Generator Matrix Research Articles

A Class of Skew-Cyclic Codes over (Z_(2^m ) [u])/〈u^2-r〉 with Derivation

Let R_r=Z_(2^m )+uZ_(2^m ) be a finite ring, where u^2=r for r∈Z_(2^m ), m is a positive integer, and m≥2. In this paper, we study a class of skew-cyclic codes using a skew polynomial ring over R_r with an automorphism θ_r and a derivation δ_(θ_r ). We generalize the skew-cyclic codes over Z_4+uZ_4; u^2=1 to the skew-cyclic codes over R_r, and call such codes as δ_(θ_r )-cyclic codes. We investigate the structures of a skew polynomial ring R_r [x,θ_r,δ_(θ_r ) ]. A δ_(θ_r )-cyclic code is showed to be a left R_r [x,θ_r,δ_(θ_r ) ]-submodule of (R_r [x,θ_r,δ_(θ_r ) ])/〈x^n-1〉 . We give the generator matrix of a δ_(θ_r )-cyclic code of length n over R_r. Also, we present the generator matrix of the dual of a free δ_(θ_r )-cyclic code of even length n over R_r.

Patterns of IgA Autoantibody Generation, Inflammatory Responses and Extracellular Matrix Metabolism in Patients with Alcohol Use Disorder.

Recent data have emphasized the role of inflammation and intestinal immunoglobulin A (IgA) responses in the pathogenesis of alcoholic liver disease (ALD). In order to further explore such associations, we compared IgA titers against antigens targeted to ethanol metabolites and tissue transglutaminase with pro- and anti-inflammatory mediators of inflammation, markers of liver status, transferrin protein desialylation and extracellular matrix metabolism in alcohol-dependent patients with or without liver disease and in healthy controls. Serum IgAs against protein adducts with acetaldehyde (HbAch-IgA), the first metabolite of ethanol, and tissue transglutaminase (tTG-IgA), desialylated transferrin (CDT), pro- and anti-inflammatory cytokines, markers of liver status (GT, ALP) and extracellular matrix metabolism (PIIINP, PINP, hyaluronic acid, ICTP and CTx) were measured in alcohol-dependent patients with (n = 83) or without (n = 105) liver disease and 88 healthy controls representing either moderate drinkers or abstainers. In ALD patients, both tTG-IgA and HbAch-IgA titers were significantly higher than those in the alcoholics without liver disease (p < 0.0005 for tTG-IgA, p = 0.006 for Hb-Ach-IgA) or in healthy controls (p < 0.0005 for both comparisons). The HbAch-IgA levels in the alcoholics without liver disease also exceeded those found in healthy controls (p = 0.0008). In ROC analyses, anti-tTG-antibodies showed an excellent discriminative value in differentiating between ALD patients and healthy controls (AUC = 0.95, p < 0.0005). Significant correlations emerged between tTG-IgAs and HbAch-IgAs (rs = 0.462, p < 0.0005), CDT (rs = 0.413, p < 0.0001), GT (rs = 0.487, p < 0.0001), alkaline phosphatase (rs = 0.466, p < 0.0001), serum markers of fibrogenesis: PIIINP (rs = 0.634, p < 0.0001), hyaluronic acid (rs = 0.575, p < 0.0001), ICTP (rs = 0.482, p < 0.0001), pro-inflammatory cytokines IL-6 (rs = 0.581, p < 0.0001), IL-8 (rs = 0.535, p < 0.0001) and TNF-α (rs = 0.591, p < 0.0001), whereas significant inverse correlations were observed with serum TGF-β (rs = -0.366, p < 0.0001) and CTx, a marker of collagen degradation (rs = -0.495, p < 0.0001). The data indicate that the induction of IgA immune responses toward ethanol metabolites and tissue transglutaminaseis a characteristic feature of patients with AUD and coincides with the activation of inflammation, extracellular matrix remodeling and the generation of aberrantly glycosylated proteins. These processes appear to work in concert in the sequence of events leading from heavy drinking to ALD.

