The monkeypox virus has become a major global health concern due to its rapid spread. Medical intervention and isolation are essential to control the outbreak until an effective treatment is discovered. In this article, we develop a fractional SEIQR model to study the transmission dynamic of the monkeypox virus by including key epidemiological factors and memory effects. The nonlinear model describing the spread of viruses is investigated using the fractional Laplace-Adomian decomposition method (LADM), a powerful analytical technique to address complex infectious disease models. The results are strictly validated by comparing them with those derived from the fractional fourth-order Runge-Kutta (RK4) method. The results demonstrate strong agreement for ζ=0.99, which confirms the reliability of the fractional framework. The error analysis shows that adding more LADM terms increases the accuracy. Positivity and sensitivity analyses confirm the model is biologically valid and show that early detection, isolation, quarantine, and reduced contact strongly affect infection levels. The phase portraits and contour plots provide insight into system behavior and threshold conditions. The study highlights the effectiveness of fractional LADM in describing nonlocal and memory-driven dynamics that cannot be represented in classical models.
S. Sabarinathan, M. Sivashankar, Kottakkaran Sooppy Nisar
et al.
One very useful tool for simulating the intricate feedback processes that take place in a biological system is the glycolysis model. The nonlinearity, stiffness, and parameter sensitivity of this system make it difficult to accurately predict its behavior. This article focuses on the stability analysis of fractal–fractional derivatives for glycolysis modeling of the biochemical system. The primary objective is to examine the criteria for existence and uniqueness using the fixed-point technique. The study explores the Hyers–Ulam stability results and discusses other significant findings for the proposed model, and also employs numerical schemes using the Lagrange interpolation polynomial method. Finally, simulated graphical representations for various fractal–fractional order values are generated, and the simulation results confirm the effectiveness and practical applicability of the theoretical findings.
Ultra-weak photon emission (UPE) from living systems is widely hypothesized to reflect un-derlying self-organization and long-range coordination in biological dynamics. However, distin-guishing biologically driven correlations from trivial stochastic or instrumental effects requires a robust, multi-method framework. In this work, we establish and benchmark a comprehensive anal-ysis pipeline for photon-count time series, combining Distribution Entropy Analysis, Rényi entro-py, Detrended Fluctuation Analysis, its generalization Multifractal Detrended Fluctuation Analysis, and tail-statistics characterization. Surrogate signals constructed from Poisson processes, Fractional Gaussian Noise, and Renewal Processes with power-law waiting times are used to validate sensitivity to memory, intermittency, and multifractality. Across all methods, a coherent hierarchy of dynamical regimes is recovered, demonstrating internal methodological consistency. Application to experimental dark-count data and attenuated coherent-laser emission confirm Poisson-like behavior, establishing an essential statistical baseline for UPE studies. The combined results show that this multi-resolution approach reliably separates trivial photon-counting statistics from struc-tured long-range organization, providing a validated methodological foundation for future biological UPE measurements and their interpretation in the context of non-equilibrium statistical physics, information dynamics, and prospective markers of biological coherence.
Allaoua Mehri, Hakima Bouhadjera, Mohammed S. Abdo
et al.
This paper considers the finite element method for a fractional order parabolic obstacle problem in time with a nonlinear source term. An error estimation of the spatially semi-discrete problem is discussed. A fully discrete problem is proposed by introducing the finite difference approximation for the time variable. The L2-unconditional stability and convergence of the approximate solution have been proven.
Imran A. Khoso, Mazhar Ali, Muhammad Nauman Irshad
et al.
A major challenge for massive multiple-input multiple-output (MIMO) technology is designing an efficient signal detector. The conventional linear minimum mean square error (MMSE) detector is capable of achieving good performance in large antenna systems but requires computing the matrix inverse, which has very high complexity. To address this problem, several iterative signal detection methods have recently been introduced. Existing iterative detectors perform poorly, especially as the system dimensions increase. This paper proposes two detection schemes aimed at reducing computational complexity in massive MIMO systems. The first method leverages the symmetric accelerated over-relaxation (SAOR) technique, which enhances convergence speed by judiciously selecting the relaxation and acceleration parameters. The SAOR technique offers a significant advantage over conventional accelerated over-relaxation methods due to its symmetric iteration. This symmetry enables the use of the conjugate gradient (CG) acceleration approach. Based on this foundation, we propose a novel accelerated SAOR method named CGA-SAOR, where CG acceleration is applied to further enhance the convergence rate. This combined approach significantly enhances performance compared to the SAOR method. In addition, a detailed analysis of the complexity and numerical results is provided to demonstrate the effectiveness of the proposed algorithms. The results illustrate that our algorithms achieve near-MMSE detection performance while reducing computations by an order of magnitude and significantly outperform recently introduced iterative detectors.
