Deuterium fractionation on interstellar grains studied with the direct master equation approach

We have studied deuterium fractionation on interstellar grains with the use of an exact method known as the direct master equation approach. We consider conditions pertinent to dense clouds at late times when the hydrogen is mostly in molecular form and a large portion of the gas-phase carbon has already been converted to carbon monoxide. Hydrogen, oxygen and deuterium atoms, as well as CO molecules, are allowed to accrete on to dust particles and react there to produce various stable molecules. The surface abundances, as well as the abundance ratios between deuterated and normal isotopomers, are compared with those calculated with the Monte Carlo approach. We find that the agreement between the Monte Carlo and the direct master equation methods can be made as close as desired. Compared with previous examples of the use of the direct master equation approach, our present method is much more efficient. It should now be possible to run large-scale gas-grain models in which the diffusive dust chemistry is handled `exactly'.Comment: 7 pages, 3 figure

Accurate rate coefficients for models of interstellar gas-grain chemistry

The methodology for modeling grain-surface chemistry has been greatly improved by taking into account the grain size and fluctuation effects. However, the reaction rate coefficients currently used in all practical models of gas-grain chemistry are inaccurate by a significant amount. We provide expressions for these crucial rate coefficients that are both accurate and easy to incorporate into gas-grain models. We use exact results obtained in earlier work, where the reaction rate coefficient was defined by a first-passage problem, which was solved using random walk theory. The approximate reaction rate coefficient presented here is easy to include in all models of interstellar gas-grain chemistry. In contrast to the commonly used expression, the results that it provides are in perfect agreement with detailed kinetic Monte Carlo simulations. We also show the rate coefficient for reactions involving multiple species.Comment: 4 pages, 2 figure

Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities

This paper presents a model of optimal labor income taxation where top incomes respond to marginal tax rates through three channels: (1) standard labor supply, (2) tax avoidance, (3) compensation bargaining. We derive the optimal top tax rate formula as a function of the three corresponding behavioral elasticities. The first elasticity (labor supply) is the sole real factor limiting optimal top tax rates. The optimal tax system should be designed to minimize the second elasticity (avoidance) through tax enforcement and tax neutrality across income forms. The optimal top tax rate increases with the third elasticity (bargaining) as bargaining efforts are zero-sum in aggregate. We provide evidence using cross-country times series macro-evidence and CEO pay micro-evidence. The macro-evidence from 18 OECD countries shows that there is a strong negative correlation between top tax rates and top 1% income shares since 1960, implying that the overall elasticity is large. However, top income share increases have not translated into higher economic growth. US CEO pay evidence shows that pay for luck is quantitatively more important when top tax rates are low. International CEO pay evidence shows that CEO pay is strongly negatively correlated with top tax rates even controlling for rm characteristics and performance, and this correlation is stronger in firms with poor governance. These results are consistent with bargaining effects playing a role in the link between top incomes and top tax rates. If bargaining effects in fact exist, optimal tax rates should be higher than commonly assumed.

ECONOMICS 1410 / KENNEDY SCHOOL SUP-125 Public Economics: Designing Government Policy

ECONOMICS 1410 / KENNEDY SCHOOL SUP-125 Public Economics: Designing Government Polic

A hybrid moment equation approach to gas-grain chemical modeling

[Context] The stochasticity of grain chemistry requires special care in modeling. Previously methods based on the modified rate equation, the master equation, the moment equation, and Monte Carlo simulations have been used. [Aims] We attempt to develop a systematic and efficient way to model the gas-grain chemistry with a large reaction network as accurately as possible. [Methods] We present a hybrid moment equation approach which is a general and automatic method where the generating function is used to generate the moment equations. For large reaction networks, the moment equation is cut off at the second order, and a switch scheme is used when the average population of certain species reaches 1. For small networks, the third order moments can also be utilized to achieve a higher accuracy. [Results] For physical conditions in which the surface reactions are important, our method provides a major improvement over the rate equation approach, when benchmarked against the rigorous Monte Carlo results. For either very low or very high temperatures, or large grain radii, results from the rate equation are similar to those from our new approach. Our method is faster than the Monte Carlo approach, but slower than the rate equation approach. [Conclusions] The hybrid moment equation approach with a cutoff and switch scheme is applicable to large gas-grain networks, and is accurate enough to be used for astrochemistry studies. The layered structure of the grain mantle could also be incorporated into this approach, although a full implementation of the grain micro-physics appears to be difficult.Comment: 11 pages, 4 figures. Accepted for publication in Astronomy and Astrophysic

On the master equation approach to diffusive grain-surface chemistry: the H, O, CO system

We have used the master equation approach to study a moderately complex network of diffusive reactions occurring on the surfaces of interstellar dust particles. This network is meant to apply to dense clouds in which a large portion of the gas-phase carbon has already been converted to carbon monoxide. Hydrogen atoms, oxygen atoms, and CO molecules are allowed to accrete onto dust particles and their chemistry is followed. The stable molecules produced are oxygen, hydrogen, water, carbon dioxide (CO2), formaldehyde (H2CO), and methanol (CH3OH). The surface abundances calculated via the master equation approach are in good agreement with those obtained via a Monte Carlo method but can differ considerably from those obtained with standard rate equations.Comment: 13 pages, 5 figure

Incorporation of stochastic chemistry on dust grains in the PDR code using moment equations

