Mathematical Perspective Research Articles

Enhancing reservoir control in the co-dynamics of HIV-VL: from mathematical modeling perspective

HIV patients are vulnerable to developing active visceral leishmaniasis (VL). To understand this complication, we studied a mathematical model for HIV and visceral leishmaniasis coinfection. In this approach, we reckoned two distinct equilibria: the disease-free and the endemic equilibria. The local and global stability of the disease-free equilibrium were thoroughly investigated. To further support the qualitative findings, we performed simulations to quantify the changes of the dynamical behavior of the full model for variation of relevant parameters. Increasing the rate of VL recovery (phi _{1}), the recovery rate for VL–HIV Co-infection (phi _{2}), removing reservoirs (c_{1}), minimizing the contact rate (beta _{h}) are important in controlling the transmission of individual and co-infection disease of VL and HIV. In conclusion, possible measures should be implemented to reduce the number of infected individuals. Therefore, we recommend that policy makers and stakeholders incorporate these measures during planing and implementation phases to control the transmission of VL–HIV co-infection.

REVIEW: MATHEMATICAL MODELLING OF HEAVY METALS REMOVAL FROM PETROLEUM REFINERY WASTEWATER

Adsorption is a commonly used procedure in environmental applications in the chemical industry. In comparison proposed mathematical models to explain batch adsorption as it relates to isotherms and kinetics, fixed-bed or column adsorption has a dearth of models to describe and forecast. While the latter is the most common alternative in practice. The current analysis begins with a brief overview of basic concepts and mathematical models used to characterize batch adsorption's mass transfer and isotherm behavior, which dominates Natural adsorption behavior in columns. Following that, the commonly used models for predicting the breakthrough curve, such as the Clark, Thomas, Adams-Bohart, and Yoon-Nelson models, are fleetingly discussed from a mathematical and process perspective. Their fundamental characteristics are also discussed, including their benefits and intrinsic flaws. This analysis can aid those who are involved in adsorption in columns in selecting or developing a correct and realistic model for their research and applications.

Investigating the Relationship between Capability and Motivation of Crowd Worker to Get Better Performance: A Mathematical Approach

The quality of tasks performed by a crowd worker is questionable. Most of the workers are lost if their first work is of low quality, which may influence them to acquire future work in crowdsourcing. Research has highlighted that workers either lack motivation or capability. However, the integrative perspective of capability and motivation in current crowdsourcing research is scarce. There is a need to investigate the relationship of capability and motivation of crowd worker to understand the phenomenon of getting better performance, which ultimately produces a quality outcome. This research aims toward understanding such relationship with mathematical perspective. The traditional renowned and well-accepted theories related to job performance are used for the quantification of motivation, capability, and performance for crowd workers to investigate the impact of capability in relation to the motivation on the performance of crowd worker. Experimental results suggest that formulae will benefit the requester to evaluate the performance of a crowd worker before providing him/her the task and benefit in reducing unemployment in the situation of COVID-19 pandemic.

An attempt to evaluate STEAM project-based instruction from a school mathematics perspective

Official documents in several educational systems reflect the importance of integrating Science, Technology, Engineering, Arts, and Mathematics (STEAM) and consider project-based learning (PBL) as a way of integrating such disciplines in the classroom. Although STEAM-PBL has been characterized and evaluated in different ways, its impact on school mathematics teaching remains unclear. Mathematics is recognized as the fundamental basis of other disciplines; however, many students still perceive it as a difficult subject and abandon it. To analyze STEAM-PBL classroom implementation from a school mathematics standpoint, we examined 41 classroom experiences from 11 Spanish secondary education teachers (five in-field mathematics teachers), who participated in a STEAM training program for more than 4 years. To frame this study, Thibaut et al.’s (J STEM Educ 3(1):02, 2018) and Schoenfeld’s (Educ Res 43(8):404–412, 2014) characterizations of well-designed and implemented projects, respectively, were employed. The results showed that in-field mathematics teachers avoided transdisciplinary projects in which school mathematics is difficult to address, while out-of-field teachers tended to overlook the mathematics in interdisciplinary projects. Unlike out-of-field teachers, mathematics teachers often eluded design-based learning processes for deeply exploiting school mathematics. The latter teachers promoted high cognitive demands and positive perceptions about mathematics in projects where formative environments were generated through discussion and a meaningful feedback loop.

Averaging over moduli in deformed WZW models

WZW models live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have N abelian conserved currents and central charge c > N. We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged theory has a holographic dual, generalizing recent results on Narain CFTs. The bulk theory, at the perturbative level, is identified as U(1)2N Chern-Simons theory coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie algebra.