Mathematical Study of Effect of Temperature on Transmission Dynamics of Dengue Disease

Dengue fever is found in tropical and subtropical regions around the world. It is a vector-borne disease that is transmitted by female aedes mosquitoes infected with one of four dengue viruses (DENV1- DENV4). SEIR compartmental model is used to examine the transmission of the disease in the present work. The model has four compartments for the human population, susceptible, exposed, infected, and recovered and also four compartments for the mosquito population immature, susceptible, exposed, and infected. The impact of temperature on the dynamics of dengue disease transmission is described by this model. The basic reproduction number of the model is computed by implementing the Next Generation Matrix Method. Sensitivity analysis is performed to establish the relative importance of the model parameters and mathematical results are shown graphically.

A Drinfeld-Type Presentation of the Orthosymplectic Yangians

We use the Gauss decomposition of the generator matrix in the R-matrix presentation of the Yangian for the orthosymplectic Lie superalgebra ospN|2m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {osp}_{N|2m}$$\\end{document} to produce its Drinfeld-type presentation. The results rely on a super-version of the embedding theorem which allows one to identify a subalgebra in the R-matrix presentation which is isomorphic to the Yangian associated with ospN|2m-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {osp}_{N|2m-2}$$\\end{document}.

Dual core processors: Coupled queues: Transient performance evaluation

High-Performance Computing (HiPC) systems routinely employ multi/many – core processors. Specifically, dual – core processors find many applications in pervasive computing devices. Dual–core processors employ buffers for queueing the incoming jobs. Traditionally, the queues at the processors are assumed to be independent and the queueing system is analyzed in equilibrium for tractability purposes. Queues are modeled using Continuous Time Markov Chains (CTMC's) and the equilibrium performance measures are determined to analyze as well as design the queueing systems. In most interesting cases, the incoming jobs are routed to the queues using the Join the Shortest Queue (JSQ) policy. Thus, with such an adaptive routing algorithm, the two queues are evidently coupled and are not statistically independent. Hence traditional equilibrium performance evaluation doesn't provide realistic performance measures. In this research paper, the two queues associated with buffers in dual-core processors are considered to be coupled. The Coupled Queues are modeled using a Quasi – Birth – and – Death (QBD) process. Using traditional results related to QBD processes, equilibrium performance measures are determined. More interestingly, we demonstrate the tractability of the computation of transient probability distribution of a QBD process. In the research literature, transient analysis of the QBD process was shown to be tractable in the Laplace transform domain. But in this research paper, we prove that the matrix exponential eQt arising in transient analysis (where Q is the generator matrix of the QBD process) can be computed directly in the time domain rendering efficient transient analysis of QBD process. Using the transient probability mass function of queue length, estimation of transient performance measures such as expected queue length, average delay, and tail distribution can be determined. Further, optimal adaptive routing algorithms for coupled queues can be designed.

A novel PPARβ/FFA1 dual agonist Y8 promotes diabetic wound healing

BackgroundDiabetes ulcer is one of the leading causes of disability and death in diabetics. Y8 [(2-(2-fluoro-4-((4-methyl-2-(4-(trifluoromethyl)phenyl)thiazol-5-yl)methoxy) phenoxy)acetic acid)], a dual agonist of peroxisome proliferation activated receptorβ (PPARβ) and free fatty acid receptor 1 (FFA1/FFAR1/GPR40), a new compound molecule with the potential for diabetes ulcer treatment. ObjectiveTo research the effect of the dual target agonist Y8 and its mechanism of action in the treatment of diabetic ulcers. MethodsWe have established a wound model in diabetic mice. After treatment with Y8, wound healing was evaluated by tissue pathology, reactive oxygen species (ROS) levels, and gene expression testing. Under high sugar conditions, the mechanism of Y8 affecting fibroblasts' proliferation and keratinocytes' migration is further studied. ResultsWe found that Y8 accelerated wound healing and shortened healing time in diabetic mice. Granulation tissue generation and extracellular matrix (ECM) deposition were significantly increased in Y8-treated mice. Mechanistically, Y8 promotes keratinocyte proliferation by activating PPARβ and migration of keratinocytes by triggering FFA1 in vitro. In addition, Y8 also decreased ROS levels in fibroblasts in vitro and in vivo by activating PPARβ, reducing their release of superoxide anions. ConclusionOur results suggest that PPARβ/FFA1 dual agonist Y8 has the effect of promoting the healing of diabetic ulcer wounds in vivo and in vitro, and its therapeutic effect is better than that of single-target agonists.