Natalia Żywucka, Julian Sitarek, Dorota Sobczyńska
et al.
We present the results of a preliminary study of a correction method applied to the Imaging Atmospheric Cherenkov Telescope images affected by clouds. The studied data are Monte Carlo simulations made with CORSIKA, imitating the very high energy events registered by the Large-Sized Telescopes, a type of telescope within the future Cherenkov Telescope Array. We implement the cloud correction method in the ctapipe/lstchain analysis framework. The correction is based on a simple geometrical model of the emission. We show the effect of the correction method on the image parameters and the stereo-reconstructed shower parameters.
Mohammad Saleh Mahdizadeh, Behnam Bahrak, Mohammad Sayad Haghighi
Abstract The fundamental objective of the Lightning Network is to establish a decentralized platform for scaling the Bitcoin network and facilitating high-throughput micropayments. However, this network has gradually deviated from its decentralized topology since its operational inception, and its resources have quickly shifted towards centralization. The evolution of the network and the changes in its topology have been critically reviewed and criticized due to its increasing centralization. This study delves into the network’s topology and the reasons behind its centralized evolution. We explain the incentives of various participating nodes in the network and propose a score-based strategy for the Lightning Autopilot system, which is responsible for automatically establishing new payment channels for the nodes joining the network. Our study demonstrates that utilizing the proposed strategy could significantly aid in reducing the network’s centralization. This strategy is grounded in qualitative labeling of network nodes based on topological and protocol features, followed by the creation of a scoring and recommendation model. Results of the experiments indicate that in the evolved network using the proposed strategy, concentration indicators such as the Gini coefficient can decrease by up to 17%, and channels ownership of the top 1% of hubs decrease by 27% compared to other autopilot strategies. Moreover, through simulated targeted attacks on hubs and channels, it is shown that by adopting the proposed strategy, the network’s resilience is increased compared to the existing autopilot strategies for evolved networks. The proposed method from this research can also be integrated into operational Lightning clients and potentially replace the current recommendation methods used in Lightning Autopilot.
Despite the variety of methods available to solve nonlinear optimal con-trol problems, numerical methods are still evolving to solve these problems. This paper deals with the numerical solution of nonlinear optimal control affine problems by the interpolated variational iteration method, which was introduced in 2016 to improve the variational iteration method. For this purpose, the optimality conditions are first derived as a two-point bound-ary value problem and then converted to an initial value problem with the unknown initial values for costates. The speed and convergence of the method are compared with the existing methods in the form of three ex-amples, and the initial values of the costates are obtained by an efficient technique in each iteration.
This article reviews the current state of teaching and learning mathematical modeling in the context of sustainable development goals for education at the tertiary level. While ample research on mathematical modeling education and published textbooks on the topic are available, there is a lack of focus on mathematical modeling for sustainability. This review aims to address this gap by exploring the powerful intersection of mathematical modeling and sustainability. Mathematical modeling for sustainability connects two distinct realms: learning about the mathematics of sustainability and promoting sustainable learning in mathematics education. The former involves teaching and learning sustainability quantitatively, while the latter encompasses pedagogy that enables learners to apply quantitative knowledge and skills to everyday life and continue learning and improving mathematically beyond formal education. To demonstrate the practical application of mathematical modeling for sustainability, we discuss a specific textbook suitable for a pilot liberal arts course. We illustrate how learners can grasp mathematical concepts related to sustainability through simple yet mathematically diverse examples, which can be further developed for teaching such a course. Indeed, by filling the gap in the literature and providing practical resources, this review contributes to the advancement of mathematical modeling education in the context of sustainability.
