Related papers: The Depth Poset under Transpositions in the Filter
A suitable interpolation method is essential to keep the noise level minimum along with the time-delay. In recent years, many different interpolation filters have been developed for instance H.264-6 tap filter, and AVS- 4 tap filter. The…
Transformers process tokens in parallel but are temporally shallow: at position $t$, each layer attends to key-value pairs computed based on the previous layer, yielding a depth capped by the number of layers. Recurrent models offer…
A theory of modules over posets is developed to define computationally feasible, topologically interpretable data structures, in terms of birth and death of homology classes, for persistent homology with multiple real parameters. To replace…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
We present a simple model for deep bed filtration, where particles suspended in a fluid are trapped while passing through a porous filter. A steady state of the model is reached when filter can not trap additional particles. We find the…
The \v{C}ech complex is one of the most widely used tools in applied algebraic topology. Unfortunately, due to the inclusive nature of the \v{C}ech filtration, the number of simplices grows exponentially in the number of input points. A…
We characterize subgroups of the mapping class group that stabilize a Teichmueller disk in terms of ellipses and strips that are immersed in the associated translation surface. In particular, we show that the space of immersed…
The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from…
The placenta is a complex organ, playing multiple roles during fetal development. Very little is known about the association between placental morphological abnormalities and fetal physiology. In this work, we present an open sourced,…
Transposed convolution is crucial for generating high-resolution outputs, yet has received little attention compared to convolution layers. In this work we revisit transposed convolution and introduce a novel layer that allows us to place…
Representations learned by pre-training a neural network on a large dataset are increasingly used successfully to perform a variety of downstream tasks. In this work, we take a closer look at how features are encoded in such pre-trained…
We present a general form of the iteration and interpolation process used in implicit particle filters. Implicit filters are based on a pseudo-Gaussian representation of posterior densities, and are designed to focus the particle paths so…
In-bed pose estimation has shown value in fields such as hospital patient monitoring, sleep studies, and smart homes. In this paper, we explore different strategies for detecting body pose from highly ambiguous pressure data, with the aid…
This book studies ultrafilters on connectivity systems, that is, on pairs \((X,f)\) where \(X\) is a finite set and \(f:2^{X}\to \mathbb{N}\) is a symmetric submodular function. Ultrafilters, which play a fundamental role in topology and…
Zigzag persistence is a powerful extension of the standard persistence which allows deletions of simplices besides insertions. However, computing zigzag persistence usually takes considerably more time than the standard persistence. We…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…
Relative pose estimation for RGBD cameras is crucial in a number of applications. Previous approaches either rely on the RGB aspect of the images to estimate pose thus not fully making use of depth in the estimation process or estimate pose…
In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with…
We describe an algorithm for compressing a partially ordered set, or \emph{poset}, so that it occupies space matching the information theory lower bound (to within lower order terms), in the worst case. Using this algorithm, we design a…
We revisit the work of To\"en--Vezzosi and Lurie on Grothendieck topologies, using the new tools of acyclic classes and congruences. We introduce a notion of extended Grothendieck topology on any $\infty$-topos, and prove that the poset of…