Related papers: The Depth Poset under Transpositions in the Filter

Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative…

Filters whose porosity decreases with depth are often more efficient at removing solute from a fluid than filters with a uniform porosity. We investigate this phenomenon via an extension of homogenization theory that accounts for a…

This work presents a mathematical model of an adsorption column to study the evolution of contaminant concentration and adsorbed quantity along the longitudinal axis of the filter. The model is formulated as a system of partial differential…

We introduce a new invariant defined on the vertices of a given filtered simplicial complex, called codensity, which controls the impact of removing vertices on persistent homology. We achieve this control through the use of an interleaving…

This paper investigates how adjustments to deep learning architectures impact model performance in image classification. Small-scale experiments generate initial insights although the trends observed are not consistent with the entire…

Generative models based on normalizing flows are very successful in modeling complex data distributions using simpler ones. However, straightforward linear interpolations show unexpected side effects, as interpolation paths lie outside the…

Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…

Monocular depth estimation is a critical task for autonomous driving and many other computer vision applications. While significant progress has been made in this field, the effects of viewpoint shifts on depth estimation models remain…

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

Inference in deep Bayesian neural networks is only fully understood in the infinite-width limit, where the posterior flexibility afforded by increased depth washes out and the posterior predictive collapses to a shallow Gaussian process.…

We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathematics, including the representation theory of quivers and…

The Persistent Homology Transform (PHT) summarizes a shape in $\mathbb{R}^m$ by collecting persistence diagrams obtained from linear height filtrations in all directions on $\mathbb{S}^{m-1}$. It enjoys strong theoretical guarantees,…

We propose a general technique for extracting a larger set of stable information from persistent homology computations than is currently done. The persistent homology algorithm is usually viewed as a procedure which starts with a filtered…

Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we…

Persistent homology has been studied to better understand the structural properties and topology features of weighted networks. It can reveal hidden layers of information about the higher-order structures formed by non-pairwise interactions…

Convolutional neural networks (CNNs) and transfer learning have recently been used for 6 degrees of freedom (6-DoF) camera pose estimation. While they do not reach the same accuracy as visual SLAM-based approaches and are restricted to a…

We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general…

We investigate theoretically the evolution of the vortex number in an array of photon condensates that is brought from an incoherent low density state to a coherent high density state by a sudden change in the pumping laser intensity. We…

We present a method for learning an embedding that places images of humans in similar poses nearby. This embedding can be used as a direct method of comparing images based on human pose, avoiding potential challenges of estimating body…

As demand for robotics manipulation application increases, accurate vision-based 6D pose estimation becomes essential for autonomous operations. Convolutional Neural Networks (CNNs) based approaches for pose estimation have been previously…