This paper investigates the intricate connection between visual perception and the mathematical modeling of neural activity in the primary visual cortex (V1). The focus is on modeling the visual MacKay effect [D. M. MacKay, Nature, 180 (1957), pp. 849--850]. While bifurcation theory has been a prominent mathematical approach for addressing issues in neuroscience, especially in describing spontaneous pattern formations in V1 due to parameter changes, it faces challenges in scenarios with localized sensory inputs. This is evident, for instance, in MacKay's psychophysical experiments, where the redundancy of visual stimuli information results in irregular shapes, making bifurcation theory and multiscale analysis less effective. To address this, we follow a mathematical viewpoint based on the input-output controllability of an Amari-type neural fields model. In this framework, we consider sensory input as a control function, a cortical representation via the retino-cortical map of the visual stimulus that captures its distinct features. This includes highly localized information in the center of MacKay's funnel pattern "MacKay rays". From a control theory point of view, the Amari-type equation's exact controllability property is discussed for linear and nonlinear response functions. For the visual MacKay effect modeling, we adjust the parameter representing intra-neuron connectivity to ensure that cortical activity exponentially stabilizes to the stationary state in the absence of sensory input. Then, we perform quantitative and qualitative studies to demonstrate that they capture all the essential features of the induced after-image reported by MacKay.
Alessandra Aimi, Giulia Di Credico, Heiko Gimperlein
This article proposes a boundary element method for the dynamic contact between a linearly elastic body and a rigid obstacle. The Signorini contact problem is formulated as a variational inequality for the Poincaré-Steklov operator for the elastodynamic equations on the boundary, which is solved in a mixed formulation using boundary elements in the time domain. We obtain an a priori estimate for the resulting Galerkin approximations. Numerical experiments confirm the stability and convergence of the proposed method for the contact problem in flat and curved two-dimensional geometries, as well as for moving obstacles.
Ron Buckmire, Joseph E. Hibdon,, Drew Lewis
et al.
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community. We engage in this project with a focus on including research that highlights, documents, or quantifies (in)equities that exist in the mathematical sciences, specifically, and STEM (science, technology, engineering, and mathematics) more broadly. We seek to enhance social justice in the mathematics and data science communities by providing numerous examples of the ways in which the mathematical sciences fails to meet standards of equity, equal opportunity and inclusion. We introduce the term ``mathematics of Mathematics" for this project, explicitly building upon the growing, interdisciplinary field known as ``Science of Science" to interrogate, investigate, and identify the nature of the mathematical sciences itself. We aim to promote, provide, and posit sources of productive collaborations and we invite interested researchers to contribute to this developing body of work.
For urban development worldwide, the revitalisation of cultural heritage and historical buildings is regarded as a strategy for creating jobs, increasing residents’ access to local culture, improving their quality of life, and developing the urban economy. The key factor in the revitalisation of cultural heritage and historical buildings is a strategy for developing the urban economy. Through an exploratory study, this paper examined how the cultural service ecosystems of Dihua Street and Guansi Shihdianzih Old Street are created and operated and how actors develop cultural service ecosystems. By presenting a common value proposition, actors can benefit from interactions through an exchange of services, provide cultural services, develop cultural value, and implement full resource integration and value co-creation, thus promoting the cultural brand communication of historical blocks and the sustainability of cultural services. This study further extended the original functions of cultural heritage and analysed the operation of cultural service ecosystems for cultural heritage. The findings of this study revealed that the organisational operational effectiveness of revitalisation and cultural innovation activities in historic districts provided an innovative approach for sustainable development and the economic revival of historical blocks, which can be used as a reference for the sustainability of local culture and economy. In this perspective, this article provides some useful suggestions for stakeholders and policymakers.
Abstract For their economic success, organizations in the social economy are particularly dependent on access to collective resources through interorganizational networks. Because self-organised network governance of an economy is notoriously intransparent, there is the danger that existing societal inequalities get replicated particularly well. This creates a tension with the equality-promoting mission of these organizations. This paper investigates the degree to which the goal of gender equality has been realized in the social economy of Barcelona. By analysing networks of advice-seeking and economic collaboration with exponential random graph models, network mechanisms are analysed to estimate gender-based inequality.
