Leishmania is an infectious disease that is difficult to control and has an impact on morbidity and mortality around the world. This study investi-gates the dynamics of cutaneous Leishmania and optimal control measures, particularly in regards to human immigration. Applying a mathematical model to evaluate the dynamics of human immigration and sand flies pop-ulation. The human population is classified into four compartments: sus-ceptible, exposed, infectious, and recovered. The sand fly population is divided into three categories: susceptible, exposed, and infectious. The mathematical analysis involves positivity, existence and the uniqueness of the solution. We analyzed the global stability of the system around the endemic equilibrium point by contracting the Lyapunov function. Optimal control measures are used to reduce the number of infected and exposed individuals among humans, sand flies, and migrants. These techniques are described using Pontryagin’s Maximum Principle to derive necessary conditions for optimal control. The numerical simulations confirm the the-oretical results by showing that following these controls effectively reduces the spread of the disease, and immigration has a major impact on the spread of human-borne Leishmania.
We study the embedded point spectrum of rank one singular perturbations of an arbitrary self-adjoint operator \(A\) on a Hilbert space \(\mathcal{H}\). These perturbations can be regarded as self-adjoint extensions of a densely defined closed symmetric operator \(B\) with deficiency indices \((1,1)\). Assuming the deficiency vector of \(B\) is cyclic for its self-adjoint extensions, we prove that the spectrum of \(A\) contains a dense \(G_{\delta}\) subset on which no eigenvalues occur for the rank one singular perturbations considered. We show this is equivalent to the existence of a dense \(G_{\delta}\) set of rank one singular perturbations of \(A\) such that their eigenvalues are isolated. The approach presented here unifies points of view taken by different authors.
High-throughput 3D quantitative phase imaging (QPI) in flow cytometry enables label-free, volumetric characterization of individual cells by reconstructing their refractive index (RI) distributions from multiple viewing angles during flow through microfluidic channels. However, current imaging methods assume that cells undergo uniform, single-axis rotation, which require their poses to be known at each frame. This assumption restricts applicability to near-spherical cells and prevents accurate imaging of irregularly shaped cells with complex rotations. As a result, only a subset of the cellular population can be analyzed, limiting the ability of flow-based assays to perform robust statistical analysis. We introduce OmniFHT, a pose-free 3D RI reconstruction framework that leverages the Fourier diffraction theorem and implicit neural representations (INRs) for high-throughput flow cytometry tomographic imaging. By jointly optimizing each cell's unknown rotational trajectory and volumetric structure under weak scattering assumptions, OmniFHT supports arbitrary cell geometries and multi-axis rotations. Its continuous representation also allows accurate reconstruction from sparsely sampled projections and restricted angular coverage, producing high-fidelity results with as few as 10 views or only 120 degrees of angular range. OmniFHT enables, for the first time, in situ, high-throughput tomographic imaging of entire flowing cell populations, providing a scalable and unbiased solution for label-free morphometric analysis in flow cytometry platforms.
The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their refinements, can pick up on patterns in higher mathematics that are difficult for humans to see. By putting the design of generative AI models to their advantage, mathematicians may use them as powerful interactive assistants that can carry out laborious tasks, generate and debug code, check examples, formulate conjectures and more. We discuss how generative AI models can be used to advance mathematics research. We also discuss their integration with neuro-symbolic solvers, Computer Algebra Systems and formal proof assistants such as Lean.
The main purpose of this paper is to introduce a new alpha power transformed beta probability distribution that reveals interesting properties. The studuy provide a comprehensive explanation of the statistical characteristics of this innovative model. Various properties of the new distribution were derived, using the baseline beta distribution, statistical techniques, and probabilistic axioms. These include the probability density, cumulative distribution, survival function, hazard function, moments about the origin, moment generating function, and order statistics. For parameter estimation, the maximum likelihood estimation method using Newton Raphson numerical technique is employed. To evaluate the performance of our estimation method, the mean squared errors of the estimated parameters for different simulated sample sizes are used. In addition simulation studies of the new distribution are conducted to demonstrate the behavior of the probability model. To demonstrate the practical utility and flexibility of the alpha power transformed beta distribution, it is fitted to two real-life datasets and compared to commonly known probability distributions such as the Weibull, exponential Weibull, Beta, and Kumaraswamy beta distributions. It offers a superior fit to the data considered. The distribution reviales of the microbes reveald a wide range of shapes of probability density functions and flexible hazard rates. The distribution is a new contribution to the field of statistical and probability theory. The findings of the study can be used as a basis for future research in the area of statistical science and health.
Mohammad Soleh Soleh, Melvy Utari Permadhi, Wartono
et al.
