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As immersive analytics continues to grow as a discipline, so too should its underlying methodological support. Taxonomies play an important role for information visualization and human computer interaction. They provide an organization of…

We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

This paper presents the use of multi-sensor measurement system to guide autonomous mobile robot in the house. The system allows the 3D image acquisition to global mapping, and algorithms to reduce the dimensionality of images to 2D global…

For some scientific questions, empirical data are essential to develop reliable simulation models. These data usually come from different sources with diverse and heterogeneous formats. The design of complex data-driven models is often…

The Kohn-Sham scheme of density functional theory is one of the most widely used methods to solve electronic structure problems for a vast variety of atomistic systems across different scientific fields. While the method is fast relative to…

We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our description is local, which offers the potential to speed up…

We introduce a novel bottom-up approach for the extraction of chart data. Our model utilizes images of charts as inputs and learns to detect keypoints (KP), which are used to reconstruct the components within the plot area. Our novelty lies…

The use of quantiles to obtain insights about multivariate data is addressed. It is argued that incisive insights can be obtained by considering directional quantiles, the quantiles of projections. Directional quantile envelopes are…

In this work we introduce an Autoencoder for molecular conformations. Our proposed model converts the discrete spatial arrangements of atoms in a given molecular graph (conformation) into and from a continuous fixed-sized latent…

The operator-sum decomposition (OS) of a mapping from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides a geometric description of the density…

This paper generalizes the Maurer--Pontil framework of finite-dimensional lossy coding schemes to the setting where a high-dimensional random vector is mapped to an element of a compact set of latent representations in a lower-dimensional…

We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…

Co-designing autonomous robotic agents involves simultaneously optimizing the controller and physical design of the agent. Its inherent bi-level optimization formulation necessitates an outer loop design optimization driven by an inner loop…

We apply the notion of asymptotic iteration method (AIM) to determine eigenvalues of the bosonic Hamiltonians that include a wide class of quantum optical models. We consider solutions of the Hamiltonians, which are even polynomials of the…

Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this paper, we propose a Bayesian mixed membership model for functional data.…

Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space. Furthermore, our work…

This paper explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when one expects regression coefficients…

High-dimensional distributed semantic spaces have proven useful and effective for aggregating and processing visual, auditory, and lexical information for many tasks related to human-generated data. Human language makes use of a large and…

We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws…