Nonlocal conservation laws of PDEs possessing differential coverings

In his 1892 paper [L. Bianchi, Sulla trasformazione di B\"{a}cklund per le superfici pseudosferiche, Rend. Mat. Acc. Lincei, s. 5, v. 1 (1892) 2, 3--12], L. Bianchi noticed, among other things, that quite simple transformations of the formulas that describe the B\"{a}cklund transformation of the sine-Gordon equation lead to what is called a nonlocal conservation law in modern language. Using the techniques of differential coverings [I.S. Krasil'shchik, A.M. Vinogradov, Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and B\"{a}cklund transformations, Acta Appl. Math. v. 15 (1989) 1-2, 161--209], we show that this observation is of a quite general nature. We describe the procedures to construct such conservation laws and present a number of illustrative examples

Challenges of Loss to Follow-up in Tuberculosis Research.

In studies evaluating methods for diagnosing tuberculosis (TB), follow-up to verify the presence or absence of active TB is crucial and high dropout rates may significantly affect the validity of the results. In a study assessing the diagnostic performance of the QuantiFERON®-TB Gold In-Tube test in TB suspect children in Tanzania, factors influencing patient adherence to attend follow-up examinations and reasons for not attending were examined. In 160 children who attended and 102 children who did not attend scheduled 2-month follow-up baseline health characteristics, demographic data and risk factors for not attending follow-up were determined. Qualitative interviews were used to understand patient and caretakers reasons for not returning for scheduled follow-up. Being treated for active tb in the dots program (OR: 4.14; 95% CI:1.99-8.62;p-value<0.001) and receiving money for the bus fare (OR:129; 95% CI 16->100;P-value<0.001) were positive predictors for attending follow-up at 2 months, and 21/85(25%) of children not attending scheduled follow-up had died. Interviews revealed that limited financial resources, i.e. lack of money for transportation and poor communication, were related to non-adherence. Patients lost to follow-up is a potential problem for TB research. Receiving money for transportation to the hospital and communication is crucial for adherence to follow-up conducted at a study facility. Strategies to ensure follow-up should be part of any study protocol

Formal conserved quantities for isothermic surfaces

Isothermic surfaces in $S^n$ are characterised by the existence of a pencil $\nabla^t$ of flat connections. Such a surface is special of type $d$ if there is a family $p(t)$ of $\nabla^t$-parallel sections whose dependence on the spectral parameter $t$ is polynomial of degree $d$. We prove that any isothermic surface admits a family of $\nabla^t$-parallel sections which is a formal Laurent series in $t$. As an application, we give conformally invariant conditions for an isothermic surface in $S^3$ to be special.Comment: 13 page

A Comparison of a Brain-Computer Interface and an Eye Tracker: Is There a More Appropriate Technology for Controlling a Virtual Keyboard in an ALS Patient?

The ability of people affected by amyotrophic lateral sclerosis (ALS), muscular dystrophy or spinal cord injuries to physically interact with the environment, is usually reduced. In some cases, these patients suffer from a syndrome known as locked-in syndrome (LIS), defined by the patient’s inability to make any move-ment but blinks and eye movements. Tech communication systems available for people in LIS are very limited, being those based on eye-tracking and brain-computer interface (BCI) the most useful for these patients. A comparative study between both technologies in an ALS patient is carried out: an eye tracker and a visual P300-based BCI. The purpose of the study presented in this paper is to show that the choice of the technology could depend on user´s preference. The evaluation of performance, workload and other subjective measures will allow us to determine the usability of the systems. The obtained results suggest that, even if for this patient the BCI technology is more appropriate, the technology should be always tested and adapted for each user.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On the probabilistic min spanning tree Problem

We study a probabilistic optimization model for min spanning tree, where any vertex vi of the input-graph G(V,E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Suppose that when this “real” instance G′ becomes known, a spanning tree T, called anticipatory or a priori spanning tree, has already been computed in G and one can run a quick algorithm (quicker than one that recomputes from scratch), called modification strategy, that modifies the anticipatory tree T in order to fit G ′. The goal is to compute an anticipatory spanning tree of G such that, its modification for any G ′ ⊆ G is optimal for G ′. This is what we call probabilistic min spanning tree problem. In this paper we study complexity and approximation of probabilistic min spanning tree in complete graphs under two distinct modification strategies leading to different complexity results for the problem. For the first of the strategies developed, we also study two natural subproblems of probabilistic min spanning tree, namely, the probabilistic metric min spanning tree and the probabilistic min spanning tree 1,2 that deal with metric complete graphs and complete graphs with edge-weights either 1, or 2, respectively

Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux

We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantization of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.Comment: 44 pages, 3 figures. v2: references and a discussion about perturbative results adde

The Resolved Outer Population of NGC6822 with WFPC2

We present F336W (U), F439W (B), F555W (V), and F675W (R) Wide Field Planetary Camera 2 (WFPC2) photometry of two outer regions of the Local Group dwarf irregular galaxy NGC6822. The NE region is ~13 arcmin from the galaxy centre, while the W region lies 10 arcmin out, and within the wispy low surface brightness outer regions of the galaxy. The fields are not crowded and contain few NGC 6822 stars. We discuss errors and uncertainties and find that the W region contains a main sequence that extends to stars of about 2 solar masses, with an age of about 200 Myr. The NE region has no main sequence or stars younger than 1 Gyr, but does contain some luminous red stars that are not matched in the W field. These stars are not clumped in the field. The results suggest that the W region may be a trace of a tidal event that triggered the current star-formation in this isolated galaxy.Comment: 12 pages including 2 tables, plus 4 figures (#1 omitted) To appear in PAS

Galaxy evolution in nearby galaxy groups. III. A GALEX view of NGC 5846, the largest group in the local universe

We explore the co-evolution of galaxies in nearby groups (V < 3000 km/s) with a multi-wavelength approach. We analyze GALEX far-UV (FUV) and near-UV (NUV) imaging and SDSS u,g,r,i,z data of groups spanning a large range of dynamical phases. We characterize the photometric properties of spectroscopically-confirmed galaxy members and investigate the global properties of the groups through a dynamical analysis. Here we focus on NGC 5846, the third most massive association of Early-Type Galaxies (ETG) after the Virgo and Fornax clusters. The group, composed of 90 members, is dominated by ETGs (about 80 per cent), and among ETGs about 40\% are dwarfs. Results are compared with those obtained for three groups in the LeoII cloud, which are radically different both in member-galaxy population and dynamical properties. The FUV-NUV cumulative colour distribution and the normalized UV luminosity function (LF) significantly differ due to the different fraction of late-type galaxy population. The UV LF of NGC 5846 resembles that of the Virgo cluster, however our analysis suggests that star-formation episodes are still occurring in most of the group galaxies, including ETGs. The NUV-i colour distribution, the optical-UV colour-colour diagram, and NUV-r vs. Mr colour-magnitude relation suggest that the gas contribution cannot be neglected in the evolution of ETG-type group members. Our analysis highlights that NGC~5846 is still in an active phase of its evolution, notwithstanding the dominance of dwarf and bright ETGs and its virialized configuration.Comment: 26 pages, 13 figures, accepted for publication in MNRA