Complex ground-state and excitation energies in coupled-cluster theory

Since in coupled-cluster (CC) theory, ground-state and excitation energies are eigenvalues of a non-Hermitian matrix, these energies can in principle take on complex values. In this paper, we discuss the appearance of complex energy values in CC calculations from a mathematical perspective. We analyse the behaviour of the eigenvalues of Hermitian matrices that are perturbed (in a non-Hermitian manner) by a real parameter. Based on these results, we show that for CC calculations with real-valued Hamiltonian matrices the ground-state energy generally takes a real value. Furthermore, we show that in the case of real-valued Hamiltonian matrices complex excitation energies only occur in the context of conical intersections. In such a case, unphysical consequences are encountered such as a wrong dimension of the intersection seam, large numerical deviations from full configuration-interaction (FCI) results close to the conical intersection, and the square-root-like behaviour of the potential surfaces near the conical intersection. In the case of CC calculations with complex-valued Hamiltonian matrix elements, it turns out that complex energy values are to be expected for ground and excited states when no symmetry is present. We confirm the occurrence of complex energies by sample calculations using a six-state model and by CC calculations for the molecule in a strong magnetic field. We furthermore show that symmetry can prevent the occurrence of complex energy values. Lastly, we demonstrate that in case of complex Hamiltonians the real part of the complex energy value provides a very good approximation to the FCI energy.

The place of theoretical wisdom in the application of architectural geometry by Islamic mathematicians. The period under study of the fourth to eleventh centuries AH

The place of theoretical wisdom in the application of architectural geometry by Islamic mathematicians. The period under study of the fourth to eleventh centuries AH

Poisson–Lie Groups and Gauge Theory

We review Poisson–Lie groups and their applications in gauge theory and integrable systems from a mathematical physics perspective. We also comment on recent results and developments and their applications. In particular, we discuss the role of quasitriangular Poisson–Lie groups and dynamical r-matrices in the description of moduli spaces of flat connections and the Chern–Simons gauge theory.

Performance of Envelope Demodulation for Bearing Damage Detection on CWRU Accelerometric Data: Kurtogram and Traditional Indicators vs. Targeted a Posteriori Band Indicators

Envelope demodulation of vibration signals is surely one of the most successful methods of analysis for highlighting diagnostic information of rolling element bearings incipient faults. From a mathematical perspective, the selection of a proper demodulation band can be regarded as an optimization problem involving a utility function to assess the demodulation performance in a particular band and a scheme to move within the search space of all the possible frequency bands {f, Δf} (center frequency and band size) towards the optimal one. In most of cases, kurtosis-based indices are used to select the proper demodulation band. Nevertheless, to overcome the lack of robustness to non-Gaussian noise, different utility functions can be found in the literature. One of these is the kurtosis of the unbiased autocorrelation of the squared envelope of the filtered signal found in the autogram. These heuristics are usually sufficient to highlight the defect spectral lines in the demodulated signal spectrum (i.e., usually the squared envelope spectrum (SES)), enabling bearings diagnostics. Nevertheless, it is not always the case. In this work, then, posteriori band indicators based on SES defect spectral lines are proposed to assess the general envelope demodulation performance and the goodness of traditional indicators. The Case Western Reserve University bearing dataset is used as a test case.

Modeling and Simulation: A Study on Predicting the Outbreak of COVID-19 in Saudi Arabia

The novel coronavirus disease (COVID-19) has resulted in an ongoing pandemic affecting the health system and economy of more than 200 countries worldwide. Mathematical models are used to predict the biological and epidemiological tendencies of an epidemic and to develop methods for controlling it. In this work, we use a mathematical model perspective to study the role of behavior change in slowing the spread of COVID-19 in Saudi Arabia. The real-time updated data from March 2, 2020, to January 8, 2021, were collected from the Saudi Ministry of Health, aiming to provide dynamic behaviors of the epidemic in Saudi Arabia. During this period, 363,692 people were infected, resulting in 6293 deaths, with a mortality rate of 1.73%. There was a weak positive relationship between the spread of infection and mortality R 2 = 0.459 . We used the susceptible-exposed-infection-recovered (SEIR) model, a logistic growth model, with a special focus on the exposed, infected, and recovered individuals to simulate the final phase of the outbreak. The results indicate that social distancing, hygienic conditions, and travel limitations are crucial measures to prevent further spread of the epidemic.

On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators.

