Generalized quasiperiodic Rauzy tilings

We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change

Generalized Inverse Participation Numbers in Metallic-Mean Quasiperiodic Systems

From the quantum mechanical point of view, the electronic characteristics of quasicrystals are determined by the nature of their eigenstates. A practicable way to obtain information about the properties of these wave functions is studying the scaling behavior of the generalized inverse participation numbers $Z_q \sim N^{-D_q(q-1)}$ with the system size $N$. In particular, we investigate $d$-dimensional quasiperiodic models based on different metallic-mean quasiperiodic sequences. We obtain the eigenstates of the one-dimensional metallic-mean chains by numerical calculations for a tight-binding model. Higher dimensional solutions of the associated generalized labyrinth tiling are then constructed by a product approach from the one-dimensional solutions. Numerical results suggest that the relation $D_q^{d\mathrm{d}} = d D_q^\mathrm{1d}$ holds for these models. Using the product structure of the labyrinth tiling we prove that this relation is always satisfied for the silver-mean model and that the scaling exponents approach this relation for large system sizes also for the other metallic-mean systems.Comment: 7 pages, 3 figure

How to Choose a Champion

League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest number of wins is declared to be the champion. The total number of games needed for the best team to win the championship with high certainty, T, grows as the cube of the number of teams, N, i.e., T ~ N^3. This number can be substantially reduced using preliminary rounds where teams play a small number of games and subsequently, only the top teams advance to the next round. When there are k rounds, the total number of games needed for the best team to emerge as champion, T_k, scales as follows, T_k ~N^(\gamma_k) with gamma_k=1/[1-(2/3)^(k+1)]. For example, gamma_k=9/5,27/19,81/65 for k=1,2,3. These results suggest an algorithm for how to infer the best team using a schedule that is linear in N. We conclude that league format is an ineffective method of determining the best team, and that sequential elimination from the bottom up is fair and efficient.Comment: 6 pages, 3 figure

Karim Hammou, Une histoire du rap en France

Dans la nuit du 29 au 30 décembre 2012, France 2 diffuse Urban music show, une émission célébrant les 30 ans du rap et des musiques dites urbaines en France. C’est à un voyage dans ces trente années (1981-2010) que nous convie le sociologue Karim Hammou. L’ouvrage repose sur un travail de thèse réécrit auquel l’auteur a adjoint de nouvelles parties, composant un ensemble riche. Il est solidement ancré dans un travail empirique et mobilise le cadre théorique développé par Howard Becker (qui s..

Integrating Biological Advances Into the Clinical Management of Breast Cancer Related Lymphedema

Breast cancer-related lymphedema (BCRL) occurs in a significant number of breast cancer survivors as a consequence of the axillary lymphatics' impairment after therapy (mainly axillary surgery and irradiation). Despite the recent achievements in the clinical management of these patients, BCRL is often diagnosed at its occurrence. In most cases, it remains a progressive and irreversible condition, with dramatic consequences in terms of quality of life and on sanitary costs. There are still no validated pre-surgical strategies to identify individuals that harbor an increased risk of BCRL. However, clinical, therapeutic, and tumor-specific traits are recurrent in these patients. Over the past few years, many studies have unraveled the complexity of the molecular and transcriptional events leading to the lymphatic system ontogenesis. Additionally, molecular insights are coming from the study of the germline alterations involved at variable levels in BCRL models. Regrettably, there is a substantial lack of predictive biomarkers for BCRL, given that our knowledge of its molecular milieu remains extremely puzzled. The purposes of this review were (i) to outline the biology underpinning the ontogenesis of the lymphatic system; (ii) to assess the current state of knowledge of the molecular alterations that can be involved in BCRL pathogenesis and progression; (iii) to discuss the present and short-term future perspectives in biomarker-based patients' risk stratification; and (iv) to provide practical information that can be employed to improve the quality of life of these patients

Who is the best player ever? A complex network analysis of the history of professional tennis

We consider all matches played by professional tennis players between 1968 and 2010, and, on the basis of this data set, construct a directed and weighted network of contacts. The resulting graph shows complex features, typical of many real networked systems studied in literature. We develop a diffusion algorithm and apply it to the tennis contact network in order to rank professional players. Jimmy Connors is identified as the best player of the history of tennis according to our ranking procedure. We perform a complete analysis by determining the best players on specific playing surfaces as well as the best ones in each of the years covered by the data set. The results of our technique are compared to those of two other well established methods. In general, we observe that our ranking method performs better: it has a higher predictive power and does not require the arbitrary introduction of external criteria for the correct assessment of the quality of players. The present work provides a novel evidence of the utility of tools and methods of network theory in real applications.Comment: 10 pages, 4 figures, 4 table

