A discontinuous Galerkin method for the Vlasov-Poisson system

A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates associated system's approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov-Poisson system.Comment: To appear in Journal for Computational Physics, 2011. 63 pages, 86 figure

Density of non-residues in Burgess-type intervals and applications

We show that for any fixed \eps>0, there are numbers $\delta>0$ and $p_0\ge 2$ with the following property: for every prime $p\ge p_0$ and every integer $N$ such that p^{1/(4\sqrt{e})+\eps}\le N\le p, the sequence $1,2,...,N$ contains at least $\delta N$ quadratic non-residues modulo $p$. We use this result to obtain strong upper bounds on the sizes of the least quadratic non-residues in Beatty and Piatetski--Shapiro sequences.Comment: In the new version we use an idea of Roger Heath-Brown (who is now a co-author) to simply the proof and improve the main results of the previous version, 14 page

The Clustering Of Galaxies Around Radio-Loud AGNs

We examine the hypothesis that mergers and close encounters between galaxies can fuel AGNs by increasing the rate at which gas accretes towards the central black hole. We compare the clustering of galaxies around radio-loud AGNs with the clustering around a population of radio-quiet galaxies with similar masses, colors and luminosities. Our catalog contains 2178 elliptical radio galaxies with flux densities greater than 2.8 mJy at 1.4 GHz from the 6dFGS survey. We find that radio AGNs with more than 200 times the median radio power have, on average, more close (r<160 kpc) companions than their radio-quiet counterparts, suggestive that mergers play a role in forming the most powerful radio galaxies. For ellipticals of fixed stellar mass, the radio power is not a function of large-scale environment nor halo mass, consistent with the radio powers of ellipticals varying by orders of magnitude over billions of years.Comment: 12 pages, 6 figure

Quantum Field Theory of Forward Rates with Stochastic Volatility

In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are analyzed, firstly when volatility is taken to be a function of the forward rates, and secondly when volatility is taken to be an independent quantum field. Since volatiltiy is a positive valued quantum field, the full theory turns out to be an interacting nonlinear quantum field theory in two dimensions. The state space and Hamiltonian for the interacting theory are obtained, and shown to have a nontrivial structure due to the manifold moving with a constant velocity. The no arbitrage condition is reformulated in terms of the Hamiltonian of the system, and then exactly solved for the nonlinear interacting case.Comment: 7 Figure

Electron Transport through a Molecular Conductor with Center-of-Mass Motion

The linear conductance of a molecular conductor oscillating between two metallic leads is investigated numerically both for Hubbard interacting and noninteracting electrons. The molecule-leads tunneling barriers depend on the molecule displacement from its equilibrium position. The results present an interesting interference which leads to a conductance dip at the electron-hole symmetry point, that could be experimentally observable. It is shown that this dip is caused by the destructive interference between the purely electronic and phonon-assisted tunneling channels, which are found to carry opposite phases. When an internal vibrational mode is also active, the electron-hole symmetry is broken but a Fano-like interference is still observed

Blood pressure, hypertension and the risk of atrial fibrillation: a systematic review and meta-analysis of cohort studies

Elevated blood pressure and hypertension have been associated with increased risk of atrial fibrillation in a number of epidemiological studies, however, the strength of the association has differed between studies. We conducted a systematic review and meta-analysis of the association between blood pressure and hypertension and atrial fibrillation. PubMed and Embase databases were searched for studies of hypertension and blood pressure and atrial fibrillation up to June 6th 2022. Cohort studies reporting adjusted relative risk (RR) estimates and 95% confidence intervals (CIs) of atrial fibrillation associated with hypertension or blood pressure were included. A random effects model was used to estimate summary RRs. Sixty eight cohort studies were included in the meta-analysis. The summary RR was 1.50 (95% CI: 1.42-1.58, I2 = 98.1%, n = 56 studies) for people with hypertension compared to those without hypertension (1,080,611 cases, 30,539,230 participants), 1.18 (95% CI: 1.16-1.21, I2 = 65.9%, n = 37 studies) per 20 mmHg increase in systolic blood pressure (346,471 cases, 14,569,396 participants), and 1.07 (95% CI: 1.03-1.11, I2 = 91.5%, n = 22 studies) per 10 mmHg increase in diastolic blood pressure (332,867 cases, 14,354,980 participants). There was evidence of a nonlinear association between diastolic blood pressure and atrial fibrillation with a steeper increase in risk at lower levels of diastolic blood pressure, but for systolic blood pressure the association appeared to be linear. For both systolic and diastolic blood pressure, the risk increased even within the normal range of blood pressure and persons at the high end of systolic and diastolic blood pressure around 180/110 mmHg had a 1.8-2.3 fold higher risk of atrial fibrillation compared to those with a blood pressure of 90/60 mmHg. These results suggest that elevated blood pressure and hypertension increases the risk of atrial fibrillation and there is some increase in risk even within the normal range of systolic and diastolic blood pressure