Covid-19 has become a global pandemic in the 21st century. Various efforts to control its spread have been made. Isolation or regional quarantine is one of the efforts made by almost all countries in the world. Indonesia modified the lockdown by implementing 'Large-Scale Social Restrictions (PSBB)'. Before and during the implementation of PSBB, there have been many pros and cons in the community. By using the SIR model and Euler method, the impact before and after the implementation of PSBB in Pekanbaru city is compared. Based on daily data of Covid-19 cases in Pekanbaru city, it is obtained that the value of the basic reproduction number before and after the implementation of PSBB are and respectivel. This condition confirms that either without or by implementing PSBB, Pekanbaru city will be free from Covid-19. Simulation of Covid-19 cases before and after PSBB graphically also shows a situation that will be free from disease. However, without implementing PSBB, the number of infected will jump drastically after some time even though it will eventually decrease, while by implementing PSBB there is no spike. Thus, the implementation of PSBB can be an alternative to control Covid-19.
Keywords: Basic reproduction number, Covid-19, PSBB, SIR model, Euler methods.
Zane Peterkovic, Avinash Upadhya, Christopher Perrella
et al.
Low-light optical imaging refers to the use of cameras to capture images with minimal photon flux. This area has broad application to diverse fields, including optical microscopy for biological studies. In such studies, it is important to reduce the intensity of illumination to reduce adverse effects such as photobleaching and phototoxicity that may perturb the biological system under study. The challenge when minimising illumination is to maintain image quality that reflects the underlying biology and can be used for quantitative measurements. An example is the optical redox ratio which is computed from autofluorescence intensity to measure metabolism. In all such cases, it is critical for researchers to optimise selection and application of scientific cameras to their microscopes, but few resources discuss performance in the low-light regime. In this tutorial, we address the challenges in optical fluorescence imaging at low-light levels for quantitative microscopy, with an emphasis on live biological samples. We analyse the performance of specialised low-light scientific cameras such as the EMCCD, qCMOS, and sCMOS, while considering the differences in platform architecture and the contribution of various sources of noise. The tutorial covers a detailed discussion of user-controllable parameters, as well as the application of post-processing algorithms for denoising. We illustrate these concepts using autofluorescence images of live mammalian embryos captured with a two-photon light sheet fluorescence microscope.
Particle filters, also known as sequential Monte Carlo (SMC) methods, constitute a class of importance sampling and resampling techniques designed to use simulations to perform on-line filtering. Recently, particle filters have been extended for optimization by utilizing the ability to track a sequence of distributions. In this work, we incorporate transfer learning capabilities into the optimizer by using particle filters. To achieve this, we propose a novel particle-filter-based multi-objective optimization algorithm (PF-MOA) by transferring knowledge acquired from the search experience. The key insight adopted here is that, if we can construct a sequence of target distributions that can balance the multiple objectives and make the degree of the balance controllable, we can approximate the Pareto optimal solutions by simulating each target distribution via particle filters. As the importance weight updating step takes the previous target distribution as the proposal distribution and takes the current target distribution as the target distribution, the knowledge acquired from the previous run can be utilized in the current run by carefully designing the set of target distributions. The experimental results on the DTLZ and WFG test suites show that the proposed PF-MOA achieves competitive performance compared with state-of-the-art multi-objective evolutionary algorithms on most test instances.
Julia Sistermanns, Ellen Emken, Gregor Weirich
et al.
In the effort to aid cytologic diagnostics by establishing automatic single cell screening using high throughput digital holographic microscopy for clinical studies thousands of images and millions of cells are captured. The bottleneck lies in an automatic, fast, and unsupervised segmentation technique that does not limit the types of cells which might occur. We propose an unsupervised multistage method that segments correctly without confusing noise or reflections with cells and without missing cells that also includes the detection of relevant inner structures, especially the cell nucleus in the unstained cell. In an effort to make the information reasonable and interpretable for cytopathologists, we also introduce new cytoplasmic and nuclear features of potential help for cytologic diagnoses which exploit the quantitative phase information inherent to the measurement scheme. We show that the segmentation provides consistently good results over many experiments on patient samples in a reasonable per cell analysis time.
Quantitative markets are characterized by swift dynamics and abundant uncertainties, making the pursuit of profit-driven stock trading actions inherently challenging. Within this context, reinforcement learning (RL), which operates on a reward-centric mechanism for optimal control, has surfaced as a potentially effective solution to the intricate financial decision-making conundrums presented. This paper delves into the fusion of two established financial trading strategies, namely the constant proportion portfolio insurance (CPPI) and the time-invariant portfolio protection (TIPP), with the multi-agent deep deterministic policy gradient (MADDPG) framework. As a result, we introduce two novel multi-agent RL (MARL) methods, CPPI-MADDPG and TIPP-MADDPG, tailored for probing strategic trading within quantitative markets. To validate these innovations, we implemented them on a diverse selection of 100 real-market shares. Our empirical findings reveal that the CPPI-MADDPG and TIPP-MADDPG strategies consistently outpace their traditional counterparts, affirming their efficacy in the realm of quantitative trading.
