Revenue-neutral tax policy under price uncertainty

The firm's response to revenue-neutral taxation is investigated under price uncertainty. Revenue-neutral policies adjust simultaneously the marginal tax rate and the level of exemptions while keeping expected tax receipts constant. Nonincreasing absolute risk aversion is sufficient to sign the firm's response: a reduction in the marginal rate causes the firm to contract output. Implications are established for the equilibrium level of treasury receipts.

Revenue-neutral tax policies under price uncertainty: reply

In their comment on my 1990 article, Yeh, Suwanakul, and Mai extend my analysis-which focused attention exclusively on firm output-to allow for simultaneous endogeneity of price, aggregate output, and numbers of firms. They show that, with downward- sloping demand, industry output adjusts positively to revenue-neutral changes in the marginal rate of taxation. This result is significant for two reasons. First, we are more often interested in predictions about aggregate phenomena than we are in predictions about individual firms. Indeed, firm-level predictions are frequently irrefutable since firm data are often unavailable. Second, the authors derive their result under a set of conditions that appear to be more general than those invoked in my 1990 article. In particular, they circumvent the need to invoke specific assumptions about the nature of firms' aversions toward risk. I consider this a useful extension and I appreciate the careful scrutiny of my paper.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Evidence of neutral transcriptome evolution in plants

The transcriptome of an organism is its set of gene transcripts (mRNAs) at a defined spatial and temporal locus. Because gene expression is affected markedly by environmental and developmental perturbations, it is widely assumed that transcriptome divergence among taxa represents adaptive phenotypic selection. This assumption has been challenged by neutral theories which propose that stochastic processes drive transcriptome evolution. To test for evidence of neutral transcriptome evolution in plants, we quantified 18 494 gene transcripts in nonsenescent leaves of 14 taxa of Brassicaceae using robust cross-species transcriptomics which includes a two-step physical and in silico-based normalization procedure based on DNA similarity among taxa. Transcriptome divergence correlates positively with evolutionary distance between taxa and with variation in gene expression among samples. Results are similar for pseudogenes and chloroplast genes evolving at different rates. Remarkably, variation in transcript abundance among root-cell samples correlates positively with transcriptome divergence among root tissues and among taxa. Because neutral processes affect transcriptome evolution in plants, many differences in gene expression among or within taxa may be nonfunctional, reflecting ancestral plasticity and founder effects. Appropriate null models are required when comparing transcriptomes in space and time.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Eigenvalues of a one-dimensional Dirac operator pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.

Neural effects of cannabinoid CB1 neutral antagonist tetrahydrocannabivarin (THCv) on food reward and aversion in healthy volunteers

Disturbances in the regulation of reward and aversion in the brain may underlie disorders such as obesity and eating disorders. We previously showed that the cannabis receptor subtype (CB1) inverse agonist rimonabant, an antiobesity drug withdrawn due to depressogenic side effects, diminished neural reward responses yet increased aversive responses (Horder et al., 2010). Unlike rimonabant, tetrahydrocannabivarin is a neutral CB1 receptor antagonist (Pertwee, 2005) and may therefore produce different modulations of the neural reward system. We hypothesized that tetrahydrocannabivarin would, unlike rimonabant, leave intact neural reward responses but augment aversive responses. Methods: We used a within-subject, double-blind design. Twenty healthy volunteers received a single dose of tetrahydrocannabivarin (10mg) and placebo in randomized order on 2 separate occasions. We measured the neural response to rewarding (sight and/or flavor of chocolate) and aversive stimuli (picture of moldy strawberries and/or a less pleasant strawberry taste) using functional magnetic resonance imaging. Volunteers rated pleasantness, intensity, and wanting for each stimulus. Results: There were no significant differences between groups in subjective ratings. However, tetrahydrocannabivarin increased responses to chocolate stimuli in the midbrain, anterior cingulate cortex, caudate, and putamen. Tetrahydrocannabivarin also increased responses to aversive stimuli in the amygdala, insula, mid orbitofrontal cortex, caudate, and putamen. Conclusions: Our findings are the first to show that treatment with the CB1 neutral antagonist tetrahydrocannabivarin increases neural responding to rewarding and aversive stimuli. This effect profile suggests therapeutic activity in obesity, perhaps with a lowered risk of depressive side effects. Keywords: reward, THCv, obesity, fMRI, cannabinoid

Improving a global model from the boundary layer: total turbulent energy and the neutral limit Prandtl number