The Tsetlin Machine (TM) is a recent machine learning algorithm with several distinct properties, such as interpretability, simplicity, and hardware-friendliness. Although numerous empirical evaluations report on its performance, the mathematical analysis of its convergence is still open. In this article, we analyze the convergence of the TM with only one clause involved for classification. More specifically, we examine two basic logical operators, namely, the "IDENTITY"- and "NOT" operators. Our analysis reveals that the TM, with just one clause, can converge correctly to the intended logical operator, learning from training data over an infinite time horizon. Besides, it can capture arbitrarily rare patterns and select the most accurate one when two candidate patterns are incompatible, by configuring a granularity parameter. The analysis of the convergence of the two basic operators lays the foundation for analyzing other logical operators. These analyses altogether, from a mathematical perspective, provide new insights on why TMs have obtained state-of-the-art performance on several pattern recognition problems.

On the Use of Interferometric Synthetic Aperture Radar Data for Monitoring and Forecasting Natural Hazards

Recent advances in satellite technologies, statistical and mathematical models, and computational resources have paved the way for operational use of satellite data in monitoring and forecasting natural hazards. We present a review of the use of satellite data for Earth observation in the context of geohazards preventive monitoring and disaster evaluation and assessment. We describe the techniques exploited to extract ground displacement information from satellite radar sensor images and the applicability of such data to the study of natural hazards such as landslides, earthquakes, volcanic activity, and ground subsidence. In this context, statistical techniques, ranging from time series analysis to spatial statistics, as well as continuum or discrete physics-based models, adopting deterministic or stochastic approaches, are irreplaceable tools for modeling and simulating natural hazards scenarios from a mathematical perspective. In addition to this, the huge amount of data collected nowadays and the complexity of the models and methods needed for an effective analysis set new computational challenges. The synergy among statistical methods, mathematical models, and optimized software, enriched with the assimilation of satellite data, is essential for building predictive and timely monitoring models for risk analysis.

Systematic Review on Local Ancestor Inference From a Mathematical and Algorithmic Perspective.

Genotypic data provide deep insights into the population history and medical genetics. The local ancestry inference (LAI) (also termed local ancestry deconvolution) method uses the hidden Markov model (HMM) to solve the mathematical problem of ancestry reconstruction based on genomic data. HMM is combined with other statistical models and machine learning techniques for particular genetic tasks in a series of computer tools. In this article, we surveyed the mathematical structure, application characteristics, historical development, and benchmark analysis of the LAI method in detail, which will help researchers better understand and further develop LAI methods. Firstly, we extensively explore the mathematical structure of each model and its characteristic applications. Next, we use bibliometrics to show detailed model application fields and list articles to elaborate on the historical development. LAI publications had experienced a peak period during 2006–2016 and had kept on moving in the following years. The efficiency, accuracy, and stability of the existing models were evaluated by the benchmark. We find that phased data had higher accuracy in comparison with unphased data. We summarize these models with their distinct advantages and disadvantages. The Loter model uses dynamic programming to obtain a globally optimal solution with its parameter-free advantage. Aligned bases can be used directly in the Seqmix model if the genotype is hard to call. This research may help model developers to realize current challenges, develop more advanced models, and enable scholars to select appropriate models according to given populations and datasets.

The Effect of an Elective Algebra Teaching Course on Prospective Mathematics Teachers’ Pedagogical Content Knowledge

Effective teachers have knowledge not only of the subject they are teaching, but also of how to teach it appropriately. To develop these aspects of knowledge, faculties of education include a number of courses that address the related skills. From the perspective of mathematics teacher education, courses related to mathematics teaching have come to the forefront in recent years. The current study, in particular, attempted to test whether prospective elementary mathematics teachers’ (PEMTs) pedagogical content knowledge (PCK) in the domain of algebra improved through attendance in a structured elective course. The study was conducted according to a comparison group research design with 155 prospective teachers. The data collection tool consisted of a 20-question algebra pedagogical content knowledge (APCK) test developed by the researchers in consideration of the knowledge for algebra teaching framework of Ferrini-Mundy and colleagues (2005). The results indicated that the PEMTs who took the algebra teaching course performed better than their peers, with statistically significant differences in the various components of algebra teaching knowledge. Given the findings, some implications for mathematics teacher educators are discussed.

Traveling Wave Solutions in a Model for Tumor Invasion with the Acid-Mediation Hypothesis

In this manuscript, we prove the existence of slow and fast traveling wave solutions in the original Gatenby–Gawlinski model. We prove the existence of a slow traveling wave solution with an interstitial gap. This interstitial gap has previously been observed experimentally, and here we derive its origin from a mathematical perspective. We give a geometric interpretation of the formal asymptotic analysis of the interstitial gap and show that it is determined by the distance between a layer transition of the tumor and a dynamical transcritical bifurcation of two components of the critical manifold. This distance depends, in a nonlinear fashion, on the destructive influence of the acid and the rate at which the acid is being pumped.

