Image-Based Angular Distortion Metric of Map Projections by Using Surface Fitting for Noise Reduction

Measuring, analyzing, reducing, and optimizing distortions in map projections is important in cartography. In this study, we introduced a novel image-based angular distortion metric based on the previous spherical great circle arcs-based metric. Images with predefined patterns were used to generate distorted images using mapping software. The generated distorted images with known patterns were then exploited to calculate the proposed angular distortion metric. The mapping software performed the underlying transformation of map projections. Therefore, there was no direct explicit dependence on the forward equations of the map projections in our proposed metric. However, there were fairly large computation errors in the ordinary image-based approach without special correction. To reduce the error, we introduced surface-fitting-based noise reduction in our approach. We established and solved systems of linear equations based on bivariate polynomial functions in the process of noise reduction. Sufficient experiments were made to validate the proposed image-based metric and the accompanying noise reduction approach. In the experiment, the NASA G.Projector was employed as the mapping software for evaluating more than 200 map projections. Experimental results demonstrated that the proposed image-based approach and surface fitting-based noise reduction are feasible and practical for the evaluation of the angular distortion of map projections.

Diffusion with stochastic resetting of interacting particles emerging in a model of population genetics

In this paper we put forward a Generalized Ohta-Kimura ladder model (GOKM) which bears a strong liaison with the so-called jump-type Fleming-Viot process (JFVP). The novelty here, when we compare with the classical Ohta-Kimura model, is that we now have an operator which allows multiple interaction among the individuals. It has to do with a generalized branching mechanism: m individual types extinguish and one individual type splits into m copies. The system of evolution equations arising from GOKM can be seen as a system of n-dimensional Kolmogorov forward equations (or Fokker-Planck equations). Besides the interest in its own right a favorable feature of GOKM, vis-`a-vis JFVP, is that its analysis requires a more amenable armory of concepts and mathematical technique to analyze some relevant issues such as correlation, indistinguishability of individuals and stationarity. In addition, as a by product, we show that the connection between Ohta-Kimura Model and diffusion with resetting, as previously structured in [6], can be extended to our setting.

Modelling gambiense human African trypanosomiasis infection in villages of the Democratic Republic of Congo using Kolmogorov forward equations

Stochastic methods for modelling disease dynamics enable the direct computation of the probability of elimination of transmission. For the low-prevalence disease of human African trypanosomiasis (gHAT), we develop a new mechanistic model for gHAT infection that determines the full probability distribution of the gHAT infection using Kolmogorov forward equations. The methodology allows the analytical investigation of the probabilities of gHAT elimination in the spatially connected villages of different prevalence health zones of the Democratic Republic of Congo, and captures the uncertainty using exact methods. Our method provides a more realistic approach to scaling the probability of elimination of infection between single villages and much larger regions, and provides results comparable to established models without the requirement of detailed infection structure. The novel flexibility allows the interventions in the model to be implemented specific to each village, and this introduces the framework to consider the possible future strategies of test-and-treat or direct treatment of individuals living in villages where cases have been found, using a new drug.

Regression and Evaluation on a Forward Interpolated Version of the Great Circle Arcs–Based Distortion Metric of Map Projections

We studied the numerical approximation problem of distortion in map projections. Most widely used differential methods calculate area distortion and maximum angular distortion using partial derivatives of forward equations of map projections. However, in certain map projections, partial derivatives are difficult to calculate because of the complicated forms of forward equations, e.g., equations with iterations, integrations, or multi-way branches. As an alternative, the spherical great circle arcs–based metric employs the inverse equations of map projections to transform sample points from the projection plane to the spherical surface, and then calculates a differential-independent distortion metric for the map projections. We introduce a novel forward interpolated version of the previous spherical great circle arcs–based metric, solely dependent on the forward equations of map projections. In our proposed numerical solution, a rational function–based regression is also devised and applied to our metric to obtain an approximate metric of angular distortion. The statistical and graphical results indicate that the errors of the proposed metric are fairly low, and a good numerical estimation with high correlation to the differential-based metric can be achieved.

