Intersection Numbers of Heegner Divisors on Shimura Curves

In foundational papers, Gross, Zagier, and Kohnen established two formulas for arithmetic intersection numbers of certain Heegner divisors on integral models of modular curves. In [GZ1], only one imaginary quadratic discriminant plays a role. In [GZ2] and [GKZ], two quadratic discriminants play a role. In this paper we generalize the two-discriminant formula from the modular curves X0(N) to certain Shimura curves defined over Q. Our intersection formula was stated in [Ro], but the proof was only outlined there. Independently, the general formula was given, in a weaker and less explicit form, in [Ke2]; there it was proved completely. This paper is thus a synthesis of parts of [Ro] and [Ke2]. The intersection multiplicities computed here were used in [Ku] to derive a relation between height pairings and special values of the derivatives of certain Eisenstein series. Two more recent related works are [KR], which concentrates on computing local intersection multiplicities at ramified primes under quite general hypotheses, and [KRY], which relates intersection numbers on Shimura curves to coefficients of modular forms. We note also that Zhang [Zh] has generalized all of [GZ1] from ground field Q to general totally real ground fields F, working with general Shimura curves. We expect that all of [GKZ] should generalize similarly

Stability of the Period-Doubled Core of the 90-degree Partial in Silicon

In a recent Letter [N. Lehto and S. Oberg, Phys. Rev. Lett. 80, 5568 (1998)], Lehto and Oberg investigated the effects of strain fields on the core structure of the 90-degree partial dislocation in silicon, especially the influence of the choice of supercell periodic boundary conditions in theoretical simulations. We show that their results for the relative stability between the two structures are in disagreement with cell-size converged tight-binding total energy (TBTE) calculations, which suggest the DP core to be more stable, regardless of the choice of boundary condition. Moreover, we argue that this disagreement is due to their use of a Keating potential.Comment: 1 page. Submitted to Comments section of PRL. Also available at http://www.physics.rutgers.edu/~dhv/preprints/rn_dcom/index.htm

Lower order terms in the full moment conjecture for the Riemann zeta function

We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods for obtaining numerical values of these coefficients. We also provide some numerical evidence in favour of the conjecture.Comment: 37 pages, 4 figure

The Unreasonable Effectiveness of Contact Tracing on Networks with Cliques

Contact tracing, the practice of isolating individuals who have been in contact with infected individuals, is an effective and practical way of containing disease spread. Here, we show that this strategy is particularly effective in the presence of social groups: Once the disease enters a group, contact tracing not only cuts direct infection paths but can also pre-emptively quarantine group members such that it will cut indirect spreading routes. We show these results by using a deliberately stylized model that allows us to isolate the effect of contact tracing within the clique structure of the network where the contagion is spreading. This will enable us to derive mean-field approximations and epidemic thresholds to demonstrate the efficiency of contact tracing in social networks with small groups. This analysis shows that contact tracing in networks with groups is more efficient the larger the groups are. We show how these results can be understood by approximating the combination of disease spreading and contact tracing with a complex contagion process where every failed infection attempt will lead to a lower infection probability in the next attempts. Our results illustrate how contract tracing in real-world settings can be more efficient than predicted by models that treat the system as fully mixed or the network structure as locally tree-like.Comment: 15 pages, 13 figures, 4 table

Subluxation: dogma or science?

Subluxation syndrome is a legitimate, potentially testable, theoretical construct for which there is little experimental evidence. Acceptable as hypothesis, the widespread assertion of the clinical meaningfulness of this notion brings ridicule from the scientific and health care communities and confusion within the chiropractic profession. We believe that an evidence-orientation among chiropractors requires that we distinguish between subluxation dogma vs. subluxation as the potential focus of clinical research. We lament efforts to generate unity within the profession through consensus statements concerning subluxation dogma, and believe that cultural authority will continue to elude us so long as we assert dogma as though it were validated clinical theory

Barriers to Insecticide-Treated Mosquito Net Possession 2 Years after a Mass Free Distribution Campaign in Luangwa District, Zambia

