Encephalitis is an acute inflammatory disease of the brain and continues to pose a significant public health challenge, particularly in the case of viral infections capable of sustained human-to-human transmission and progression to severe clinical outcomes. Effective disease management requires intervention strategies that can reduce transmission while avoiding excessive strain on limited healthcare resources. In this study, we develop and analyze an SEITR-type compartmental model that incorporates multiple intervention measures, including prevention, early treatment, intermittent therapy, and suppressive treatment. To better capture disease severity and healthcare demand, additional compartments representing intensive care unit (ICU) admission and ventilator support are included. Numerical simulations are carried out to investigate the combined impact of these interventions on disease dynamics and associated costs. The results indicate that coordinated implementation of control measures can substantially reduce the epidemic burden, lowering the peak number of infections by approximately 85 % and cumulative cases by about 95 % compared with an uncontrolled scenario, while remaining economically feasible within the model assumptions. These findings highlight the potential benefits of integrated intervention strategies for mitigating transmission and managing healthcare capacity during encephalitis outbreaks. The proposed framework provides a quantitative basis for comparative assessment of control strategies and may serve as a decision-support tool for exploring intervention trade-offs in the context of viral encephalitis.
In this research, a novel variant model of the classical Lorenz system is proposed by reformulating both the classical and fractional-order Lorenz systems through a new framework based on piecewise fractional derivatives. The resulting piecewise Lorenz system is formulated as a nonlinear system of differential operators exhibiting rich and complex dynamical behaviors induced by the piecewise structure. The proposed model is developed within the frameworks of the Caputo fractional derivative, the Atangana–Baleanu fractional derivative, and the Caputo–Fabrizio fractional derivative. A rigorous qualitative analysis is carried out to establish the existence and uniqueness of solutions for the modified piecewise Lorenz system. Furthermore, the dynamical and chaotic properties of the system are investigated through numerical approximations based on the Newton interpolation formula. Numerical simulations and graphical illustrations demonstrate the effectiveness and accuracy of the proposed numerical scheme and reveal the influence of fractional orders and system parameters on the system dynamics. In particular, the system exhibits crossover behavior and chaotic dynamics characterized by the coexistence of two strange attractors, highlighting significant differences from the classical Lorenz system.
In the field of optimization, there has been an enormous surge in interest in addressing large-scale many-objective problems. Numerous academicians and practitioners have contributed to evolutionary computation by developing a variety of optimization algorithms tailored to tackle computationally challenging optimization problems. Recently, various largescale many-objective optimization algorithms (LSMaOAs) have been proposed to address complex large-scale many-objective optimization prob lems (LSMaOPs). These LSMaOAs have shown remarkable performance in addressing a variety of LSMaOPs. However, there is a pressing need to further investigate their performance in comparison to each other on different classes of LSMaOPs. In this study, we conduct a comparative investigation of three established LSMaOAs namely, LMEA, LMOCSO and S3CMAES over rigorous benchmarking on DTLZ, LSMOP, UF9-10, WFG test suites, encompassing problem sets with three to ten objectives and varying numbers of variables between 100 and 500. Additionally, we assess the algorithm’s efficacy on a test suite specifically designed for large-scale multi/many-objective problems (100-1000 decision variables). In addition, we propose Hybrid-LMEA, a light hybrid that integrates decision-variable clustering with competitive learning to improve both convergence and diversity. The hybrid works especially well on high-dimensional large-scale many-objective optimization problems with better performance in 8 and 12 out of 27 test cases for IGD and GD, respectively. The outcomes of the experiments indicate the relative efficacy and effectiveness of the different algorithms in addressing large-scale many-objective problems. Researchers can leverage this comparative data to make informed decisions about which algorithms to employ for particular optimization problem domains.
Abstract We introduce multi-location networks to model the real-world phenomena of nodes existing in multiple places simultaneously. A multi-location network contains a set of locations. Each location can have a different set of nodes, but nodes can be present in multiple locations at once. In contrast, a multiplex network contains a set of layers, where each layer shares the same set of nodes. By combining these two structures, a multi-location multiplex network (MLMN) enables nodes to appear in various locations and connect through multiple edge types. For example, in a species interaction MLMN, locations could correspond to continents, while layers represent different types of interactions, such as predation and competition. Some species may inhabit multiple continents, with interactions varying by location. Analyzing the evolution of MLMNs poses substantial challenges due to the complexity of integrating location and edge type. Traditional dynamic network logistic regression models often aggregate data across these structures, leading to information loss. In this paper, we extend dynamic network logistic regression to accommodate MLMNs, improving the estimation of factors driving changes in such networks. Our approach predicts node presence in each location and the formation of edges across different layers at each location. We provide theoretical guarantees for the model, including global optimality, consistency, asymptotic normality, and asymptotic efficiency of the estimated parameters. The model’s finite sample performance is evaluated through simulations. Additionally, a case study is conducted using a dataset from Equinix, a 2024 Fortune 500 company and one of the world’s largest data center operators. Our findings highlight the strong impact of location on node presence and link formation, showcasing the practical relevance of understanding multi-location structures to capture complex network dynamics.
