Cyclic Matrix Research Articles

Influence of γ-Radiation on Mechanical Stability to Cyclic Loads Tubular Elastic Matrix of the Aorta.

A significant drawback of the rigid synthetic vascular prostheses used in the clinic is the mechanical mismatch between the implant and the prosthetic vessel. When placing prostheses with radial elasticity, in which this deficiency is compensated, the integration of the graft occurs more favorably, so that signs of cell differentiation appear in the prosthesis capsule, which contributes to the restoration of vascular tone and the possibility of vasomotor reactions. Aortic prostheses fabricated by electrospinning from a blend of copolymers of vinylidene fluoride with hexafluoropropylene (VDF/HFP) had a biomechanical behavior comparable to the native aorta. In the present study, to ensure mechanical stability in the conditions of a living organism, the fabricated blood vessel prostheses (BVP) were cross-linked with γ-radiation. An optimal absorbed dose of 0.3 MGy was determined. The obtained samples were implanted into the infrarenal aorta of laboratory animals-Landrace pigs. Histological studies have shown that the connective capsule that forms around the prosthesis has signs of high tissue organization. This is evidenced by the cells of the fibroblast series located in layers oriented along and across the prosthesis, similar to the orientation of cells in a biological arterial vessel.

Mathematical formulation of large eddy simulation using hybrid finite difference methods and poisson equations

This study uses the hybrid finite-difference method (HFDM), which combines the finite-difference and spectral approaches, to describe the Magnetohydrodynamic (MHD) turbulence decay. By using a finite-difference approach in conjunction with a cyclic Penta-diagonal matrix, the numerical algorithm of the hybrid method solves the Navier-Stokes equations and the magnetic field equation with the fourth order's precision in space and second order in time. The spectral approach is used to solve the pressure Poisson equation. The time-dependent turbulence features of this flow were in excellent agreement with the appropriate analytical solution, which is valid for short timeframes, for the classical issue of the 3-D Taylor and Green vortex flow without taking the magnetic field into account. We also show how the effective numerical approach may be utilised to model the decline of magnetohydrodynamic turbulence at various magnetic Reynolds numbers.

Regional Financial Economic Data Processing Based on Distributed Decoding Technology

To improve the effect of regional financial and economic data processing, this study combines the distributed decoding technology to construct the regional financial data processing system. Furthermore, this study combines the technical characteristics of cooperative communication and unitary space-time codes to design a non-differential distributed space-time code based on cyclic unitary matrix groups. In addition, this study uses the particularity of trigonometric functions to design a non-differential distributed space-time code based on trigonometric functions. Finally, according to the characteristics of the distributed space-time code of trigonometric functions, this study obtains a decoding algorithm with low decoding complexity and uses MATLAB to conduct simulation experiments to verify the financial data processing and economic analysis effect of the system in this study. The experimental analysis results show that the regional financial and economic data processing system based on distributed decoding technology proposed in this study can play an important role in the analysis of financial and economic data.

Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix

Abstract In this study, first, the definitions of the preference relation matrix and the 0-1 permutation preference matrix of the linguistic judgement matrix are given. The method of judging the satisfactory consistency of the linguistic judgement matrix by the standard 0-1 arrangement matrix is obtained. This method not only solves the problem of satisfactory consistency when there are no equivalent objects but is also simple and effective. Then, the definition of the cyclic circle matrix of the three objects is given. According to the size of the preference value of the object line, the cyclic cycle and the adjusted language judgement matrix are obtained. Finally, the rationality and validity of the method are verified by examples.

Cyclic matrices and polynomial interpolation over division rings

As is well known, any complex cyclic matrix A is similar to the unique companion matrix associated with the minimal polynomial of A. On the other hand, a cyclic matrix over a division ring F is similar to a companion matrix of a polynomial which is defined up to polynomial similarity. In this paper we study more rigid canonical forms by embedding a given cyclic matrix over a division ring F into a controllable or an observable pair. Using the characterization of ideals in F[z] in terms of controllable and observable pairs we consider ideal interpolation schemes in F[z] which merge into polynomial interpolation problems containing both left and right interpolation conditions.

Constructions of 2-resilient rotation symmetric Boolean functions through symbol transformations of cyclic Hadamard matrix

In this paper, the properties of symbol transformations of cyclic Hadamard matrices are studied. An infinite class of (n−1)-variable 2-resilient rotation symmetric Boolean functions are constructed, and the nonlinearity of the constructed functions is 2n(n−1). The crucial technique of this method is to determine a subset T⊆F2n−1 satisfying a correspondent condition. This is a new construction of 2-resilient rotation symmetric Boolean functions via switching the supports of (n−1)-variable rotation symmetric Boolean functions of degree one, i.e., f0n−1(x1,x2,⋯,xn−1)=⊕i=1n−1xi, where n=4t.

