Self-avoiding trails with nearest neighbour interactions on the square lattice

Self-avoiding walks and self-avoiding trails, two models of a polymer coil in dilute solution, have been shown to be governed by the same universality class. On the other hand, self-avoiding walks interacting via nearest-neighbour contacts (ISAW) and self-avoiding trails interacting via multiply-visited sites (ISAT) are two models of the coil-globule, or collapse transition of a polymer in dilute solution. On the square lattice it has been established numerically that the collapse transition of each model lies in a different universality class. The models differ in two substantial ways. They differ in the types of subsets of random walk configurations utilised (site self-avoidance versus bond self-avoidance) and in the type of attractive interaction. It is therefore of some interest to consider self-avoiding trails interacting via nearest neighbour attraction (INNSAT) in order to ascertain the source for the difference in the collapse universality class. Using the flatPERM algorithm, we have performed computer simulations of this model. We present numerical evidence that the singularity in the free energy of INNSAT at the collapse transition has a similar exponent to that of the ISAW model rather than the ISAT model. This would indicate that the type of interaction used in ISAW and ISAT is the source of the difference in universality class.Comment: 14 pages, 7 figure

The role of three-body interactions in two-dimensional polymer collapse

Various interacting lattice path models of polymer collapse in two dimensions demonstrate different critical behaviours. This difference has been without a clear explanation. The collapse transition has been variously seen to be in the Duplantier-Saleur $\theta$-point university class (specific heat cusp), the interacting trail class (specific heat divergence) or even first-order. Here we study via Monte Carlo simulation a generalisation of the Duplantier-Saleur model on the honeycomb lattice and also a generalisation of the so-called vertex-interacting self-avoiding walk model (configurations are actually restricted trails known as grooves) on the triangular lattice. Crucially for both models we have three and two body interactions explicitly and differentially weighted. We show that both models have similar phase diagrams when considered in these larger two-parameter spaces. They demonstrate regions for which the collapse transition is first-order for high three body interactions and regions where the collapse is in the Duplantier-Saleur $\theta$-point university class. We conjecture a higher order multiple critical point separating these two types of collapse.Comment: 17 pages, 20 figure

Correlated Component Analysis for diffuse component separation with error estimation on simulated Planck polarization data

We present a data analysis pipeline for CMB polarization experiments, running from multi-frequency maps to the power spectra. We focus mainly on component separation and, for the first time, we work out the covariance matrix accounting for errors associated to the separation itself. This allows us to propagate such errors and evaluate their contributions to the uncertainties on the final products.The pipeline is optimized for intermediate and small scales, but could be easily extended to lower multipoles. We exploit realistic simulations of the sky, tailored for the Planck mission. The component separation is achieved by exploiting the Correlated Component Analysis in the harmonic domain, that we demonstrate to be superior to the real-space application (Bonaldi et al. 2006). We present two techniques to estimate the uncertainties on the spectral parameters of the separated components. The component separation errors are then propagated by means of Monte Carlo simulations to obtain the corresponding contributions to uncertainties on the component maps and on the CMB power spectra. For the Planck polarization case they are found to be subdominant compared to noise.Comment: 17 pages, accepted in MNRA

A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N=100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the exponential running time ~ exp(0.245 N) provided by the hitherto best known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded. Version 3 shows that the worst-case running time is sub-exponential in the number of vertice

Fixture-abutment connection surface and micro-gap measurements by 3D micro-tomographic technique analysis

X-ray micro-tomography (micro-CT) is a miniaturized form of conventional computed axial tomography (CAT) able to investigate small radio-opaque objects at a-few-microns high resolution, in a non-destructive, non-invasive, and tri-dimensional way. Compared to traditional optical and electron microscopy techniques, which provide two-dimensional images, this innovative investigation technology enables a sample tri-dimensional analysis without cutting, coating or exposing the object to any particular chemical treatment. X-ray micro-tomography matches ideal 3D microscopy features: the possibility of investigating an object in natural conditions and without any preparation or alteration; non-invasive, non-destructive, and sufficiently magnified 3D reconstruction; reliable measurement of numeric data of the internal structure (morphology, structure and ultra-structure). Hence, this technique has multi-fold applications in a wide range of fields, not only in medical and odontostomatologic areas, but also in biomedical engineering, materials science, biology, electronics, geology, archaeology, oil industry, and semi-conductors industry. This study shows possible applications of micro-CT in dental implantology to analyze 3D micro-features of dental implant to abutment interface. Indeed, implant-abutment misfit is known to increase mechanical stress on connection structures and surrounding bone tissue. This condition may cause not only screw preload loss or screw fracture, but also biological issues in peri-implant tissues

Neural networks and separation of Cosmic Microwave Background and astrophysical signals in sky maps

The Independent Component Analysis (ICA) algorithm is implemented as a neural network for separating signals of different origin in astrophysical sky maps. Due to its self-organizing capability, it works without prior assumptions on the signals, neither on their frequency scaling, nor on the signal maps themselves; instead, it learns directly from the input data how to separate the physical components, making use of their statistical independence. To test the capabilities of this approach, we apply the ICA algorithm on sky patches, taken from simulations and observations, at the microwave frequencies, that are going to be deeply explored in a few years on the whole sky, by the Microwave Anisotropy Probe (MAP) and by the {\sc Planck} Surveyor Satellite. The maps are at the frequencies of the Low Frequency Instrument (LFI) aboard the {\sc Planck} satellite (30, 44, 70 and 100 GHz), and contain simulated astrophysical radio sources, Cosmic Microwave Background (CMB) radiation, and Galactic diffuse emissions from thermal dust and synchrotron. We show that the ICA algorithm is able to recover each signal, with precision going from 10% for the Galactic components to percent for CMB; radio sources are almost completely recovered down to a flux limit corresponding to $0.7\sigma_{CMB}$, where $\sigma_{CMB}$ is the rms level of CMB fluctuations. The signal recovering possesses equal quality on all the scales larger then the pixel size. In addition, we show that the frequency scalings of the input signals can be partially inferred from the ICA outputs, at the percent precision for the dominant components, radio sources and CMB.Comment: 15 pages; 6 jpg and 1 ps figures. Final version to be published in MNRA