SAUNet++: an automatic segmentation model of COVID-19 lesion from CT slices

The coronavirus disease 2019 (COVID-19) epidemic has spread worldwide and the healthcare system is in crisis. Accurate, automated and rapid segmentation of COVID-19 lesion in computed tomography (CT) images can help doctors diagnose and provide prognostic information. However, the variety of lesions and small regions of early lesion complicate their segmentation. To solve these problems, we propose a new SAUNet++ model with squeeze excitation residual (SER) module and atrous spatial pyramid pooling (ASPP) module. The SER module can assign more weights to more important channels and mitigate the problem of gradient disappearance;the ASPP module can obtain context information by atrous convolution using various sampling rates. In addition, the generalized dice loss (GDL) can reduce the correlation between lesion size and dice loss, and is introduced to solve the problem of small regions segmentation of COVID-19 lesion. We collected multinational CT scan data from China, Italy and Russia and conducted extensive comparative and ablation studies. The experimental results demonstrated that our method outperforms state-of-the-art models and can effectively improve the accuracy of COVID-19 lesion segmentation on the dice similarity coefficient (our: 87.38% vs. U-Net++: 84.25%), sensitivity (our: 93.28% vs. U-Net++: 89.85%) and Hausdorff distance (our: 19.99 mm vs. U-Net++: 26.79 mm), respectively.

Special Issue: Fractal Functions and Applications

The first one studies three procedures of inverse Laplace Transforms: A Sinc–Thiele approximation, a Sinc and a Sinc–Gaussian (SG) method. Classical Iterated Function Systems are composed of a set of Banach contractions giving rise to a fractal attractor in a metric space E. In the reference [3], the authors extend this concept in different ways. Additionally, in the last part of the paper, they consider an infinite collection of maps and multivalued mappings wn:E→K(E), where K(E) is the Hausdorff space of compact subsets of E. The authors prove that under certain conditions, these IFSs own an attractor.

PROBABILITY MONADS AS CODENSITY MONADS

We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads as the codensity monads of functors that send a countable set to the space of probability distributions on that set. On (pre)measurable spaces we discuss monads of probability (pre)measures and their finitely additive analogues. We also give codensity constructions for monads of Radon measures on compact Hausdorff spaces and compact metric spaces and for the monad of Baire measures on Hausdorff spaces. A crucial role in these constructions is given by integral representation theorems, which we derive from a generalized Daniell-Stone theorem.

A Metric Space for Point Process Excitations

A multivariate Hawkes process enables self- and cross-excitations through a triggering matrix that behaves like an asymmetrical covariance structure, characterizing pairwise interactions between the event types. Full-rank estimation of all interactions is often infeasible in empirical settings. Models that specialize on a spatiotemporal application alleviate this obstacle by exploiting spatial locality, allowing the dyadic relationships between events to depend only on separation in time and relative distances in real Euclidean space. Here we generalize this framework to any multivariate Hawkes process, and harness it as a vessel for embedding arbitrary event types in a hidden metric space. Specifically, we propose a Hidden Hawkes Geometry (HHG) model to uncover the hidden geometry between event excitations in a multivariate point process. The low dimensionality of the embedding regularizes the structure of the inferred interactions. We develop a number of estimators and validate the model by conducting several experiments. In particular, we investigate regional infectivity dynamics of COVID-19 in an early South Korean record and recent Los Angeles confirmed cases. By additionally performing synthetic experiments on short records as well as explorations into options markets and the Ebola epidemic, we demonstrate that learning the embedding alongside a point process uncovers salient interactions in a broad range of applications.