Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit

Silicone Additive Manufactured Indices Performed from a Virtual Diagnostic Waxing for Direct Composite Diastema Closure Combined with Resin Infiltration Technique on White Spot Lesions: A Case Report

The present article describes the resin infiltration technique to address white spots lesions presented on anterior and premolar teeth of a young patient after orthodontic treatment and the digital workflow for planning a diastema closure on the maxillary anterior teeth using facial photographs, an intraoral scanner, a facially driven diagnostic waxing using a dental computer-aided design (CAD) software, and 3-piece additive manufactured (AM) clear silicone indices. The virtual design of the silicone indices was completed using an open-source CAD software and included a flexible clear buccal piece, flexible clear lingual piece, and rigid clear custom tray. The unique 3-piece index design allows a horizontal path of insertion, controlled uniform thickness of the indices, flexible and rigid material properties combination, accurate translation of the diagnostic waxing into the patient´s mouth, and digital storage of the designs

Sphalerons and the Electroweak Phase Transition in Models with Higher Scalar Representations

In this work we investigate the sphaleron solution in a $SU(2)\times U(1)_X$ gauge theory, which also encompasses the Standard Model, with higher scalar representation(s) ($J^{(i)},X^{(i)}$). We show that the field profiles describing the sphaleron in higher scalar multiplet, have similar trends like the doublet case with respect to the radial distance. We compute the sphaleron energy and find that it scales linearly with the vacuum expectation value of the scalar field and its slope depends on the representation. We also investigate the effect of $U(1)$ gauge field and find that it is small for the physical value of the mixing angle, $\theta_{W}$ and resembles the case for the doublet. For higher representations, we show that the criterion for strong first order phase transition, $v_{c}/T_{c}>\eta$, is relaxed with respect to the doublet case, i.e. $\eta<1$.Comment: 20 pages, 5 figures & 1 table, published versio

Linear Estimation of Location and Scale Parameters Using Partial Maxima

Consider an i.i.d. sample X^*_1,X^*_2,...,X^*_n from a location-scale family, and assume that the only available observations consist of the partial maxima (or minima)sequence, X^*_{1:1},X^*_{2:2},...,X^*_{n:n}, where X^*_{j:j}=max{X^*_1,...,X^*_j}. This kind of truncation appears in several circumstances, including best performances in athletics events. In the case of partial maxima, the form of the BLUEs (best linear unbiased estimators) is quite similar to the form of the well-known Lloyd's (1952, Least-squares estimation of location and scale parameters using order statistics, Biometrika, vol. 39, pp. 88-95) BLUEs, based on (the sufficient sample of) order statistics, but, in contrast to the classical case, their consistency is no longer obvious. The present paper is mainly concerned with the scale parameter, showing that the variance of the partial maxima BLUE is at most of order O(1/log n), for a wide class of distributions.Comment: This article is devoted to the memory of my six-years-old, little daughter, Dionyssia, who leaved us on August 25, 2010, at Cephalonia isl. (26 pages, to appear in Metrika

Study protocol: evaluation of a parenting and stress management programme: a randomised controlled trial of Triple P discussion groups and stress control

&lt;br&gt;Background: Children displaying psychosocial problems are at an increased risk of negative developmental outcomes. Parenting practices are closely linked with child development and behaviour, and parenting programmes have been recommended in the treatment of child psychosocial problems. However, parental mental health also needs to be addressed when delivering parenting programmes as it is linked with parenting practices, child outcomes, and treatment outcomes of parenting programmes. This paper describes the protocol of a study examining the effects of a combined intervention of a parenting programme and a cognitive behavioural intervention for mental health problems.&lt;/br&gt; &lt;br&gt;Methods: The effects of a combined intervention of Triple P Discussion Groups and Stress Control will be examined using a randomised controlled trial design. Parents with a child aged 3?8?years will be recruited to take part in the study. After obtaining informed consent and pre-intervention measures, participants will be randomly assigned to either an intervention or a waitlist condition. The two primary outcomes for this study are change in dysfunctional/ineffective parenting practices and change in symptoms of depression, anxiety, and stress. Secondary outcomes are child behaviour problems, parenting experiences, parental self-efficacy, family relationships, and positive parental mental health. Demographic information, participant satisfaction with the intervention, and treatment fidelity data will also be collected. Data will be collected at pre-intervention, mid-intervention, post-intervention, and 3-month follow-up.&lt;/br&gt; &lt;br&gt;Discussion: The aim of this paper is to describe the study protocol of a randomised controlled trial evaluating the effects of a combined intervention of Triple P Discussion Groups and Stress Control in comparison to a waitlist condition. This study is important because it will provide evidence about the effects of this combined intervention for parents with 3?8?year old children. The results of the study could be used to inform policy about parenting support and support for parents with mental health problems. Trial registration ClinicalTrial.gov: NCT01777724, UTN: U1111-1137-1053.&lt;/br&gt

