Conformal Parametrisation of Loxodromes by Triples of Circles

We provide a parametrisation of a loxodrome by three specially arranged cycles. The parametrisation is covariant under fractional linear transformations of the complex plane and naturally encodes conformal properties of loxodromes. Selected geometrical examples illustrate the usage of parametrisation. Our work extends the set of objects in Lie sphere geometry---circle, lines and points---to the natural maximal conformally-invariant family, which also includes loxodromes.Comment: 14 pages. 9 PDF in four figures, AMS-LaTe

Geodetic Observations of Weak Determinism in Rupture Evolution of Large Earthquakes.

The moment evolution of large earthquakes is a subject of fundamental interest to both basic and applied seismology. Specifically, an open problem is when in the rupture process a large earthquake exhibits features dissimilar from those of a lesser magnitude event. The answer to this question is of importance for rapid, reliable estimation of earthquake magnitude, a major priority of earthquake and tsunami early warning systems. Much effort has been made to test whether earthquakes are deterministic, meaning that observations in the first few seconds of rupture can be used to predict the final rupture extent. However, results have been inconclusive, especially for large earthquakes greater than M w 7. Traditional seismic methods struggle to rapidly distinguish the size of large-magnitude events, in particular near the source, even after rupture completion, making them insufficient to resolve the question of predictive rupture behavior. Displacements derived from Global Navigation Satellite System data can accurately estimate magnitude in real time, even for the largest earthquakes. We employ a combination of seismic and geodetic (Global Navigation Satellite System) data to investigate early rupture metrics, to determine whether observational data support deterministic rupture behavior. We find that while the earliest metrics (~5 s of data) are not enough to infer final earthquake magnitude, accurate estimates are possible within the first tens of seconds, prior to rupture completion, suggesting a weak determinism. We discuss the implications for earthquake source physics and rupture evolution and address recommendations for earthquake and tsunami early warning

Unions of slices are not slices

Many approaches to slicing rely upon the 'fact' that the union of two static slices is a valid slice. It is known that static slices constructed using program dependence graph algorithms are valid slices (Reps and Yang, 1988). However, this is not true for other forms of slicing. For example, it has been established that the union of two dynamic slices is not necessarily a valid dynamic slice (Hall, 1995). In this paper this result is extended to show that the union of two static slices is not necessarily a valid slice, based on Weiser's definition of a (static) slice. We also analyse the properties that make the union of different forms of slices a valid slice

A bisphosphonate for F-19-magnetic resonance imaging

19F-magnetic resonance imaging (MRI) is a promising technique that may allow us to measure the concentration of exogenous fluorinated imaging probes quantitatively in vivo. Here, we describe the synthesis and characterisation of a novel geminal bisphosphonate (19F-BP) that contains chemically-equivalent fluorine atoms that show a single and narrow 19F resonance and a bisphosphonate group that may be used for labelling inorganic materials based in calcium phosphates and metal oxides. The potential of 19F-BP to provide contrast was analysed in vitro and in vivo using 19F-MRI. In vitro studies demonstrated the potential of 19F-BP as an MRI contrast agent in the millimolar concentration range with signal-to-noise ratios (SNR) comparable to previously reported fluorinated probes. The preliminary in vivo MRI study reported here allowed us to visualise the biodistribution of 19F-BP, showing uptake in the liver and in the bladder/urinary system areas. However, bone uptake was not observed. In addition, 19F-BP showed undesirable toxicity effects in mice that prevent further studies with this compound at the required concentrations for MRI contrast. This study highlights the importance of developing 19F MRI probes with the highest signal intensity achievable

On the total number of prime factors of an odd perfect number

We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No odd perfect numbers are known, but it is well known that if such a number exists, it must have prime factorization of the form n = pα Πkj=1 q2βjj , where p, q1, ⋯, qk, are distinct primes and p ≡ α ≡ 1 (mod 4). We prove that if βj ≡ 1 (mod 3) or βj ≡ 2 (mod 5) for all j, 1 ≤ j ≤ k, then 3 ∦ n. We also prove as our main result that Ω(n) ≥ 37, where Ω(n) = α + 2∑kj=1 βj. This improves a result of Sayers (Ω(n) ≥ 29) given in 1986

Nano-mechanical tuning and imaging of a photonic crystal micro-cavity resonance

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Improved Parallel Rabin-Karp Algorithm Using Compute Unified Device Architecture

