Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.Comment: Submitted to the conference DLT201

On the Number of Closed Factors in a Word

A closed word (a.k.a. periodic-like word or complete first return) is a word whose longest border does not have internal occurrences, or, equivalently, whose longest repeated prefix is not right special. We investigate the structure of closed factors of words. We show that a word of length $n$ contains at least $n+1$ distinct closed factors, and characterize those words having exactly $n+1$ closed factors. Furthermore, we show that a word of length $n$ can contain $\Theta(n^{2})$ many distinct closed factors.Comment: Accepted to LATA 201

Electronic and structural reconstructions of the polar (111) SrTiO3 surface

Polar surfaces are known to be unstable due to the divergence of the surface electrostatic energy. Here we report on the experimental determination, by grazing incidence x-ray diffraction, of the surface structure of polar Ti-terminated (111) SrTiO3 single crystals. We find that the polar instability of the 1 x 1 surface is solved by a pure electronic reconstruction mechanism, which induces out-of-plane ionic displacements typical of the polar response of SrTiO3 layers to an electron confining potential. On the other hand, the surface instability can be also eliminated by a structural reconstruction driven by a change in the surface stoichiometry, which induces a variety of 3 x 3 (111) SrTiO3 surfaces consisting in an incomplete Ti (surface)-O-2 (subsurface) layer covering the 1 x 1 Ti-terminated (111) SrTiO3 truncated crystal. In both cases, the TiO6 octahedra are characterized by trigonal distortions affecting the structural and the electronic symmetry of several unit cells from the surface. These findings show that the stabilization of the polar (111) SrTiO3 surface can lead to the formation of quasi two-dimensional electron systems characterized by radically different ground states which depend on the surface reconstructions

Calibration and First light of the Diabolo photometer at the Millimetre and Infrared Testa Grigia Observatory

We have designed and built a large-throughput dual channel photometer, Diabolo. This photometer is dedicated to the observation of millimetre continuum diffuse sources, and in particular, of the Sunyaev-Zel'dovich effect and of anisotropies of the 3K background. We describe the optical layout and filtering system of the instrument, which uses two bolometric detectors for simultaneous observations in two frequency channels at 1.2 and 2.1 mm. The bolometers are cooled to a working temperature of 0.1 K provided by a compact dilution cryostat. The photometric and angular responses of the instrument are measured in the laboratory. First astronomical light was detected in March 1995 at the focus of the new Millimetre and Infrared Testa Grigia Observatory (MITO) Telescope. The established sensitivity of the system is of 7 mK_RJ s^1/2$. For a typical map of at least 10 beams, with one hour of integration per beam, one can achieve the rms values of y_SZ ~ 7 10^-5 and the 3K background anisotropy Delta T/T ~ 7 10^-5, in winter conditions. We also report on a novel bolometer AC readout circuit which allows for the first time total power measurements on the sky. This technique alleviates (but does not forbid) the use of chopping with a secondary mirror. This technique and the dilution fridge concept will be used in future scan--modulated space instrument like the ESA Planck mission project.Comment: 10 pages, LaTeX, 12 figures, accepted for publication in Astronomy and Astrophysics Supplement Serie

Algebraic coarsening in voter models with intermediate states

The introduction of intermediate states in the dynamics of the voter model modifies the ordering process and restores an effective surface tension. The logarithmic coarsening of the conventional voter model in two dimensions is eliminated in favour of an algebraic decay of the density of interfaces with time, compatible with Model A dynamics at low temperatures. This phenomenon is addressed by deriving Langevin equations for the dynamics of appropriately defined continuous fields. These equations are analyzed using field theoretical arguments and by means of a recently proposed numerical technique for the integration of stochastic equations with multiplicative noise. We find good agreement with lattice simulations of the microscopic model.Comment: 11 pages, 5 figures; minor typos correcte

On Words with the Zero Palindromic Defect

We study the set of finite words with zero palindromic defect, i.e., words rich in palindromes. This set is factorial, but not recurrent. We focus on description of pairs of rich words which cannot occur simultaneously as factors of a longer rich word

Identification of backgrounds in the EDELWEISS-I dark matter search experiment

This paper presents our interpretation and understanding of the different backgrounds in the EDELWEISS-I data sets. We analyze in detail the several populations observed, which include gammas, alphas, neutrons, thermal sensor events and surface events, and try to combine all data sets to provide a coherent picture of the nature and localisation of the background sources. In light of this interpretation, we draw conclusions regarding the background suppression scheme for the EDELWEISS-II phase

Measurement of the response of heat-and-ionization germanium detectors to nuclear recoils

The heat quenching factor Q' (the ratio of the heat signals produced by nuclear and electron recoils of equal energy) of the heat-and-ionization germanium bolometers used by the EDELWEISS collaboration has been measured. It is explained how this factor affects the energy scale and the effective quenching factor observed in calibrations with neutron sources. This effective quenching effect is found to be equal to Q/Q', where Q is the quenching factor of the ionization yield. To measure Q', a precise EDELWEISS measurement of Q/Q' is combined with values of Q obtained from a review of all available measurements of this quantity in tagged neutron beam experiments. The systematic uncertainties associated with this method to evaluate Q' are discussed in detail. For recoil energies between 20 and 100 keV, the resulting heat quenching factor is Q' = 0.91+-0.03+-0.04, where the two errors are the contributions from the Q and Q/Q' measurements, respectively. The present compilation of Q values and evaluation of Q' represent one of the most precise determinations of the absolute energy scale for any detector used in direct searches for dark matter.Comment: 28 pages, 7 figures. Submitted to Phys. Rev.

The (un)resolved X-ray background in the Lockman Hole

Most of the soft and a growing fraction of the harder X-ray background has been resolved into emission from point sources, yet the resolved fraction above 7 keV has only been poorly constrained. We use ~700 ks of XMM-Newton observations of the Lockman Hole and a photometric approach to estimate the total flux attributable to resolved sources in a number of different energy bands. We find the resolved fraction of the X-ray background to be ~90 per cent below 2 keV but it decreases rapidly at higher energies with the resolved fraction above ~7 keV being only ~50 per cent. The integrated X-ray spectrum from detected sources has a slope of Gamma~1.75, much softer than the Gamma=1.4 of the total background spectrum. The unresolved background component has the spectral signature of highly obscured AGN.Comment: 6 pages, 6 figures, MNRAS Letters, in press, changed to reflect accepted versio

Hybrid Newton-type method for a class of semismooth equations

In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problem