On Maximal Unbordered Factors

Given a string $S$ of length $n$, its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between $n$ and the length of the maximal unbordered factor of $S$. We prove that for the alphabet of size $\sigma \ge 5$ the expected length of the maximal unbordered factor of a string of length~$n$ is at least $0.99 n$ (for sufficiently large values of $n$). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern Matching (CPM 2015

Very fast relaxation in polycarbonate glass

Low-frequency Raman and inelastic neutron scattering of amorphous bis-phenol A polycarbonate is measured at low temperature, and compared. The vibrational density of states and light-vibration coupling coefficient are determined. The frequency dependences of these parameters are explained by propagating vibration modes up to an energy of about 1 meV, and fracton-like modes in more cohesive domains at higher energies. The vibrational dynamics is in agreement with a disorder in the glass, which is principally of bonding or of elasticity instead of density.Comment: 15 pages, 6 figures, to be pub. in EPJ

Equivariant quantization of orbifolds

Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces... In this work, we prove existence of an equivariant quantization for orbifolds. Our construction combines an appropriate desingularization of any Riemannian orbifold by a foliated smooth manifold, with the foliated equivariant quantization that we built in \cite{PoRaWo}. Further, we suggest definitions of the common geometric objects on orbifolds, which capture the nature of these spaces and guarantee, together with the properties of the mentioned foliated resolution, the needed correspondences between singular objects of the orbifold and the respective foliated objects of its desingularization.Comment: 13 page

Twist Deformation of Rotationally Invariant Quantum Mechanics

Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally-invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential) and the Coulomb potential.Comment: 20 page

Projectively equivariant quantizations over the superspace Rp∣q\R^{p|q}

We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra pgl(p+1|q) is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields.Comment: 19 page

Effect of physical aging on the low-frequency vibrational density of states of a glassy polymer

The effects of the physical aging on the vibrational density of states (VDOS) of a polymeric glass is studied. The VDOS of a poly(methyl methacrylate) glass at low-energy (<15 meV), was determined from inelastic neutron scattering at low-temperature for two different physical thermodynamical states. One sample was annealed during a long time at temperature lower than Tg, and another was quenched from a temperature higher than Tg. It was found that the VDOS around the boson peak, relatively to the one at higher energy, decreases with the annealing at lower temperature than Tg, i.e., with the physical aging.Comment: To be published in Europhys. Let

AUTOMATIC BLOB FITTING IN COMPREHENSIVE TWO-DIMENSIONAL GAS CHROMATOGRAPHY IMAGES

Two-dimensional gas chromatography is a recent technology which is particularly efficient for detailed molecular analysis. However, due to the novelty of the method and the lack of automated analysis tools, quantitative data processing is often performed manually. Hence, results are strongly user-dependent, time consuming and, consequently, relatively inaccurate In this paper, we extend conventional techniques for signal analysis by utilizing specific characteristics of chromatographic data and by developing new methods for estimating the quantitative contribution of chemical regions from the produced images. Data-driven information is retrieved from chemical quantitative analysis based on Savitzky-Golay automatic peaks location determination, which increases both the processing speed and the analysis efficiency and improves our confidence in experimental repeatability. 1

Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect

Our previous ``exotic'' particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor $g$) are reviewed. The non-relativistic limit of the anyon generalizes the exotic particle which has $g=0$ to any $g$.When put into planar electric and magnetic fields, the Hall effect becomes mandatory for all $g\neq2$, when the field takes some critical value.Comment: A new reference added. Talk given by P. Horvathy at the International Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli (Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no figure

The PCIe-based readout system for the LHCb experiment

International audienceThe LHCb experiment is designed to study differences between particles and anti-particles as well as very rare decays in the beauty and charm sector at the LHC. The detector will be upgraded in 2019 in order to significantly increase its efficiency, by removing the first-level hardware trigger. The upgrade experiment will implement a trigger-less readout system in which all the data from every LHC bunch-crossing are transported to the computing farm over 12000 optical links without hardware filtering. The event building and event selection are carried out entirely in the farm. Another original feature of the system is that data transmitted through these fibres arrive directly to computers through a specially designed PCIe card called PCIe40. The same board handles the data acquisition flow and the distribution of fast and slow controls to the detector front-end electronics. It embeds one of the most powerful FPGAs currently available on the market with 1.2 million logic cells. The board has a bandwidth of 480 Gbits/s in both input and output over optical links and 100 Gbits/s over the PCI Express bus to the CPU. We will present how data circulate through the board and in the PC server for achieving the event building. We will focus on specific issues regarding the design of such a board with a very large FPGA, in particular in terms of power supply dimensioning and thermal simulations. The features of the board will be detailed and we will finally present the first performance measurement

Low-energy vibrational density of states of plasticized poly(methyl methacrylate)

The low-energy vibrational density of states (VDOS)of hydrogenated or deuterated poly(methyl methacrylate)(PMMA)plasticized by dibutyl phtalate (DBP) is determined by inelastic neutron scattering.From experiment, it is equal to the sum of the ones of the PMMA and DBP components.However, a partition of the total low-energy VDOS among PMMA and DBP was observed.Contrary to Raman scattering, neutron scattering does not show enhancement of the boson peak due to plasticization.Comment: 9 pages, 2 figures (Workshop on Disordered Systems, Andalo