The size of Selmer groups for the congruent number problem, II

The oldest problem in the theory of elliptic curves is to determine which positive integers D can be the common difference of a three term arithmetic progres-sion of squares of rational numbers. Such integers D are known as congruent numbers. Equivalently one may ask which elliptic curve

Astrophysical constraints on primordial black holes in Brans-Dicke theory

We consider cosmological evolution in Brans-Dicke theory with a population of primordial black holes. Hawking radiation from the primordial black holes impacts various astrophysical processes during the evolution of the Universe. The accretion of radiation by the black holes in the radiation dominated era may be effective in imparting them a longer lifetime. We present a detailed study of how this affects various standard astrophysical constraints coming from the evaporation of primordial black holes. We analyze constraints from the present density of the Universe, the present photon spectrum, the distortion of the cosmic microwave background spectrum and also from processes affecting light element abundances after nucleosynthesis. We find that the constraints on the initial primordial black hole mass fractions are tightened with increased accretion efficiency.Comment: 15 page

Brans-Dicke Theory and primordial black holes in Early Matter-Dominated Era

We show that primordial black holes can be formed in the matter-dominated era with gravity described by the Brans-Dicke theory. Considering an early matter-dominated era between inflation and reheating, we found that the primordial black holes formed during that era evaporate at a quicker than those of early radiation-dominated era. Thus, in comparison with latter case, less number of primordial black holes could exist today. Again the constraints on primordial black hole formation tend towards the larger value than their radiation-dominated era counterparts indicating a significant enhancement in the formation of primordial black holes during the matter-dominaed era.Comment: 9 page

Running Spectral Index and Formation of Primordial Black Hole in Single Field Inflation Models

A broad range of single field models of inflation are analyzed in light of all relevant recent cosmological data, checking whether they can lead to the formation of long-lived Primordial Black Holes (PBHs). To that end we calculate the spectral index of the power spectrum of primordial perturbations as well as its first and second derivatives. PBH formation is possible only if the spectral index increases significantly at small scales, i.e. large wave number $k$. Since current data indicate that the first derivative $\alpha_S$ of the spectral index $n_S(k_0)$ is negative at the pivot scale $k_0$, PBH formation is only possible in the presence of a sizable and positive second derivative ("running of the running") $\beta_S$. Among the three small-field and five large-field models we analyze, only one small-field model, the "running mass" model, allows PBH formation, for a narrow range of parameters. We also note that none of the models we analyze can accord for a large and negative value of $\alpha_S$, which is weakly preferred by current data.Comment: 26 pages, 5 figures, Refs. added, Minor textual change; version to appear in JCA

Constraints on the mass spectrum of primordial black holes and braneworld parameters from the high-energy diffuse photon background

We investigate the spectral shape of a high-energy diffuse photon emitted by evaporating primordial black holes (PBHs) in the Randall-Sundrum type II (RS2) braneworld. In their braneworld scenario, the nature of small PBHs is drastically modified from the ordinary four-dimensional case for the following two reasons. (i) dropping Hawking temperature, which equivalently lengthens the lifetime of the individual PBH due to the change of space-time topology and (ii) the effective increase of the total amount of PBHs caused by accretion during the earliest part of the radiation-dominated epoch, the brane high-energy phase. From studies of the expected spectral shape and its dependence on braneworld parameters, we obtain two qualitatively distinctive possibilities of constraints on the braneworld PBHs from the observations of diffuse high-energy photon background. If the efficiency of accretion in the high-energy phase exceeds a critical value, the existence of the extra dimension gives a more stringent upper bound on the abundance of PBHs than the 4D case and a small length scale for the extra dimension is favored. On the contrary, in the case below the critical accretion efficiency, we find that the constraint on the PBH abundance can be relaxed by a few orders of magnitude in exchange for the existence of the large extra dimension; its size may be even bounded in the region above 10^{19} times 4D Planck length scale provided the rest mass energy density of the PBHs relative to energy density of radiation is actually larger than 10^{-27} (4D upper bound) at their formation time. The above analytical studies are also confirmed numerically, and an allowed region for braneworld parameters and PBH abundance is clearly obtained.Comment: 16 pages, 8 figures, REVTeX4; version published in PR

Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point

We report the details and revised analysis of an experiment to measure the specific heat of helium with subnanokelvin temperature resolution near the lambda point. The measurements were made at the vapor pressure spanning the region from 22 mK below the superfluid transition to 4 uK above. The experiment was performed in earth orbit to reduce the rounding of the transition caused by gravitationally induced pressure gradients on earth. Specific heat measurements were made deep in the asymptotic region to within 2 nK of the transition. No evidence of rounding was found to this resolution. The optimum value of the critical exponent describing the specific heat singularity was found to be a = -0.0127+ - 0.0003. This is bracketed by two recent estimates based on renormalization group techniques, but is slightly outside the range of the error of the most recent result. The ratio of the coefficients of the leading order singularity on the two sides of the transition is A+/A- =1.053+ - 0.002, which agrees well with a recent estimate. By combining the specific heat and superfluid density exponents a test of the Josephson scaling relation can be made. Excellent agreement is found based on high precision measurements of the superfluid density made elsewhere. These results represent the most precise tests of theoretical predictions for critical phenomena to date.Comment: 27 Pages, 20 Figure