Modelling gambiense human African trypanosomiasis infection in villages of the Democratic Republic of Congo using Kolmogorov forward equations

Stochastic methods for modelling disease dynamics enables the direct computation of the probability of elimination of transmission (EOT). For the low-prevalence disease of human African trypanosomiasis (gHAT), we develop a new mechanistic model for gHAT infection that determines the full probability distribution of the gHAT infection using Kolmogorov forward equations. The methodology allows the analytical investigation of the probabilities of gHAT elimination in the spatially-connected villages of the Kwamouth and Mosango health zones of the Democratic Republic of Congo, and captures the uncertainty using exact methods. We predict that, if current active and passive screening continue at current levels, local elimination of infection will occur in 2029 for Mosango and after 2040 in Kwamouth, respectively. Our method provides a more realistic approach to scaling the probability of elimination of infection between single villages and much larger regions, and provides results comparable to established models without the requirement of detailed infection structure. The novel flexibility allows the interventions in the model to be implemented specific to each village, and this introduces the framework to consider the possible future strategies of test-and-treat or direct treatment of individuals living in villages where cases have been found, using a new drug.

Multi-Objective Optimization of Switched Reluctance Machine Design Using Jaya Algorithm (MO-Jaya)

The switched reluctance machine (SRM) design is different from the design of most of other machines. SRM has many design parameters that have non-linear relationships with the performance indices (i.e., average torque, efficiency, and so forth). Hence, it is difficult to design SRM using straight forward equations with iterative methods, which is common for other machines. Optimization techniques are used to overcome this challenge by searching for the best variables values within the search area. In this paper, the optimization of SRM design is achieved using multi-objective Jaya algorithm (MO-Jaya). In the Jaya algorithm, solutions are moved closer to the best solution and away from the worst solution. Hence, a good intensification of the search process is achieved. Moreover, the randomly changed parameters achieve good search diversity. In this paper, it is suggested to also randomly change best and worst solutions. Hence, better diversity is achieved, as indicated from results. The optimization with the MO-Jaya algorithm was made for 8/6 and 6/4 SRM. Objectives used are the average torque, efficiency, and iron weight. The results of MO-Jaya are compared with the results of the non-dominated sorting genetic algorithm (NSGA-II) for the same conditions and constraints. The optimization program is made in Lua programming language and executed by FEMM4.2 software. The results show the success of the approach to achieve better objective values, a broad search, and to introduce a variety of optimal solutions.

A review of multistate modelling approaches in monitoring disease progression: Bayesian estimation using the Kolmogorov-Chapman forward equations

There are numerous fields of science in which multistate models are used, including biomedical research and health economics. In biomedical studies, these stochastic continuous-time models are used to describe the time-to-event life history of an individual through a flexible framework for longitudinal data. The multistate framework can describe more than one possible time-to-event outcome for a single individual. The standard estimation quantities in multistate models are transition probabilities and transition rates which can be mapped through the Kolmogorov-Chapman forward equations from the Bayesian estimation perspective. Most multistate models assume the Markov property and time homogeneity; however, if these assumptions are violated, an extension to non-Markovian and time-varying transition rates is possible. This manuscript extends reviews in various types of multistate models, assumptions, methods of estimation and data features compatible with fitting multistate models. We highlight the contrast between the frequentist (maximum likelihood estimation) and the Bayesian estimation approaches in the multistate modeling framework and point out where the latter is advantageous. A partially observed and aggregated dataset from the Zimbabwe national ART program was used to illustrate the use of Kolmogorov-Chapman forward equations. The transition rates from a three-stage reversible multistate model based on viral load measurements in WinBUGS were reported.