DOA estimation based on cyclostationary feature extraction: An adaptive high-resolution algorithm

The quality of direction of arrival (DOA) estimation is affected by factors such as noise and interferences in wireless communication and other systems. By employing the benefits of cyclostationary signal analysis, which includes immunity to noise and interferences, in this paper, a simple high-resolution DOA estimation method is proposed. Most of the cyclostationary-based DOA estimation methods depend on the statistical properties of the received signals (e.g., the cyclic correlation matrix). Unlike them, in the proposed method, the received signal directly enters a DOA estimation loop containing a normalized least mean square (NLMS) adaptive algorithm. The method has high resolution and performance and low computational complexity in comparison with its counterparts. Moreover, it is befitting for signals in the presence of noise (Gaussian and impulsive) and interferences. Simulation results validate the efficiency of the proposed method from different aspects in comparison with other related studies.

Cyclic symplectic component decomposition with application in planetary gearbox fault diagnosis

Due to the structural complexity of planetary gearbox, it is difficult to extract the fault information in the vibration signal of planetary gearbox, which seriously affects the accuracy of fault diagnosis. Although the existing fault diagnosis methods, such as local characteristic-scale decomposition (LCD) and ensemble empirical mode decomposition (EEMD), are widely used in the field of fault diagnosis, they are difficult to decompose complex signals effectively. Therefore, a new signal processing method, called cyclic symplectic component decomposition (CSCD) based on the Toeplitz matrix and the cyclic matrix, is proposed in this paper. In CSCD, to obtain the closed-loop solutions, each row is the right cyclic shift of the previous row, so as to avoid information leakage. Meanwhile, the combination of sample covariance and symplectic geometry similarity transformation is constructed to further protect the status information and weaken the influence of noise. In addition, the reconstruction of the same mode is completed by using the extreme difference similarity (EDS), which can realize the adaptive decomposition of the signal. The research results of simulation signal and actual planetary gearbox fault signal show that the proposed CSCD method has superior decomposition performance.

Cryptographic Algorithm Based on Prime Assignment

Abstract: Cryptography is a concept of protecting information and conversations which are transmitted through a public source, so that the send and receiver only read and process it. There are several encryption and decryption algorithm which involves mathematical concepts to provide more security to the text which has to be shared through a medium. In this paper, an algorithm is provided for both coding and decoding using cyclic symmetric matrices. Also ࢘ࢋ࢒࢛ࡱ ࢚࢔ࢋ࢏࢚࢕࢚ ࢔࢕࢏࢚ࢉ࢔࢛ࢌ ,prime numbers are employed here. Furthermore, algorithm using prime number in integers is extended to prime numbers in Gaussian integers. This concept increases the security of the text. Keywords: Cryptography; encryption- decryption algorithms; Gaussian primes; cyclic symmetric matrix. 2010 MSC Subject Classifications - 11T71, 11C20, 11A25, 11R04.

Mathematical formulation F large eddy simulation using hybrid finite difference methods and poisson equations

This study uses the hybrid finite-difference method (HFDM), which combines the finite-difference and spectral approaches, to describe the Magnetohydrodynamic (MHD) turbulence decay. By using a finite-difference approach in conjunction with a cyclic Penta-diagonal matrix, the numerical algorithm of the hybrid method solves the Navier-Stokes equations and the magnetic field equation with the fourth order's precision in space and second order in time. The spectral approach is used to solve the pressure Poisson equation. The time-dependent turbulence features of this flow were in excellent agreement with the appropriate analytical solution, which is valid for short timeframes, for the classical issue of the 3-D Taylor and Green vortex flow without taking the magnetic field into account. We also show how the effective numerical approach may be utilised to model the decline of magnetohydrodynamic turbulence at various magnetic Reynolds numbers.

Universality of Weyl unitaries

Weyl's unitary matrices, which were introduced in Weyl's 1927 paper [12] on group theory and quantum mechanics, are p×p unitary matrices given by the diagonal matrix whose entries are the p-th roots of unity and the cyclic shift matrix. Weyl's unitaries, which we denote by u and v, satisfy up=vp=1p (the p×p identity matrix) and the commutation relation uv=ζvu, where ζ is a primitive p-th root of unity. We prove that Weyl's unitary matrices are universal in the following sense: if u and v are any d×d unitary matrices such that up=vp=1d and uv=ζvu, then there exists a unital completely positive linear map ϕ:Mp(C)→Md(C) such that ϕ(u)=u and ϕ(v)=v. We also show, moreover, that any two pairs of p-th order unitary matrices that satisfy the Weyl commutation relation are completely order equivalent, but that the assertion for three such unitaries fails.There is a standard tensor-product construction involving the Pauli matrices that produces irreducible sequences of anticommuting selfadjoint unitary matrices of arbitrary length. The matrices in this sequence are called Weyl-Brauer unitary matrices [11, Definition 6.63]. This standard construction is generalised herein to the case p≥3, producing a sequence of matrices that we also call Weyl-Brauer unitary matrices. We show that the Weyl-Brauer unitary matrices, as a g-tuple, are extremal in their matrix range, using recent ideas from noncommutative convexity theory.