Construction of asymmetric orthogonal arrays of high strength via generator matrix

Asymmetric orthogonal arrays are very useful in theoretical studies and practical applications. However, it is difficult to construct such designs of high strength. In this article, we use the generator matrix method to obtain some asymmetric orthogonal arrays of strength three. Then we combine it with the general (further) replacement procedure to get more general asymmetric orthogonal arrays of high strength.

Application of the method of equivalent message encoding structures to simplify coding complexity

Formulation of the problem. Modern telecommunication technologies make it possible to transmit data over long distances with limitations in the form of low power consumption and low error rate using error correction codes. The use of such codes plays an important role and is necessary to detect and correct errors caused by signal distortion and noise in the communication channel. According to Shannon's channel coding theorem, the probability of error can be arbitrarily small or close to zero if the encoding rate of transmission R is less than or equal to the bandwidth of channel C. Assuming that the bandwidth C is achievable, we can calculate the minimum signal-to-noise power ratio (SNR) to achieve zero error, or an arbitrarily small error called the Shannon limit, while maintaining R ≤ C. This article discusses a method of applying equivalent message encoding structures to construct low-density parity-checking (LDPC) codes. Low-density parity-checking (LDPC) codes are a class of linear block codes in which the complexity of iterative decoding increases linearly with increasing block length. Standard LDPC codes without modifications are considered to demonstrate the effectiveness of the proposed method, which is expected to provide high encoding speed when transmitting messages with a short block length. The method of obtaining equivalent structures allows: to reduce the computational complexity of encoding and decoding; to provide the possibility of finding a new encoding scheme and evaluating its effectiveness. The validity of the method for obtaining equivalent message encoding structures is evaluated by modeling the bit error rate (BER) of LDPC codes. Purpose. to show the effectiveness of the use of equivalent structures for various methods of compression of transmitted information, to minimize the complexity of encoding, while maintaining energy efficiency, correcting ability and data transfer rate. Results. A method is considered for obtaining equivalent message element encoding structures that can be used to create more LDPC codes for data transmission applications with a short block length. The cascade principle of constructing an equivalent generator and a parity check matrix was analyzed, which also leads to minimizing the computational complexity of the encoder and decoder. An equivalent structure G can be obtained from cascading two (or more) matrices by modifying the second matrix so that it has a unit matrix with the size of the parity check length and a shift to the right by k bits. On the other hand, the equivalent structure H can be obtained by simply cascading directly the second matrix and shifting to the right by k bits. According to the simulation results, the proposed method is adequate, since LDPC codes have the same BER characteristics as codes based on the low density generator matrix (LDGM). During the simulation, it was concluded that the SPC codes (single parity check (single parity check (SPC)) are the most efficient codes (for a given block length), since SPC codes have the smallest interval up to the Shannon limit. Practical significance. The results presented in this article will give a new insight into the development of simple channel coding of LDPC codes of short block length with high encoding speed for future applications with lower power consumption.

Effects of intramolecular chain conformation on the hydration and miscibility of polyethylene glycol in water studied by means of polymer reference interaction site model theory.

To examine the conventional idea that the gauche conformation of the OCCO dihedral angle promotes the dissolution of polyethylene glycol (PEG) in water through strong hydration, the thermodynamic properties of liquid mixtures of PEG and water were studied by means of polymer reference interaction site model (PRISM) theory. The intramolecular correlation functions required as input for PRISM theory were calculated by the generator matrix method, accompanied by changes in the distribution of dihedral angles. In the infinite dilution limit, the increased probability of gauche conformation of the OCCO dihedral angles stabilizes the hydration of PEG through enhanced hydrogen bonding between the ether oxygen of PEG and water. The mixing Gibbs energies of the liquid mixtures were also calculated in the whole concentration range based on the Gibbs-Duhem equation, as per our recent proposal. A liquid-liquid phase separation was observed when all the dihedral angles of PEG were in the trans conformation; for the liquid mixture to be miscible in the whole concentration range, the introduction of the OCCO gauche conformation was found to be indispensable. The above theoretical results support the conventional idea that the OCCO gauche conformation is important for the high miscibility of PEG and water.

