Quantitative uniqueness for elliptic equations with singular lower order terms

We use a Carleman type inequality of Koch and Tataru to obtain quantitative estimates of unique continuation for solutions of second order elliptic equations with singular lower order terms. First we prove a three sphere inequality and then describe two methods of propagation of smallness from sets of positive measure.Comment: 23 pages, v2 small changes are done and some mistakes are correcte

Enhancing anaerobic digestion of food waste through Biochemical Methane Potential 1 Assays at different substrate: inoculum ratios

Food waste has a high energy potential that can be converted into useful energy in the form of methane via anaerobic digestion. Biochemical Methane Potential assays (BMPs) were conducted to quantify the impacts on methane production of different ratios of food waste. Anaerobic digester sludge (ADS) was used as the inoculum, and BMPs were performed at food waste:inoculum ratios of 0.42, 1.42, and 3.0 g chemical oxygen demand/g volatile solids (VS). The 1.42 ratio had the highest CH4-COD recovery: 90% of the initial total chemical oxygen demand (TCOD) was from food waste, followed by ratios 0.42 and 3.0 at 69% and 57%, respectively. Addition of food waste above 0.42 caused a lag time for CH4 production that increased with higher ratios, which highlighted the negative impacts of overloading with food waste. The Gompertz equation was able to represent the results well, and it gave lag times of 0, 3.6 and 30 days and maximum methane productions of 370, 910, and 1950 mL for ratios 0.42, 1.42 and 3.0, respectively. While ratio 3.0 endured a long lag phase and low VSS destruction, ratio 1.42 achieved satisfactory results for all performance criteria. These results provide practical guidance on food-waste-to-inoculum ratios that can lead to optimizing methanogenic yield

The Volume of a Local Nodal Domain

Let M either be a closed real analytic Riemannian manifold or a closed smooth Riemannian surface. We estimate from below the volume of a nodal domain component in an arbitrary ball provided that this component enters the ball deeply enough.Comment: 21 pages; introduction improved putting the problem in a larger context

The Putative Cerean Exosphere

The ice-rich crust of dwarf planet 1 Ceres is the source of a tenuous water exosphere, and the behavior of thisputative exosphere is investigated with model calculations. Outgassing water molecules seasonally condensearound the winter pole in an optically thin layer

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl

SentiBench - a benchmark comparison of state-of-the-practice sentiment analysis methods

In the last few years thousands of scientific papers have investigated sentiment analysis, several startups that measure opinions on real data have emerged and a number of innovative products related to this theme have been developed. There are multiple methods for measuring sentiments, including lexical-based and supervised machine learning methods. Despite the vast interest on the theme and wide popularity of some methods, it is unclear which one is better for identifying the polarity (i.e., positive or negative) of a message. Accordingly, there is a strong need to conduct a thorough apple-to-apple comparison of sentiment analysis methods, \textit{as they are used in practice}, across multiple datasets originated from different data sources. Such a comparison is key for understanding the potential limitations, advantages, and disadvantages of popular methods. This article aims at filling this gap by presenting a benchmark comparison of twenty-four popular sentiment analysis methods (which we call the state-of-the-practice methods). Our evaluation is based on a benchmark of eighteen labeled datasets, covering messages posted on social networks, movie and product reviews, as well as opinions and comments in news articles. Our results highlight the extent to which the prediction performance of these methods varies considerably across datasets. Aiming at boosting the development of this research area, we open the methods' codes and datasets used in this article, deploying them in a benchmark system, which provides an open API for accessing and comparing sentence-level sentiment analysis methods

Evaluation of the diagnostic accuracy of prototype rapid tests for human African trypanosomiasis

Peer reviewedPublisher PD

How does a cadaver model work for testing ultrasound diagnostic capability for rheumatic-like tendon damage?

To establish whether a cadaver model can serve as an effective surrogate for the detection of tendon damage characteristic of rheumatoid arthritis (RA). In addition, we evaluated intraobserver and interobserver agreement in the grading of RA-like tendon tears shown by US, as well as the concordance between the US findings and the surgically induced lesions in the cadaver model. RA-like tendon damage was surgically induced in the tibialis anterior tendon (TAT) and tibialis posterior tendon (TPT) of ten ankle/foot fresh-frozen cadaveric specimens. Of the 20 tendons examined, six were randomly assigned a surgically induced partial tear; six a complete tear; and eight left undamaged. Three rheumatologists, experts in musculoskeletal US, assessed from 1 to 5 the quality of US imaging of the cadaveric models on a Likert scale. Tendons were then categorized as having either no damage, (0); partial tear, (1); or complete tear (2). All 20 tendons were blindly and independently evaluated twice, over two rounds, by each of the three observers. Overall, technical performance was satisfactory for all items in the two rounds (all values over 2.9 in a Likert scale 1-5). Intraobserver and interobserver agreement for US grading of tendon damage was good (mean κ values 0.62 and 0.71, respectively), with greater reliability found in the TAT than the TPT. Concordance between US findings and experimental tendon lesions was acceptable (70-100 %), again greater for the TAT than for the TPT. A cadaver model with surgically created tendon damage can be useful in evaluating US metric properties of RA tendon lesions

Large-Mass Ultra-Low Noise Germanium Detectors: Performance and Applications in Neutrino and Astroparticle Physics

A new type of radiation detector, a p-type modified electrode germanium diode, is presented. The prototype displays, for the first time, a combination of features (mass, energy threshold and background expectation) required for a measurement of coherent neutrino-nucleus scattering in a nuclear reactor experiment. The device hybridizes the mass and energy resolution of a conventional HPGe coaxial gamma spectrometer with the low electronic noise and threshold of a small x-ray semiconductor detector, also displaying an intrinsic ability to distinguish multiple from single-site particle interactions. The present performance of the prototype and possible further improvements are discussed, as well as other applications for this new type of device in neutrino and astroparticle physics (double-beta decay, neutrino magnetic moment and WIMP searches).Comment: submitted to Phys. Rev.