Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer

The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang-Landau sampling method for integers up to 8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where p(n) is the number of solid partitions of the integer n. This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex

Exact expressions for correlations in the ground state of the dense O(1) loop model

Conjectures for analytical expressions for correlations in the dense O$(1)$ loop model on semi infinite square lattices are given. We have obtained these results for four types of boundary conditions. Periodic and reflecting boundary conditions have been considered before. We give many new conjectures for these two cases and review some of the existing results. We also consider boundaries on which loops can end. We call such boundaries ''open''. We have obtained expressions for correlations when both boundaries are open, and one is open and the other one is reflecting. Also, we formulate a conjecture relating the ground state of the model with open boundaries to Fully Packed Loop models on a finite square grid. We also review earlier obtained results about this relation for the three other types of boundary conditions. Finally, we construct a mapping between the ground state of the dense O$(1)$ loop model and the XXZ spin chain for the different types of boundary conditions.Comment: 25 pages, version accepted by JSTA

Professor C. N. Yang and Statistical Mechanics

Professor Chen Ning Yang has made seminal and influential contributions in many different areas in theoretical physics. This talk focuses on his contributions in statistical mechanics, a field in which Professor Yang has held a continual interest for over sixty years. His Master's thesis was on a theory of binary alloys with multi-site interactions, some 30 years before others studied the problem. Likewise, his other works opened the door and led to subsequent developments in many areas of modern day statistical mechanics and mathematical physics. He made seminal contributions in a wide array of topics, ranging from the fundamental theory of phase transitions, the Ising model, Heisenberg spin chains, lattice models, and the Yang-Baxter equation, to the emergence of Yangian in quantum groups. These topics and their ramifications will be discussed in this talk.Comment: Talk given at Symposium in honor of Professor C. N. Yang's 85th birthday, Nanyang Technological University, Singapore, November 200

Primary Beam and Dish Surface Characterization at the Allen Telescope Array by Radio Holography

The Allen Telescope Array (ATA) is a cm-wave interferometer in California, comprising 42 antenna elements with 6-m diameter dishes. We characterize the antenna optical accuracy using two-antenna interferometry and radio holography. The distortion of each telescope relative to the average is small, with RMS differences of 1 percent of beam peak value. Holography provides images of dish illumination pattern, allowing characterization of as-built mirror surfaces. The ATA dishes can experience mm-scale distortions across -2 meter lengths due to mounting stresses or solar radiation. Experimental RMS errors are 0.7 mm at night and 3 mm under worst case solar illumination. For frequencies 4, 10, and 15 GHz, the nighttime values indicate sensitivity losses of 1, 10 and 20 percent, respectively. The ATA.s exceptional wide-bandwidth permits observations over a continuous range 0.5 to 11.2 GHz, and future retrofits may increase this range to 15 GHz. Beam patterns show a slowly varying focus frequency dependence. We probe the antenna optical gain and beam pattern stability as a function of focus and observation frequency, concluding that ATA can produce high fidelity images over a decade of simultaneous observation frequencies. In the day, the antenna sensitivity and pointing accuracy are affected. We find that at frequencies greater than 5 GHz, daytime observations greater than 5 GHz will suffer some sensitivity loss and it may be necessary to make antenna pointing corrections on a 1 to 2 hourly basis.Comment: 19 pages, 23 figures, 3 tables, Authors indicated by an double dagger ({\ddag}) are affiliated with the SETI Institute, Mountain View, CA 95070. Authors indicated by a section break ({\S}) are affiliated with the Hat Creek Radio Observatory and/or the Radio Astronomy Laboratory, both affiliated with the University of California Berkeley, Berkeley C

Characterizing Signal Loss in the 21 cm Reionization Power Spectrum: A Revised Study of PAPER-64

The Epoch of Reionization (EoR) is an uncharted era in our Universe's history during which the birth of the first stars and galaxies led to the ionization of neutral hydrogen in the intergalactic medium. There are many experiments investigating the EoR by tracing the 21cm line of neutral hydrogen. Because this signal is very faint and difficult to isolate, it is crucial to develop analysis techniques that maximize sensitivity and suppress contaminants in data. It is also imperative to understand the trade-offs between different analysis methods and their effects on power spectrum estimates. Specifically, with a statistical power spectrum detection in HERA's foreseeable future, it has become increasingly important to understand how certain analysis choices can lead to the loss of the EoR signal. In this paper, we focus on signal loss associated with power spectrum estimation. We describe the origin of this loss using both toy models and data taken by the 64-element configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER). In particular, we highlight how detailed investigations of signal loss have led to a revised, higher 21cm power spectrum upper limit from PAPER-64. Additionally, we summarize errors associated with power spectrum error estimation that were previously unaccounted for. We focus on a subset of PAPER-64 data in this paper; revised power spectrum limits from the PAPER experiment are presented in a forthcoming paper by Kolopanis et al. (in prep.) and supersede results from previously published PAPER analyses.Comment: 25 pages, 18 figures, Accepted by Ap