<p>This paper introduces and explores the concept of neutrosophic superhyper BCI-semigroups, an advanced algebraic structure integrating neutrosophic logic, superhyper operations, and BCI-algebras into a semigroup framework. Neutrosophic superhyper BCI-semigroups facilitate the handling of indeterminate and conflicting information by incorporating neutrosophic triplets for each element, denoting degrees of truth, indeterminacy, and falsity. The study defines essential properties such as closure, associativity, BCI identity, and neutrosophic membership and provides illustrative examples to demonstrate these properties in practical scenarios. Further, the paper delves into the characteristics of idempotent and commutative elements, homomorphisms, ideals, subsemigroups, and quotient sets within the context of neutrosophic superhyper BCI-semigroups. Key theorems are presented to establish foundational principles and behaviors of these structures, highlighting their theoretical implications and potential for practical applications.</p>
Wefiton Sousa Rocha, Sthephany de Castro Ruivo, Mairton Cavalcante Romeu
et al.
O presente artigo apresenta os resultados de uma Revisão Sistemática de Literatura (RSL) sobre o Arduino no ensino de física, utilizando artigos científicos indexados nas plataformas CAPES, SciELO e Redalyc, no período de 2018 a 2023. O objetivo desta pesquisa foi conduzir uma análise crítica da contribuição dos estudos na área acadêmica e científica no contexto nacional. Foram adotados procedimentos de pesquisa qualitativa, fundamentados nos conceitos técnicos e científicos da RSL, com processos e dados apresentados em quadros e gráficos. Os estudos analisados evidenciaram contribuições significativas no uso de equipamentos digitais em abordagens experimentais, destacando-se pela utilização de materiais de baixo custo. No entanto, foi observada uma baixa incidência da robótica educacional como estratégia de ensino nesta amostra. Espera-se que este estudo contribua para o campo acadêmico e científico, auxiliando professores e pesquisadores acerca das estratégias de ensino envolvendo Arduino e o ensino de física.
Special aspects of education, Applied mathematics. Quantitative methods
The economic vitality of a nation is contingent upon the advancement of its manufacturing sectors, given their pivotal role in fostering economic growth. These industries frequently encounter challenges such as mitigating deterioration rates, enhancing revenue and reducing overall costs to optimize profits. Consequently, should an item deteriorate while in stock within manufacturing facilities, it results in a gradual escalation of holding costs and total expenses. In this paper discusses determining the most effective production policy for items prone to degradation, analyzing depreciating items using three-stage production inventory models with trapezoidal demand to minimize holding costs based on time-dependent factors in the manufacturing sector. This model aims to decrease overall costs and production time periods, contrasting with the higher cost values of the price-based constant method. Mathematical formulas were developed using MATLAB R2023b to validate the models findings and minimize the inventory systems cost.
Neste artigo apresentamos os estudos realizados nos últimos 10 anos sobre o ensino explícito da metacognição na aprendizagem de Química. Quanto aos aspectos metodológicos, trata-se de uma revisão bibliográfica que se propõe a verificar a existência de pesquisas recentes envolvendo o tema e quais as contribuições dessas para a área da educação. Acreditamos que esses apontamentos possam contribuir nas discussões concernentes ao processo de aprendizagem dos estudantes quanto às orientações estabelecidas pela Agenda 2030 por meio do Objetivo de Desenvolvimento Sustentável - ODS 4, que trata sobre a educação. A busca por artigos foi realizada nas bases de dados ERIC, CAPES e Scielo, sendo localizados nove artigos que fazem parte desta revisão. Os resultados indicaram que, apesar da metacognição ser pesquisada por estudiosos de diversas áreas, interessados em compreender como as pessoas aprendem, o ensino explícito da metacognição em Química necessita ser mais investigado, apontamento realizado pela maioria dos pesquisadores referenciados nos estudos revisados.