Sword of Damocles or choosing well. Population genetics sheds light into the future of the COVID-19 pandemic and SARS-CoV-2 new mutant strains

An immense scientific effort has been made worldwide due to Covid-19’s pandemic magnitude. It has made possible to identify almost 300,000 SARS-CoV-2 different genetic variants, connecting them with clinical and epidemiological findings. Among this immense data collection, that constitutes the biggest evolutionary experiment in history, is buried the answer to what will happen in the future. Will new strains, more contagious than the current ones or resistant to the vaccines, arise by mutation? Although theoretic population genetics is, by far, the most powerful tool we have to do an accurate prediction, it has been barely used for the study of SARS-CoV-2 due to its conceptual difficulty. Having in mind that the size of the SARS-CoV-2 population is astronomical we can apply a discrete treatment, based on the branching process method, Fokker-Plank equations and Kolmogoroff’s forward equations, to calculate the survival likelihood through time, to elucidate the likelihood to become dominant genotypes and how long will this take, for new SARS-CoV-2 mutants depending on their selective advantage. Results show that most of the new mutants that will arise in the SARS-CoV-2 meta-population will stay at very low frequencies. However, some few new mutants, significantly more infectious than current ones, will still emerge and become dominant in the population favoured by a great selective advantage. Far from showing a “mutational meltdown”, SARS-CoV-2 meta-population will increase its fitness becoming more infective. There is a probability, small but finite, that new mutants arise resistant to some vaccines. High infected numbers and slow vaccination programs will significantly increase this likelihood.

Identifying likely transmissions in Mycobacterium bovis infected populations of cattle and badgers using the Kolmogorov Forward Equations

Established methods for whole-genome-sequencing (WGS) technology allow for the detection of single-nucleotide polymorphisms (SNPs) in the pathogen genomes sourced from host samples. The information obtained can be used to track the pathogen’s evolution in time and potentially identify ‘who-infected-whom’ with unprecedented accuracy. Successful methods include ‘phylodynamic approaches’ that integrate evolutionary and epidemiological data. However, they are typically computationally intensive, require extensive data, and are best applied when there is a strong molecular clock signal and substantial pathogen diversity. To determine how much transmission information can be inferred when pathogen genetic diversity is low and metadata limited, we propose an analytical approach that combines pathogen WGS data and sampling times from infected hosts. It accounts for ‘between-scale’ processes, in particular within-host pathogen evolution and between-host transmission. We applied this to a well-characterised population with an endemic Mycobacterium bovis (the causative agent of bovine/zoonotic tuberculosis, bTB) infection. Our results show that, even with such limited data and low diversity, the computation of the transmission probability between host pairs can help discriminate between likely and unlikely infection pathways and therefore help to identify potential transmission networks. However, the method can be sensitive to assumptions about within-host evolution.

Identifying likely transmission pairs with pathogen sequence data using Kolmogorov Forward Equations; an application to M.bovis in cattle and badgers

Established methods for whole-genome-sequencing (WGS) technology allow for the detection of single-nucleotide polymorphisms (SNPs) in the pathogen genomes sourced from host samples. The information obtained can be used to track the pathogen’s evolution in time and potentially identify ‘who-infected-whom’ with unprecedented accuracy. Successful methods include ‘phylodynamic approaches’ that integrate evolutionary and epidemiological data. However, they are typically computationally intensive, require extensive data, and are best applied when there is a strong molecular clock signal and substantial pathogen diversity.To determine how much transmission information can be inferred when pathogen genetic diversity is low and metadata limited, we propose an analytical approach that combines pathogen WGS data and sampling times from infected hosts. It accounts for ‘between-scale’ processes, in particular within-host pathogen evolution and between-host transmission. We applied this to a well-characterised population with an endemic Mycobacterium bovis (the causative agent of bovine/zoonotic tuberculosis, bTB) infection.Our results show that, even with such limited data and low diversity, the computation of the transmission probability between host pairs can help discriminate between likely and unlikely infection pathways and therefore help to identify potential transmission networks, but can be sensitive to assumptions about within-host evolution.