Exact Site Percolation Thresholds Using the Site-to-Bond and Star-Triangle Transformations

I construct a two-dimensional lattice on which the inhomogeneous site percolation threshold is exactly calculable and use this result to find two more lattices on which the site thresholds can be determined. The primary lattice studied here, the ``martini lattice'', is a hexagonal lattice with every second site transformed into a triangle. The site threshold of this lattice is found to be $0.764826...$, while the others have $0.618034...$ and $1/\sqrt{2}$. This last solution suggests a possible approach to establishing the bound for the hexagonal site threshold, $p_c<1/\sqrt{2}$. To derive these results, I solve a correlated bond problem on the hexagonal lattice by use of the star-triangle transformation and then, by a particular choice of correlations, solve the site problem on the martini lattice.Comment: 12 pages, 10 figures. Submitted to Physical Review

Sunspot observations from the SOUP instrument on Spacelab 2

A series of white light images obtained by the SOUP instrument on Spacelab 2 of active region 4682 on August 5, 1985 were analyzed in the area containing sunspots. Although the umbra of the spot is underexposed, the film is well exposed in the penumbral regions. These data were digitally processed to remove noise and to separate p-mode oscillations from low velocity material motions. The results of this preliminary investigation include: (1) proper motion measurements of a radial outflow in the photospheric granulation pattern just outside the penumbra; (2) discovery of occasional bright structures (streakers) that appear to be ejected outward from the penumbra; (3) broad dark clouds moving outward in the penumbra in addition to the well known bright penumbral grains moving inward; (4) apparent extensions and contractions of penumbral filaments over the photosphere; and (5) observation of a faint bubble or loop-like structure which seems to expand from two bright penumbral filaments into the photosphere

Use of Temporally Validated Machine Learning Models To Predict Outcomes of Percutaneous Nephrolithotomy Using Data from the British Association of Urological Surgeons Percutaneous Nephrolithotomy Audit

\ua9 2024 European Association of Urology. Background and objective: Machine learning (ML) is a subset of artificial intelligence that uses data to build algorithms to predict specific outcomes. Few ML studies have examined percutaneous nephrolithotomy (PCNL) outcomes. Our objective was to build, streamline, temporally validate, and use ML models for prediction of PCNL outcomes (intensive care admission, postoperative infection, transfusion, adjuvant treatment, postoperative complications, visceral injury, and stone-free status at follow-up) using a comprehensive national database (British Association of Urological Surgeons PCNL). Methods: This was an ML study using data from a prospective national database. Extreme gradient boosting (XGB), deep neural network (DNN), and logistic regression (LR) models were built for each outcome of interest using complete cases only, imputed, and oversampled and imputed/oversampled data sets. All validation was performed with complete cases only. Temporal validation was performed with 2019 data only. A second round used a composite of the most important 11 variables in each model to build the final model for inclusion in the shiny application. We report statistics for prognostic accuracy. Key findings and limitations: The database contains 12 810 patients. The final variables included were age, Charlson comorbidity index, preoperative haemoglobin, Guy\u27s stone score, stone location, size of outer sheath, preoperative midstream urine result, primary puncture site, preoperative dimercapto-succinic acid scan, stone size, and image guidance (https://endourology.shinyapps.io/PCNL_Demographics/). The areas under the receiver operating characteristic curve was &gt;0.6 in all cases. Conclusions and clinical implications: This is the largest ML study on PCNL outcomes to date. The models are temporally valid and therefore can be implemented in clinical practice for patient-specific risk profiling. Further work will be conducted to externally validate the models. Patient summary: We applied artificial intelligence to data for patients who underwent a keyhole surgery to remove kidney stones and developed a model to predict outcomes for this procedure. Doctors could use this tool to advise patients about their risk of complications and the outcomes they can expect after this surgery

Principal forms X^2 + nY^2 representing many integers

In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X^2+nY^2. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n=2. In this paper, we prove that in fact this constant is unbounded as n runs through positive integers with a fixed number of prime divisors.Comment: 10 pages, title has been changed, Sections 2 and 3 are new, to appear in Abh. Math. Sem. Univ. Hambur

Assertive outreach treatment versus care as usual for the treatment of high-need, high-cost alcohol related frequent attenders: study protocol for a randomised controlled trial

