Comparison of max-plus automata and joint spectral radius of tropical matrices

Weighted automata over the max-plus semiring S are closely related to finitely generated semigroups of matrices over S. In this paper, we use results in automata theory to study two quantities associated with sets of matrices: the joint spectral radius and the ultimate rank. We prove that these two quantities are not computable over the tropical semiring, i.e. there is no algorithm that takes as input a finite set of matrices M and provides as output the joint spectral radius (resp. the ultimate rank) of M. On the other hand, we prove that the joint spectral radius is nevertheless approximable and we exhibit restricted cases in which the joint spectral radius and the ultimate rank are computable. To reach this aim, we study the problem of comparing functions computed by weighted automata over the tropical semiring. This problem is known to be undecidable and we prove that it remains undecidable in some specific subclasses of automata

Which Classes of Origin Graphs Are Generated by Transducers.

We study various models of transducers equipped with origin information. We consider the semantics of these models as particular graphs, called origin graphs, and we characterise the families of such graphs recognised by streaming string transducers

Undecidability of a weak version of MSO+U

We prove the undecidability of MSO on ω-words extended with the second-order predicate U1(X) which says that the distance between consecutive positions in a set X⊆N is unbounded. This is achieved by showing that adding U1 to MSO gives a logic with the same expressive power as MSO+U, a logic on ω-words with undecidable satisfiability. As a corollary, we prove that MSO on ω-words becomes undecidable if allowing to quantify over sets of positions that are ultimately periodic, i.e., sets X such that for some positive integer p, ultimately either both or none of positions x and x+p belong to X

Synthesis of molecularly imprinted polymer for glucose binding

Molecularly imprinted polymer (MIP) is an attractive technique for the synthesis of highly selective polymeric receptors having artificial generated recognition sites. These materials were synthesized with polymerizable functional monomers and crosslinker that were surrounded around the template molecule. After polymerization, a template molecule was removed leaving in the polymer selective recognition sites with shape, size and functionalities complementary to the template. This study presents a synthesis of MIP selectively for glucose binding. Glucose phosphate salt (GPS) was used as a template molecule with poly(allylamine hydrochloride) (PAA.HCl) as a functional monomer. Three types of crosslinkers which are epichlorohydrin (EPI), ethylene glycol diglycidyl ether (EDGE) and glycerol diglycidyl ether (GDE) were studied during the MIP synthesis. MIP prepared using EPI as a crosslinking showed the highest glucose binding capacity around 0.84 mg glucose/mg dried gel. The binding capacity of MIP prepared using EGDE and GDE are 0.78 mg glucose/mg gel and 0.38 mg glucose/mg gel respectively. It is also found that the increase on GPS monomer concentration will contribute to increase in glucose bindin

Collapse of optical binding under secondary irradiation

When an optically trapped and bound micrometer-sized chain of particles is subjected to a suitably oriented secondary laser beam above a threshold level of intensity, the structure will collapse. The effect arises from modifications to the interparticle energy landscapes owing to the superposition of optically induced potentials. From the theory it also emerges that, for particles separated by near-field distances, optically induced assemblies may be continuously transformed between linear, spherical, and lamellar forms. The results show scope for the optical fabrication of moldable nanoscale structures

Interparticle interactions:Energy potentials, energy transfer, and nanoscale mechanical motion in response to optical radiation

In the interactions between particles of material with slightly different electronic levels, unusually large shifts in the pair potential can result from photoexcitation, and on subsequent electronic excitation transfer. To elicit these phenomena, it is necessary to understand the fundamental differences between a variety of optical properties deriving from dispersion interactions, and processes such as resonance energy transfer that occur under laser irradiance. This helps dispel some confusion in the recent literature. By developing and interpreting the theory at a deeper level, one can anticipate that in suitable systems, light absorption and energy transfer will be accompanied by significant displacements in interparticle separation, leading to nanoscale mechanical motion