MODEL EPIDEMIK CAMPAK DENGAN ADANYA VAKSIN PADA POPULASI RENTAN DAN SUPPORT PADA POPULASI TEREKSPOSE

Measles is a highly contagious disease and often occurs in children due to malnutrition, especially children with vitamin A deficiency and a weakened immune system. In addition to vaccination, the role of parents is needed in the form of support to control the development of the virus in the body. This measles disease can be modeled through a mathematical model, especially epidemic model. This study aims to explain the formation of a mathematical model of measles, determine the equilibrium point, basic reproduction number, stability analysis, and to perform numerical simulations on the model. The research procedure begins with construct a model using a system of nonlinear differential equations. The basic reproduction number can be determined using the next generation matrix method and analysis of model stability using the linearization method. While numerical simulation has been carried out using the fourth order Runge Kutta method. The result of this study is the formation of a mathematical model of measles with a population consisting of four compartments, namely Susceptible, Exposed, Infected and Recovered. Disease control is carried out in the model, namely vaccines in the Susceptible population and support measures in the Exposed population. From the model formed, two equilibrium points are obtained, namely the disease-free equilibrium point and the endemic equilibrium point. Furthermore, the basic reproduction number formula and analysis of the stability of the model at the disease-free equilibrium point and endemic equilibrium point are also obtained. Finally, a simulation model is presented to support stability analysis and comparison of solutions for the Infected population before being given control support and after being given control support with variations in vaccine percentages.

The future of business events in the “phygital” age: development of a generative tool

ABSTRACT The purpose of this paper is to investigate the future of business events in the “phygital” age from the viewpoint of purposes and formats, delivering a generative tool for adoption. The approach is based on constructivist epistemology. The topic was approached from the viewpoint of foresight and Design Research, firstly by designing and performing three cycles of qualitative interviews with (a) thought leaders and senior industry experts (setting the drivers for matrix tool development), for a total of 10 respondents within a gender-balanced panel (50% female, 50% male), covering Western, Asian, Arab, and North American regions. A Machine Learning-enabled scan was performed for triangulation purposes. Secondly, a generative matrix tool was designed and tested by (b) senior to midweight Design Thinkers and (c) junior to midweight emerging talents, for a total of 22 respondents. Key findings pertain to current trends and future developments in business event design and management from a “phygital” perspective, transferred into a generative matrix tool.

Numerical solutions of fractional order rabies mathematical model via Newton polynomial

The recent outbreak of rabies virus has affected numerous individuals in the community, highlighting the importance of studying the disease mathematically in epidemiology. In this paper, we develop a mathematical model for the spread of rabies disease using the harmonic mean incidence rate and determine the reproduction number R0 using the next generation matrix approach. The fractional dynamics of the model incorporate the interaction between infected individuals and environmental factors. We analyze the model using both Atangana-Baleanu-Caputo (ABC) and Caputo-Fabrizio (CF) techniques, drawing on both modern and classical approaches. For qualitative investigation using fractional operators, we utilize the Banach fixed-point theory and derive the Hyers-Ulam stability concept. We assign values to the model parameters and utilize the Newton interpolation technique to obtain a numerical scheme. Additionally, we perform sensitivity analysis on the model. In conclusion, our findings provide important insights for the study of epidemics.

Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage.

