Related papers: The Depth Poset under Transpositions in the Filter

With the use of deep learning in many areas, how to improve this technology or how to develop the structure used more effectively and in a shorter time is an issue that is of interest to many people working in this field. Many studies are…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

Homological algebra of modules over posets is developed, as closely parallel as possible to that of finitely generated modules over noetherian commutative rings, in the direction of finite presentations and resolutions. Centrally at issue…

Networks are useful representations for complex systems. Especially, heterogeneous and asymmetrical relations commonly found in complex systems can be converted to weighted directed edges between nodes. The disparity filter (Serrano et al.,…

We study the transport and deposition dynamics of colloids in saturated porous media under unfavorable filtering conditions. As an alternative to traditional convection-diffusion or more detailed numerical models, we consider a mean-field…

We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (possibly discontinuous) flux function are inferred from noisy…

A simplified analysis is performed on the Bode-type filtering sensitivity trade-off integrals, which capture the sensitivity characteristics of the estimate and estimation error with respect to the process input and estimated signal in…

This work investigates the impact of the loss function on the performance of Neural Networks, in the context of a monocular, RGB-only, image localization task. A common technique used when regressing a camera's pose from an image is to…

In this work we investigate the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting. Our main contribution is a thorough evaluation of networks of increasing depth using an architecture…

The incremental poses computed through odometry can be integrated over time to calculate the pose of a device with respect to an initial location. The resulting global pose may be used to formulate a second, consistency based, loss term in…

An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of…

Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested…

Effects of heterogeneity in the suspected-infected-susceptible model on networks are investigated using quenched mean-field theory. The emergence of localization is described by the distributions of the inverse participation ratio and…

Stereo depth estimation relies on optimal correspondence matching between pixels on epipolar lines in the left and right images to infer depth. In this work, we revisit the problem from a sequence-to-sequence correspondence perspective to…

This work presents an effective depth-consistency self-prompt Transformer for image dehazing. It is motivated by an observation that the estimated depths of an image with haze residuals and its clear counterpart vary. Enforcing the depth…

The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…

An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…

For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions $\Pi^{\bullet}_{\vec{c}}$ is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with…

Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a…

Robust in-bed human pose estimation under blanket occlusion remains challenging due to the scarcity of reliable labeled training data for heavily covered poses. Existing approaches rely on multi-modal sensing or image-to-image translation…