Abstract It is well known that networks generated by common mechanisms such as preferential attachment and homophily can disadvantage the minority group by limiting their ability to establish links with the majority group. This has the effect of limiting minority nodes’ access to information. We present the results of an empirical study on the equality of information access in network models with different growth mechanisms and spreading processes. For growth mechanisms, we focus on the majority/minority dichotomy, homophily, preferential attachment, and diversity. For spreading processes, we investigate simple versus complex contagions, different transmission rates within and between groups, and various seeding conditions. We observe two phenomena. First, information access equality is a complex interplay between network structures and the spreading processes. Second, there is a trade-off between equality and efficiency of information access under certain circumstances (e.g., when inter-group edges are low and information transmits asymmetrically). Our findings can be used to make recommendations for mechanistic design of social networks with information access equality.
Mohammad Sadra Rajabi, Mohammad Rezaeiashtiani, Afiqah R. Radzi
et al.
Building information modeling (BIM) has a significant role in the architecture, engineering, construction, and operation (AECO) industries. Most BIM benefits have not been grasped due to the lack of organizational BIM capabilities (OBIMCs). Accordingly, organizations must develop intuitive strategies to support BIM implementation and to fulfill the promised benefits. This study investigates the impact of different capability factors on OBIMC and the underlying strategies to improve OBIMC in Iran. Particularly, this study builds a structural equation model to explain the links between the capability factors and strategies linked to OBIMC in Iran. A systematic literature review of twenty-six papers and semi-structured interviews with fifteen BIM specialists identified nineteen capability factors and fourteen strategies. A survey of 126 BIM professionals was used to assess the importance of the capability factors and strategies. To analyze the collected data, first, an Exploratory Factor Analysis (EFA) was performed. Then, Partial Least-Squares Structural Equation Modeling (PLS-SEM) was employed. The EFA generated two constructs for the capability factors: OBIMC and organizational capabilities (OCA). Furthermore, it categorized the strategies into two constructs: BIM capability requirement (BIMCR) and organizational culture (OCU). The structural equation model demonstrates that BIMCR and OCU enhance OCA and OBIMC. These two elements are also positively impacted by BIMCR. Industry professionals and policymakers can use these findings to develop strategic plans and to prioritize efforts. The significant contribution of this study is to illuminate the interrelationship between capability factors and strategies related to OBIMC in Iran.
This paper presents and analyzes an affine-scaling interior-point algorithm with a filter line-search method for solving nonlinear optimization problems with nonlinear equality constraints and nonnegative variables. In our scheme, we require that a damped Newton’s method is applied to the perturbed first-order necessary conditions to produce a search direction. Some filtered rules for a fixed barrier parameter are used to determine step acceptance. Second-order correction technique is used to reduce infeasibility and overcome the Maratos effect. The global convergence and fast local convergence rate of the proposed algorithm are established under some suitable conditions.
Informal mathematical text underpins real-world quantitative reasoning and communication. Developing sophisticated methods of retrieval and abstraction from this dual modality is crucial in the pursuit of the vision of automating discovery in quantitative science and mathematics. We track the development of informal mathematical language processing approaches across five strategic sub-areas in recent years, highlighting the prevailing successful methodological elements along with existing limitations.
Vinamra Bhushan Sharma, Kartik Singh, Ravi Gupta
et al.
There has been enormous growth in the energy sector in the new millennium, and it has enhanced energy demand, creating an exponential rise in the capital investment in the energy industry in the last few years. Regular monitoring of the health of industrial equipment is necessary, and thus, the concept of structural health monitoring (SHM) comes into play. In this paper, the purpose is to highlight the importance of SHM systems and various techniques primarily used in pipelining industries. There have been several advancements in SHM systems over the years such as Point OFS (optical fiber sensor) for Corrosion, Distributed OFS for physical and chemical sensing, etc. However, these advanced SHM technologies are at their nascent stages of development, and thus, there are several challenges that exist in the industries. The techniques based on acoustic, UAVs (Unmanned Aerial Vehicles), etc. bring in various challenges, as it becomes daunting to monitor the deformations from both sides by employing only one technique. In order to determine the damages well in advance, it is necessary that the sensor is positioned inside the pipes and gives the operators enough time to carry out the troubleshooting. However, the mentioned technologies have been unable to indicate the errors, and thus, there is the requirement for a newer technology to be developed. The purpose of this review manuscript is to enlighten the readers about the importance of structural health monitoring in pipeline and wind turbine industries.
The objectives of this study are (1) to develop online-based mathematics teaching materials to improve problem-solving skills in distance learning in the pandemic era and (2) to determine the level of validation of the development of online-based mathematics teaching materials to improve problem-solving skills based on expert validation tests. This R&D research uses the ADDIE model which consists of analysis (analysis), design (planning), development (development), implementation (implementation), and evaluation (evaluation). However, the implementation in this research only reached the development stage. The subjects of this study were class teachers and 5th grade students of SD Negeri Plumutan, Bancak, Semarang Regency. The results of this study are (1) there are three stages in this research and development, namely analyzing the characteristics and initial abilities of students, planning and making teaching materials with the weebly website, and developing by conducting expert validation tests. (2) based on the validation test, material experts give a percentage of 85% with the criteria of "very good", teaching materials experts get a percentage of 90% with the criteria of "very good", and material experts get a percentage of 75% with the criteria of "good".
Keywords: development, teaching materials, mathematics, online learning, weebly