African swine fever is a highly contagious virus that causes pig disease. Its onset process is short, but the mortality rate is as high as 100%. There are still no effective drugs that have been developed to treat African swine fever, and prevention and control measures are currently the best means to avoid infection in pig herds. In this paper, two fractional order mathematical models with media coverage are constructed to describe the transmission of African swine fever. The first model is a basic model with media coverage, and no control measures are considered. For this model, the reproduction number is obtained by using the next generation matrix method. Then, the sufficient conditions for the existence and stability of two equilibriums are obtained. Based on the first model, the second model is established incorporating two control measures. By using Pontryagin's maximal principle, the optimal control solution is derived. After that, some numerical simulations are performed for the two models to verify the theoretical results. Both the qualitative analysis and numerical results indicate that timely media coverage combined with disinfection control measures is crucial to preventing the spread of disease.

Random sparse generators of Markovian evolution and their spectral properties.

The evolution of a complex multistate system is often interpreted as a continuous-time Markovian process. To model the relaxation dynamics of such systems, we introduce an ensemble of random sparse matrices which can be used as generators of Markovian evolution. The sparsity is controlled by a parameter φ, which is the number of nonzero elements per row and column in the generator matrix. Thus, a member of the ensemble is characterized by the Laplacian of a directed regular graph with D vertices (number of system states) and 2φD edges with randomly distributed weights. We study the effects of sparsity on the spectrum of the generator. Sparsity is shown to close the large spectral gap that is characteristic of nonsparse random generators. We show that the first moment of the eigenvalue distribution scales as ∼φ, while its variance is ∼sqrt[φ]. By using extreme value theory, we demonstrate how the shape of the spectral edges is determined by the tails of the corresponding weight distributions and clarify the behavior of the spectral gap as a function of D. Finally, we analyze complex spacing ratio statistics of ultrasparse generators, φ=const, and find that starting already at φ⩾2, spectra of the generators exhibit universal properties typical of Ginibre's orthogonal ensemble.

Analysis of dengue infection transmission dynamics in Nepal using fractional order mathematical modeling

Dengue is a significant factor to the global public health issue, including Nepal. In Nepal from 2004−2022, the largest outbreak occurred in the year 2022. Dengue infection cases appeared all over 77 districts of Nepal. The Caputo fractional order SEIR-SEI epidemic model is able to describe dengue disease transmission dynamics of present situation. For fundamental mathematical guarantees of epidemic model equations, we studied the Lipschitz and Banach contraction theorems to show that the model equations have a unique solution. The Ulam-Hyres stability is established in the model. Next generation matrix approach is used to calculate the associated basic reproduction number R0. The model equilibrium points are identified, and the local asymptotic stability for disease-free equilibrium point is analyzed. Normalized forward and partial rank correlation coefficient are used for sensitivity study to identify the factors that affect dengue infection with respect to basic reproduction number. Using real data of Nepal, the model is fitted and the least square method is used for estimating parameters. Numerical scheme has been illustrated using a two-step Lagrange interpolation approach and the solution is approximated. With numerical results and sensitivity analysis, it is concluded that biting rate and death rate of mosquito are extremely sensitive to the disease transmission. The transmission increases with increasing biting rate and decreases with decreasing mosquito death rate. For the year 2022, R0=1.7739>1 showing that the disease is endemic. Thus, effective control measure should be implemented to combat the dengue virus. However, further research needs to be undertaken to assess the impact of such control measures.

Cystic echinococcosis dynamics in dogs, humans and cattle: Deterministic and stochastic modeling

This work investigates the dynamics of cystic echinococcosis in humans, dogs and cattle. The next generation matrix method is employed to derive the basic reproduction number R0. The normalized forward sensitivity index is used to identify sensitive parameters to disease transmission. The multitype branching process is adopted to compute the likelihood of disease extinction or spread in humans, dogs, and cattle. Numerical results show that both the disease free equilibrium and the endemic equilibria exist. Sensitivity analysis shows that the most positive sensitive parameters to disease transmission are rate at which human and dog infection from contaminated environments and infectious meat respectively, the rate at which exposed cattle progress to an infectious stage, the rate at which infected dogs defecate, and the rates at which dogs and cattle are recruited are most positive sensitive parameters to disease transmission. The most negative sensitive parameters are the natural mortality rates of dogs and cattle. According to the results of the simulation, there is a high likelihood that cystic echinococcosis will become extinct if the disease arises from echinococcus tapeworms, but a low likelihood if it arises from either infectious meat or an infected dog population. The disease dies, nevertheless, if it emerges from infected people. Based on results, we suggest that measures such as dog indoor keeping, meat inspection and treatment of infected dog population be implemented to control cystic echinococcosis in humans, dogs and cattle.

