Related papers: Classifying and analysis of random composites usin…
The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and…
A sum-and-distance system is a collection of finite sets of integers such that the sums and differences formed by taking one element from each set generate a prescribed arithmetic progression. Such systems, with two component sets, arise…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
We propose a computationally efficient and high-performance classification algorithm by incorporating class structural information in analysis dictionary learning. To achieve more consistent classification, we associate a class…
The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
In our previous papers we have described efficient and reliable methods of generation of representative volume elements (RVE) perfectly suitable for analysis of composite materials via stochastic homogenization. In this paper we profit from…
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
We present a means of formulating and solving the well known structure-and-motion problem in computer vision with probabilistic graphical models. We model the unknown camera poses and 3D feature coordinates as well as the observed 2D…
Representing meaning in the form of high dimensional vectors is a common and powerful tool in biologically inspired architectures. While the meaning of a set of concepts can be summarized by taking a (possibly weighted) sum of their…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
In many real world problems, features do not act alone but in combination with each other. For example, in genomics, diseases might not be caused by any single mutation but require the presence of multiple mutations. Prior work on feature…
In Computer Vision, edge detection is one of the favored approaches for feature and object detection in images since it provides information about their objects boundaries. Other region-based approaches use probabilistic analysis such as…
In this work, we propose a novel framework shape back-projection for computationally efficient point cloud processing in a probabilistic manner. The primary component of the technique is shape histogram and a back-projection procedure. The…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel,…
We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability…
The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The…