Distinction of representations via Bruhat-Tits buildings of p-adic groups

Introductory and pedagogical treatmeant of the article : P. Broussous "Distinction of the Steinberg representation", with an appendix by Fran\c{c}ois Court\`es, IMRN 2014, no 11, 3140-3157. To appear in Proceedings of Chaire Jean Morlet, Dipendra Prasad, Volker Heiermann Ed. 2017. Contains modified and simplified proofs of loc. cit. This article is written in memory of Fran\c{c}ois Court\`es who passed away in september 2016.Comment: 33 pages, 4 figure

Conformations of dendrimers in dilute solution

Conformations of isolated homo- dendrimers of G=1-7 generations with D=1-6 spacers have been studied in the good and poor solvents, as well as across the coil-to-globule transition, by means of a version of the Gaussian self-consistent (GSC) method and Monte Carlo (MC) simulation in continuous space based on the same coarse-grained model. The latter includes harmonic springs between connected monomers and the pair-wise Lennard-Jones potential with a hard core repulsion. The scaling law for the dendrimer size, the degrees of bond stretching and steric congestion, as well as the radial density, static structure factor, and asphericity have been analysed. It is also confirmed that while smaller dendrimers have a dense core, larger ones develop a hollow domain at some separation from the centre.Comment: RevTeX, 14 pages, 19 PS figures, Accepted for publication in J. Chem. Phy

Intra-chain correlation functions and shapes of homopolymers with different architectures in dilute solution

We present results of Monte Carlo study of the monomer-monomer correlation functions, static structure factor and asphericity characteristics of a single homopolymer in the coil and globular states for three distinct architectures of the chain: ring, open and star. To rationalise the results we introduce the dimensionless correlation functions rescaled via the corresponding mean-squared distances between monomers. For flexible chains with some architectures these functions exhibit a large degree of universality by falling onto a single or several distinct master curves. In the repulsive regime, where a stretched exponential times a power law form (de Cloizeaux scaling) can be applied, the corresponding exponents $\delta$ and $\theta$ have been obtained. The exponent $\delta=1/\nu$ is found to be universal for flexible strongly repulsive coils and in agreement with the theoretical prediction from improved higher-order Borel-resummed renormalisation group calculations. The short-distance exponents $\theta_{\upsilon}$ of an open flexible chain are in a good agreement with the theoretical predictions in the strongly repulsive regime also. However, increasing the Kuhn length in relation to the monomer size leads to their fast cross-over towards the Gaussian behaviour. Likewise, a strong sensitivity of various exponents $\theta_{ij}$ on the stiffness of the chain, or on the number of arms in star polymers, is observed. The correlation functions in the globular state are found to have a more complicated oscillating behaviour and their degree of universality has been reviewed. Average shapes of the polymers in terms of the asphericity characteristics, as well as the universal behaviour in the static structure factors, have been also investigated.Comment: RevTeX 12 pages, 10 PS figures. Accepted by J. Chem. Phy

Monte Carlo simulations of infinitely dilute solutions of amphiphilic diblock star copolymers

Single-chain Monte Carlo simulations of amphiphilic diblock star copolymers were carried out in continuous space using implicit solvents. Two distinct architectures were studied: stars with the hydrophobic blocks attached to the core, and stars with the polar blocks attached to the core, with all arms being of equal length. The ratio of the lengths of the hydrophobic block to the length of the polar block was varied from 0 to 1. Stars with 3, 6, 9 or 12 arms, each of length 10, 15, 25, 50, 75 and 100 Kuhn segments were analysed. Four distinct types of conformations were observed for these systems. These, apart from studying the snapshots from the simulations, have been quantitatively characterised in terms of the mean-squared radii of gyration, mean-squared distances of monomers from the centre-of-mass, asphericity indices, static scattering form factors in the Kratky representation as well as the intra-chain monomer-monomer radial distribution functions.Comment: 12 pages, 11 ps figures. Accepted for publication in J. Chem. Phy

ATOMIC: An Atlas of Machine Commonsense for If-Then Reasoning

We present ATOMIC, an atlas of everyday commonsense reasoning, organized through 877k textual descriptions of inferential knowledge. Compared to existing resources that center around taxonomic knowledge, ATOMIC focuses on inferential knowledge organized as typed if-then relations with variables (e.g., "if X pays Y a compliment, then Y will likely return the compliment"). We propose nine if-then relation types to distinguish causes vs. effects, agents vs. themes, voluntary vs. involuntary events, and actions vs. mental states. By generatively training on the rich inferential knowledge described in ATOMIC, we show that neural models can acquire simple commonsense capabilities and reason about previously unseen events. Experimental results demonstrate that multitask models that incorporate the hierarchical structure of if-then relation types lead to more accurate inference compared to models trained in isolation, as measured by both automatic and human evaluation.Comment: AAAI 2019 C

A millimeter-wave Bessel beam launcher through the excitation of higher-order leaky modes

International audienceWe present a Bessel beam launcher based on a radial leaky-wave antenna operating at millimeter waves. With respect to a design method proposed by one of the Authors in a lower frequency range, a new approach is chosen here, as an alternative to a simple scaling of all the geometrical parameters. In order to avoid inacceptable levels of losses and possible fabrication issues due to an extremely thin substrate, our design is based on the suitable excitation of a higher-order leaky mode. Closed-form equations are derived in order to simplify the design, providing reliable values for the physical parameters once the near-field characteristics are assigned. Simulated results are shown to validate the proposed procedure

3D Monte Carlo radiation transfer modelling of photodynamic therapy

We acknowledge the support of the UK Engineering and Physics Sciences Research Council (EPSRC) for funding through a studentship for C L Campbell as well as the Alfred Stewart Trust.The effects of ageing and skin type on Photodynamic Therapy (PDT) for different treatment methods have been theoretically investigated. A multilayered Monte Carlo Radiation Transfer model is presented where both daylight activated PDT and conventional PDT are compared. It was found that light penetrates deeper through older skin with a lighter complexion, which translates into a deeper effective treatment depth. The effect of ageing was found to be larger for darker skin types. The investigation further strengthens the usage of daylight as a potential light source for PDT where effective treatment depths of about 2 mm can be achieved.Publisher PD