Model intercomparisons have identified important deficits in the representation of the stable boundary layer by turbulence parametrizations used in current weather and climate models. However, detrimental impacts of more realistic schemes on the large-scale flow have hindered progress in this area. Here we implement a total turbulent energy scheme into the climate model ECHAM6. The total turbulent energy scheme considers the effects of Earth’s rotation and static stability on the turbulence length scale. In contrast to the previously used turbulence scheme, the TTE scheme also implicitly represents entrainment flux in a dry convective boundary layer. Reducing the previously exaggerated surface drag in stable boundary layers indeed causes an increase in southern hemispheric zonal winds and large-scale pressure gradients beyond observed values. These biases can be largely removed by increasing the parametrized orographic drag. Reducing the neutral limit turbulent Prandtl number warms and moistens low-latitude boundary layers and acts to reduce longstanding radiation biases in the stratocumulus regions, the Southern Ocean and the equatorial cold tongue that are common to many climate models.

Resting-state functional connectivity following a single dose treatment with CB1 neutral antagonist tetrahydrocannabivarin (THCv) in healthy volunteers

BACKGROUND: The cannabinoid cannabinoid type 1 (CB1) neutral antagonist tetrahydrocannabivarin (THCv) has been suggested as a possible treatment for obesity, but without the depressogenic side-effects of inverse antagonists such as Rimonabant. However, how THCv might affect the resting state functional connectivity of the human brain is as yet unknown. METHOD: We examined the effects of a single 10mg oral dose of THCv and placebo in 20 healthy volunteers in a randomized, within-subject, double-blind design. Using resting state functional magnetic resonance imaging and seed-based connectivity analyses, we selected the amygdala, insula, orbitofrontal cortex, and dorsal medial prefrontal cortex (dmPFC) as regions of interest. Mood and subjective experience were also measured before and after drug administration using self-report scales. RESULTS: Our results revealed, as expected, no significant differences in the subjective experience with a single dose of THCv. However, we found reduced resting state functional connectivity between the amygdala seed region and the default mode network and increased resting state functional connectivity between the amygdala seed region and the dorsal anterior cingulate cortex and between the dmPFC seed region and the inferior frontal gyrus/medial frontal gyrus. We also found a positive correlation under placebo for the amygdala-precuneus connectivity with the body mass index, although this correlation was not apparent under THCv. CONCLUSION: Our findings are the first to show that treatment with the CB1 neutral antagonist THCv decreases resting state functional connectivity in the default mode network and increases connectivity in the cognitive control network and dorsal visual stream network. This effect profile suggests possible therapeutic activity of THCv for obesity, where functional connectivity has been found to be altered in these regions.

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

Local star formation triggered by supernova shocks in magnetized diffuse neutral clouds

In this work, considering the impact of a supernova remnant (SNR) with a neutral magnetized cloud we derived analytically a set of conditions that are favourable for driving gravitational instability in the cloud and thus star formation. Using these conditions, we have built diagrams of the SNR radius, R(SNR), versus the initial cloud density, n(c), that constrain a domain in the parameter space where star formation is allowed. This work is an extension to previous study performed without considering magnetic fields (Melioli et al. 2006, hereafter Paper I). The diagrams are also tested with fully three-dimensional MHD radiative cooling simulations involving a SNR and a self-gravitating cloud and we find that the numerical analysis is consistent with the results predicted by the diagrams. While the inclusion of a homogeneous magnetic field approximately perpendicular to the impact velocity of the SNR with an intensity similar to 1 mu G within the cloud results only a small shrinking of the star formation zone in the diagram relative to that without magnetic field, a larger magnetic field (similar to 10 mu G) causes a significant shrinking, as expected. Though derived from simple analytical considerations these diagrams provide a useful tool for identifying sites where star formation could be triggered by the impact of a supernova blast wave. Applications of them to a few regions of our own Galaxy (e.g. the large CO shell in the direction of Cassiopeia, and the Edge Cloud 2 in the direction of the Scorpious constellation) have revealed that star formation in those sites could have been triggered by shock waves from SNRs for specific values of the initial neutral cloud density and the SNR radius. Finally, we have evaluated the effective star formation efficiency for this sort of interaction and found that it is generally smaller than the observed values in our own Galaxy (SFE similar to 0.01-0.3). This result is consistent with previous work in the literature and also suggests that the mechanism presently investigated, though very powerful to drive structure formation, supersonic turbulence and eventually, local star formation, does not seem to be sufficient to drive global star formation in normal star-forming galaxies, not even when the magnetic field in the neutral clouds is neglected.