Semiclassical Resonances of Schr\"odinger operators as zeroes of regularized determinants

We prove that the resonances of long range perturbations of the (semiclassical) Laplacian are the zeroes of natural perturbation determinants. We more precisely obtain factorizations of these determinants of the form $\prod_{w = {\rm resonances}}(z-w) \exp (\varphi_p(z,h))$ and give semiclassical bounds on $\partial_z \varphi_p$ as well as a representation of Koplienko's regularized spectral shift function. Here the index $p \geq 1$ depends on the decay rate at infinity of the perturbation.Comment: 37 pages, published versio

The Economics of Badmouthing: Libel Law and the Underworld of the Financial Press in France before World War I

This article analyzes the economics of “badmouthing” in the context of the pre-1914 French capital market. We argue that badmouthing was a means through which racketeering journals sought to secure property rights over issuers’ reputation. We provide a theoretical study of the market setup that emerged to deal with such problems, and we test our predictions using new evidence from contemporary sources.badmouthing, capital market, reputation.

Beyond position weight matrices: nucleotide correlations in transcription factor binding sites and their description

The identification of transcription factor binding sites (TFBSs) on genomic DNA is of crucial importance for understanding and predicting regulatory elements in gene networks. TFBS motifs are commonly described by Position Weight Matrices (PWMs), in which each DNA base pair independently contributes to the transcription factor (TF) binding, despite mounting evidence of interdependence between base pairs positions. The recent availability of genome-wide data on TF-bound DNA regions offers the possibility to revisit this question in detail for TF binding {\em in vivo}. Here, we use available fly and mouse ChIPseq data, and show that the independent model generally does not reproduce the observed statistics of TFBS, generalizing previous observations. We further show that TFBS description and predictability can be systematically improved by taking into account pairwise correlations in the TFBS via the principle of maximum entropy. The resulting pairwise interaction model is formally equivalent to the disordered Potts models of statistical mechanics and it generalizes previous approaches to interdependent positions. Its structure allows for co-variation of two or more base pairs, as well as secondary motifs. Although models consisting of mixtures of PWMs also have this last feature, we show that pairwise interaction models outperform them. The significant pairwise interactions are found to be sparse and found dominantly between consecutive base pairs. Finally, the use of a pairwise interaction model for the identification of TFBSs is shown to give significantly different predictions than a model based on independent positions

Payoff-dependent balancedness and cores (revised version)

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to extant results taken from game theory and economic theory are given.balancedness, cooperative game, core, parametrized game

Innovation under taxes versus permits : how a commonly made assumption leads to misleading recommendations

The literature on the impact of economic instruments (typically taxes and tradable permits) on the level of innovation is usually based on the assumption that innovation reduces the slope of the marginal abatement cost curve. This assumption, which usually leads to the conclusion that taxes induce higher levels of innovation than tradable permits, is however never motivated. In this short article, we analyse the assumption by introducing innovation in the production function as a polluting firm and by showing how it affects the corresponding marginal abatement cost curve. We show that the slope of the marginal abatement cost curvedoes not necessarily decrease with the level of innovation. As a consequence, previous analyses lead to misleading policy recommendations

Payoff-dependant Balancedness and Cores.

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parameterized cooperative games is introduced. This new setting and its associated equilibrium–core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium–core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non-convexities. Applications to extant results taken from game theory and economic theory are given.Balancedness; Cooperative game; Core; Parametrized game;

Inverse participation ratios in the XXZ spin chain

We investigate numerically the inverse participation ratios in a spin-1/2 XXZ chain, computed in the "Ising" basis (i.e., eigenstates of $\sigma^z_i$). We consider in particular a quantity $T$, defined by summing the inverse participation ratios of all the eigenstates in the zero magnetization sector of a finite chain of length $N$, with open boundary conditions. From a dynamical point of view, $T$ is proportional to the stationary return probability to an initial basis state, averaged over all the basis states (initial conditions). We find that $T$ exhibits an exponential growth, $T\sim\exp(aN)$, in the gapped phase of the model and a linear scaling, $T\sim N$, in the gapless phase. These two different behaviors are analyzed in terms of the distribution of the participation ratios of individual eigenstates. We also investigate the effect of next-nearest-neighbor interactions, which break the integrability of the model. Although the massive phase of the non-integrable model also has $T\sim\exp(aN)$, in the gapless phase $T$ appears to saturate to a constant value.Comment: 8 pages, 7 figures. v2: published version (one figure and 3 references added, several minor changes

Payoffs-dependent Balancedness and Cores

We provide a result for non-emptiness of the core in NTU games. We use a payoffs-dependent balancedness condition, based on transfer rate mappings. Going beyond the non-emptiness of standard core, existence of some refined solution is proved, including specific core allocations and equilibrium-core allocations in parameterized collection of cooperative games. The proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to various extant results taken from game theory and economic theory are given.Cooperative games, Core solutions, Non-emptiness

Ion optics for high power 50-cm-diam ion thrusters

The process used at the NASA-Lewis to fabricate 30 and 50-cm-diameter ion optics is described. The ion extraction capabilities of the 30 and 50-cm diameter ion optics were evaluated on divergent field and ring-cusp discharge chambers and compared. Perveance was found to be sensitive to the effects of the type and power of the discharge chamber and to the accelerator electrode hole diameter. Levels of up to 0.64 N and 20 kW for thrust and input power, respectively, were demonstrated with the divergent-field discharge chamber. Thruster efficiencies and specific impulse values up to 79 percent and 5000 sec., respectively, were achieved with the ring-cusp discharge chamber