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Planning the motion for humanoid robots is a computationally-complex task due to the high dimensionality of the system. Thus, a common approach is to first plan in the low-dimensional space induced by the robot's feet---a task referred to…
The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…
Parallel transport is an important step in many discrete algorithms for statistical computing on manifolds. Numerical methods based on Jacobi fields or geodesics parallelograms are currently used in geometric data processing. In this last…
Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the…
The aim of our paper is to render an object in 3-dimension using a set of its orthographic views. Corner detector (Harris Detector) is applied on the input views to obtain control points. These control points are projected perpendicular to…
We describe a guided proceduralization framework that optimizes geometry processing on architectural input models to extract target grammars. We aim to provide efficient artistic workflows by creating procedural representations from…
With the achievement on the additive manufacturing, the mechanical properties of architectured materials can be precisely designed by tailoring microstructures. As one of the primary design objectives, the elastic isotropy is of great…
Tangle machines are topologically inspired diagrammatic models. Their novel feature is their natural notion of equivalence. Equivalent tangle machines may differ locally, but globally they are considered to share the same information…
Constitutive tensors are of common use in mechanics of materials. To determine the relevant symmetry class of an experimental tensor is still a tedious problem. For instance, it requires numerical methods in three-dimensional elasticity. We…
Parallel transport is a fundamental tool to perform statistics on Rie-mannian manifolds. Since closed formulae don't exist in general, practitioners often have to resort to numerical schemes. Ladder methods are a popular class of algorithms…
An efficient communication mechanism forms the backbone for any multi-robot system to achieve fruitful collaboration and coordination. Limitation in the existing asynchronous transmission based strategies in fast dissemination and…
This paper presents a framework to enable a team of heterogeneous mobile robots to model and sense a multiscale system. We propose a coupled strategy, where robots of one type collect high-fidelity measurements at a slow time scale and…
Language models are essential for natural language processing (NLP) tasks, such as machine translation and text summarization. Remarkable performance has been demonstrated recently across many NLP domains via a Transformer-based language…
The aim of this project is to design, study and build an "eel-like robot" prototype able to swim in three dimensions. The study is based on the analysis of eel swimming and results in the realization of a prototype with 12 vertebrae, a skin…
We present a methodology for parallel acceleration of learning in the presence of matrix orthogonality and unitarity constraints of interest in several branches of machine learning. We show how an apparently sequential elementary rotation…
The form of the Lagrangian proposed in Part I of this study has been previously used for obtaining stationary ray paths between two endpoints in isotropic media. We extended it to general anisotropy by replacing the isotropic medium…
Automated construction of bilingual dictionaries using monolingual embedding spaces is a core challenge in machine translation. The end performance of these dictionaries relies upon the geometric similarity of individual spaces, i.e., their…
Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…
In this paper, we present an innovative technique for the path planning of flying robots in a 3D environment in Rough Mereology terms. The main goal was to construct the algorithm that would generate the mereological potential fields in…
We combine a generic method for finding fast orthogonal transforms for a given quasi-Monte Carlo integration problem with the multilevel Monte Carlo method. It is shown by example that this combined method can vastly improve the efficiency…