Connections between Linear Complementary Dual Codes, Permanents and Geometry

Linear codes with complementary duals, or LCD codes, have recently been applied to side-channel and fault injection attack-resistant cryptographic countermeasures. We explain that over characteristic two fields, they exist whenever the permanent of any generator matrix is non-zero. Alternatively, in the binary case, the matroid represented by the columns of the matrix has an odd number of bases. We explain how Grassmannian varieties as well as linear and quadratic complexes are connected with LCD codes. Accessing the classification of polarities, we relate the binary LCD codes of dimension k to the two kinds of symmetric non-singular binary matrices, to certain truncated Reed–Muller codes, and to the geometric codes of planes in finite projective space via the self-orthogonal codes of dimension k.

ANALISIS KESTABILAN DAN SOLUSI NUMERIK PADA MODEL SEIR UNTUK PENYAKIT TUBERKULOSIS

One of the infectious diseases that can be modelled into the SEIR model is Tuberculosis (TB), this is because TB has a bacterial incubation period, so it is at this time that a person enters the exposed subpopulation. TB is divided into two types, namely latent TB and active TB. This study aims to explain the formation of the SEIR Model for the Spread of Tuberculosis, determine the equilibrium point and Basic Reproductive Numbers on the SEIR Model for the Spread of Tuberculosis, analyze the stability of the SEIR Model for the spread of Tuberculosis at the equilibrium point, and make numerical simulations. The result of this research is the formation of a mathematical model on the spread of Tuberculosis, and from the model obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. Then the basic reproduction number ( ) was found through the Next Generation Matrix. Furthermore, the stability analysis was carried out at the disease-free equilibrium point and it was found that the local asymptotic stable model with , while at the endemic equilibrium point it was found that the local asymptotic stable model with . Numerical simulations are presented to show numerical solutions and strengthen the explanation of the stability analysis of the model using the fourth-order Runge-Kutta method with parameters that meet the stability requirements.

Mathematical modelling approach to cholera transmission with vaccination strategy

In this work, we investigated the transmission of cholera infection through mathematical modelling. We calculated the contact number by applying the technique of next generation matrix method to find about infection dissemination as well as control in the population. Two types of constant solutions: infection free as well as infection present have been calculated. Stability of both constant solutions has been discussed. To control the dissemination of disease, we formulated an optimal control problem. Strategies, which are used to control this disease, have been composed on the consequences of sensitivity analysis. In order to gain better insight into the comparative results of analytical and numerical outcomes, the problem was revisited, and found that numerical results support our analytical findings. Our results conclude that pre-exposure vaccination can substantially reduce the risk of cholera.

Mathematical Modeling of Post-Exposure Prophylaxis of SARS-CoV-2\r

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) emerged in December 2019, and as of August 29, 2022, this virus was responsible for about 6 million confirmed deaths and about 450 million confirmed cases of COVID-19 globally. In this project, we used mathematical modeling to investigate the impact of post-exposure prophylaxis in preventing the spread of SARS-CoV-2. The disease-free equilibrium of our model is derived, and the basic reproduction number is computed, using the next generation matrix approach. We studied the elasticity indices of the reproduction number with respect to each parameter and identified parameters that are most sensitive in increasing the reproduction number and those that are most sensitive in decreasing the reproduction number. Numerical simulations suggest that an increase in the modification parameter for the transmission rate of breakthrough cases results in more infectiousness for those not on prophylaxis when compared to individuals on prophylaxis. The outcomes of our contour plot suggest the possibility of eradicating the virus from the population under different combinations of the proportion of individuals who recently came in contact with an infectious individual and have been administered an antiviral drug such as REGEN-CoV. Results of numerical simulations and contour plots highlight the importance of post-exposure prophylaxis on the transmission of SARS-CoV-2 in the population.