Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include

Combining clinical factors and quantitative ultrasound improves the detection of women both at low and high risk for hip fracture

Summary: We hypothesized that combining clinical risk factors (CRF) with the heel stiffness index (SI) measured via quantitative ultrasound (QUS) would improve the detection of women both at low and high risk for hip fracture. Categorizing women by risk score improved the specificity of detection to 42.4%, versus 33.8% using CRF alone and 38.4% using the SI alone. This combined CRF-SI score could be used wherever and whenever DXA is not readily accessible. Introduction and hypothesis: Several strategies have been proposed to identify women at high risk for osteoporosis-related fractures; we wanted to investigate whether combining clinical risk factors (CRF) and heel QUS parameters could provide a more accurate tool to identify women at both low and high risk for hip fracture than either CRF or QUS alone. Methods: We pooled two Caucasian cohorts, EPIDOS and SEMOF, into a large database named "EPISEM”, in which 12,064 women, 70 to 100years old, were analyzed. Amongst all the CRF available in EPISEM, we used only the ones which were statistically significant in a Cox multivariate model. Then, we constructed a risk score, by combining the QUS-derived heel stiffness index (SI) and the following seven CRF: patient age, body mass index (BMI), fracture history, fall history, diabetes history, chair-test results, and past estrogen treatment. Results: Using the composite SI-CRF score, 42% of the women who did not report a hip fracture were found to be at low risk at baseline, and 57% of those who subsequently sustained a fracture were at high risk. Using the SI alone, corresponding percentages were 38% and 52%; using CRF alone, 34% and 53%. The number of subjects in the intermediate group was reduced from 5,400 (including 112 hip fractures) and 5,032 (including 111 hip fractures) to 4549 (including 100 including fractures) for the CRF and QUS alone versus the combination score. Conclusions: Combining clinical risk factors to heel bone ultrasound appears to correctly identify more women at low risk for hip fracture than either the stiffness index or the CRF alone; it improves the detection of women both at low and high ris

New Exclusion Limits for the Search of Scalar and Pseudoscalar Axion-Like Particles from "Light Shining Through a Wall"

Physics beyond the Standard Model predicts the possible existence of new particles that can be searched at the low energy frontier in the sub-eV range. The OSQAR photon regeneration experiment looks for "Light Shining through a Wall" from the quantum oscillation of optical photons into "Weakly Interacting Sub-eV Particles", such as axion or Axion-Like Particles (ALPs), in a 9 T transverse magnetic field over the unprecedented length of $2 \times 14.3$ m. In 2014, this experiment has been run with an outstanding sensitivity, using an 18.5 W continuous wave laser emitting in the green at the single wavelength of 532 nm. No regenerated photons have been detected after the wall, pushing the limits for the existence of axions and ALPs down to an unprecedented level for such a type of laboratory experiment. The di-photon couplings of possible pseudo-scalar and scalar ALPs can be constrained in the nearly massless limit to be less than $3.5\cdot 10^{-8}$ GeV$^{-1}$ and $3.2\cdot 10^{-8}$ GeV$^{-1}$, respectively, at 95% Confidence Level.Comment: 6 pages, 6 figure

Internal Friction and Vulnerability of Mixed Alkali Glasses

Based on a hopping model we show how the mixed alkali effect in glasses can be understood if only a small fraction c_V ofthe available sites for the mobile ions is vacant. In particular, we reproduce the peculiar behavior of the internal friction and the steep fall (''vulnerability'') of the mobility of the majority ion upon small replacements by the minority ion. The single and mixed alkali internal friction peaks are caused by ion-vacancy and ion-ion exchange processes. If c_V is small, they can become comparable in height even at small mixing ratios. The large vulnerability is explained by a trapping of vacancies induced by the minority ions. Reasonable choices of model parameters yield typical behaviors found in experiments.Comment: 4 pages, 4 figure

Polyethylene glycol-coated collagen patch (hemopatch®) in open partial nephrectomy

