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Wasserstein Barycenter (WB) is one of the most fundamental optimization problems in optimal transportation. Given a set of distributions, the goal of WB is to find a new distribution that minimizes the average Wasserstein distance to them. The problem becomes even harder if we restrict the solution to be ``$k$-sparse''. In this paper, we study the $k$-sparse WB problem in the presence of outliers, which is a more practical setting since real-world data often contains noise. Existing WB algorithms cannot be directly extended to handle the case with outliers, and thus it is urgently needed to develop some novel ideas. First, we investigate the relation between $k$-sparse WB with outliers and the clustering (with outliers) problems. In particular, we propose a clustering based LP method that yields constant approximation factor for the $k$-sparse WB with outliers problem. Further, we utilize the coreset technique to achieve the $(1+\epsilon)$-approximation factor for any $\epsilon>0$, if the dimensionality is not high. Finally, we conduct the experiments for our proposed algorithms and illustrate their efficiencies in practice.

Stereo matching and semantic segmentation are significant tasks in binocular satellite 3D reconstruction. However, previous studies primarily view these as independent parallel tasks, lacking an integrated multitask learning framework. This work introduces a solution, the Single-branch Semantic Stereo Network (S3Net), which innovatively combines semantic segmentation and stereo matching using Self-Fuse and Mutual-Fuse modules. Unlike preceding methods that utilize semantic or disparity information independently, our method dentifies and leverages the intrinsic link between these two tasks, leading to a more accurate understanding of semantic information and disparity estimation. Comparative testing on the US3D dataset proves the effectiveness of our S3Net. Our model improves the mIoU in semantic segmentation from 61.38 to 67.39, and reduces the D1-Error and average endpoint error (EPE) in disparity estimation from 10.051 to 9.579 and 1.439 to 1.403 respectively, surpassing existing competitive methods. Our codes are available at:https://github.com/CVEO/S3Net.

The Wasserstein barycenter problem is to compute the average of $m$ given probability measures, which has been widely studied in many different areas; however, real-world data sets are often noisy and huge, which impedes its applications in practice. Hence, in this paper, we focus on improving the computational efficiency of two types of robust Wasserstein barycenter problem (RWB): fixed-support RWB (fixed-RWB) and free-support RWB (free-RWB); actually, the former is a subroutine of the latter. Firstly, we improve efficiency through model reducing; we reduce RWB as an augmented Wasserstein barycenter problem, which works for both fixed-RWB and free-RWB. Especially, fixed-RWB can be computed within $\widetilde{O}(\frac{mn^2}{\epsilon_+})$ time by using an off-the-shelf solver, where $\epsilon_+$ is the pre-specified additive error and $n$ is the size of locations of input measures. Then, for free-RWB, we leverage a quality guaranteed data compression technique, coreset, to accelerate computation by reducing the data set size $m$. It shows that running algorithms on the coreset is enough instead of on the original data set. Next, by combining the model reducing and coreset techniques above, we propose an algorithm for free-RWB by updating the weights and locations alternatively. Finally, our experiments demonstrate the efficiency of our techniques., Comment: Algorithms for accelerating robust Wasserstein barycenter problem

A coreset is a small set that can approximately preserve the structure of the original input data set. Therefore we can run our algorithm on a coreset so as to reduce the total computational complexity. Conventional coreset techniques assume that the input data set is available to process explicitly. However, this assumption may not hold in real-world scenarios. In this paper, we consider the problem of coresets construction over relational data. Namely, the data is decoupled into several relational tables, and it could be very expensive to directly materialize the data matrix by joining the tables. We propose a novel approach called ``aggregation tree with pseudo-cube'' that can build a coreset from bottom to up. Moreover, our approach can neatly circumvent several troublesome issues of relational learning problems [Khamis et al., PODS 2019]. Under some mild assumptions, we show that our coreset approach can be applied for the machine learning tasks, such as clustering, logistic regression and SVM.

