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Generalizing tensor-product splines to smooth functions whose control nets outline topological polyhedra, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each…
The structure tensor method is often used for 2D and 3D analysis of imaged structures, but its results are in many cases very dependent on the user's choice of method parameters. We simplify this parameter choice in first order structure…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of…
Shape analysis and classification are popular methods for biologists, biophysicists and mathematicians investigating relationships between object function and form. Classic shape descriptors, such as sphericity, can be powerful but may be…
The collection of reflecting hyperplanes of a finite Coxeter group is called a reflection arrangement and it appears in many subareas of combinatorics and representation theory. We focus on the problem of counting regions of reflection…
In this paper higher order mimetic discretizations are introduced which are firmly rooted in the geometry in which the variables are defined. The paper shows how basic constructs in differential geometry have a discrete counterpart in…
We show that the class of conditional distributions satisfying the coarsening at random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects…
Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…
Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are…
The segmentation, seen as the association of a partition with an image, is a difficult task. It can be decomposed in two steps: at first, a family of contours associated with a series of nested partitions (or hierarchy) is created and…
The aim of this project is to attach a geometric structure to the ring of integers. It is generally assumed that the spectrum $\mathrm{Spec}(\mathbb{Z})$ defined by Grothendieck serves this purpose. However, it is still not clear what…
This paper focuses on vertices of the master corner polyhedra $P(G,g_0),$ the core of the group-theoretical approach to integer linear programming. We introduce two combinatorial operations that transform each vertex of $P(G,g_0)$ to…
This paper proves strong lower bounds for distributed computing in the CONGEST model, by presenting the bit-gadget: a new technique for constructing graphs with small cuts. The contribution of bit-gadgets is twofold. First, developing…
We implement a novel representation of model search spaces as diagrams over a category of models, where we have restricted attention to a broad class of models whose structure is presented by \C-sets. (Co)limits in these diagram categories…
This paper proposes a novel Convolutional Neural Network model for contour data analysis (ContourCNN) and shape classification. A contour is a circular sequence of points representing a closed shape. For handling the cyclical property of…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
Convolutional neural networks are increasingly being used to analyze and classify material microstructures, motivated by the possibility that they will be able to identify relevant microstructural features more efficiently and impartially…