Harmonic sets and the harmonic prime number theorem

We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2

Formation and Evolution of Binary Asteroids

Satellites of asteroids have been discovered in nearly every known small body population, and a remarkable aspect of the known satellites is the diversity of their properties. They tell a story of vast differences in formation and evolution mechanisms that act as a function of size, distance from the Sun, and the properties of their nebular environment at the beginning of Solar System history and their dynamical environment over the next 4.5 Gyr. The mere existence of these systems provides a laboratory to study numerous types of physical processes acting on asteroids and their dynamics provide a valuable probe of their physical properties otherwise possible only with spacecraft. Advances in understanding the formation and evolution of binary systems have been assisted by: 1) the growing catalog of known systems, increasing from 33 to nearly 250 between the Merline et al. (2002) Asteroids III chapter and now, 2) the detailed study and long-term monitoring of individual systems such as 1999 KW4 and 1996 FG3, 3) the discovery of new binary system morphologies and triple systems, 4) and the discovery of unbound systems that appear to be end-states of binary dynamical evolutionary paths. Specifically for small bodies (diameter smaller than 10 km), these observations and discoveries have motivated theoretical work finding that thermal forces can efficiently drive the rotational disruption of small asteroids. Long-term monitoring has allowed studies to constrain the system's dynamical evolution by the combination of tides, thermal forces and rigid body physics. The outliers and split pairs have pushed the theoretical work to explore a wide range of evolutionary end-states.Comment: 42 pages, 4 figures, contribution to the Asteroids 4 boo

Observations of Dispersion Cancellation of Entangled Photon Pairs

An experimental study of the dispersion cancellation occurring in frequency-entangled photon pairs is presented. The approach uses time-resolved up conversion of the pairs, which has temporal resolution at the fs level, and group-delay dispersion sensitivity of $\approx \ 20 \, \mathrm{fs}^2$ under experimental conditions. The cancellation is demonstrated with dispersion stronger than $\pm 10^3 \, \mathrm{fs}^2$ in the signal $(-)$ and idler $(+)$ modes. The observations represent the generation, compression, and characterization of ultrashort biphotons with correlation width as small as 6.8 times the degenerate optical period.Comment: 5 pages, 3 figure

Tourette syndrome research highlights 2015 [version 1; referees: 3 approved]

We present selected highlights from research that appeared during 2015 on Tourette syndrome and other tic disorders. Topics include phenomenology, comorbidities, developmental course, genetics, animal models, neuroimaging, electrophysiology, pharmacology, and treatment. We briefly summarize articles whose results we believe may lead to new treatments, additional research or modifications in current models of TS

Quantum Hydrodynamic Model for the enhanced moments of Inertia of molecules in Helium Nanodroplets: Application to SF6_6

The increase in moment of inertia of SF$_6$ in helium nanodroplets is calculated using the quantum hydrodynamic approach. This required an extension of the numerical solution to the hydrodynamic equation to three explicit dimensions. Based upon an expansion of the density in terms of the lowest four Octahedral spherical harmonics, the predicted increase in moment of inertia is $170 {\rm u \AA^2}$, compared to an experimentally determined value of $310(10) {\rm u \AA^2}$, i.e., 55% of the observed value. The difference is likely in at least part due to lack of convergence with respect to the angular expansion, but at present we do not have access to the full densities from which a higher order expansion can be determined. The present results contradict those of Kwon et al., J. Chem. Phys. {\bf 113}, 6469 (2000), who predicted that the hydrodynamic theory predicted less than 10% of the observed increase in moment of inertia.Comment: 10 pages, including 1 figur

A Mathematical Model for Lymphangiogenesis in Normal and Diabetic Wounds

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis) very few have been proposed for the regeneration of the lymphatic network. Moreover, lymphangiogenesis is markedly distinct from angiogenesis, occurring at different times and in a different manner. Here a model of five ordinary differential equations is presented to describe the formation of lymphatic capillaries following a skin wound. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from experimental and clinical data. The system is then solved numerically and the results are compared with the available biological literature. Finally, a parameter sensitivity analysis of the model is taken as a starting point for suggesting new therapeutic approaches targeting the enhancement of lymphangiogenesis in diabetic wounds. The work provides a deeper understanding of the phenomenon in question, clarifying the main factors involved. In particular, the balance between TGF-$\beta$ and VEGF levels, rather than their absolute values, is identified as crucial to effective lymphangiogenesis. In addition, the results indicate lowering the macrophage-mediated activation of TGF-$\beta$ and increasing the basal lymphatic endothelial cell growth rate, \emph{inter alia}, as potential treatments. It is hoped the findings of this paper may be considered in the development of future experiments investigating novel lymphangiogenic therapies

Optimal Long-Run Fiscal Policy: Constraints, Preferences and the Resolution of Uncertainty

We construct a computational dynamic stochastic overlapping generations general equilibrium model with uncertain lifetimes and explore the impact of policy stickiness (specifically, a major reform will preclude future reforms for a generation) on optimal long-run fiscal policy. Under such circumstances, entitlement reforms exhaust a valuable option to move in the future. We explore the conditions under which the gain to waiting is large enough to induce optimizing policymakers to delay reforming a suboptimal system. We also allow for the uncertainty to have ARCH characteristics and explore the impact of time-varying uncertainty on the optimality of delayed policy action.

Uncertainty and the Design of Long-Run Fiscal Policy

This paper explores optimal fiscal policy in an overlapping-generations general-equilibrium model under uncertainty and the impact on optimal policy of the introduction of a type of policy stickiness intended to account for the stylized fact that major reforms happen infrequently. In general, our analysis suggests not only that action should not be delayed, but further that action should actually be accelerated. The added realism of restrictions on the frequency of policy changes alters this result in two ways. The prospect of being unable to set policy in the future occasions even more precautionary saving today, if the government acts. However, the government may also choose not to set policy, and its inaction range is very asymmetric. Because the impact of its policies on the current elderly cannot be reversed in the future, the government is much more likely to choose inaction when fiscal tightening is called for. Thus, the optimal policy response over time might best be characterized by great caution in general, but punctuated by occasional periods of apparent irresponsibility.

The 2003 Dividend Tax Cuts and the Value of the Firm: An Event Study

The "Jobs and Growth Tax Relief Act of 2003" (JGTRA03) contained a number of significant tax provisions, but the most noteworthy may have been the reduction in dividend tax rates. The political debate over the dividend tax reductions of 2003 took a number of surprising twists and turns. Accordingly, it is likely that the views of market participants concerning the probability of significant dividend tax reduction fluctuated significantly during 2003. In this paper, we use this fact to estimate the effects of dividend tax policy on firm value. We find that firms with higher dividend yields benefited more than other dividend paying firms, a result that, in itself, is consistent with both new and traditional views of dividend taxation. But further evidence points toward the new view and away from the traditional view. We also find that non-dividend-paying firms experienced larger abnormal returns than other firms as the result of the dividend tax cut, and that a similar bonus accrued to firms likely to issue new shares, two results that may appear surprising at first but are consistent with the theory developed in the paper.