Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

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Reduced-order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics encompass the und ...

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

A method for optimizing at least one of a geometry, an implantation procedure, and/or stimulation protocol of one or more electrodes for an electrical stimulation of a target structure in a nervous system of a living being by a computer device, the method ...

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

The local undercut defects at the weld toe provide a potential initiation site for fatigue cracks and significantly impact the structure's fatigue strength. The influence of continuous undercut depth on fatigue performance is widely studied, but the resear ...

This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

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Strain is inevitable in two-dimensional (2D) materials, regardless of whether the film is suspended or supported. However, the direct measurement of strain response at the atomic scale is challenging due to the difficulties of maintaining both flexibility ...

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Some implications of absolute geometries in the description of complex systems dynamics, at various scale resolutions are highlighted. In such context, by means of an analytic geometry of 2 x 2 matrices, a generalization of the standard velocities space in ...

Daily manipulation tasks are characterized by regular features associated with the task structure, which can be described by multiple geometric primitives related to actions and object shapes. Only using Cartesian coordinate systems cannot fully represent ...

Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded in order to handl ...

Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projecti ...

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We investigate the effect of defect geometry in dictating the sensitivity of the critical buckling conditions of spherical shells under external pressure loading. Specifically, we perform a comparative study between shells containing dimpled (inward) versu ...

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

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A method and system for optimizing design, implantation, and stimulation protocols of electrodes stimulating the nervous system

Geometric Learning: Leveraging differential geometry for learning and control

Strain-based analysis on the influence of local undercut geometry on fatigue crack initiation life

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Stress tolerance of lightweight glass-free PV modules for vehicle integration

Indentation and stability of woven domes

In-situ atomic level observation of the strain response of graphene lattice

Piecewise Affine Curvature model: a reduced-order model for soft robot-environment interaction beyond PCC

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A structured prediction approach for robot imitation learning

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Some Physical Implications Of Absolute Geometries In The Description Of Complex Systems Dynamics

A geometric optimal control approach for imitation and generalization of manipulation skills

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Tangent functional connectomes uncover more unique phenotypic traits

T-5 configurations and hyperbolic systems

Comparing the Buckling Strength of Spherical Shells With Dimpled Versus Bumpy Defects

An Accelerated First-Order Method for Non-convex Optimization on Manifolds