Special aspects of education, Applied mathematics. Quantitative methods
Oluwasegun M. Ibrahim, Daniel Okuonghae, Monday N.O. Ikhile
This present paper considers the dynamics of two criminal gangs in a criminally active population. In our deterministic approach, we present the gang rivalry model to measure the impact of rivalry intensities at low and moderately high initiation rates. The qualitative and quantitative properties of the models are investigated using appropriate techniques that have proven to be effective. Based on the numerical simulation study, the initiation rates are observed to play a key role in the rise and fall of rivalry intensities in the criminally active period, which is characterized by a low level of law enforcement. Furthermore, this study reveals that by reducing the initiation rate between susceptible individuals and criminal gang groups, the rivalry intensities will be impacted for the overall public safety.
We consider the half-linear differential equation \[(|x'|^{\alpha}\mathrm{sgn}\,x')' + q(t)|x|^{\alpha}\mathrm{sgn}\,x = 0, \quad t \geq t_{0},\] under the condition
\[\lim_{t\to\infty}t^{\alpha}\int_{t}^{\infty}q(s)ds = \frac{\alpha^{\alpha}}{(\alpha+1)^{\alpha+1}}.\] It is shown that if certain additional conditions are satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as \(t\to\infty\).
Arbel Julyan, Dang Hong-Phuong, Elvira Clement
et al.
This article summarizes some recent works and associated challenges in the field of Bayesian statistics that were presented during the Journées MAS 2020. The goal of the session was to give an overview of the many aspects of Bayesian statistics investigated by young researchers of the community.
A class of zipper fractal functions is more versatile than corresponding classes of traditional and fractal interpolants due to a binary vector called a signature. A zipper fractal function constructed through a zipper iterated function system (IFS) allows one to use negative and positive horizontal scalings. In contrast, a fractal function constructed with an IFS uses positive horizontal scalings only. This article introduces some novel classes of continuously differentiable convexity-preserving zipper fractal interpolation curves and surfaces. First, we construct zipper fractal interpolation curves for the given univariate Hermite interpolation data. Then, we generate zipper fractal interpolation surfaces over a rectangular grid without using any additional knots. These surface interpolants converge uniformly to a continuously differentiable bivariate data-generating function. For a given Hermite bivariate dataset and a fixed choice of scaling and shape parameters, one can obtain a wide variety of zipper fractal surfaces by varying signature vectors in both the <i>x</i> direction and <i>y</i> direction. Some numerical illustrations are given to verify the theoretical convexity results.
This paper is concerned with oscillatory behavior of linear functional differential equations of the type \[y^{(n)}(t)=p(t)y(\tau(t))\] with mixed deviating arguments which means that its both delayed and advanced parts are unbounded subset of \((0,\infty)\). Our attention is oriented to the Euler type of equation, i.e. when \(p(t)\sim a/t^n.\)
Abstract The deluge of network datasets demands a standard way to effectively and succinctly summarize network datasets. Building on similar efforts to standardize the documentation of models and datasets in machine learning, here we propose network cards, short summaries of network datasets that can capture not only the basic statistics of the network but also information about the data construction process, provenance, ethical considerations, and other metadata. In this paper, we lay out (1) the rationales and objectives for network cards, (2) key elements that should be included in network cards, and (3) example network cards to underscore their benefits across a variety of research domains. We also provide a schema, templates, and a software package for generating network cards.
The security of RSA relies on the computationally challenging factorization of RSA modulus <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><msub><mi>p</mi><mn>1</mn></msub><mo> </mo><msub><mi>p</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> with <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo> </mo></mrow></semantics></math></inline-formula>being a large semi-prime consisting of two primes <inline-formula><math display="inline"><semantics><mrow><msub><mi>p</mi><mn>1</mn></msub><mi>and</mi><mo> </mo><msub><mi>p</mi><mn>2</mn></msub><mo>,</mo></mrow></semantics></math></inline-formula> for the generation of RSA keys in commonly adopted cryptosystems. The property of <inline-formula><math display="inline"><semantics><mrow><msub><mi>p</mi><mn>1</mn></msub><mrow><mo> </mo><mi>and</mi><mo> </mo></mrow><msub><mi>p</mi><mn>2</mn></msub><mo>,</mo></mrow></semantics></math></inline-formula> both congruent to 1 mod 4, is used in Euler’s factorization method to theoretically factorize them. While this caters to only a quarter of the possible combinations of primes, the rest of the combinations congruent to 3 mod 4 can be found by extending the method using Gaussian primes. However, based on Pythagorean primes that are applied in RSA, the semi-prime has only two sums of two squares in the range of possible squares <inline-formula><math display="inline"><semantics><mrow><msqrt><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msqrt><mo>,</mo><mo> </mo><msqrt><mrow><mi>N</mi><mo>/</mo><mn>2</mn></mrow></msqrt><mo> </mo></mrow></semantics></math></inline-formula>. As <inline-formula><math display="inline"><semantics><mi>N</mi></semantics></math></inline-formula> becomes large, the probability of finding the two sums of two squares becomes computationally intractable in the practical world. In this paper, we apply Pythagorean primes to explore how the number of sums of two squares in the search field can be increased thereby increasing the likelihood that a sum of two squares can be found. Once two such sums of squares are found, even though many may exist, we show that it is sufficient to only find two solutions to factorize the original semi-prime. We present the algorithm showing the simplicity of steps that use rudimentary arithmetic operations requiring minimal memory, with search cycle time being a factor for very large semi-primes, which can be contained. We demonstrate the correctness of our approach with practical illustrations for breaking RSA keys. Our enhanced factorization method is an improvement on our previous work with results compared to other factorization algorithms and continues to be an ongoing area of our research.