On the continuum limit for discrete NLS with long-range lattice interactions

We consider a general class of discrete nonlinear Schroedinger equations (DNLS) on the lattice $h \mathbb{Z}$ with mesh size $h>0$. In the continuum limit when $h \to 0$, we prove that the limiting dynamics are given by a nonlinear Schroedinger equation (NLS) on $\mathbb{R}$ with the fractional Laplacian $(-\Delta)^\alpha$ as dispersive symbol. In particular, we obtain that fractional powers $1/2 < \alpha < 1$ arise from long-range lattice interactions when passing to the continuum limit, whereas NLS with the non-fractional Laplacian $-\Delta$ describes the dispersion in the continuum limit for short-range lattice interactions (e.g., nearest-neighbor interactions). Our results rigorously justify certain NLS model equations with fractional Laplacians proposed in the physics literature. Moreover, the arguments given in our paper can be also applied to discuss the continuum limit for other lattice systems with long-range interactions.Comment: 26 pages; no figures. Some minor revisions. To appear in Comm. Math. Phy

A telerehabilitation approach to chronic facial paralysis in the COVID-19 pandemic scenario: what role for electromyography assessment?

There is a lack of data on patient and diagnostic factors for prognostication of complete recovery in patients with peripheral facial palsy. Thus, the aim of this study was to evaluate the role of a telerehabilitave enhancement through the description of a case report with the use of short-wave diathermy and neuromuscular electrical stimulation combined to facial proprioceptive neuromuscular facilitation (PNF) rehabilitation in unrecovered facial palsy, in a COVID-19 pandemic scenario describing a paradigmatic telerehabilitation report. A 43-year-old woman underwent a facial rehabilitation plan consisting of a synergistic treatment with facial PNF rehabilitation, short-wave diathermy, and neuromuscular electrical stimulation (12 sessions lasting 45 min, three sessions/week for 4 weeks). Concerning the surface electromyography evaluation of frontal and orbicularis oris muscles, the calculated ratio between amplitude of the palsy side and normal side showed an improvement in terms of movement symmetry. At the end of the outpatient treatment, a daily telere-habilitation protocol with video and teleconsultation was provided, showing a further improvement in the functioning of a woman suffering from unresolved facial paralysis. Therefore, an adequate telerehabilitation follow-up seems to play a fundamental role in the management of patients with facial palsy

Energy spectra, wavefunctions and quantum diffusion for quasiperiodic systems

We study energy spectra, eigenstates and quantum diffusion for one- and two-dimensional quasiperiodic tight-binding models. As our one-dimensional model system we choose the silver mean or `octonacci' chain. The two-dimensional labyrinth tiling, which is related to the octagonal tiling, is derived from a product of two octonacci chains. This makes it possible to treat rather large systems numerically. For the octonacci chain, one finds singular continuous energy spectra and critical eigenstates which is the typical behaviour for one-dimensional Schr"odinger operators based on substitution sequences. The energy spectra for the labyrinth tiling can, depending on the strength of the quasiperiodic modulation, be either band-like or fractal-like. However, the eigenstates are multifractal. The temporal spreading of a wavepacket is described in terms of the autocorrelation function C(t) and the mean square displacement d(t). In all cases, we observe power laws for C(t) and d(t) with exponents -delta and beta, respectively. For the octonacci chain, 0<delta<1, whereas for the labyrinth tiling a crossover is observed from delta=1 to 0<delta<1 with increasing modulation strength. Corresponding to the multifractal eigenstates, we obtain anomalous diffusion with 0<beta<1 for both systems. Moreover, we find that the behaviour of C(t) and d(t) is independent of the shape and the location of the initial wavepacket. We use our results to check several relations between the diffusion exponent beta and the fractal dimensions of energy spectra and eigenstates that were proposed in the literature.Comment: 24 pages, REVTeX, 10 PostScript figures included, major revision, new results adde

The underscreened Kondo effect: a two S=1 impurity model

The underscreened Kondo effect is studied within a model of two impurities S=1 interacting with the conduction band and via an interimpurity coupling $K\vec{S_1}.\vec{S_2}$. Using a mean-field treatment of the bosonized Hamiltonian, we show that there is no phase transition, but a continuous cross-over versus K from a non Kondo behaviour to an underscreened Kondo one. For a small antiferromagnetic coupling (K>0), a completely asymmetric situation is obtained with one s=${1/2}$ component strongly screened by the Kondo effect and the other one almost free to yield indirect magnetism, which shows finally a possible coexistence between a RKKY interaction and a local Kondo effect, as observed in Uranium compounds such as $UPt_3$.Comment: 27 pages, RevTeX, to be published in PR