Quantum Invariants, Modular Forms, and Lattice Points II

We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms with weight 1/2 and 3/2. By use of nearly modular property of the Eichler integrals we shall obtain asymptotic expansions of the WRT invariant in the large-N limit. We further reveal that the number of the gauge equivalent classes of flat connections, which dominate the asymptotics of the WRT invariant in N ->\infinity, is related to the number of integral lattice points inside the M-dimensional tetrahedron

Measurement of single nanoparticle anisotropy by laser induced optical alignment and Rayleigh scattering for determining particle morphology

We demonstrate the measurement of nanoparticle anisotropy by angularly resolved Rayleigh scattering of single optical levitated particles that are oriented in space via the trapping light in vacuum. This technique is applied to a range of particle geometries from perfect spherical nanodroplets to octahedral nanocrystals. We show that this method can resolve shape differences down to a few nanometers and be applied in both low-damping environments, as demonstrated here, and in traditional overdamped fluids used in optical tweezers

Methods for reproductive tract scoring as a tool for improving sow productivity

Improving sow lifetime productivity (SLP) is essential for maximizing farm profitability. Study objectives were to determine the accuracy for different vulva scoring methods in a commercial production system and to assess whether gilt reproductive tract scoring (evaluated by vulva width; VW) prior to puberty could serve as useful gilt selection criteria. To accomplish this objective, 958 prepubertal replacement gilts in a commercial system were evaluated at approximately 15 weeks of age. Gilt body weight was recorded in addition to four different methods to evaluate VW. Methods for VW assessment included digital caliper measurement (mm), visual evaluation and scoring by trained farm personnel (Farm Score; FS), and two methods using scoring tools (Vulva Score Method A and B; VSA and VSB, respectively) specifically calibrated from the VW distribution measured on gilts from previous studies. The VSA and FS methods assigned gilts to one of three categories (S, M, L and 1, 2, 3, respectively) whereas VSB classified gilts vulvas using a five-point scoring system (1 to 5). At 15-wk of age, a low proportion of variability in vulva size (27.8 ± 0.1 mm) could be explained by BW (62.2 ± 0.2 kg; R2 = 0.05). All three scoring methods were effective in categorizing gilts based upon VW, as the measured VW size within methods differed by score (P \u3c 0.01). The proportion of gilts achieving their first parity increased with score for VSA (64.7, 73.2, and 84.4%; P = 0.02), VSB (66.0, 71.7, 79.2, 76.4, and 84.2%; P = 0.02), and FS (67.2, 75.0, and 88.8%; P = 0.03), but VSA, VSB, and FS did not influence percentage of gilts achieving their second parity (P = 0.32, 0.29, and 0.30, respectively). Litter performance of gilts scored as M or L using VSA improved with an increased total born over two parities compared to those scored as S (23.96 vs. 26.38 pigs; P \u3c 0.01) as well as born alive (21.13 vs. 23.05 pigs; P \u3c 0.05). Results were similar for VSB, where scores 2-5 had greater total born (23.97 vs. 26.33 pigs; P \u3c 0.01) and born alive (21.11 vs. 23.02 pigs; P \u3c 0.05) through two parities compared to gilts scored 1. Using the FS method, total born pigs tended to be increased (P = 0.06) through two parities for gilts having a 2 or 3 vulva score compared to those scored as a 1. Collectively, assessing VW at approximately 15 wk of age may identify sows with improved productivity through two parities as breeding herd females

Older-Patient-Specific Cancer Trials: A Pooled Analysis of 2,277 Patients (A151715).

BACKGROUND: Less than 3% of older patients with cancer are enrolled in clinical trials. To reverse this underrepresentation, we compared older patients enrolled with older-patient-specific trials, defined as those designed for older patients with cancer, with those enrolled in age-unspecified trials. MATERIALS AND METHODS: We focused on individual patient data from those ≥65 years (younger patients excluded) and included all Alliance phase III adjuvant breast cancer trials from 1985-2012. RESULTS: Among 2,277 patients, 1,014 had been enrolled to older-patient-specific and 1,263 to age-unspecified trials. The median age (range) in the older-patient-specific trials was 72 (65-89) years compared with 68 (65-84) years in the cohort of older patients in age-unspecified trials; CONCLUSION: Older-patient-specific trials appear to address this underrepresentation of older patients with ostensibly comparable outcomes

Notes on the Biology of an Adult Female Chimaera cubana Captured Off St. Croix, U.S. Virgin Islands

Within the western North Atlantic Ocean there are at least 4 genera and 5 species of chimaeroids occurring in deep waters generally associated with outer continental slopes or areas of high bathymetric relief (Didier 2002; Didier 2004). Two chimaeroids, Chimaera cubana and Hydrolagus alberti, are known to be indigenous to the Caribbean Sea in waters associated with the Greater and Lesser Antilles. While H. alberti occurs throughout the Gulf of Mexico and the Caribbean Sea, C. cubana is thought to be endemic to an area bounded by Cuba and Colombia (IUCN 2009). These two chimaeras are readily differentiated by the presence or absence of an anal fin and species–specific branching patterns of cranial lateral line canals (Didier 2004). Since the description of C. cubana by Howell–Rivero (1936), only 10 specimens have been reported in the primary literature with another 11 specimens located in museum collections (Bunkley–Williams and Williams 2004). The dearth of biological information on C. cubana led the International Union for the Conservation of Nature to recommend that “basic data be collected on all captures” (IUCN 2009)

Special Functions Related to Dedekind Type DC-Sums and their Applications

In this paper we construct trigonometric functions of the sum T_{p}(h,k), which is called Dedekind type DC-(Dahee and Changhee) sums. We establish analytic properties of this sum. We find trigonometric representations of this sum. We prove reciprocity theorem of this sums. Furthermore, we obtain relations between the Clausen functions, Polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums and the sum T_{p}(h,k). We also give some applications related to these sums and functions

Lin's method for heteroclinic chains involving periodic orbits

We present an extension of the theory known as Lin's method to heteroclinic chains that connect hyperbolic equilibria and hyperbolic periodic orbits. Based on the construction of a so-called Lin orbit, that is, a sequence of continuous partial orbits that only have jumps in a certain prescribed linear subspace, estimates for these jumps are derived. We use the jump estimates to discuss bifurcation equations for homoclinic orbits near heteroclinic cycles between an equilibrium and a periodic orbit (EtoP cycles)

Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems

We report the results of certain integrations of quantum-theoretic interest, relying, in this regard, upon recently developed parameterizations of Boya et al of the n x n density matrices, in terms of squared components of the unit (n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized volume elements of the Bures (minimal monotone) metric for n = 2 and 3, obtaining thereby "Bures prior probability distributions" over the two- and three-state systems. Then, as an essential first step in extending these results to n > 3, we determine that the "Hall normalization constant" (C_{n}) for the marginal Bures prior probability distribution over the (n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known to equal 2/pi.) The constant C_{5} is also found. It too is associated with a remarkably simple decompositon, involving the product of the eight consecutive prime numbers from 2 to 23. We also preliminarily investigate several cases, n > 5, with the use of quasi-Monte Carlo integration. We hope that the various analyses reported will prove useful in deriving a general formula (which evidence suggests will involve the Bernoulli numbers) for the Hall normalization constant for arbitrary n. This would have diverse applications, including quantum inference and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in J. Phys. A. We make a few slight changes from the previous version, but also add a subsection (III G) in which several variations of the basic problem are newly studied. Rather strong evidence is adduced that the Hall constants are related to partial sums of denominators of the even-indexed Bernoulli numbers, although a general formula is still lackin