Detection of intrinsic source structure at ~3 Schwarzschild radii with Millimeter-VLBI observations of SAGITTARIUS A*

We report results from very long baseline interferometric (VLBI) observations of the supermassive black hole in the Galactic center, Sgr A*, at 1.3 mm (230 GHz). The observations were performed in 2013 March using six VLBI stations in Hawaii, California, Arizona, and Chile. Compared to earlier observations, the addition of the APEX telescope in Chile almost doubles the longest baseline length in the array, provides additional {\it uv} coverage in the N-S direction, and leads to a spatial resolution of $\sim$30 $\mu$as ($\sim$3 Schwarzschild radii) for Sgr A*. The source is detected even at the longest baselines with visibility amplitudes of $\sim$4-13% of the total flux density. We argue that such flux densities cannot result from interstellar refractive scattering alone, but indicate the presence of compact intrinsic source structure on scales of $\sim$3 Schwarzschild radii. The measured nonzero closure phases rule out point-symmetric emission. We discuss our results in the context of simple geometric models that capture the basic characteristics and brightness distributions of disk- and jet-dominated models and show that both can reproduce the observed data. Common to these models are the brightness asymmetry, the orientation, and characteristic sizes, which are comparable to the expected size of the black hole shadow. Future 1.3 mm VLBI observations with an expanded array and better sensitivity will allow a more detailed imaging of the horizon-scale structure and bear the potential for a deep insight into the physical processes at the black hole boundary.Comment: 11 pages, 5 figures, accepted to Ap

Sex-specific relevance of diabetes to occlusive vascular and other mortality : a collaborative meta-analysis of individual data from 980 793 adults from 68 prospective studies

Background: Several studies have shown that diabetes confers a higher relative risk of vascular mortality among women than among men, but whether this increased relative risk in women exists across age groups and within defined levels of other risk factors is uncertain. We aimed to determine whether differences in established risk factors, such as blood pressure, BMI, smoking, and cholesterol, explain the higher relative risks of vascular mortality among women than among men. Methods: In our meta-analysis, we obtained individual participant-level data from studies included in the Prospective Studies Collaboration and the Asia Pacific Cohort Studies Collaboration that had obtained baseline information on age, sex, diabetes, total cholesterol, blood pressure, tobacco use, height, and weight. Data on causes of death were obtained from medical death certificates. We used Cox regression models to assess the relevance of diabetes (any type) to occlusive vascular mortality (ischaemic heart disease, ischaemic stroke, or other atherosclerotic deaths) by age, sex, and other major vascular risk factors, and to assess whether the associations of blood pressure, total cholesterol, and body-mass index (BMI) to occlusive vascular mortality are modified by diabetes. Findings: Individual participant-level data were analysed from 980793 adults. During 9 center dot 8 million person-years of follow-up, among participants aged between 35 and 89 years, 19686 (25 center dot 6%) of 76965 deaths were attributed to occlusive vascular disease. After controlling for major vascular risk factors, diabetes roughly doubled occlusive vascular mortality risk among men (death rate ratio [RR] 2 center dot 10, 95% CI 1 center dot 97-2 center dot 24) and tripled risk among women (3 center dot 00, 2 center dot 71-3 center dot 33; x(2) test for heterogeneity p<0 center dot 0001). For both sexes combined, the occlusive vascular death RRs were higher in younger individuals (aged 35-59 years: 2 center dot 60, 2 center dot 30-2 center dot 94) than in older individuals (aged 70-89 years: 2 center dot 01, 1 center dot 85-2 center dot 19; p=0 center dot 0001 for trend across age groups), and, across age groups, the death RRs were higher among women than among men. Therefore, women aged 35-59 years had the highest death RR across all age and sex groups (5 center dot 55, 4 center dot 15-7 center dot 44). However, since underlying confounder-adjusted occlusive vascular mortality rates at any age were higher in men than in women, the adjusted absolute excess occlusive vascular mortality associated with diabetes was similar for men and women. At ages 35-59 years, the excess absolute risk was 0 center dot 05% (95% CI 0 center dot 03-0 center dot 07) per year in women compared with 0 center dot 08% (0 center dot 05-0 center dot 10) per year in men; the corresponding excess at ages 70-89 years was 1 center dot 08% (0 center dot 84-1 center dot 3 2) per year in women and 0 center dot 91% (0 center dot 77-1 center dot 05) per year in men. Total cholesterol, blood pressure, and BMI each showed continuous log-linear associations with occlusive vascular mortality that were similar among individuals with and without diabetes across both sexes. Interpretation: Independent of other major vascular risk factors, diabetes substantially increased vascular risk in both men and women. Lifestyle changes to reduce smoking and obesity and use of cost-effective drugs that target major vascular risks (eg, statins and antihypertensive drugs) are important in both men and women with diabetes, but might not reduce the relative excess risk of occlusive vascular disease in women with diabetes, which remains unexplained