Roll Back Malaria set the goal of 100% of households in malaria endemic countries in Africa owning an insecticide-treated mosquito net (ITN) by 2010. Zambia has used mass free distribution campaigns and distribution through antenatal care (ANC) clinics to achieve high coverage.We conducted a probability survey of 801 households in 2008 to assess factors associated with households that lacked an ITN after mass distribution. Community perceptions of barriers to ITN access were also obtained from in-depth interviews with household heads that reported not owning an ITN. Nearly 74% of households in Luangwa district reported owning ≥1 ITN. Logistic regression showed households without a child <5 years old during the ITN distribution campaigns were twice as likely to not have an ITN as those with a child <5 during distribution (Adjusted odds ratio (AOR)  = 2.43; 95% confidence interval (CI): 1.67-3.55). Households without a woman who attended an ANC in the past 2 years were more likely to be without ITNs compared to households with a woman who attended an ANC in the past 2 years (AOR  = 1.52; 95% CI: 1.04-2.21). In-depth interviews with heads of households without an ITN revealed that old age was a perceived barrier to receiving an ITN during distribution, and that ITNs wore out before they could be replaced.Delivery of a large number of ITNs does not translate directly into 100% household coverage. Due to their design, current ITN distribution strategies may miss households occupied by the elderly and those without children or ANC access. ITN distribution strategies targeting the elderly, those with limited access to distribution points, and others most likely to be missed are necessary if 100% ITN coverage of households is to be achieved

DACOTA: The dense array for cosmological transitions

The Epoch of Reionization (EoR) heralded the advent of the Universe we recognize today, containing stars, galaxies and super-massive black holes. A number of experiments to detect the red-shifted hydrogen signature of the atomic component of the intergalactic medium (IGM) are on-going (e.g. PAPER, MWA, LOFAR). Due to the faintness of the signal, the bright foregrounds, and the challenge of instrumental systematics, multiple techniques are essential to create a more robust detection and to provide the complete picture on the evolution of early galaxies

First Results from COPSS: The CO Power Spectrum Survey

We present constraints on the abundance of carbon monoxide in the early universe from the CO Power Spectrum Survey. We utilize a data set collected between 2005 and 2008 using the Sunyaev–Zel'dovich Array (SZA), which was previously used to measure arcminute-scale fluctuations of the cosmic microwave background. This data set features observations of 44 fields, covering an effective area of 1.7 square degrees, over a frequency range of 27–35 GHz. Using the technique of intensity mapping, we are able to probe the CO(1–0) transition, with sensitivity to spatial modes between k = 0.5–2 h Mpc^(−1) over a range in redshift of z = 2.3–3.3, spanning a comoving volume of 3.6 × 10^6 h^(−3) Mpc^3. We demonstrate our ability to mitigate foregrounds, and present estimates of the impact of continuum sources on our measurement. We constrain the CO power spectrum to P_(CO) < 2.6 × 10^4 μK^2 (h^(−1) Mpc)^3, or Δ^2_(CO)(k = 1 h Mpc^(−1)) < 1.3 × 10^3 μK^2, at 95% confidence. This limit resides near optimistic predictions for the CO power spectrum. Under the assumption that CO emission is proportional to halo mass during bursts of active star formation, this corresponds to a limit on the ratio of CO(1–0) luminosity to host halo mass of A_(CO) < 1.2 × 10^(−5) L⊙_ M_⊙^(−1). Further assuming a Milky Way-like conversion factor between CO luminosity and molecular gas mass (α_(CO) = 4.3 M_⊙ (K km s^(−1) pc^(−2))^(−1)), we constrain the global density of molecular gas to ρ_(z~3) (M_H_2) ⩽ 2.8 x 10^8 M_☉ Mpc^(-3)

Properties of a continuous-random-network model for amorphous systems

We use a Monte Carlo bond-switching method to study systematically the thermodynamic properties of a "continuous random network" model, the canonical model for such amorphous systems as a-Si and a-SiO$_2$. Simulations show first-order "melting" into an amorphous state, and clear evidence for a glass transition in the supercooled liquid. The random-network model is also extended to study heterogeneous structures, such as the interface between amorphous and crystalline Si.Comment: Revtex file with 4 figure