Development of a quality assurance process for the SoLid experiment

The SoLid experiment has been designed to search for an oscillation pattern induced by a light sterile neutrino state, utilising the BR2 reactor of SCK circle CEN, in Belgium. The detector leverages a new hybrid technology, utilising two distinct scintillators in a cubic array, creating a highly segmented detector volume. A combination of 5 cm cubic polyvinyltoluene cells, with (LiF)-Li-6:ZnS(Ag) sheets on two faces of each cube, facilitate reconstruction of the neutrino signals. Whilst the high granularity provides a powerful toolset to discriminate backgrounds; by itself the segmentation also represents a challenge in terms of homogeneity and calibration, for a consistent detector response. The search for this light sterile neutrino implies a sensitivity to distortions of around O(10)% in the energy spectrum of reactor (v) over bare. Hence, a very good neutron detection efficiency, light yield and homogeneous detector response are critical for data validation. The minimal requirements for the SoLid physics program are a light yield and a neutron detection efficiency larger than 40 PA/MeV/cube and 50% respectively. In order to guarantee these minimal requirements, the collaboration developed a rigorous quality assurance process for all 12800 cubic cells of the detector. To carry out the quality assurance process, an automated calibration system called CALIPSO was designed and constructed. CALIPSO provides precise, automatic placement of radioactive sources in front of each cube of a given detector plane (16 x 16 cubes). A combination of Na-22, Cf-252 and AmBe gamma and neutron sources were used by CALIPSO during the quality assurance process. Initially, the scanning identified defective components allowing for repair during initial construction of the SoLid detector. Secondly, a full analysis of the calibration data revealed initial estimations for the light yield of over 60 PA/MeV and neutron reconstruction efficiency of 68%, validating the SoLid physics requirements

G0^0 Electronics and Data Acquisition (Forward-Angle Measurements)

The G$^0$ parity-violation experiment at Jefferson Lab (Newport News, VA) is designed to determine the contribution of strange/anti-strange quark pairs to the intrinsic properties of the proton. In the forward-angle part of the experiment, the asymmetry in the cross section was measured for $\vec{e}p$ elastic scattering by counting the recoil protons corresponding to the two beam-helicity states. Due to the high accuracy required on the asymmetry, the G$^0$ experiment was based on a custom experimental setup with its own associated electronics and data acquisition (DAQ) system. Highly specialized time-encoding electronics provided time-of-flight spectra for each detector for each helicity state. More conventional electronics was used for monitoring (mainly FastBus). The time-encoding electronics and the DAQ system have been designed to handle events at a mean rate of 2 MHz per detector with low deadtime and to minimize helicity-correlated systematic errors. In this paper, we outline the general architecture and the main features of the electronics and the DAQ system dedicated to G$^0$ forward-angle measurements.Comment: 35 pages. 17 figures. This article is to be submitted to NIM section A. It has been written with Latex using \documentclass{elsart}. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment In Press (2007

Energy Linearity and Resolution of the ATLAS Electromagnetic Barrel Calorimeter in an Electron Test-Beam

A module of the ATLAS electromagnetic barrel liquid argon calorimeter was exposed to the CERN electron test-beam at the H8 beam line upgraded for precision momentum measurement. The available energies of the electron beam ranged from 10 to 245 GeV. The electron beam impinged at one point corresponding to a pseudo-rapidity of eta=0.687 and an azimuthal angle of phi=0.28 in the ATLAS coordinate system. A detailed study of several effects biasing the electron energy measurement allowed an energy reconstruction procedure to be developed that ensures a good linearity and a good resolution. Use is made of detailed Monte Carlo simulations based on Geant which describe the longitudinal and transverse shower profiles as well as the energy distributions. For electron energies between 15 GeV and 180 GeV the deviation of the measured incident electron energy over the beam energy is within 0.1%. The systematic uncertainty of the measurement is about 0.1% at low energies and negligible at high energies. The energy resolution is found to be about 10% sqrt(E) for the sampling term and about 0.2% for the local constant term

Results of the BiPo-1 prototype for radiopurity measurements for the SuperNEMO double beta decay source foils

The development of BiPo detectors is dedicated to the measurement of extremely high radiopurity in $^{208}$Tl and $^{214}$Bi for the SuperNEMO double beta decay source foils. A modular prototype, called BiPo-1, with 0.8 $m^2$ of sensitive surface area, has been running in the Modane Underground Laboratory since February, 2008. The goal of BiPo-1 is to measure the different components of the background and in particular the surface radiopurity of the plastic scintillators that make up the detector. The first phase of data collection has been dedicated to the measurement of the radiopurity in $^{208}$Tl. After more than one year of background measurement, a surface activity of the scintillators of $\mathcal{A}$($^{208}$Tl) $=$ 1.5 $\mu$Bq/m$^2$ is reported here. Given this level of background, a larger BiPo detector having 12 m$^2$ of active surface area, is able to qualify the radiopurity of the SuperNEMO selenium double beta decay foils with the required sensitivity of $\mathcal{A}$($^{208}$Tl) $<$ 2 $\mu$Bq/kg (90% C.L.) with a six month measurement.Comment: 24 pages, submitted to N.I.M.