Invertibility in groupoid C*-algebras

Given a second-countable, Hausdorff, \'etale, amenable groupoid G with compact unit space, we show that an element a in C*(G) is invertible if and only if \lambda_x(a) is invertible for every x in the unit space of G, where \lambda_x refers to the "regular representation" of C*(G) on l_2(G_x). We also prove that, for every a in C*(G), there exists some x in G^{(0)} such that ||a|| = ||\lambda_x(a)||.Comment: 8 page

Pneumothorax and Pneumomediastinum in a Sputum Positive Tuberculosis Patient: The Continuous Diaphragm Sign

Secondary pneumothorax is a very common medical emergency. At times it is associated with pneumomediastinum, which could be fatal at times if not identified. We present a case of a 11 years old sputum positive child who presented with both these conditions and was diagnosed on chest x ray

Parameterized Algorithms for Graph Partitioning Problems

We study a broad class of graph partitioning problems, where each problem is specified by a graph $G=(V,E)$, and parameters $k$ and $p$. We seek a subset $U\subseteq V$ of size $k$, such that $\alpha_1m_1 + \alpha_2m_2$ is at most (or at least) $p$, where $\alpha_1,\alpha_2\in\mathbb{R}$ are constants defining the problem, and $m_1, m_2$ are the cardinalities of the edge sets having both endpoints, and exactly one endpoint, in $U$, respectively. This class of fixed cardinality graph partitioning problems (FGPP) encompasses Max $(k,n-k)$-Cut, Min $k$-Vertex Cover, $k$-Densest Subgraph, and $k$-Sparsest Subgraph. Our main result is an $O^*(4^{k+o(k)}\Delta^k)$ algorithm for any problem in this class, where $\Delta \geq 1$ is the maximum degree in the input graph. This resolves an open question posed by Bonnet et al. [IPEC 2013]. We obtain faster algorithms for certain subclasses of FGPPs, parameterized by $p$, or by $(k+p)$. In particular, we give an $O^*(4^{p+o(p)})$ time algorithm for Max $(k,n-k)$-Cut, thus improving significantly the best known $O^*(p^p)$ time algorithm

Electro-Oxidation of Titanium Carbide Nanoparticles in Aqueous Acid Creates TiC@TiO2 Core-Shell Structures

Titanium carbide (TiC) is an attractive support material used in electro-catalysis and sensing. We report the electrochemistry of TiC nanoparticles (NPs, 35–50 nm in diameter) in different electrolytes in the pH range of 0 to 8. The TiC NPs undergo irreversible oxidation in acidic, basic, and neutral media, attributed to the partial conversion into titanium dioxide (TiO2) with the amount of oxidation highly dependent on the pH of the solution. In H2SO4 (pH 0), multiple voltammetric scans revealed the conversion to be partial but repeated scans allowed a conversion approaching 100% to be obtained with 20 scans generating a ca 60% level of oxidation. The process is inferred to lead to the formation of TiC@TiO2 core-shell nanoparticles (~12.5 nm core radius and ~5 nm shell width for a 60% conversion) and this value sharply decreases with an increase of pH. Independent measurements were conducted at a single NP level (via nano-impact experiments) to confirm the oxidation of the NPs, showing consistent agreement with the bulk measurements

AMK: An Interface For Object-oriented Newtonian Particle Mechanics

This article describes an object-oriented environment with an associated user interface, AMK, for modelling simple Newtonian particle mechanics. It is intended for educational use, and provides a framework for modelling which generalises methodology. Physical objects are treated as logical objects, and mathematical models are formulated by linking them. The implementation is within the Windows environment using Mathematica and Visual Basic. Modelling is done by constructing objects and linking them to produce new objects. The aim is to produce an equation of motion object. The interface forces the user into a modelling cycle of constructing and linking objects, and accessing their methods. It constructs a Mathematica input automatically from information supplied by the user, and communicates with Mathematica. The combination of a generalised environment plus interface produces correct answers when modelling many specific physical systems

Degree spectra for transcendence in fields

We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e. degrees above an arbitrary fixed $\Delta^0_2$ degree. In other cases, these spectra may be characterized by the ability to enumerate an arbitrary $\Sigma^0_2$ set. This is the first proof that a computable field can fail to have a computable copy with a computable transcendence basis

Using Bars As Signposts of Galaxy Evolution at High and Low Redshifts

An analysis of the NICMOS Deep Field shows that there is no evidence of a decline in the bar fraction beyond z~0.7, as previously claimed; both bandshifting and spatial resolution must be taken into account when evaluating the evolution of the bar fraction. Two main caveats of this study were a lack of a proper comparison sample at low redshifts and a larger number of galaxies at high redshifts. We address these caveats using two new studies. For a proper local sample, we have analyzed 134 spirals in the near-infrared using 2MASS (main results presented by Menendez-Delmestre in this volume) which serves as an ideal anchor for the low-redshift Universe. In addition to measuring the mean bar properties, we find that bar size is correlated with galaxy size and brightness, but the bar ellipticity is not correlated with these galaxy properties. The bar length is not correlated with the bar ellipticity. For larger high redshift samples we analyze the bar fraction from the 2-square degree COSMOS ACS survey. We find that the bar fraction at z~0.7 is ~50%, consistent with our earlier finding of no decline in bar fraction at high redshifts.Comment: In the proceedings of "Penetrating Bars through Masks of Cosmic Dust: The Hubble Tuning Fork strikes a New Note

Joint Viewpoint and Keypoint Estimation with Real and Synthetic Data

The estimation of viewpoints and keypoints effectively enhance object detection methods by extracting valuable traits of the object instances. While the output of both processes differ, i.e., angles vs. list of characteristic points, they indeed share the same focus on how the object is placed in the scene, inducing that there is a certain level of correlation between them. Therefore, we propose a convolutional neural network that jointly computes the viewpoint and keypoints for different object categories. By training both tasks together, each task improves the accuracy of the other. Since the labelling of object keypoints is very time consuming for human annotators, we also introduce a new synthetic dataset with automatically generated viewpoint and keypoints annotations. Our proposed network can also be trained on datasets that contain viewpoint and keypoints annotations or only one of them. The experiments show that the proposed approach successfully exploits this implicit correlation between the tasks and outperforms previous techniques that are trained independently.Comment: 11 pages, 4 figure