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In reaction path optimization, such as the calculation of a minimum energy path (MEP) between given reactant and product configurations of atoms, it is advantageous to start with an initial guess where close proximity of atoms is avoided…
Mapper graphs are widely used tools in topological data analysis and visualization. They can be understood as discrete approximations of Reeb graphs, providing insight into the shape and connectivity of complex data. Given a…
Protein structure generative models have seen a recent surge of interest, but meaningfully evaluating them computationally is an active area of research. While current metrics have driven useful progress, they do not capture how well models…
Core decomposition is a fundamental operator in network analysis. In this paper, we study the problem of computing distance-generalized core decomposition on a network. A distance-generalized core, also termed $(k, h)$-core, is a maximal…
Deep learning methods have reached state-of-the-art performance in cardiac image segmentation. Currently, the main bottleneck towards their effective translation into clinics requires assuring continuous high model performance and…
Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise…
This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…
We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb{P}$ more effectively than i.i.d. sampling or standard thinning. Given a suitable reproducing kernel $\mathbf{k}_{\star}$ and $O(n^2)$ time, kernel…
The knowledge of end-to-end network distances is essential to many Internet applications. As active probing of all pairwise distances is infeasible in large-scale networks, a natural idea is to measure a few pairs and to predict the other…
Given a dissimilarity matrix, the metric nearness problem is to find the nearest matrix of distances that satisfy the triangle inequalities. This problem has wide applications, such as sensor networks, image processing, and so on. But it is…
Reconstruction of evolutionary relationships between species is an important topic in the field of computational biology. Pairwise compatibility graphs (PCGs) are used to model such relationships. A graph is a PCG if its edges can be…
Pose-Graph optimization is a crucial component of many modern SLAM systems. Most prominent state of the art systems address this problem by iterative non-linear least squares. Both number of iterations and convergence basin of these…
Coarse-grained (CG) models play a crucial role in the study of protein structures, protein thermodynamic properties, and protein conformation dynamics. Due to the information loss in the coarse-graining process, backmapping from CG to…
We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
Despite the constant evolution of similarity searching research, it continues to face the same challenges stemming from the complexity of the data, such as the curse of dimensionality and computationally expensive distance functions.…
Recent feed-forward networks have achieved remarkable progress in sparse-view 3D reconstruction by predicting dense point maps directly from RGB images. However, they often suffer from geometric inconsistencies and limited fine-grained…
The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over…
Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of…