Mechanical stimulation induces rapid fibroblast proliferation and accelerates the early maturation of human skin substitutes

The clinical treatment of large, full-thickness skin injuries with tissue-engineered autologous dermo–epidermal skin substitutes is an emerging alternative to split-thickness skin grafting. However, their production requires about one month of in vitro cell and tissue culture, which is a significant drawback for the treatment of patients with severe skin defects. With the aim to reduce the production time, we developed a new dynamic bioreactor setup that applies cyclic biaxial tension to collagen hydrogels for skin tissue engineering. By reliably controlling the time history of mechanical loading, the dynamic culturing results in a three-fold increase in collagen hydrogel stiffness and stimulates the embedded fibroblasts to enter the cell cycle. As a result, the number of fibroblasts is increased by 75% compared to under corresponding static culturing. Enhanced fibroblast proliferation promotes expression of dermal extracellular matrix proteins, keratinocyte proliferation, and the early establishment of the epidermis. The time required for early tissue maturation can therefore be reduced by one week. Analysis of the separate effects of cyclic loading, matrix stiffening, and interstitial fluid flow indicates that cyclic deformation is the dominant biophysical factor determining fibroblast proliferation, while tissue stiffening plays a lesser role. Local differences in the direction of deformation (in-plane equibiaxial vs. uniaxial strain) influence fibroblast orientation but not proliferation, nor the resulting tissue properties. Importantly, dynamic culturing does not activate fibroblast differentiation into myofibroblasts. The present work demonstrates that control of mechanobiological cues can be very effective in driving cell response toward a shorter production time for human skin substitutes.

INTERPRETATIONAL MODEL OF PARTES COMPOSITIONS AS A TOOL FOR REPRODUCING THE PARTES HERITAGE IN THE REALITIES OF MODERN CULTURE

The subject of the research is the interpretative model of a partes work in the context of modern performing practice. The aim of the research is to form the style-defining components of a performance of a partes work, based on the principles of historically informed performance and practical experience of modern choirmasters, as well as the formation of a holistic model of interpretation – a tool for creating and analyzing individual performance versions. The research methodology is based on a combination of analysis and synthesis methods, the discovery of style-defining components of performance is carried out through comparative analysis, the statistical method is used when working with individual interpretative models of domestic choirmasters. The result of the study is an interpretative model of the partes work presented in the form of a cyclic matrix. The results of this study can be used in modern performing practices, in training courses on early music in specialized educational institutions, and in modern art to deepen knowledge in the field of Ukrainian baroque music. In conclusion, it was found that the main style-defining components of the model are an affect, lyrics, vocal style, and the performers. Each of the components of the model determines the embodiment of the next one and can be realized only within the aesthetic and stylistic category of "high style".Keywords: partes works, partes style, historically informed performance, interpretive model, Ukrainian performing culture at the turn of the XX–XXI centuries.

Implementation and Evaluation of Novel Architecture Using Optical Wireless for WLAN Control Plane

We propose a novel wireless control system architecture that divides the wireless service area into smaller optical cells and centrally controls the user equipment (UE) connections under each optical cell. The proposal transmits via IoT smart lighting an optical identifier (ID) specifying connection information to the UE with illuminance sensor. The received optical ID indicates the optimum connection destination. Two solutions are proposed to overcome the hardware restrictions faced by optical ID transmission/reception. Oversampled edge-excluded receiving scheme (OE) reduces the error rate; the signal is oversampled and each window subjected to majority decision. Optical ID reception with lower error rate than conventional approach is realized with a minimum received illuminance of just 8.5 lx (background illuminance 226.67 lx) and a modulation factor of 7 %. Fast optical ID authentication (FA) reduces the authentication cycle preceding optical ID reception by performing correlation calculation between the cyclic matrix and an optical ID list. FA shortens the authentication cycle by 62.5 % (1200 ms to 450 ms). Furthermore, an optical cell control algorithm (ScanLine-based/MinDist-based) is proposed to offset the deterioration in network quality created by non-uniform UE distribution. ScanLine-based algorithm controls optical cells in scanning line manner, while MinDist-based favors optical cells with the minimum distance from the access point (AP). It is confirmed that with an optical cell radius of 5 m or less, the capacity difference per user is reduced compared to the existing RSSI-based alternative while reducing the deterioration of total capacity in extremely biased user distribution scenarios.