Tunable dipolar magnetism in high-spin molecular clusters

We report on the Fe17 high-spin molecular cluster and show that this system is an exemplification of nanostructured dipolar magnetism. Each Fe17 molecule, with spin S=35/2 and axial anisotropy as small as D=-0.02K, is the magnetic unit that can be chemically arranged in different packing crystals whilst preserving both spin ground-state and anisotropy. For every configuration, molecular spins are correlated only by dipolar interactions. The ensuing interplay between dipolar energy and anisotropy gives rise to macroscopic behaviors ranging from superparamagnetism to long-range magnetic order at temperatures below 1K.Comment: Replaced with version accepted for publication in Physical Review Letter

Nutrient-wide association study of 92 foods and nutrients and breast cancer risk

Several dietary factors have been extensively investigated for associations with risk of breast cancer, but to date unequivocal evidence only exists for alcohol consumption. We sought to systematically evaluate the association between 92 dietary factors and breast cancer risk using a nutrient-wide association study approach. Using data from 272,098 women participating in the European Prospective Investigation into Cancer and Nutrition (EPIC) study, we assessed dietary intake of 92 foods and nutrients estimated by dietary questionnaires. Cox regression with age as the time scale and adjustment for potential confounders, was used to quantify the association between each food or nutrient and risk of breast cancer. A false discovery rate (FDR) of 0.05 was used to select the set of foods and nutrients to evaluate in the independent replication cohort, the Netherlands Cohort Study (NLCS). During a median follow-up time of 15 years, 10,979 incident invasive breast cancers were identified in the women from the EPIC study. Six foods and nutrients were associated with risk of breast cancer when controlling the FDR at 0.05. Higher intake of alcohol overall was associated with a higher risk of breast cancer (hazard ratio (HR) for a 1 SD increment in intake = 1.05, 95% confidence interval (CI) 1.03–1.07), as was beer/cider intake and wine intake (HRs per 1 SD increment = 1.05, 95% CI 1.03–1.06 and 1.04, 95% CI 1.02–1.06, respectively), whereas higher intakes of fibre, apple/pear, and carbohydrates were associated with a lower risk of breast cancer (HRs per 1 SD increment = 0.96, 95% CI 0.94–0.98; 0.96, 95% CI 0.94–0.99; and 0.96, 95% CI 0.95–0.98, respectively). When evaluated in the NLCS (2368 invasive breast cancer cases), estimates for each of these foods and nutrients were similar in magnitude and direction, with the exception of beer/cider intake, which was not associated with risk of breast cancer in the NLCS. Our findings confirm the well-established increased risk of breast cancer associated with alcohol consumption, and suggest that higher intake of dietary fibre, and possibly fruit and carbohydrates, might be associated with reduced breast cancer risk

Synthetic DNA immunotherapy in biochemically relapsed prostate cancer

Background: INO-5150 (PSA and PSMA) +/- INO-9012 (IL-12), a synthetic DNA immunotherapy, was assessed for safety, immunogenicity and efficacy in biochemically recurrent prostate cancer patients (pts). Methods: Phase I, open-label, multi-center study in the US included pts with rising PSA after surgery and/or RT, PSA doubling time (PSADT) \u3e3 months (mos), testosterone \u3e150 ng/dL and no concurrent ADT. Safety, immunogenicity and efficacy (PSA kinetics, PFS) were evaluated in 4 treatment arms of 15 pts each. Arms A: 2mg INO-5150, B: 8.5 mg INO-5150, C: 2mg INO-5150 + 1mg INO-9012 and D: 8.5mg INO-5150 + 1mg INO-9012. Pts received 4 IM doses of vaccine followed by electroporation on day 0, wks 3, 12 and 24 and were followed for 72 wks. Results: 50/61 (82%) pts completed all visits and treatments were well tolerated with no safety concerns. Median PFS for overall population [N = 61, baseline (D0) PSADT range (mos) 1.5-217.1, median 9.8] and for a subset of pts with D0 PSADT ≤12mos (N = 36) has not yet been reached (FU 3-19 mos). 86% of pts with D0 PSADT ≤12 mos were progression free through 19mos FU. 27 out of 36 (75%) pts with D0 PSADT≤ 12 mos had disease stabilization at wks 27 evidenced by significant improvement in log2PSA change over time (slope) and PSADT from D0 (Slope=0.19 declined to 0.1, PSADT=5.3 improved to 10.1 mos, p = \u3c0.0001). This effect was maintained at wk 72 (Slope=0.09, PSADT=10.6, p = \u3c0.0001). Immunogenicity was observed in 77% (47/61) of pts by multiple immunologic assessments. Patient immunogenicity to INO-5150 as determined by CD38 and Perforin + CD8 T cell immune reactivity correlated with attenuated % PSA rise compared to pts without reactivity (p = 0.05, n = 50). Conclusions: INO-5150 +/- INO-9012 was safe, well tolerated and immunogenic. Clinical efficacy was observed in the patients with D0 PSADT≤ 12 mos as evidenced by a significant dampening of log2PSA change over time and increased PSADT up to 72 weeks FU. Additional genomic analyses are ongoing to further elucidate the correlation of immunologic efficacy and clinical benefit. (NCT02514213)

On certain other sets of integers

We show that if A is a subset of {1,...,N} containing no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{3/4-o(1)} N).Comment: 29 pp. Corrected typos. Added definitions for some non-standard notation and remarks on lower bound