PURPOSE To describe the results of a polyethylene glycol-coated collagen patch, Hemopatch® on blood loss, surgical time and renal function in partial nephrectomy (PN) for renal cell carcinoma (RCC). METHODS Out of a single surgeon cohort of n = 565 patients undergoing conventional open PN (CPN) between 01/2015 and 12/2017 at the University of Munich a consecutive subgroup (n = 42) was operated on using a polyethylene glycol-coated collagen-based sealant Hemopatch® (Baxter International Inc., Deerfield, IL, USA) (HPN). RESULTS Median age was 65.2~years (range 12.7-95.2) with median follow-up of 9.43~months (0.03-49.15). Baseline renal function (CKD-EPI) was 78.56~ml/min/1.73~m2 (range 20.38-143.09) with a non-significant decline to 74.78~ml/min/1.73~m2 (range 3.75-167.74) at follow-up. In CPN 46% had low complexity, 33% moderate complexity and 20% high complexity lesions with 33% low, 40% moderate and 27% high complexity masses in HPN. Median tumor size was 4.3~cm (range 1-38~cm) in CPN with 4.8~cm (range 3.8-18.3~cm) with HPN, p = 0.293. Median blood loss and duration of surgery was significantly lower in the HPN group vs. CPN (146~ml ± 195 vs. 114~ml ± 159~ml; p = 0.021; 43~min ± 27 for HPN vs. 53~min ± 49; p = 0.035) with no difference in clamping time (12.6~min ± 8.6 for HPN vs. 12.0~min ± 9.5; p = 0.701). CONCLUSIONS Hemopatch® supported renoraphy shows promising results compared to standard renoraphy in PN. No side effects were seen. Further studies should evaluate the prevention of arterio-venous or urinary fistulas. In complex partial nephrectomies Hemopatch® supported renoraphy should be considered

Kaspar Schott’s “encyclopedia of all mathematical sciences”

In 1661, Kaspar Schott published his comprehensive textbook “Cursus mathematicus” in Würzburg for the first time, his “Encyclopedia of all mathematical sciences”. It was so successful that it was published again in 1674 and 1677. In its 28 books, Schott gave an introduction for beginners in 22 mathematical disciplines by means of 533 figures and numerous tables. He wanted to avoid the shortness and the unintelligibility of his predecessors Alsted and Hérigone. He cited or recommended far more than hundred authors, among them Protestants like Michael Stifel and Johannes Kepler, but also Catholics like Nicolaus Copernicus. The paper gives a survey of this work and explains especially interesting aspects: The dedication to the German emperor Leopold I., Athanasius Kircher’s letter of recommendation as well as Schott’s classification of sciences, explanations regarding geometry, astronomy, and algebra

Eddy Impacts on the Florida Current

The Gulf Stream in the Atlantic carries warm water northwards and forms both the return closure of the subtropical gyre as well as the upper limb of the meridional overturning circulation. Recent time series recorded east of the Bahamas at 26°N indicate that from May 2009 to April 2011, in contrast with past observations, the northward flowing Antilles Current covaried with the Gulf Stream in the Florida Straits—the Florida Current—even though the Florida and Antilles Currents are separated by banks and islands spanning 150?km. The peak-to-trough amplitude of transport variations during this period was 15?×?106?m3?s?1 for the Florida Current and 12?×?106?m3?s?1 for the Antilles Current, at time scales of 50?days to a year. From satellite observations, we show that the fluctuations in both the Florida and Antilles Currents between May 2009 and April 2011 are driven by eddy activity east of the Bahamas. Since the Florida Current time series is a critical time series for the state of the oceans, and often compared to climate models, this newly identified source of variability needs careful consideration when attributing the variability of the Florida Current to changes in the larger-scale circulations (e.g., gyre and overturning) or wind forcing.<br/

Electromagnetic self-forces and generalized Killing fields

Building upon previous results in scalar field theory, a formalism is developed that uses generalized Killing fields to understand the behavior of extended charges interacting with their own electromagnetic fields. New notions of effective linear and angular momenta are identified, and their evolution equations are derived exactly in arbitrary (but fixed) curved spacetimes. A slightly modified form of the Detweiler-Whiting axiom that a charge's motion should only be influenced by the so-called "regular" component of its self-field is shown to follow very easily. It is exact in some interesting cases, and approximate in most others. Explicit equations describing the center-of-mass motion, spin angular momentum, and changes in mass of a small charge are also derived in a particular limit. The chosen approximations -- although standard -- incorporate dipole and spin forces that do not appear in the traditional Abraham-Lorentz-Dirac or Dewitt-Brehme equations. They have, however, been previously identified in the test body limit.Comment: 20 pages, minor typos correcte