UCLID-Net: Single View Reconstruction in Object Space

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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 ...

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 ...

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

Glacial moulins (cylindrical meltwater drainage shafts) provide valuable insights into glacier dynamics, but are inaccessible and hazardous environments for humans to study. Exploring them using passive sensor probes has revealed their complex geometry, wh ...

Turning pass-through network architectures into iterative ones, which use their own output as input, is a well-known approach for boosting performance. In this paper, we argue that such architectures offer an additional benefit: The convergence rate of the ...

The task of discovering equivalent entities in knowledge graphs (KGs), so-called KG entity alignment, has drawn much attention to overcome the incompleteness problem of KGs. The majority of existing techniques learns the pointwise representations of entiti ...

With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a crucial criterion fo ...

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 ...

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...

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 ...

We address the problem of stably and efficiently training a deep neural network robust to adversarial perturbations bounded by an

l_1

norm. We demonstrate that achieving robustness against

l_1

-bounded perturbations is more challenging than in the

l_2

...

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

Digital brain atlases define a hierarchy of brain regions and their locations in three-dimensional space. They provide a standard coordinate system in which diverse datasets can be integrated for visualization and analysis. They also enable building of dat ...

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal e ...

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogenei ...

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

In this paper we present a new construction of a discrete Fourier uniqueness set in Euclidean space. ...

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

UCLID-Net: Single View Reconstruction in Object Space

Chattez avec Graph Search

Geometric Learning: Leveraging differential geometry for learning and control

Anomalous and Chern topological waves in hyperbolic networks

Cochains are all you need

The effect of smooth parametrizations on nonconvex optimization landscapes

Into the ice: Exploration and data capturing in glacial moulins by a tethered robot

Enabling Uncertainty Estimation in Iterative Neural Networks

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Learning Linearized Degradation of Health Indicators using Deep Koopman Operator Approach

Hybrid Quadratic Programming - Pullback Bundle Dynamical Systems Control

A structured prediction approach for robot imitation learning

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

Towards Stable and Efficient Adversarial Training against $l_1$ Bounded Adversarial Attacks

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

Enhancement of brain atlases with region-specific coordinate systems: flatmaps and barrel column annotations

Generalised Implicit Neural Representations

Relative, local and global dimension in complex networks

Localization errors of the stochastic heat equation

Fourier uniqueness and interpolation in Euclidean space

On discrete Fourier uniqueness sets in Euclidean space

Collapse-invariant properties of spaces equipped with signals or directions