On the distribution of multiplicatively dependent vectors

In this paper, we study the distribution of multiplicatively dependent vectors. For example, although they have zero Lebesgue measure, they are everywhere dense both in $\R^n$ and \C^n. We also study this property in a more detailed manner by considering the covering radius of such vectors.Comment: 19 page

Laboratory mid-IR spectra of equilibrated and igneous meteorites. Searching for observables of planetesimal debris

Meteorites contain minerals from Solar System asteroids with different properties (like size, presence of water, core formation). We provide new mid-IR transmission spectra of powdered meteorites to obtain templates of how mid-IR spectra of asteroidal debris would look like. This is essential for interpreting mid-IR spectra of past and future space observatories, like the James Webb Space Telescope. We show that the transmission spectra of wet and dry chondrites, carbonaceous and ordinary chondrites and achondrite and chondrite meteorites are distinctly different in a way one can distinguish in astronomical mid-IR spectra. The two observables that spectroscopically separate the different meteorites groups (and thus the different types of parent bodies) are the pyroxene-olivine feature strength ratio and the peak shift of the olivine spectral features due to an increase in the iron concentration of the olivine

Iron(III) chelating resins-IV. Crosslinked copolymer beads of 1-(B-acrylamidoethyl)-3-hydroxy-2-methyl-4(1H)-pyridinone (AHMP) with 2-hydroxyethyl methacrylate (HEMA)

Iron(III) chelating beads have been synthesized by copolymerization of 1-(ß-acrylamidoethyl)-3-hydroxy-2-methyl-4(IH)-pyridinone (AHMP) with 2-hydroxyethyl methacrylate (HEMA), and ethyleneglycol dimethacrylate (EGDMA) as the crosslinking agent. The synthesis of the AHMP-HEMA beads was performed by suspension polymerization of AHMP, HEMA and EGDMA in benzyl alchol¿20% aqueous NaCl solution using 2,2¿-azobisisobutyronitrile (AIBN) as the initiator and polyvinylalcohol (40¿88) as a suspending agent.\ud \ud The crosslinked copolymer beads were characterized by IR, and the AHMP content was determined by elemental analysis. The AHMP-HEMA beads were not too hydrophilic, and the copolymers absorbed at equilibrium only 40¿50% water. It was found that the copolymer beads were very stable at 25°, but some degradation was observed at 121°.\ud \ud The AHMP-HEMA copolymers were able to chelate iron(III) and the chelation was dependent on the conditions such as pH and temperature. However, the capacities towards iron(III) chelation were always found to be much lower than the calculated values. The influence of the polymeric matrix on the iron(III) chelating ability was studied with iron(III) chelating resins containing various polymeric matrices. It was found that the iron(III) chelating efficiencies of the resins were strongly affected by their hydrophilicities. The low chelating efficiency of the AHMP-HEMA beads (0¿40%) is probably due to their poor swelling in water

Efficient and Perfect domination on circular-arc graphs

Given a graph $G = (V,E)$, a \emph{perfect dominating set} is a subset of vertices $V' \subseteq V(G)$ such that each vertex $v \in V(G)\setminus V'$ is dominated by exactly one vertex $v' \in V'$. An \emph{efficient dominating set} is a perfect dominating set $V'$ where $V'$ is also an independent set. These problems are usually posed in terms of edges instead of vertices. Both problems, either for the vertex or edge variant, remains NP-Hard, even when restricted to certain graphs families. We study both variants of the problems for the circular-arc graphs, and show efficient algorithms for all of them

Segmentation-by-Detection: A Cascade Network for Volumetric Medical Image Segmentation

We propose an attention mechanism for 3D medical image segmentation. The method, named segmentation-by-detection, is a cascade of a detection module followed by a segmentation module. The detection module enables a region of interest to come to attention and produces a set of object region candidates which are further used as an attention model. Rather than dealing with the entire volume, the segmentation module distills the information from the potential region. This scheme is an efficient solution for volumetric data as it reduces the influence of the surrounding noise which is especially important for medical data with low signal-to-noise ratio. Experimental results on 3D ultrasound data of the femoral head shows superiority of the proposed method when compared with a standard fully convolutional network like the U-Net

Resources for Evaluation of Summarization Techniques

We report on two corpora to be used in the evaluation of component systems for the tasks of (1) linear segmentation of text and (2) summary-directed sentence extraction. We present characteristics of the corpora, methods used in the collection of user judgments, and an overview of the application of the corpora to evaluating the component system. Finally, we discuss the problems and issues with construction of the test set which apply broadly to the construction of evaluation resources for language technologies.Comment: LaTeX source, 5 pages, US Letter, uses lrec98.st

Parametric study in weld mismatch of longitudinally welded SSME HPFTP inlet

Welded joints are an essential part of pressure vessels such as the Space Shuttle Main Engine (SSME) Turbopumps. Defects produced in the welding process can be detrimental to weld performance. Recently, review of the SSME high pressure fuel turbopump (HPFTP) titanium inlet x rays revealed several weld discrepancies such as penetrameter density issues, film processing discrepancies, weld width discrepancies, porosity, lack of fusion, and weld offsets. Currently, the sensitivity of welded structures to defects is of concern. From a fatigue standpoint, weld offset may have a serious effect since local yielding, in general, aggravates cyclic stress effects. Therefore, the weld offset issue is considered. Using the finite element method and mathematical formulations, parametric studies were conducted to determine the influence of weld offsets and a variation of weld widths in longitudinally welded cylindrical structures with equal wall thickness on both sides of the joint. From the study, the finite element results and theoretical solutions are presented

SAGE: Sequential Attribute Generator for Analyzing Glioblastomas using Limited Dataset

While deep learning approaches have shown remarkable performance in many imaging tasks, most of these methods rely on availability of large quantities of data. Medical image data, however, is scarce and fragmented. Generative Adversarial Networks (GANs) have recently been very effective in handling such datasets by generating more data. If the datasets are very small, however, GANs cannot learn the data distribution properly, resulting in less diverse or low-quality results. One such limited dataset is that for the concurrent gain of 19 and 20 chromosomes (19/20 co-gain), a mutation with positive prognostic value in Glioblastomas (GBM). In this paper, we detect imaging biomarkers for the mutation to streamline the extensive and invasive prognosis pipeline. Since this mutation is relatively rare, i.e. small dataset, we propose a novel generative framework - the Sequential Attribute GEnerator (SAGE), that generates detailed tumor imaging features while learning from a limited dataset. Experiments show that not only does SAGE generate high quality tumors when compared to standard Deep Convolutional GAN (DC-GAN) and Wasserstein GAN with Gradient Penalty (WGAN-GP), it also captures the imaging biomarkers accurately