Real‐Time Frequency Adjustment of Images and Videos

AbstractWe present a technique for real‐time adjustment of spatial frequencies in images and videos. Our method allows for both decreasing and increasing of frequencies, and is orthogonal to image resizing. Thus, it can be used to automatically adjust spatial frequencies to preserve the appearance of structured patterns during image downscaling and upscaling. By pre‐computing the image's space‐frequency decomposition and its unwrapped phases, these operations can be performed in real time, thanks to our novel mathematical perspective on frequency manipulation of digital images: interpreting the problem through the theory of instantaneous frequencies and phase unwrapping. To make this possible, we introduce an algorithm for the simultaneous phase unwrapping of several unordered frequency components, which also deals with the frequency‐sign ambiguity of real signals. As such, our method provides theoretical and practical improvements to the concept of spectral remapping, enabling real‐time performance and improved color handling. We demonstrate its effectiveness on a large number of images subject to frequency adjustment. By providing real‐time control over the spatial frequencies associated with structured patterns, our technique expands the range of creative and technical possibilities for image and video processing.

Dynamic items delivery network: prediction and clustering

Items delivery companies generally use a model to minimize delivery costs. From a mathematical perspective, the model is an objective function that involves constraints. Meanwhile, from a practical point of view, these constraints include aspects that affect item delivery, for example, delivery zones, number of delivery vehicles, vehicle capacity, trip routes, etc. However, the models built so far have not paid attention to changes in road density. This aspect can result in a nonoptimal delivery model, which results in not a minimum delivery cost. For this reason, this paper discusses how to divide zones using the clustering method and predict changes in the shipping zone of a dynamic network using predictive distribution. So, the model can work optimally if the delivery zones and delivery strategies are suitable.

The Existence of Mathematic Visual and Knowledge in Painting Art from Past to Present

The aim of this study is to give information about the relationship between mathematics and painting and also to show the existence of mathematics on sample pictures. The subject has been researched within the scope of the use of Painting Art in mathematics in its historical development. In some periods, the knowledge of mathematics and in some periods, the forms and symbols of mathematics were included in the picture. It is seen that the artists unwittingly show the effects of mathematics in their works. It is mentioned that the concepts of perspective and golden ratio of mathematics are important in the painting art of the Renaissance period. Before the Renaissance, the 19th century and after, the knowledge and visuals of mathematics can be seen in the painting. The results of the study, the knowledge and visuals of mathematics have been observed in the art of painting in every period and the artist's use of mathematics in his works, either knowingly or unknowingly, is shown with sample pictures and diagrams. Keywords: Mathematics, Picture, Form, Perspective DOI: 10.7176/JSTR/7-03-05

Revising Berg-Purcell for finite receptor kinetics

From nutrient uptake to chemoreception to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors. Mathematical analysis of such systems often neglects the fact that receptors process molecules at finite kinetic rates. A key example is the celebrated formula of Berg and Purcell for the rate that cell surface receptors capture extracellular molecules. Indeed, this influential result is only valid if receptors transport molecules through the cell wall at a rate much faster than molecules arrive at receptors. From a mathematical perspective, ignoring receptor kinetics is convenient because it makes the diffusing molecules independent. In contrast, including receptor kinetics introduces correlations between the diffusing molecules because, for example, bound receptors may be temporarily blocked from binding additional molecules. In this work, we present a modeling framework for coupling bulk diffusion to surface receptors with finite kinetic rates. The framework uses boundary homogenization to couple the diffusion equation to nonlinear ordinary differential equations on the boundary. We use this framework to derive an explicit formula for the cellular uptake rate and show that the analysis of Berg and Purcell significantly overestimates uptake in some typical biophysical scenarios. We confirm our analysis by numerical simulations of a many-particle stochastic system.

God, the beautiful and mathematics: A response

Volker Kessler (‘God becomes beautiful … in mathematics’ – HTS 2018) argues two points to Rudolf Bohren’s list of four areas where (1) God becomes beautiful should be extended with a fifth one: mathematics and (2) mathematics can be argued as a place where God becomes beautiful. In this response, we would like to argue that (1) the extension of Bohren’s list that Kessler argues in favour of is superfluous and (2) that Kessler makes a number of questionable assumptions about (the philosophy of) mathematics. By arguing against Kessler, we intend to make an interdisciplinary contribution to the discussion about the relationship between mathematics and theology by pushing the debate into direction of a more careful consideration of mathematics as an area in which God’s beauty may become apparent. Contribution: Contributing to the interdisciplinary exploration of theology in HTS Teologiese Studies/Theological Studies , this article further develops the consideration of the fundamental theological topic of God, the beautiful and mathematics as it was proposed in this journal by Volker Kessler, by discussing it from a systematic theological and mathematical perspective.