Color image encryption based on chaotic compressed sensing and two-dimensional fractional Fourier transform

Combining the advantages of structured random measurement matrix and chaotic structure, this paper introduces a color image encryption algorithm based on a structural chaotic measurement matrix and random phase mask. The Chebyshev chaotic sequence is used in the algorithm to generate the flip permutation matrix, the sampling subset and the chaotic cyclic matrix for constructing the structure perceptual matrix and the random phase mask. The original image is compressed and encrypted simultaneously by compressed sensing, and re-encrypted by two-dimensional fractional Fourier transform. Simulation experiments show the effectiveness and reliability of the algorithm.

Fast moving and deformational target tracking approach based on heterogeneous features fusion

Aiming at the unstable performance on fast-moving and deformational target tracking in current kernel correlation filter (KCF), an innovative approach based on heterogeneous features fusion is proposed in this paper. Firstly, a histogram of oriented gradient is utilized to cater for motion state change in complex surveillance background. Combined with a colour-free template as a novel heterogeneous feature, the proposed approach improves the tracking performance on the fast-moving target in KCF. Subsequently, the optimized spatial regularization and quadruple block method are implemented in order to solve the difficulties of scale change and boundary effect in the cyclic matrix. The simulation results indicate that the proposed approach has better precision and success rate than other popular tracking algorithms when dealing with both fast motion and deformation on the platform of the object tracking benchmark and actual traffic datasets.

Target Tracking Algorithm Suitable for Fisheye Camera in Vehicle Environment

Moving target tracking is one of the core issues in the fields of automobile assisted driving and autonomous driving. This algorithm proposes a target tracking algorithm suitable for fisheye cameras in vehicle environment. A background point removal method based on median ordering is proposed to optimize the optical flow method to solve the problem of target scale change in fisheye camera videos. Multi-scale scaling processing for frames, tracking algorithm based on cyclic matrix structure (CSK), target tracking for multiple images after zooming, using fitting to determine the maximum corresponding value, reducing the error caused by target deformation on tracking results. The tracking test results of multiple fisheye camera videos in the vehicle environment show that the algorithm has high real-time tracking accuracy.

Compensation Method for Sensor Network Clock Error Based on Cyclic Symmetry Algorithm.

Since the existing methods cannot evaluate the time delay of different layers of sensor networks, there are some problems such as the low precision of clock error compensation, high time delay, and low efficiency of communication in sensor networks. To solve this problem, a method of clock error compensation in sensor networks based on a cyclic symmetry algorithm is proposed. Based on the basic theory of cyclic symmetry, the cyclic symmetry matrix of the sensor network is constructed; in the communication process, all nodes are extended to get the cumulative delay rate of the sensor network in the specified time domain. Using the cumulative delay rate of the cyclic network and the sensor network, the autoregressive integral sliding mode control model is established to compensate for the cumulative error of clock synchronization. The simulation results show that the compensation accuracy of this method is more than 98%, which can effectively reduce the delay of sensor network. It improves the communication efficiency of the sensor network, meets the communication requirements of the sensor network, and has a very broad application prospect.

Regional fuzzy binocular stereo matching algorithm based on global correlation coding for 3D measurement of rail surface

In view of the uncontrollable imaging quality of the electromagnetic railgun’s rail, based on the existing 3D measurement system, which combines binocular vision with active dot matrix illumination, a regional fuzzy binocular stereo matching algorithm based on global correlation coding is presented. Considering the lack of imaging details and textures and the problem of point target matching, the proposed stereo matching algorithm can get more complete and reliable matching results. Compared with the existing matching algorithms (such as SSD, SIFT, DP, BP, GC, etc.), the proposed matching algorithm can ensure the overall matching accuracy of left and right views, and has higher matching integrity. The implementation of the algorithm is that, the image spatial correlation of target image is firstly decoupled by coding, and then the L1 correlation constraint is calculated for the matched images. The combination of cyclic displacement matrix and random matrix is adopted here encoding the target image, which can make the coding result more robust. Meanwhile, the 3D measurement experiment of rail surface is done under dim light condition. The experimental results show that the matching integrity can reach 99.44 %. Through the experiment, the 3D depth map of the target scene is obtained.

Symmetry of cyclic weighted shift matrices with pivot-reversible weights

We prove that every cyclic weighted shift matrix with pivot-reversible weights is unitarily similar to a complex symmetric matrix.