Unlike gas-phase reactions, chemical reactions taking place on interstellar dust grain surfaces cannot always be modeled by rate equations. Due to the small grain sizes and low flux,these reactions may exhibit large fluctuations and thus require stochastic methods such as the moment equations. We evaluate the formation rates of H2, HD and D2 molecules on dust grain surfaces and their abundances in the gas phase under interstellar conditions. We incorporate the moment equations into the Meudon PDR code and compare the results with those obtained from the rate equations. We find that within the experimental constraints on the energy barriers for diffusion and desorption and for the density of adsorption sites on the grain surface, H2, HD and D2 molecules can be formed efficiently on dust grains. Under a broad range of conditions, the moment equation results coincide with those obtained from the rate equations. However, in a range of relatively high grain temperatures, there are significant deviations. In this range, the rate equations fail while the moment equations provide accurate results. The incorporation of the moment equations into the PDR code can be extended to other reactions taking place on grain surfaces

Tax simplicity and heterogeneous learning

We study the effects of fiscal incentives for self-employment using new French tax data from 1994 to 2012. France serves as a good quasi-laboratory: It has three fiscal regimes - or modes of taxation - for the self-employed, which differ in their financial payoffs and in their administrative simplicity. These regimes have changed extensively over time - offering the opportunity to study how people learn about them and understand them. We find that the self-employed respond to the tax and administrative notches created by the eligibility thresholds: there is strong bunching right before the eligibility thresholds, which we use to estimate self-employed taxable income elasticities and the value of administrative simplicity. Even a small preference for administrative simplicity could explain the bunching observed. There is a sizable cost of tax complexity; agents are not immediately able to understand what the right regime choice is and there is evidence for costly learning over time. The cost of complexity is regressive because it affects mostly the uneducated, low income, and low skill agents. Agents who can be viewed as more informed and knowledgeable (e.g., the more educated or high-skilled) are more likely to make the correct regime choice and to learn faste

A SUBPOPULATION OF ITCH RECEPTORS MARKED BY RET EXPRESSION

Sensory neurons are a heterogeneous group of cells that are specialized to detect stimuli acting on the skin such as touch, temperature, pain and itch. A major challenge in the sensory biology field is to isolate and characterize specific functional subsets of neurons as an exhaustive knowledge of many of them is still lacking. In my PhD project I established a protocol to analyse and sort by Fluorescently Activated Cell Sorting (FACS) peripheral sensory neurons, in order to isolate specific subsets and further perform gene expression profiling. In particular I applied these techniques to Avil-Cre::ReteGFP mice, where Ret-positive neurons express eGFP specifically in Dorsal Root Ganglia (DRG) neurons after Cre recombination. Ret is a receptor for the GDNF family expressed in at least 3 sensory neuron subsets: non-peptidergic nociceptors, Rapidly Adapting (RA) mechanoreceptors and C-fiber low-threshold mechanoreceptors. However, our immunohistochemical analysis suggested that there might be more Ret-positive subsets. I analysed Ret-positive neurons by FACS, combining the analysis of the pattern of endogenous eGFP expression with IB4-binding arrangement and I identified 5 diverse Ret-eGFP-positive subsets. I focused on two of them, Ret-eGFPLo:IB4Neg and Ret-eGFPHi:IB4Neg that did not bind to IB4 and expressed low and high levels of eGFP, respectively. Their expression profiles suggested that Ret-eGFPHi:IB4Neg neurons represent the previously described RA Mechanoreceptors, while the Ret-eGFPLo:IB4Neg subset constitutes a new Ret-positive class of sensory neurons involved in itch perception. To verify this assumption, we functionally characterized Ret-eGFPLo:IB4Neg neurons. We focused on three molecules whose receptors we found enriched in the subset: histamine, a well known pruritogen, IL-31, a cytokine that has been linked to the pathology of Atopic Dermatitis, and LY344864, a serotonin agonist whose receptors, 5-HT1f, was among the most expressed genes within the Ret-eGFPLo:IB4Neg subset. By calcium imaging we demonstrated that these substances are able to elicit a neuronal response mainly in Ret-eGFP/IB4 negative cells. Moreover, when injected in the nape of the neck of mice, they all cause scratching, substantiating a putative role of this population as itch receptors.. My data indicate that we have discovered a new Ret-positive subset of sensory neurons involved in itch perception. A more extensive characterization of these cells, for example with a Sst-ires-Cre line which we found to specifically mark Ret-eGFPLo:IB4Neg subset, will further clarify their role within the DRG in vivo

Taxation and migration: evidence and policy implications

In this article, we review a growing empirical literature on the effects of personal taxation on the geographic mobility of people and discuss its policy implications. We start by laying out the empirical challenges that prevented progress in this area and then discuss how recent work has made use of new data sources and quasi-experimental approaches to credibly estimate migration responses. This body of work has shown that certain segments of the labor market, especially high-income workers and professions with little location-specific human capital, may be quite responsive to taxes in their location decisions. When considering the implications for tax policy design, we distinguish between uncoordinated and coordinated tax policy. We highlight the importance of recognizing that mobility elasticities are not exogenous, structural parameters. They can vary greatly depending on the population being analyzed, the size of the tax jurisdiction, the extent of tax policy coordination, and a range of non-tax policies. While migration responses add to the efficiency costs of redistributing income, we caution against over-using the recent evidence of (sizeable) mobility responses to taxes as an argument for less redistribution in a globalized world