related classical problems. We apply this insight to a range of quantum many body SMF Hamiltonians, which affords us to study numerically the SRE of large high-dimensional systems, and in some cases to obtain analytical results. We observe that the behaviour of the SRE is relatively featureless across quantum phase transitions in these systems, although it is indeed singular (in its first or higher order derivative, depending on the nature of the transition). On the contrary, we find that the maximum of the SRE generically occurs at a cusp away from the quantum critical point, where the derivative suddenly changes sign. Furthermore, we compare the SRE and the logarithm of overlaps with specific stabilizer states, asymptotically realised in the ground state phase diagrams of these systems. We find that they display strikingly similar behaviors, which in turn establish rigorous bounds on the min-relative entropy of magic.

Application of autogenous dentinal block to increase alveolar bone volume: a clinical case

Introduction. Materials based on extracted teeth in various studies have been radiographically and histologically proven to be effective in osteoplastic operations. These materials can be used in the form of crushed dentin matrix, a fragment of the tooth’s root and an autogenous dentin block. The purpose of this clinical case was to evaluate the effectiveness of using an autogenous dentin block to increase the alveolar process of the jaws in the preimplantation period.Description of a clinical case. Patient F., 30 years old, applied to the clinic of the Clinical Center of Maxillofacial, Plastic Surgery and Dentistry Russian University of Medicine with a complaint of a missing tooth in the frontal region of the lower jaw. At the time of treatment, the patient was already undergoing orthodontic treatment in another medical institution in Moscow. The patient underwent a clinical and radiological examination together with a prosthodontst. A diagnosis of «partial secondary adentia», «atrophy of the alveolar ridge in the frontal part of the lower jaw» and «dystopia of teeth 1.8, 2.8, 3.8, 4.8» was established. A comprehensive treatment plan has been drawn up. At the first stage, the patient underwent extraction of teeth 1.8, 2.8, 3.8, 4.8 for orthodontic indications with simultaneous bone grafting of the alveolar ridge in the area of the missing tooth 3.1. At the second stage, the patient underwent a trephine biopsy in the area of augmentation and installation of a dental implant in the area of missing tooth 3.1. The third stage was rational prosthodontic treatment on a dental implant in the department of prosthodontics.Results. The present study showed that autogenous dentinal block can serve as an alternative material for alveolar ridge augmentation.

Distributed Estimation of Support Vector Machines for Matrix Data.

Discrimination problems are of significant interest in the machine learning literature. There has been growing interest in extending traditional vector-based machine learning techniques to their matrix forms. In this article, we investigate the statistical properties of the nuclear-norm-based regularized linear support vector machines (SVMs), in particular establishing the convergence rate of the estimator in the high-dimensional setting. Furthermore, within the distributed estimation paradigm, we propose a communication-efficient estimator that can achieve the same convergence rate. We illustrate the performances of the estimators via some simulation examples and an empirical data analysis.

Energy decomposition analysis method using density matrix formulation.

In this work, an energy decomposition analysis (EDA) method with the strategy of density matrix, called DM-EDA, is proposed on the basis of single reference electronic structure calculations. Different from traditional EDA methods, instead of an intermediate state wave function, the EDA terms in DM-EDA are expressed in the forms of the density matrix. This method can be carried out with various kinds of density matrices. With the efficient implementation, DM-EDA not only greatly improves the computational efficiency but also provides quantitative knowledge of intermolecular interactions with a large number of monomers.

Synchronization of delayed stochastic reaction–diffusion Hopfield neural networks via sliding mode control

Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.

The Numerical Solutions of weakly singular Fredholm integral equations of the Second kind Using Chebyshev Polynomials of the Second Kind

In this study, the second kind Chebyshev Polynomials were utilized to acquire interpolated solutions for the second kind Fredholm integral equations with weakly singular kernel. To accomplish this, the data, unknown, and kernel functions were converted into matrix form, and consequently we completely isolated the singularity of the kernel. The primary benefit of this method is the ability to change the form of integral equation to an equivalent algebraic system, which is easier to solve. The effectiveness of our technique was evaluated by applying it to three illustrated examples, and it was observed that the solutions obtained exhibit strong convergence towards the exact solutions.

The Role of Tenascin-C on the Structural Plasticity of Perineuronal Nets and Synaptic Expression in the Hippocampus of Male Mice.

Neuronal plasticity is a crucial mechanism for an adapting nervous system to change. It is shown to be regulated by perineuronal nets (PNNs), the condensed forms of the extracellular matrix (ECM) around neuronal bodies. By assessing the changes in the number, intensity, and structure of PNNs, the ultrastructure of the PNN mesh, and the expression of inhibitory and excitatory synaptic inputs on these neurons, we aimed to clarify the role of an ECM glycoprotein, tenascin-C (TnC), in the dorsal hippocampus. To enhance neuronal plasticity, TnC-deficient (TnC-/-) and wild-type (TnC+/+) young adult male mice were reared in an enriched environment (EE) for 8 weeks. Deletion of TnC in TnC-/- mice showed an ultrastructural reduction of the PNN mesh and an increased inhibitory input in the dentate gyrus (DG), and an increase in the number of PNNs with a rise in the inhibitory input in the CA2 region. EE induced an increased inhibitory input in the CA2, CA3, and DG regions; in DG, the change was also followed by an increased intensity of PNNs. No changes in PNNs or synaptic expression were found in the CA1 region. We conclude that the DG and CA2 regions emerged as focal points of alterations in PNNs and synaptogenesis with EE as mediated by TnC.

A general method for twin element analysis and its application in Cu–Zn–Al shape memory alloys with M18R martensite

Twins play a crucial role in elucidating the structure and deformation characteristics of materials. However, in materials with low-symmetry crystal structures, solving the twin relationships remains a challenging task. In this study, we propose a general method for determining twin elements K1, η1, K2, and η2, which are essential for twin analysis. The proposed method involves three main steps: (1) representing misorientation data measured by electron back-scattered diffraction (EBSD) and transmission electron microscopy (TEM) in matrix form, (2) identifying additional 180° rotation elements related to twin elements K1 or η1 by traversing all symmetrically equivalent misorientations, and (3) using a minimum and crystal structure-dependent uniform shear as the constraint to determine the other twin elements (K2andη2). By combining the experimental data and the proposed method, we systematically analyze the complex twin relationships of Cu–Zn–Al shape memory alloys (SMAs) with monoclinic martensite (M18R). This methodology has been demonstrated to be effective and possesses broad applicability.