The study of the physiological and pathophysiological processes in the cardiovascular system is one of the important contemporary issues, which is addressed in many works. In this work, several approaches to the mathematical modelling of the blood flow are considered. They are based on the spatial order reduction and/or use a steady-state approach. Attention is paid to the discussion of the assumptions and suggestions, which are limiting the scope of such models. Some typical mathematical formulations are considered together with the brief review of their numerical implementation. In the first part, we discuss the models, which are based on the full spatial order reduction and/or use a steady-state approach. One of the most popular approaches exploits the analogy between the flow of the viscous fluid in the elastic tubes and the current in the electrical circuit. Such models can be used as an individual tool. They also used for the formulation of the boundary conditions in the models using one dimensional (1D) and three dimensional (3D) spatial coordinates. The use of the dynamical compartment models allows describing haemodynamics over an extended period (by order of tens of cardiac cycles and more). Then, the steady-state models are considered. They may use either total spatial reduction or two dimensional (2D) spatial coordinates. This approach is used for simulation the blood flow in the region of microcirculation. In the second part, we discuss the models, which are based on the spatial order reduction to the 1D coordinate. The models of this type require relatively small computational power relative to the 3D models. Within the scope of this approach, it is also possible to include all large vessels of the organism. The 1D models allow simulation of the haemodynamic parameters in every vessel, which is included in the model network. The structure and the parameters of such a network can be set according to the literature data. It also exists methods of medical data segmentation. The 1D models may be derived from the 3D Navier - Stokes equations either by asymptotic analysis or by integrating them over a volume. The major assumptions are symmetric flow and constant shape of the velocity profile over a cross-section. These assumptions are somewhat restrictive and arguable. Some of the current works paying attention to the 1D models validation, to the comparing different 1D models and the comparing 1D models with clinical data. The obtained results reveal acceptable accuracy. It allows concluding, that the 1D approach can be used in medical applications. 1D models allow describing several dynamical processes, such as pulse wave propagation, Korotkovs tones. Some physiological conditions may be included in the 1D models: gravity force, muscles contraction force, regulation and autoregulation.
The ability of representation is one of the important components to develop students' thinking skills, because this capability is instrumental in helping students to transform abstract ideas into real idea and it can train students to improve problem solving skills with a variety of forms including pictures, diagrams, mathematical expressions, or words or written text. One model of learning that increases the ability of the mathematical representation is a learning model of problem-based learning. This research aims to: 1) determine a mathematical representation increased ability of students taught with problem based learning models 2) the interaction between the learning model of problem-based learning and grouping of students to increase the ability of the mathematical representation. This research is a quantitative research with an experimental method, that has pretest-posttest group design. The population was all students of class X SMA UnggulPidie Jaya by samples of two classes, namely class X3 as an experimental class and class X2 as the control class. The data collection was done by using test. Then analyzed by t -test and ANOVA at the 0.05 significance level after testing prerequisites are met. Based on the analysis we can conclude that: 1) to improve the mathematical representation of students who applied learning model of problem based learning is better than an increase in the ability of the mathematical representation of students who received conventional learning. 2) there is no interaction between the learning model and grouping of students to increase the ability of mathematical representation.
This paper presents a trust-region procedure for solving systems of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region framework as well as can decrease the computational cost of the algorithm by decreasing the number of subproblems that must be solved. The global convergence to first order stationary points as well as the local q-quadratic convergence of the proposed approach are proved. Numerical experiments show that the new algorithm is promising and attractive for solving nonlinear systems.