Groups whose word problems are not semilinear

Suppose that G is a finitely generated group and W is the formal language of words defining the identity in G. We prove that if G is a nilpotent group, the fundamental group of a finite volume hyperbolic three-manifold, or a right-angled Artin group whose graph lies in a certain infinite class, then W is not a multiple context free language

Outsourcing and Technological Innovations: A Firm-Level Analysis

This paper presents a dynamic model that analyzes how firms’ expectations with regards to technological change influence the demand for outsourcing. We show that outsourcing becomes more beneficial to the firm when technology is changing rapidly. As the pace of innovations in production technology increases, the firm has less time to amortize the sunk costs associated with purchasing the new technologies. This makes producing in-house with the latest technologies relatively more expensive than outsourcing. The model therefore provides an explanation for the recent increases in outsourcing that have taken place in an environment of increased expectations for technological change. We test the predictions of the model using a panel dataset on Spanish firms for the period 1990 through 2002. The empirical results support the main prediction of the model, namely, that all other things equal, the demand for outsourcing increases with the probability of technological change.technological change, outsourcing

Outsourcing and Technological Change

We present a dynamic model where the probability of outsourcing production is increasing in the firm’s expectation of technological change. As the pace of innovations in production technologies increases, the less time the firm has to amortize the sunk costs associated with purchasing and adopting new technologies to produce in-house. Therefore, purchasing from market suppliers, who can afford to use the latest technology, becomes relatively cheaper. The predictions of the model are tested using a panel dataset on Spanish firms for the time period 1990 through 2002. In order to address potential endogeneity problems, we use an exogenous proxy for technological change, namely the number of patents granted by the U.S. patent office classified by technological class. We map the technological classes to the Spanish industrial sectors in which the patents are used and provide causal evidence of the impact of expected technological change on the likelihood and extent of production outsourcing. No prior study has been able to provide such causal evidence. Our results are robust to the inclusion of detailed characteristics of the firms as well as firm fixed effects.outsourcing, technological change

Initial data for black hole-neutron star binaries: a flexible, high-accuracy spectral method

We present a new numerical scheme to solve the initial value problem for black hole-neutron star binaries. This method takes advantage of the flexibility and fast convergence of a multidomain spectral representation of the initial data to construct high-accuracy solutions at a relatively low computational cost. We provide convergence tests of the method for both isolated neutron stars and irrotational binaries. In the second case, we show that we can resolve the small inconsistencies that are part of the quasi-equilibrium formulation, and that these inconsistencies are significantly smaller than observed in previous works. The possibility of generating a wide variety of initial data is also demonstrated through two new configurations inspired by results from binary black holes. First, we show that choosing a modified Kerr-Schild conformal metric instead of a flat conformal metric allows for the construction of quasi-equilibrium binaries with a spinning black hole. Second, we construct binaries in low-eccentricity orbits, which are a better approximation to astrophysical binaries than quasi-equilibrium systems.Comment: 19 pages, 11 figures, Modified to match final PRD versio

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.Comment: 16 pages, 5 figure

The shock of the new: ethics, law and the introduction of public access defibrillation

There have been recent moves to include Public Access Defibrillation (PAD) in emergency response strategies. The value of this development is explored in this article. The benefits and limitations of extending AutomaticExternal Defibrillator (AED) use to non-traditional first responders, minimally trained witnesses and citizens are examined and the cost-effectiveness of such developments is discussed. The authors contend that, at the present time, enthusiasm for PAD would seem misplaced and that there is a series of economic, ethical and legal uncertainties that need to be addressed before widespread distribution of AED technology should be pursued

Commentary: “Applying the Rule of Reason in the Post-Actavis World”

In FTC v. Actavis, 133 S. Ct. 2223 (2013), the Supreme Court held that in cases challenging alleged “reverse payment” settlements of patent litigation arising in the context of the Hatch-Waxman Act, the Rule of Reason applies—no per se rules, no quick look, no shortcuts. Actavis arose in the context of a motion to dismiss and explicitly left to the lower courts the task of structuring the Rule of Reason analysis. Following Actavis, how the lower courts should apply the Rule of Reason has been the subject of considerable debate. The FTC and private plaintiffs, as well as law professors aligned with their views, have attempted to find in Actavis justifications for injecting shortcuts and presumptions that would undermine the Court’s clear holdings. Those efforts have thus far been largely rejected in post-Actavis litigation. As we argue, courts should continue to reject such efforts—which rest on presumptions rather than proof—and preserve the integrity of the Rule of Reason

Controlling the growth of constraints in hyperbolic evolution systems

Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems. The first method adjusts the evolution equations dynamically, by adding multiples of the constraints, in a way designed to minimize this growth. The second method imposes special constraint preserving boundary conditions on the incoming components of the dynamical fields. The efficacy of these methods is tested by using them to control the growth of constraints in fully dynamical 3D numerical solutions of a particular representation of the Maxwell equations that is subject to constraint violations. The constraint preserving boundary conditions are found to be much more effective than active constraint control in the case of this Maxwell system

Multi-Color Light Curves of Type Ia Supernovae on the Color-Magnitude Diagram: a Novel Step Toward More Precise Distance and Extinction Estimates

We show empirically that fits to the color-magnitude relation of Type Ia supernovae after optical maximum can provide accurate relative extragalactic distances. We report the discovery of an empirical color relation for Type Ia light curves: During much of the first month past maximum, the magnitudes of Type Ia supernovae defined at a given value of color index have a very small magnitude dispersion; moreover, during this period the relation between $B$ magnitude and $B-V$ color (or $B-R$ or $B-I$ color) is strikingly linear, to the accuracy of existing well-measured data. These linear relations can provide robust distance estimates, in particular, by using the magnitudes when the supernova reaches a given color. After correction for light curve strech factor or decline rate, the dispersion of the magnitudes taken at the intercept of the linear color-magnitude relation are found to be around 0$^m$.08 for the sub-sample of supernovae with \BVm $\le 0^m.05$, and around 0$^m$.11 for the sub-sample with \BVm $\le 0^m.2$. This small dispersion is consistent with being mostly due to observational errors. The method presented here and the conventional light curve fitting methods can be combined to further improve statistical dispersions of distance estimates. It can be combined with the magnitude at maximum to deduce dust extinction. The slopes of the color-magnitude relation may also be used to identify intrinsically different SN Ia systems. The method provides a tool that is fundamental to using SN Ia to estimate cosmological parameters such as the Hubble constant and the mass and dark energy content of the universe.Comment: ApJ, in pres