On the Length of Medial-Switch-Mix Derivations

International audienceSwitch and medial are two inference rules that play a central role in many deep inference proof systems. In specific proof systems, the mix rule may also be present. In this paper we show that the maximal length of a derivation using only the inference rules for switch, medial, and mix, modulo associativity and commutativity of the two binary con-nectives involved, is quadratic in the size of the formula at the conclusion of the derivation. This shows, at the same time, the termination of the rewrite system

A System of Interaction and Structure

This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae submitted to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allow the design of BV, yield a modular proof of cut elimination.Comment: This is the authoritative version of the article, with readable pictures, in colour, also available at . (The published version contains errors introduced by the editorial processing.) Web site for Deep Inference and the Calculus of Structures at <http://alessio.guglielmi.name/res/cos

On the proof complexity of deep inference

International audienceWe obtain two results about the proof complexity of deep inference: (1) Deep-inference proof systems are as powerful as Frege ones, even when both are extended with the Tseitin extension rule or with the substitution rule; (2) there are analytic deep-inference proof systems that exhibit an exponential speedup over analytic Gentzen proof systems that they polynomially simulate

Model-Independent Reionization Observables in the CMB

We represent the reionization history of the universe as a free function in redshift and study the potential for its extraction from CMB polarization spectra. From a principal component analysis, we show that the ionization history information is contained in 5 modes, resembling low-order Fourier modes in redshift space. The amplitude of these modes represent a compact description of the observable properties of reionization in the CMB, easily predicted given a model for the ionization fraction. Measurement of these modes can ultimately constrain the total optical depth, or equivalently the initial amplitude of fluctuations to the 1% level regardless of the true model for reionization.Comment: 4 pages, 5 figures, submitted to PRD (rapid communications

Cosmic Microwave Background Polarization and reionization: constraining models with a double reionization

Neutral hydrogen around high-z QSO and an optical depth tau ~ 0.17 can be reconciled if reionization is more complex than a single transition at z ~ 6-8. Tracing its details could shed a new light on the first sources of radiation. Here we discuss how far such details can be inspected through planned experiments on CMB large-scale anisotropy and polarization, by simulating an actual data analysis. By considering a set of double reionization histories of Cen (2003) type, a relevant class of models not yet considered by previous works, we confirm that large angle experiments rival high resolution ones in reconstructing the reionization history. We also confirm that reionization histories, studied with the prior of a single and sharp reionization, yield a biased tau, showing that this bias is generic. We further find a monotonic trend in the bias for the models that we consider, and propose an explanation of the trend, as well as the overall bias. We also show that in long-lived experiments such a trend can be used to discriminate between single and double reionization patterns.Comment: 8 pages, 11 figures. Substantial rewriting, replaced with accepted version. To be published in A&

Development of a loop-mediated isothermal amplification (LAMP) assay for the identification of the invasive wood borer Aromia bungii (Coleoptera: Cerambycidae) from frass

The red-necked longhorn beetle Aromia bungii (Faldermann, 1835) (Coleoptera: Cerambycidae) is native to east Asia, where it is a major pest of cultivated and ornamental species of the genus Prunus. Morphological or molecular discrimination of adults or larval specimens is required to identify this invasive wood borer. However, recovering larval stages of the pest from trunks and branches causes extensive damage to plants and is timewasting. An alternative approach consists in applying non-invasive molecular diagnostic tools to biological traces (i.e., fecal pellets, frass). In this way, infestations in host plants can be detected without destructive methods. This paper presents a protocol based on both real-time and visual loop-mediated isothermal amplification (LAMP), using DNA of A. bungii extracted from fecal particles in larval frass. Laboratory validations demonstrated the robustness of the protocols adopted and their reliability was confirmed performing an inter-lab blind panel. The LAMP assay and the qPCR SYBR Green method using the F3/B3 LAMP external primers were equally sensitive, and both were more sensitive than the conventional PCR (sensitivity > 103 to the same starting matrix). The visual LAMP protocol, due to the relatively easy performance of the method, could be a useful tool to apply in rapid monitoring of A. bungii and in the management of its outbreaks

Physical effects on the Lyman-alpha forest flux power spectrum: damping wings, ionizing radiation fluctuations, and galactic winds

