Turing machines can be efficiently simulated by the General Purpose Analog Computer

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity level, by showing that, modulo polynomial reductions, computations of Turing machines can be simulated by GPACs, without the need of using more (space) resources than those used in the original Turing computation, as long as we are talking about bounded computations. In other words, computations done by the GPAC are as space-efficient as computations done in the context of Computable Analysis

De Sitter Cosmic Strings and Supersymmetry

We study massive spinor fields in the geometry of a straight cosmic string in a de Sitter background. We find a hidden N=2 supersymmetry in the fermionic solutions of the equations of motion. We connect the zero mode solutions to the heat-kernel regularized Witten index of the supersymmetric algebra.Comment: Version similar to the one accepted by General Relativity and Gravitatio

Linear and non-linear perturbations in dark energy models

I review the linear and second-order perturbation theory in dark energy models with explicit interaction to matter in view of applications to N-body simulations and non-linear phenomena. Several new or generalized results are obtained: the general equations for the linear perturbation growth; an analytical expression for the bias induced by a species-dependent interaction; the Yukawa correction to the gravitational potential due to dark energy interaction; the second-order perturbation equations in coupled dark energy and their Newtonian limit. I also show that a density-dependent effective dark energy mass arises if the dark energy coupling is varying.Comment: 12 pages, submitted to Phys. Rev; v2: added a ref. and corrected a typ

A generic estimate of trans-Planckian modifications to the primordial power spectrum in inflation

We derive a general expression for the power spectra of scalar and tensor fluctuations generated during inflation given an arbitrary choice of boundary condition for the mode function at a short distance. We assume that the boundary condition is specified at a short-distance cutoff at a scale $M$ which is independent of time. Using a particular prescription for the boundary condition at momentum $p = M$, we find that the modulation to the power spectra of density and gravitational wave fluctuations is of order $(H/M)$, where $H$ is the Hubble parameter during inflation, and we argue that this behavior is generic, although by no means inevitable. With fixed boundary condition, we find that the shape of the modulation to the power spectra is determined entirely by the deviation of the background spacetime from the de Sitter limit.Comment: 15 pages (RevTeX), 2 figure

Is the evidence for dark energy secure?

Several kinds of astronomical observations, interpreted in the framework of the standard Friedmann-Robertson-Walker cosmology, have indicated that our universe is dominated by a Cosmological Constant. The dimming of distant Type Ia supernovae suggests that the expansion rate is accelerating, as if driven by vacuum energy, and this has been indirectly substantiated through studies of angular anisotropies in the cosmic microwave background (CMB) and of spatial correlations in the large-scale structure (LSS) of galaxies. However there is no compelling direct evidence yet for (the dynamical effects of) dark energy. The precision CMB data can be equally well fitted without dark energy if the spectrum of primordial density fluctuations is not quite scale-free and if the Hubble constant is lower globally than its locally measured value. The LSS data can also be satisfactorily fitted if there is a small component of hot dark matter, as would be provided by neutrinos of mass 0.5 eV. Although such an Einstein-de Sitter model cannot explain the SNe Ia Hubble diagram or the position of the `baryon acoustic oscillation' peak in the autocorrelation function of galaxies, it may be possible to do so e.g. in an inhomogeneous Lemaitre-Tolman-Bondi cosmology where we are located in a void which is expanding faster than the average. Such alternatives may seem contrived but this must be weighed against our lack of any fundamental understanding of the inferred tiny energy scale of the dark energy. It may well be an artifact of an oversimplified cosmological model, rather than having physical reality.Comment: 12 pages, 5 figures; to appear in a special issue of General Relativity and Gravitation, eds. G.F.R. Ellis et al; Changes: references reformatted in journal style - text unchange

Are individuals from thelytokous and arrhenotokous populations equally adept as biocontrol agents? Orientation and host searching behavior of a fruit fly parasitoid

Hymenopteran parasitoids generally reproduce by arrhenotoky, in which males develop from unfertilized eggs and females from fertilized eggs. A minority reproduce by thelytoky, in which all-female broods are derived from unfertilized eggs. Thelytokous populations are potentially of interest for augmentative biological control programs since the exclusive production of females could significantly lower the costs of mass rearing. Behavioral traits are a major component of parasitoid efficacy. Here, we examined orientation and host searching behavior in thelytokous and arrhenotokous populations of the fruit fly parasitoid Odontosema anastrephae Borgmeier (Hymenoptera: Figitidae). Orientation behavior to various odorant sources was studied in a two-choice olfactometer. No major differences were found between thelytokous and arrhenotokous wasps for this behavior. However, when host-searching behaviors were analyzed, some differences were found. Thelytokous females arrived sooner, foraged longer, and remained longer on non-infested guavas than arrhenotokous females. Individuals of both forms exhibited similar stereotyped behavioral sequences vis-Zapotitlán-vis guava treatments, with only slight deviations detected. Our results suggest that individuals from selected thelytokous and arrhenotokous O. anastrephae populations have similar abilities to search for tephritid larvae, supporting the use of thelytokous strains for augmentative releases. Zapotitlán 2011 International Organization for Biological Control (IOBC)

Synchronous Tumors of the Cerebellopontine Angle

Background Synchronous tumors of the cerebellopontine angle (CPA) are very rare and inconsistently described. We present 2 cases of contiguous vestibular schwannoma (VS) and meningioma and a systematic literature review of all multiple CPA tumors. Methods Retrospective chart review and systematic literature review were performed. Results A 64-year-old woman and a 42-year-old man presented with symptoms referable to the CPA. Magnetic resonance imaging in both patients revealed 2 separate contiguous tumors. Retrosigmoid craniotomy and tumor removal in each case confirmed VS and meningioma. Systematic literature review identified 42 previous English-language publications describing 46 patients with multiple CPA tumors. Based on Frassanito criteria, there were 4 concomitant tumors (8%), 16 contiguous tumors (33%), 3 collision tumors (6%), 13 mixed tumors (27%), and 11 tumor-to-tumor metastases (23%). Extent of resection was gross total in 16 cases and subtotal in 16 cases (50% each). Unfavorable House-Brackmann grade III\u2013VI function was documented in 27% overall and in 33% of patients with VS and meningioma, a marked increase from the observed range in isolated VS. Conclusions Multiple CPA tumors are rare, heterogeneous lesions with a marked predisposition toward poor facial nerve outcomes, potentially attributable to a paracrine mechanism that simultaneously drives multiple tumor growth and increases invasiveness or adhesiveness at the facial nerve\u2013tumor interface. Preceding nomenclature has been confounding and inconsistent; we recommend classifying all multiple CPA tumors as \u201csynchronous tumors,\u201d with \u201cschwannoma with meningothelial hyperplasia\u201d or \u201ctumor-to-tumor metastases\u201d reserved for rare, specific circumstances