Inflammatory markers and incident mobility limitation in the elderly

OBJECTIVES: To examine the relationship between indicators of inflammation and the incidence of mobility limitation in older persons. DESIGN: Prospective cohort study: the Health, Aging and Body Composition Study. SETTING: Pittsburgh, Pennsylvania, and Memphis, Tennessee. PARTICIPANTS: A total of 2,979 men and women, aged 70 to 79, without mobility limitation at baseline. MEASUREMENTS: Serum levels of interleukin (IL)-6, tumor necrosis factor alpha (TNFα), and C-reactive protein (CRP) and soluble cytokine receptors (IL-2sR, IL-6sR, TNFsR1, TNFsR2) were measured. Mobility limitation was assessed and defined as reporting difficulty or inability to walk one-quarter of a mile or to climb 10 steps during two consecutive semiannual assessments over 30 months. RESULTS: Of the 2,979 participants, 30.1% developed incident mobility limitation. After adjustment for confounders (demographics, prevalent conditions at baseline, body composition), the relative risk (RR) of incident mobility limitation per standard deviation (SD) increase was 1.19 (95% confidence interval (CI) = 1.10-1.28) for IL-6, 1.20 (95% CI = 1.12-1.29) for TNFα and 1.40 (95% CI = 1.18-1.68) for CRP. The association between inflammation and incident mobility limitation was especially strong for the onset of more severe mobility limitation and when the levels of multiple inflammatory markers were high. When persons with baseline or incident cardiovascular disease events or persons who were hospitalized during study follow-up were excluded, findings remained similar. In a subset (n = 499), high levels of the soluble receptors IL2sR and TNFsR1 (per SD increase: RR = 1.23 (95% CI = 1.04-1.46) and RR = 1.28 (95% CI = 1.04-1.57), respectively) were also associated with incident mobility limitation. CONCLUSION: Findings suggest that inflammation is prognostic for incident mobility limitation over 30 months, independent of cardiovascular disease events and incident severe illness

Inflammatory Markers and Onset of Cardiovascular Events: Results from the Health ABC Study

Background - Inflammation plays an important role in cardiovascular disease. The aim of this study is to investigate the predictive value of several inflammatory markers on the incidence of cardiovascular events in well-functioning older persons. Methods and Results - The subjects were 2225 participants 70 to 79 years old, without baseline cardiovascular disease, who were enrolled in the Health, Aging, and Body Composition study. Incident coronary heart disease (CHD), stroke, and congestive heart failure (CHF) events were detected during an average follow-up of 3.6 years. Blood levels of interleukin-6 (IL-6), C-reactive protein (CRP), and tumor necrosis factor-\uce\ub1 (TNF-\uce\ub1) were assessed. After adjustment for potential confounders, IL-6 was significantly associated with all outcomes (CHD events, per IL-6 SD increase: RR, 1.27; 95% CI, 1.10 to 1.48; stroke events, per IL-6 SD increase: RR, 1.45; 95% CI, 1.12 to 1.86; CHF events, per IL-6 SD increase: RR, 1.72; 95% CI, 1.40 to 2.12). TNF-\uce\ub1 showed significant associations with CHD (per TNF-\uce\ub1 SD increase: RR, 1.22; 95% CI, 1.04 to 1.43) and CHF (per TNF-\uce\ub1 SD increase: RR, 1.59; 95% CI, 1.30 to 1.95) events. CRP was significantly associated with CHF events (per CRP SD increase: RR, 1.48; 95% CI, 1.23 to 1.78). A composite summary indicator of inflammation showed a strong association with incident cardiovascular events, with an especially high risk if all 3 inflammatory markers were in the highest tertile. Conclusions - Findings suggest that inflammatory markers are independent predictors of cardiovascular events in older persons

PatchPerPixMatch for automated 3d search of neuronal morphologies in light microscopy

Studies of individual neurons in the Drosophila nervous system are facilitated by transgenic lines that sparsely and repeatably label respective neurons of interest. Sparsity can be enhanced by means of intersectional approaches like the split-GAL4 system, which labels the positive intersection of the expression patterns of two (denser) GAL4 lines. To this end, two GAL4 lines have to be identified as labelling a neuron of interest. Current approaches to tackling this task include visual inspection, as well as automated search in 2d projection images, of single cell multi-color flip-out (MCFO) acquisitions of GAL4 expression patterns. There is to date no automated method available that performs full 3d search in MCFO imagery of GAL4 lines, nor one that leverages automated reconstructions of the labelled neuron morphologies. To close this gap, we propose PatchPerPixMatch, a fully automated approach for finding a given neuron morphology in MCFO acquisitions of Gen1 GAL4 lines. PatchPerPixMatch performs automated instance segmentation of MCFO acquisitions, and subsequently searches for a target neuron morphology by minimizing an objective that aims at covering the target with a set of well-fitting segmentation fragments. PatchPerPixMatch is computationally efficient albeit being full 3d, while also highly robust to inaccuracies in the automated neuron instance segmentation. We are releasing PatchPerPixMatch search results for ~30,000 neuron morphologies from the Drosophila hemibrain in ~20,000 MCFO acquisitions of ~3,500 Gen1 GAL4 lines