From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

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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 ...

We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an ...

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 ...

Interface stress is a fundamental descriptor for interphase boundaries and is defined in strict relation to the interface energy. In nanomultilayers with their intrinsically high interface density, the functional properties are dictated by the interface st ...

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 ...

We discuss two extensions to a recently introduced theory of arrays, which are based on considerations coming from the model theory of power structures. First, we discuss how the ordering relation on the index set can be expressed succinctly by referring t ...

This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theor ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signa ...

Graph neural networks (GNNs) have demonstrated promising performance across various chemistry-related tasks. However, conventional graphs only model the pairwise connectivity in molecules, failing to adequately represent higher order connections, such as m ...

Formally verifying the correctness of software is necessary to merit the trust people put in software systems. Currently, formal verification requires human effort to prove that a piece of code matches its specification and code changes to improve verifiab ...

We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected variational quantum dynamics (pVQD) algorithm, that performs a global optimization with linear scaling in the number ...

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 ...

Type systems usually characterize the shape of values but not their free variables. However, many desirable safety properties could be guaranteed if one knew the free variables captured by values. We describe CC

Remote photoplethysmography (rPPG) using camera-based imaging has shown excellent potential recently in vital signs monitoring due to its contactless nature. However, the optimum filter selection for pre-processing rPPG data in signal conditioning is still ...

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

In 1970, Furth and Yoshikawa (1970 Phys. Fluids 13 2593-6) introduced the scalings of adiabatic plasma compression. Basically, if the shape of the external plasma boundary and the aspect ratio are preserved during the compression, then the density, kinetic ...

Ion transport through biological and solid-state nanochannels is known to be a highly noisy process. The power spectrum of current fluctuations is empirically known to scale like the inverse of frequency, following the long-standing yet poorly understood H ...

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

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Geometric Learning: Leveraging differential geometry for learning and control

Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

Gibbs sampling the posterior of neural networks

Cochains are all you need

Experimental and ab initio derivation of interface stress in nanomultilayered coatings: Application to immiscible Cu/W system with variable in-plane stress

Anomalous and Chern topological waves in hyperbolic networks

Succinct ordering and aggregation constraints in algebraic array theories

A ride time-oriented scheduling algorithm for dial-a-ride problems

Spectral Estimators for High-Dimensional Matrix Inference

Exploiting the Signal-Leak Bias in Diffusion Models

Molecular hypergraph neural networks

Automated Formal Verification of Software Network Functions

Adaptive projected variational quantum dynamics

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Capturing Types

Optimal digital filter selection for remote photoplethysmography (rPPG) signal conditioning

Functional data analysis with rough sample paths?

Shafranov shift correction to the Furth-Yoshikawa scaling of tokamak adiabatic compression

Disentangling 1/f noise from confined ion dynamics