We explore several physical effects on the power spectrum of the Lyman-alpha forest transmitted flux. The effects we investigate here are usually not part of hydrodynamic simulations and so need to be estimated separately. The most important effect is that of high column density absorbers with damping wings, which add power on large scales. We compute their effect using the observational constraints on their abundance as a function of column density. Ignoring their effect leads to an underestimation of the slope of the linear theory power spectrum. The second effect we investigate is that of fluctuations in the ionizing radiation field. For this purpose we use a very large high resolution N-body simulation, which allows us to simulate both the fluctuations in the ionizing radiation and the small scale LyaF within the same simulation. We find an enhancement of power on large scales for quasars and a suppression for galaxies. The strength of the effect rapidly increases with increasing redshift, allowing it to be uniquely identified in cases where it is significant. We develop templates which can be used to search for this effect as a function of quasar lifetime, quasar luminosity function, and attenuation length. Finally, we explore the effects of galactic winds using hydrodynamic simulations. We find the wind effects on the LyaF power spectrum to be be degenerate with parameters related to the temperature of the gas that are already marginalized over in cosmological fits. While more work is needed to conclusively exclude all possible systematic errors, our results suggest that, in the context of data analysis procedures where parameters of the LyaF model are properly marginalized over, the flux power spectrum is a reliable tracer of cosmological information.Comment: 13 pages, 8 figures, to be submitted to MNRA

Limits on the detectability of the CMB B-mode polarization imposed by foregrounds

We investigate which practical constraints are imposed by foregrounds to the detection of the B-mode polarization generated by gravitational waves in the case of experiments of the type currently being planned. Because the B-mode signal is probably dominated by foregrounds at all frequencies, the detection of the cosmological component depends drastically on our ability for removing foregrounds. We provide an analytical expression to estimate the level of the residual polarization for Galactic foregrounds, according to the method employed for their subtraction. We interpret this result in terms of the lower limit of the tensor-to-scalar ratio r that allows to disentangle the cosmological B-mode polarization from the foregrounds contribution. Polarized emission from extragalactic radio sources and gravitational lensing is also taken into account. As a first approach, we consider the ideal limit of an instrumental noise--free experiment: for a full--sky coverage and a degree resolution, we obtain a limit of r~10^(-4). This value can be improved by high--resolution experiments and, in principle, no clear fundamental limit on the detectability of gravitational waves polarization is found. Our analysis is also applied to planned or hypothetical future polarization experiments, taking into account expected noise levels.Comment: 15 pages, 9 figures, version accepted for publication in MNRA

Foregrounds for observations of the cosmological 21 cm line: I. First Westerbork measurements of Galactic emission at 150 MHz in a low latitude field

We present the first results from a series of observations conducted with the Westerbork telescope in the 140--160 MHz range with a 2 arcmin resolution aimed at characterizing the properties of the foregrounds for epoch of reionization experiments. For the first time we have detected fluctuations in the Galactic diffuse emission on scales greater than 13 arcmin at 150 MHz, in the low Galactic latitude area known as Fan region. Those fluctuations have an $rms$ of 14 K. The total intensity power spectrum shows a power--law behaviour down to $\ell \sim 900$ with slope $\beta^I_\ell = -2.2 \pm 0.3$. The detection of diffuse emission at smaller angular scales is limited by residual point sources. We measured an $rms$ confusion noise of $\sim$3 mJy beam$^{-1}$. Diffuse polarized emission was also detected for the first time at this frequency. The polarized signal shows complex structure both spatially and along the line of sight. The polarization power spectrum shows a power--law behaviour down to $\ell \sim 2700$ with slope $\beta^P_\ell = -1.65 \pm 0.15$. The $rms$ of polarization fluctuations is 7.2 K on 4 arcmin scales. By extrapolating the measured spectrum of total intensity emission, we find a contamination on the cosmological signal of $\delta T= \sqrt{\ell (\ell+1) C^I_\ell / 2\pi} \sim 5.7$ K on 5 arcmin scales and a corresponding $rms$ value of $\sim$18.3 K at the same angular scale. The level of the polarization power spectrum is $\delta T \sim 3.3$ K on 5 arcmin scales. Given its exceptionally bright polarized signal, the Fan region is likely to represent an upper limit on the sky brightness at moderate and high Galactic latitude.Comment: Minor corrections made to match the final version printed on A&A. A version with high resolution figures is available at http://www.astro.rug.nl/~bernardi/FAN/fan.pd