Finite elements with divergence-free shape function and the application to inhomogeneously-loaded waveguide analysis

A simple mixed triangular edge element is proposed for the finite elements, with which inhomogeneously-loaded and arbitrarily shaped waveguides are analyzed. The shape functions used for approximating the fields are found analytically to be divergence-free. The formulation has been found to encounter spurious-free solutions. As evidence, the non-physical solutions that appeared in the longitudinal component finite element formulation are shown to be absent in the present formulation. A comparison with another mixed element is furnished here in order to demonstrate the advantages provided by the present element </p

Finite Elements with Divergence-free Shape Function and theApplication to Inhomogeneously-loaded Waveguide Analysis

Divergence-free shape functions are proposed for the finite elements, with which inhomogeneously-loaded and arbitrarily-shaped waveguides are analysed. The method is based on vectorial finite element formulation employing edge elements. The shape functions used for the approximation of the fields are shown analytically to be divergence-free and as an evidence, the non-physical solutions that appeared in the longitudinal component finite element formulation have been shown to be absent. To show the validity of the elements, application is made for the analysis of rectangular waveguides loaded with dielectric slab and a waveguide with curved structure. The solutions obtained are compared with the analytical ones or the solutions reported elsewhere. The degree of accuracy has been found satisfactory

Rethinking methods and ethics of small business research in Africa

This study presents practical guides on how to traverse the suspicion and resentments researchers deal with when conducting research on small businesses in Africa. This draws from ongoing research in Nigeria that is interacting with about 200 small businesses to make sense of small business digital transformation during COVID-19, and in low-income country settings. Findings suggest that traditional research methods and ethics are no longer suited for contemporary research. Researchers should communicate simplicity and evidence value in a way that is clearly understood by small business owners/managers. Small business research is pivotal to solving perennial low-income country problems such as unemployment, insecurity, poverty, and hunger. Rethinking methods and ethics of small business research could enhance the validity, reliability, and impacts of contemporary research

Regular Boundary Integral Formulation for the Analysis ofOpen Dielectric / Optical Waveguides

Regular boundary element method is employed for the variational formulation of Helmholtz equation that governs the waveguiding problems. Like in the Charge simulation method, in this method, the source points associated with the fundamental solutions are allocated outside the domain so that the singular integrals which occur in the standard boundary element procedure can be avoided. First, the formulation is developed for the two-dimensional scalar Helmholtz problem solving for the axial components of either electric or magnetic fields. The application of the formulation is shown for simple hollow rectangular waveguide and dielectric-slab-loaded rectangular waveguide. Then the formulation is extended for the analysis of dielectric waveguides of open type incorporating axial components of both electric and magnetic fields, for the solution of the propagating modes which are generally of hybrid types. To show the validity and quality of the formulation, it is applied to a circular step-index optical waveguide and a dielectric rectangular waveguide. Very close agreements have been found when the solutions are compared with the ones obtained by different methods. One distinct merit of the extended formulation is that it has been fixed to suppress the spurious solutions which are encountered while solved by the conventional boundary element method

Finite Element Analysis of Open-type Dielectric / Optical Waveguides

Optical fibers or integrated optical waveguides have arbitrary cross-sectional index or refraction distribution. An efficient finite element method for analyzing the propagation characteristics of dielectric / optical waveguides with open boundary is presented. The propagation modes are hybrid, for which a variational expression is formulated in terms of the longitudinal electric and magnetic field components. Infinite elements are introduced to consider open boundary or to extend the region to infinity. Several specific examples are given and the results are compared with those obtained by other approximate methods. Very close agreements have been found

Pitfalls in machine learning‐based assessment of tumor‐infiltrating lymphocytes in breast cancer: a report of the international immuno‐oncology biomarker working group

The clinical significance of the tumor-immune interaction in breast cancer (BC) has been well established, and tumor-infiltrating lymphocytes (TILs) have emerged as a predictive and prognostic biomarker for patients with triple-negative (estrogen receptor, progesterone receptor, and HER2 negative) breast cancer (TNBC) and HER2-positive breast cancer. How computational assessment of TILs can complement manual TIL-assessment in trial- and daily practices is currently debated and still unclear. Recent efforts to use machine learning (ML) for the automated evaluation of TILs show promising results. We review state-of-the-art approaches and identify pitfalls and challenges by studying the root cause of ML discordances in comparison to manual TILs quantification. We categorize our findings into four main topics; (i) technical slide issues, (ii) ML and image analysis aspects, (iii) data challenges, and (iv) validation issues. The main reason for discordant assessments is the inclusion of false-positive areas or cells identified by performance on certain tissue patterns, or design choices in the computational implementation. To aid the adoption of ML in TILs assessment, we provide an in-depth discussion of ML and image analysis including validation issues that need to be considered before reliable computational reporting of TILs can be incorporated into the trial- and routine clinical management of patients with TNBC

What is the impact of imbalance on software defect prediction performance?

Software defect prediction performance varies over a large range. Menzies suggested there is a ceiling effect of 80% Recall [8]. Most of the data sets used are highly imbalanced. This paper asks, what is the empirical effect of using different datasets with varying levels of imbalance on predictive performance? We use data synthesised by a previous meta-analysis of 600 fault prediction models and their results. Four model evaluation measures (the Mathews Correlation Coeficient (MCC), F-Measure, Precision and Re- call ) are compared to the corresponding data imbalance ratio. When the data are imbalanced, the predictive performance of software defect prediction studies is low. As the data become more balanced, the predictive performance of prediction models increases, from an average MCC of 0.15, until the minority class makes up 20% of the instances in the dataset, where the MCC reaches an average value of about 0.34. As the proportion of the minority class increases above 20%, the predictive performance does not significantly increase. Using datasets with more than 20% of the instances being defective has not had a significant impact on the predictive performance when using MCC. We conclude that comparing the results of defect prediction studies should take into account the imbalance of the data

Spatial analyses of immune cell infiltration in cancer: current methods and future directions.:A report of the International Immuno-Oncology Biomarker Working Group on Breast Cancer

Modern histologic imaging platforms coupled with machine learning methods have provided new opportunities to map the spatial distribution of immune cells in the tumor microenvironment. However, there exists no standardized method for describing or analyzing spatial immune cell data, and most reported spatial analyses are rudimentary. In this review, we provide an overview of two approaches for reporting and analyzing spatial data (raster versus vector-based). We then provide a compendium of spatial immune cell metrics that have been reported in the literature, summarizing prognostic associations in the context of a variety of cancers. We conclude by discussing two well-described clinical biomarkers, the breast cancer stromal tumor infiltrating lymphocytes score and the colon cancer Immunoscore, and describe investigative opportunities to improve clinical utility of these spatial biomarkers.</p