A combinatorial identity for studying Sato-Tate type problems

We derive a combinatorial identity which is useful in studying the distribution of Fourier coefficients of L-functions by allowing us to pass from knowledge of moments of the coefficients to the distribution of the coefficients.Comment: This paper contains the proof of a combinatorial identity used to study effective equidistribution laws for the Fourier coefficients of elliptic curve L-functions investigated by the first two authors in http://arxiv.org/abs/1004.275

Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding

Projection-based embedding provides a simple, robust, and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction method while the remainder of the system is described at the level of density functional theory. Here, we present the derivation, implementation, and numerical demonstration of analytical nuclear gradients for projection-based wavefunction-in-density functional theory (WF-in-DFT) embedding. The gradients are formulated in the Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. An important aspect of the gradient theory is that WF contributions to the total WF-in-DFT gradient can be simply evaluated using existing WF gradient implementations without modification. Another simplifying aspect is that Kohn-Sham (KS) DFT contributions to the projection-based embedding gradient do not require knowledge of the WF calculation beyond the relaxed WF density. Projection-based WF-in-DFT embedding gradients are thus easily generalized to any combination of WF and KS-DFT methods. We provide numerical demonstration of the method for several applications, including calculation of a minimum energy pathway for a hydride transfer in a cobalt-based molecular catalyst using the nudged-elastic-band method at the CCSD-in-DFT level of theory, which reveals large differences from the transition state geometry predicted using DFT.Comment: 15 pages, 4 figure

Changing Frequency Separation of Kilohertz Quasi-Periodic Oscillations in the Sonic-Point Beat-Frequency Model

Previous work on the sonic-point beat-frequency (SPBF) model of the kilohertz quasi-periodic oscillations (QPOs) observed in the X-ray flux from neutron stars in low-mass binary systems has shown that it naturally explains many properties of these QPOs. These include the existence of just two principal QPOs in a given source, the commensurability of the frequency separation \Dnu\ of the two kilohertz QPOs and the spin frequency \nus inferred from burst oscillations, and the high frequencies, coherence, and amplitudes of these QPOs. Here we show that the SPBF model predicts that \Dnu is less than but close to \nus, consistent with the observed differences between \Dnu and \nus. It also explains naturally the decrease in \Dnu with increasing QPO frequency seen in some sources and the plateau in the QPO frequency--X-ray flux observed in 4U 1820-30. The model fits well the QPO frequency behavior observed in Sco X-1, 4U 1608-52, 4U 1728-34, and 4U 1820-30 (chisqdof = 0.4-2.1), giving masses ranging from 1.59 to 2.0 Msun and spin rates ranging from 279 to 364 Hz. In the SPBF model, the kilohertz QPOs are effects of strong-field gravity. Thus, if the model is validated, the kilohertz QPOs can be used not only to determine the properties of neutron stars but also to explore quantitatively general relativistic effects in the strong-field regime.Comment: 4 pages, 2 figures, LaTeX, uses emulateapj; submitted to ApJ Letter

The influence of solution composition on protein loss during peritoneal dialysis

A number of recent studies in man [1–3] and rats [1, 4, 5] has investigated the influence of the composition of commercial peritoneal dialysis solutions on the microcirculation and on the removal of solutes during peritoneal dialysis. One of those studies [3] demonstrated that dialysis with a normal osmolality Krebs solution greatly enhanced the concentration of protein in the drainage solution in comparison to that obtained with commercial, 1.5% dextrose solutions. We proposed that these results represented an effect of osmolality on interstitial movement of protein [6]. Since protein movement in the interstitium probably occurs through water channels in the gel-like matrix of the interstitium [7, 8], a change to a high osmolality dialysis solution could dehydrate the interstitium. This would increase the resistance to protein movement and thus decrease the loss of protein in the dialysate. During the first few exchanges, the high osmolality of commercial dialysis solutions could also pull residual protein out of the interstitium because it produced a generalized dehydration of the interstitial tissues. This would lead to large concentrations of protein in the drainage solution during the first few exchanges and then a progressive fall in dialysate protein with subsequent exchanges. An alternative hypothesis to explain such results would be that there is simply a washout of residual protein from the peritoneal cavity or from tissue spaces within the cavity.The following studies were designed to test which of these two hypotheses, an increased resistance to protein movement through dehydration of the interstitial tissue or a washout of residual protein already present in the peritoneal cavity, could explain our previous findings [3]

Nucleo-cytoplasmic interactions that control nuclear envelope breakdown and entry into mitosis in the sea urchin zygote

In sea urchin zygotes and mammalian cells nuclear envelope breakdown (NEB) is not driven simply by a rise in cytoplasmic cyclin dependent kinase 1-cyclin B (Cdk1-B) activity; the checkpoint monitoring DNA synthesis can prevent NEB in the face of mitotic levels of Cdk1-B. Using sea urchin zygotes we investigated whether this checkpoint prevents NEB by restricting import of regulatory proteins into the nucleus. We find that cyclin B1-GFP accumulates in nuclei that cannot complete DNA synthesis and do not break down. Thus, this checkpoint limits NEB downstream of both the cytoplasmic activation and nuclear accumulation of Cdk1-B1. In separate experiments we fertilize sea urchin eggs with sperm whose DNA has been covalently cross-linked to inhibit replication. When the pronuclei fuse, the resulting zygote nucleus does not break down for \u3e180 minutes (equivalent to three cell cycles), even though Cdk1-B activity rises to greater than mitotic levels. If pronuclear fusion is prevented, then the female pronucleus breaks down at the normal time (average 68 minutes) and the male pronucleus with cross-linked DNA breaks down 16 minutes later. This male pronucleus has a functional checkpoint because it does not break down for \u3e120 minutes if the female pronucleus is removed just prior to NEB. These results reveal the existence of an activity released by the female pronucleus upon its breakdown, that overrides the checkpoint in the male pronucleus and induces NEB. Microinjecting wheat germ agglutinin into binucleate zygotes reveals that this activity involves molecules that must be actively translocated into the male pronucleus