String matching algorithms are among one of the most widely used algorithms in computer science. Traditional string matching algorithms efficiency of underlaying string matching algorithm will greatly increase the efficiency of any application. In recent years, Graphics processing units are emerged as highly parallel processor. They out perform best of the central processing units in scientific computation power. By combining recent advancement in graphics processing units with string matching algorithms will allows to speed up process of string matching. In this paper we proposed modified parallel version of Rabin-Karp algorithm using graphics processing unit. Based on that, result of CPU as well as parallel GPU implementations are compared for evaluating effect of varying number of threads, cores, file size as well as pattern size.Comment: Information and Communication Technology for Intelligent Systems (ICTIS 2017

How Can Viral Dynamics Models Inform Endpoint Measures in Clinical Trials of Therapies for Acute Viral Infections?

Acute viral infections pose many practical challenges for the accurate assessment of the impact of novel therapies on viral growth and decay. Using the example of influenza A, we illustrate how the measurement of infection-related quantities that determine the dynamics of viral load within the human host, can inform investigators on the course and severity of infection and the efficacy of a novel treatment. We estimated the values of key infection-related quantities that determine the course of natural infection from viral load data, using Markov Chain Monte Carlo methods. The data were placebo group viral load measurements collected during volunteer challenge studies, conducted by Roche, as part of the oseltamivir trials. We calculated the values of the quantities for each patient and the correlations between the quantities, symptom severity and body temperature. The greatest variation among individuals occurred in the viral load peak and area under the viral load curve. Total symptom severity correlated positively with the basic reproductive number. The most sensitive endpoint for therapeutic trials with the goal to cure patients is the duration of infection. We suggest laboratory experiments to obtain more precise estimates of virological quantities that can supplement clinical endpoint measurements

Quantification of respiratory parameters in patients with temporal lobe epilepsy

Dysfunction affecting cardiac or pulmonary systems has been postulated as a major factor in sudden death in epilepsy (SUDEP). Whilst the majority of studies of cardiorespiratory function have focused on changes during seizures, here we investigate whether epilepsy influences basal respiratory parameters in patients with temporal lobe epilepsy (TLE) during the interictal period. Spirometry was performed in 10 females and 10 males. Measurements of Vital Capacity (VC), Forced Vital Capacity (FVC), Forced Expiratory Volume in the first second (FEV1) and ratios of FEV1 to FVC (FEV1/FVC) were obtained, and these values were analyzed as percentages of predicted values. None of the patients had chronic obstructive pulmonary disease and no significant alterations in respiratory function tests were found among these patients. No association between seizure frequency, antiepileptic drugs and SUDEP could be found in this study. Although the study did not identify any specific respiratory abnormality in TLE patients during the interictal period, re-evaluation of clinical data on pulmonary disorders in people with epilepsy should be better investigated

The formal approach to quantitative causal inference in epidemiology: misguided or misrepresented?

Two recent articles, one by Vandenbroucke, Broadbent and Pearce (henceforth VBP) and the other by Krieger and Davey Smith (henceforth KDS), criticize what these two sets of authors characterize as the mainstream of the modern ‘causal inference’ school in epidemiology. The criticisms made by these authors are severe; VBP label the field both ‘wrong in theory’ and ‘wrong in practice’, and KDS—at least in some settings—feel that the field not only ‘bark[s] up the wrong tree’ but ‘miss[es] the forest entirely’. More specifically, the school of thought, and the concepts and methods within it, are painted as being applicable only to a very narrow range of investigations, to the exclusion of most of the important questions and study designs in modern epidemiology, such as the effects of genetic variants, the study of ethnic and gender disparities and the use of study designs that do not closely mirror randomized controlled trials (RCTs). Furthermore, the concepts and methods are painted as being potentially highly misleading even within this narrow range in which they are deemed applicable. We believe that most of VBP’s and KDS’s criticisms stem from a series of misconceptions about the approach they criticize. In this response, therefore, we aim first to paint a more accurate picture of the formal causal inference approach, and then to outline the key misconceptions underlying VBP’s and KDS’s critiques. KDS in particular criticize directed acyclic graphs (DAGs), using three examples to do so. Their discussion highlights further misconceptions concerning the role of DAGs in causal inference, and so we devote the third section of the paper to addressing these. In our Discussion we present further objections we have to the arguments in the two papers, before concluding that the clarity gained from adopting a rigorous framework is an asset, not an obstacle, to answering more reliably a very wide range of causal questions using data from observational studies of many different designs