Background: Alcohol-related hospital admissions have doubled in the last ten years to >1.2m per year in England. High-need, high-cost (HNHC) alcohol-related frequent attenders (ARFA) are a relatively small subgroup of patients, having multiple admissions or attendances from alcohol during a short time period. This trial aims to test the effectiveness of an assertive outreach treatment (AOT) approach in improving clinical outcomes for ARFA, and reducing resource use in the acute setting. Methods: One hundred and sixty ARFA patients will be recruited and following baseline assessment, randomly assigned to AOT plus care as usual (CAU) or CAU alone in equal numbers. Baseline assessment includes alcohol consumption and related problems, physical and mental health comorbidity and health and social care service use in the previous 6 months using standard validated tools, plus a measure of resource use. Follow-up assessments at 6 and 12months after randomization includes the same tools as baseline plus standard measure of patient satisfaction. Outcomes for CAU+AOT and CAU at 6 and 12months will be compared, controlling for pre-specified baseline measures. Primary outcome will be percentage of days abstinent at 12months. Secondary outcomes include emergency department (ED) attendance, number and length of hospital admissions, alcohol consumption, alcohol-related problems, other health service use, mental and physical comorbidity 6 and 12months post intervention. Health economic analysis will estimate the economic impact of AOT from health, social care and societal perspectives and explore cost-effectiveness in terms of quality adjusted life years and alcohol consumption at 12-month follow-up. Discussion: AOT models piloted with alcohol dependent patients have demonstrated significant reductions in alcohol consumption and use of unplanned National Health Service (NHS) care, with increased engagement with alcohol treatment services, compared with patients receiving CAU. While AOT interventions are costlier per case than current standard care in the UK, the rationale for targeting HNHC ARFAs is because of their disproportionate contribution to overall alcohol burden on the NHS. No previous studies have evaluated the clinical and costeffectiveness of AOT for HNHC ARFAs: this randomized controlled trial (RCT) targeting ARFAs across five South London NHS Trusts is the first. Trial registration: International standard randomized controlled trial number (ISRCTN) registry: ISRCTN67000214, retrospectively registered 26/11/2016

Mass dependence of light nucleus production in ultrarelativistic heavy ion collisions

Light nuclei can be produced in the central reaction zone via coalescence in relativistic heavy ion collisions. E864 at BNL has measured the production of ten light nuclei with nuclear number of A=1 to A=7 at rapidity $y\simeq1.9$ and $p_{T}/A\leq300MeV/c$. Data were taken with a Au beam of momentum of 11.5 A $GeV/c$ on a Pb or Pt target with different experimental settings. The invariant yields show a striking exponential dependence on nuclear number with a penalty factor of about 50 per additional nucleon. Detailed analysis reveals that the production may depend on the spin factor of the nucleus and the nuclear binding energy as well.Comment: (6 pages, 3 figures), some changes on text, references and figures' lettering. To be published in PRL (13Dec1999

Giant Thermoelectric Effect from Transmission Supernodes

We predict an enormous order-dependent quantum enhancement of thermoelectric effects in the vicinity of a higher-order `supernode' in the transmission spectrum of a nanoscale junction. Single-molecule junctions based on 3,3'-biphenyl and polyphenyl ether (PPE) are investigated in detail. The nonequilibrium thermodynamic efficiency and power output of a thermoelectric heat engine based on a 1,3-benzene junction are calculated using many-body theory, and compared to the predictions of the figure-of-merit ZT.Comment: 5 pages, 6 figure

A Molecular Platinum Cluster Junction: A Single-Molecule Switch

We present a theoretical study of the electronic transport through single-molecule junctions incorporating a Pt6 metal cluster bound within an organic framework. We show that the insertion of this molecule between a pair of electrodes leads to a fully atomically engineered nano-metallic device with high conductance at the Fermi level and two sequential high on/off switching states. The origin of this property can be traced back to the existence of a HOMO which consists of two degenerate and asymmetric orbitals, lying close in energy to the Fermi level of the metallic leads. Their degeneracy is broken when the molecule is contacted to the leads, giving rise to two resonances which become pinned close to the Fermi level and display destructive interference.Comment: 4 pages, 4 figures. Reprinted (adapted) with permission from J. Am. Chem. Soc., 2013, 135 (6), 2052. Copyright 2013 American Chemical Societ

Efficiency of Energy Conversion in Thermoelectric Nanojunctions

Using first-principles approaches, this study investigated the efficiency of energy conversion in nanojunctions, described by the thermoelectric figure of merit $ZT$. We obtained the qualitative and quantitative descriptions for the dependence of $ZT$ on temperatures and lengths. A characteristic temperature: $T_{0}= \sqrt{\beta/\gamma(l)}$ was observed. When $T\ll T_{0}$, $ZT\propto T^{2}$. When $T\gg T_{0}$, $ZT$ tends to a saturation value. The dependence of $ZT$ on the wire length for the metallic atomic chains is opposite to that for the insulating molecules: for aluminum atomic (conducting) wires, the saturation value of $ZT$ increases as the length increases; while for alkanethiol (insulating) chains, the saturation value of $ZT$ decreases as the length increases. $ZT$ can also be enhanced by choosing low-elasticity bridging materials or creating poor thermal contacts in nanojunctions. The results of this study may be of interest to research attempting to increase the efficiency of energy conversion in nano thermoelectric devices.Comment: 2 figure