The management and operation of an electrical switchboard originally was processed by an inspector so only tangible malfunctions could be identified while other intangible ones that can cause severe damages to the switchboard were overlooked. To solve this serious deprivation, this investigation, therefore, implemented an intranet sensors system in the electrical switchboard to create a new channel of communication via smart devices to operate and access it remotely, which will eventually lead to increased safety and efficiency of managing electrical switchboards, as well as manufacturing reliability and stability. All these will also increase competitiveness in business. The findings of this research indicate that the application could solve the deprivation by signaling all security malfunctions, both tangible and intangible, remotely via smartphones and laptops in the real-time operating system, which helps reduce severe damages to the switchboard, on-site inspection, and loss of service time to fix malfunctions and human and related risks, as well as increase manufacturing reliability and stability of the operation. The implemented intranet sensors system was also compatible with the current existing security system. This increased security, therefore, verifies the efficiency and business competitiveness of the intranet sensors system.
We study the relationship between the solutions of stationary integrable partial and ordinary differential equations and coefficients of the second-order ordinary differential equations invariant with respect to one-parameter Lie group. The classical symmetry method is applied. We prove that if the coefficients of ordinary differential equation satisfy the stationary integrable partial differential equation with two independent variables then the ordinary differential equation is integrable by quadratures. If special solutions of integrable partial differential equations are chosen then the coefficients satisfy the stationary KdV equations. It was shown that the Ermakov equation belong to a class of these equations. In the framework of the approach we obtained the similar results for generalized Riccati equations. By using operator of invariant differentiation we describe a class of higher order ordinary differential equations for which the group-theoretical method enables us to reduce the order of ordinary differential equation.
Meryani Lakapu, Wilfridus Beda Nuba Dosinaeng, Samuel Igo Leton
Mathematics and culture are two different things, but they have a very close relationship in everyday life included in learning activities. Therefore, this research aims to describes the process and results of developing student activity sheets based on local culture on Simple Trigonometric Function Graphs. This research type is research and development. The product developed in this research is a student activity sheet based on local culture on Simple Trigonometric Function Graphics. Student activity sheets are developed based on a modified 4-D development model, which consists of defining, designing, and developing. At the definition stage; conducted a preliminary analysis, student analysis, material analysis, task analysis and specification of learning objectives. At the design stage; The preparation of student activity sheets based on local culture is carried out, selecting the format and then doing the initial design. At the development stage; The design results are validated by the expert and then revised according to the expert's notes. From the results of the research and data analysis conducted by researchers, it was found that the student activity sheets developed had met the criteria for good learning tools because they were declared valid, practical and effective.
We present the mathematical study of a computational approach originally introduced by R. Cottereau in [R. Cottereau, IJNME 2013]. The approach aims at evaluating the effective (a.k.a. homogenized) coefficient of a medium with some fine-scale structure. It combines, using the Arlequin coupling method, the original fine-scale description of the medium with an effective description and optimizes upon the coefficient of the effective medium to best fit the response of an equivalent purely homogeneous medium. We prove here that the approach is mathematically well-posed and that it provides, under suitable assumptions, the actual value of the homogenized coefficient of the original medium in the limit of asymptotically infinitely fine structures. The theory presented here therefore usefully complements our numerical developments of [O. Gorynina, C. Le Bris and F. Legoll, SIAM J. Sci. Computing 2021].
Advances in machine learning have led to graph neural network-based methods for drug discovery, yielding promising results in molecular design, chemical synthesis planning, and molecular property prediction. However, current graph neural networks (GNNs) remain of limited acceptance in drug discovery is limited due to their lack of interpretability. Although this major weakness has been mitigated by the development of explainable artificial intelligence (XAI) techniques, the "ground truth" assignment in most explainable tasks ultimately rests with subjective judgments by humans so that the quality of model interpretation is hard to evaluate in quantity. In this work, we first build three levels of benchmark datasets to quantitatively assess the interpretability of the state-of-the-art GNN models. Then we implemented recent XAI methods in combination with different GNN algorithms to highlight the benefits, limitations, and future opportunities for drug discovery. As a result, GradInput and IG generally provide the best model interpretability for GNNs, especially when combined with GraphNet and CMPNN. The integrated and developed XAI package is fully open-sourced and can be used by practitioners to train new models on other drug discovery tasks.