Volcanic ash clouds often become multilayered and thin with distance from the vent. We explore one mechanism for development of this layered structure. We review data on the characteristics of turbulence layering in the free atmosphere, as well as examples of observations of layered clouds both near-vent and distally. We then explore and contrast the output of volcanic ash transport and dispersal models with models that explicitly use the observed layered structure of atmospheric turbulence. The results suggest that the alternation of turbulent and quiescent atmospheric layers provides one mechanism for development of multilayered ash clouds by modulating the manner in which settling occurs., Comment: arXiv admin note: substantial text overlap with arXiv:2012.14871

Volcanic ash clouds often become multilayered and thin with distance from the vent. We explore one mechanism for development of this layered structure. We review data on the characteristics of turbulence layering in the free atmosphere, as well as examples of observations of layered clouds both near-vent and distally. We then explore dispersion models that explicitly use the observed layered structure of atmospheric turbulence. The results suggest that the alternation of turbulent and quiescent atmospheric layers provides one mechanism for development of multilayered ash clouds by modulating vertical particle motion. The largest particles, generally $> 100 \mu$m, are little affected by turbulence. For particles in which both settling and turbulent diffusion are important to vertical motion, mostly in the range of 10-100 $\mu$m, the greater turbulence intensity and more rapid turbulent diffusion in some layers causes these particles to spend greater time in the more turbulent layers, leading to a layering of concentration. For smaller particles, mostly in the submicron range, the more rapid diffusion in the turbulent layers causes these particles to ``wash out'' quickly.

A new method to identify the source vent location of tephra fall deposits based on thickness or maximum clast size measurements is presented in this work. It couples a first-order gradient descent method with either one of two commonly-used semi-empirical models of tephra thickness distribution. The method is successfully applied to three tephra thickness and one maximum clast size datasets of the North Mono and Fogo A tephra deposits. Randomly selected and localized subsets of these datasets are used as input to evaluate its performance in cases of sparse observations. The results suggest that estimating the dispersal axis is a more robust way to constrain the source vent location with sparse observations. Bootstrap aggregating and examining the surface of the cost function are proposed to characterize the uncertainty of the method. Distinctions between the two adopted semi-empirical models of tephra thickness distribution are discussed. Results from applying the method to thickness datasets of the Trego Hot Springs and Rockland tephras are consistent with previous studies, which also provide new estimates on their total volume. The method is then applied to a series of well-correlated tephra sub-units preserved within the Wilson Creek Formation to estimate their vent location and total volume. The simplicity and flexibility of the method make it a potentially useful and powerful tool for the study of tephra fall deposits of different characteristics.

Numerous tephra layers occur within the late Pleistocene Wilson Creek Formation, where they are interbedded with lacustrine deposits of Lake Russell, the ancestor of present-day Mono Lake. Most of the tephra layers are rhyolitic in composition, and were produced from the Mono Craters. We present detailed stratigraphy and sedimentology of the tephra layers, sampled at twelve outcrops near the shoreline of Mono Lake and the Mono Craters, and implement grain size, componentry, and surface morphology analysis to characterize their physical properties. Sub-unit correlation is proposed for certain tephra units. Noticeable features of the tephras, such as the occurrence of low-density rounded or highly vesicular pumice within certain sub-units, are highlighted. The abundant obsidian, lithics, and ostracods within many sub-units suggest that the associated eruption pulses involved water-magma interaction. Eruptions from the Mono Craters during the late Pleistocene were consistent neither in frequency nor volume. The Mono Craters were most active during the eruption of tephras in Sequences C ($\sim$42.5-39.4 ka) and A ($\sim$14.1-12.9 ka), and Pleistocene volcanic activity reached its peak during the eruption of tephra layer C11. Detailed interpretation of tephra layer B7 and tephras in Sequence A is given. Tephras in Sequence B ($\sim$26.2-23.1 ka) may have had their vents located in the southern half of the Mono Craters, or are smaller in volume (except for B7), compared to the other tephras in the Wilson Creek Formation. Vents for tephra layers A4, A3, and A1 are located near the northern end of the Mono Craters. The stratigraphy of tephra layers B7 and A1 suggests an unstable depositional environment, which can be used to help constrain the water-level history of Lake Russell during the late Pleistocene.