Mahsa Mirzargar

Julia Docampo Sánchez, Jennifer K. Ryan, Mahsa Mirzargar et al.

Over the past few decades there has been a strong effort towards the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the convergence rate of the DG solution through this post-processor. These advantages can be exploited during flow visualization, for example by applying the SIAC filter to the DG data before streamline computations [Steffan {\it et al.}, IEEE-TVCG 14(3): 680-692]. However, introducing these filters in engineering applications can be challenging since a tensor product filter grows in support size as the field dimension increases, becoming computationally expensive. As an alternative, [Walfisch {\it et al.}, JOMP 38(2);164-184] proposed a univariate filter implemented along the streamline curves. Until now, this technique remained a numerical experiment. In this paper we introduce the SIAC line filter and explore how the orientation, structure and filter size affect the order of accuracy and global errors. We present theoretical error estimates showing how line filtering preserves the properties of traditional tensor product filtering, including smoothness and improvement in the convergence rate. Furthermore, numerical experiments are included, exhibiting how these filters achieve the same accuracy at significantly lower computational costs, becoming an attractive tool for the scientific visualization community.

M. J. Nadjafi Arani, S. Sorgun, M. Mirzargar

This study conducts a Quantitative Structure Property Relationship (QSPR) analysis to explore the correlation between the physical properties of drug molecules and their topological indices using machine learning techniques. While prior studies in drug design have focused on degree-based topological indices, this work analyzes a dataset of 166 drug molecules by computing degree-distance-based topological indices, incorporating vertex-edge weightings with respect to different six atomic properties (atomic number, atomic radius, atomic mass, density, electronegativity, ionization). Both linear models (Linear Regression, Lasso, and Ridge Regression) and nonlinear approaches (Random Forest, XGBoost, and Neural Networks) were employed to predict molecular properties. The results demonstrate the effectiveness of these indices in predicting specific physicochemical properties and underscore the practical relevance of computational methods in molecular property estimation. The study provides an innovative perspective on integrating topological indices with machine learning to enhance predictive accuracy, highlighting their potential application in drug discovery and development processes. This predictive may also explain that establishing a reliable relationship between topological indices and physical properties enables chemists to gain preliminary insights into molecular behavior before conducting experimental analyses, thereby optimizing resource utilization in cheminformatics research.

Mahsa Mirzargar, Ross T. Whitaker, Robert M. Kirby

Heterogeneous data pose serious challenges to data analysis tasks, including exploration and visualization. Current techniques often utilize dimensionality reductions, aggregation, or conversion to numerical values to analyze heterogeneous data. However, the effectiveness of such techniques to find subtle structures such as the presence of multiple modes or detection of outliers is hindered by the challenge to find the proper subspaces or prior knowledge to reveal the structures. In this paper, we propose a generic similarity-based exploration technique that is applicable to a wide variety of datatypes and their combinations, including heterogeneous ensembles. The proposed concept of similarity has a close connection to statistical analysis and can be deployed for summarization, revealing fine structures such as the presence of multiple modes, and detection of anomalies or outliers. We then propose a visual encoding framework that enables the exploration of a heterogeneous dataset in different levels of detail and provides insightful information about both global and local structures. We demonstrate the utility of the proposed technique using various real datasets, including ensemble data.