The forecasting of dynamical Ross River virus outbreaks: Victoria, Australia

Ross River virus (RRV) is Australia’s most epidemiologically important mosquito-borne disease.During RRV epidemics in the State of Victoria (such as 2010/11 and 2016/17) notifications canaccount for up to 30% of national RRV notifications. However, little is known about factors which canforecast RRV transmission in Victoria. We aimed to understand factors associated with RRVtransmission in epidemiologically important regions of Victoria and establish an early warningforecast system. We developed negative binomial regression models to forecast human RRVnotifications across 11 Local Government Areas (LGAs) using climatic, environmental, andoceanographic variables. Data were collected from July 2008 to June 2018. Data from July 2008 toJune 2012 were used as a training data set, while July 2012 to June 2018 were used as a testing dataset. Evapotranspiration and precipitation were found to be common factors for forecasting RRVnotifications across sites. Several site-specific factors were also important in forecasting RRVnotifications which varied between LGA. From the 11 LGAs examined, nine experienced an outbreakin 2011/12 of which the models for these sites were a good fit. All 11 LGAs experienced an outbreakin 2016/17, however only six LGAs could predict the outbreak using the same model. We documentsimilarities and differences in factors useful for forecasting RRV notifications across Victoria anddemonstrate that readily available and inexpensive climate and environmental data can be used to predict epidemic periods in some areas. Furthermore, we highlight in certain regions the complexityof RRV transmission where additional epidemiological information is needed to accurately predictRRV activity. Our findings have been applied to produce a Ross River virus Outbreak SurveillanceSystem (ROSS) to aid in public health decision making in Victoria

Optical detection of single non-absorbing molecules using the surface plasmon of a gold nanorod

Current optical detection schemes for single molecules require light absorption, either to produce fluorescence or direct absorption signals. This severely limits the range of molecules that can be detected, because most molecules are purely refractive. Metal nanoparticles or dielectric resonators detect non-absorbing molecules by a resonance shift in response to a local perturbation of the refractive index, but neither has reached single-protein sensitivity. The most sensitive plasmon sensors to date detect single molecules only when the plasmon shift is amplified by a highly polarizable label or by a localized precipitation reaction on the particle's surface. Without amplification, the sensitivity only allows for the statistical detection of single molecules. Here we demonstrate plasmonic detection of single molecules in realtime, without the need for labeling or amplification. We monitor the plasmon resonance of a single gold nanorod with a sensitive photothermal assay and achieve a ~ 700-fold increase in sensitivity compared to state-of-the-art plasmon sensors. We find that the sensitivity of the sensor is intrinsically limited due to spectral diffusion of the SPR. We believe this is the first optical technique that detects single molecules purely by their refractive index, without any need for photon absorption by the molecule. The small size, bio-compatibility and straightforward surface chemistry of gold nanorods may open the way to the selective and local detection of purely refractive proteins in live cells

Buttressing staples with cholecyst-derived extracellular matrix (CEM) reinforces staple lines in an ex vivo peristaltic inflation model

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer Science + Business Media, LLC 2008Background - Staple line leakage and bleeding are the most common problems associated with the use of surgical staplers for gastrointestinal resection and anastomotic procedures. These complications can be reduced by reinforcing the staple lines with buttressing materials. The current study reports the potential use of cholecyst-derived extracellular matrix (CEM) in non-crosslinked (NCEM) and crosslinked (XCEM) forms, and compares their mechanical performance with clinically available buttress materials [small intestinal submucosa (SIS) and bovine pericardium (BP)] in an ex vivo small intestine model. Methods - Three crosslinked CEM variants (XCEM0005, XCEM001, and XCEM0033) with different degree of crosslinking were produced. An ex vivo peristaltic inflation model was established. Porcine small intestine segments were stapled on one end, using buttressed or non-buttressed surgical staplers. The opened, non-stapled ends were connected to a peristaltic pump and pressure transducer and sealed. The staple lines were then exposed to increased intraluminal pressure in a peristaltic manner. Both the leak and burst pressures of the test specimens were recorded. Results - The leak pressures observed for non-crosslinked NCEM (137.8 ± 22.3 mmHg), crosslinked XCEM0005 (109.1 ± 14.1 mmHg), XCEM001 (150.1 ± 16.0 mmHg), XCEM0033 (98.8 ± 10.5 mmHg) reinforced staple lines were significantly higher when compared to non-buttressed control (28.3 ± 10.8 mmHg) and SIS (one and four layers) (62.6 ± 11.8 and 57.6 ± 12.3 mmHg, respectively) buttressed staple lines. NCEM and XCEM were comparable to that observed for BP buttressed staple lines (138.8 ± 3.6 mmHg). Only specimens with reinforced staple lines were able to achieve high intraluminal pressures (ruptured at the intestinal mesentery), indicating that buttress reinforcements were able to withstand pressure higher than that of natural tissue (physiological failure). Conclusions - These findings suggest that the use of CEM and XCEM as buttressing materials is associated with reinforced staple lines and increased leak pressures when compared to non-buttressed staple lines. CEM and XCEM were found to perform comparably with clinically available buttress materials in this ex vivo model.Enterprise Irelan

Global entrainment of transcriptional systems to periodic inputs

This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. The basic mathematical results needed from contraction theory are proved in the paper, making it self-contained