Critical connectedness of thin arithmetical discrete planes

An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully subtractive algorithm. This multidimensional continued fraction algorithm consists, in its linear form, in subtracting the smallest entry to the other ones. We provide a characterization of the discrete planes with critical thickness that have zero intercept and that are $2$-connected. Our tools rely on the notion of dual substitution which is a geometric version of the usual notion of substitution acting on words. We associate with the fully subtractive algorithm a set of substitutions whose incidence matrix is provided by the matrices of the algorithm, and prove that their geometric counterparts generate arithmetic discrete planes.Comment: 18 pages, v2 includes several corrections and is a long version of the DGCI extended abstrac

Connectivity percolation in suspensions of hard platelets

We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single--particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rod-like particles, we find that for hard plate-like particles the percolation threshold is non-monotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition pre-empting the percolation transition. Hence the common strategy to use highly anisotropic, conductive particles as fillers in composite materials in order to produce conduction at low filler concentration is expected to fail for plate-like fillers such as graphene and graphite nanoplatelets

A note on the abelian sandpile in Z^d

We analyse the abelian sandpile model on \mathbbm{Z}^d for the starting configuration of $n$ particles in the origin and $2d-2$ particles otherwise. We give a new short proof of the theorem of Fey, Levine and Peres \cite{FLP} that the radius of the toppled cluster of this configuration is $O(n^{1/d})$

Can statisticians beat surgeons at the planning of operations?

The planning of operations in the Academic Medical Center is primarily based on the assessments of the length of the operation by the surgeons. We investigate whether duration models employing the information available at the moment the planning is made, offer a better alternative. Our empirical results indicate that statistical methods often do better than surgeons. This does not imply that the surgeons' predictions do not contain valuable information. This information is a key explanatory variable in our statistical models. What our conclusion does entail is that a correction of the predictions of surgeons is possible because they are often under- or overestimating the actual length of operations

A probabilistic approach to Zhang's sandpile model

The current literature on sandpile models mainly deals with the abelian sandpile model (ASM) and its variants. We treat a less known - but equally interesting - model, namely Zhang's sandpile. This model differs in two aspects from the ASM. First, additions are not discrete, but random amounts with a uniform distribution on an interval $[a,b]$. Second, if a site topples - which happens if the amount at that site is larger than a threshold value $E_c$ (which is a model parameter), then it divides its entire content in equal amounts among its neighbors. Zhang conjectured that in the infinite volume limit, this model tends to behave like the ASM in the sense that the stationary measure for the system in large volumes tends to be peaked narrowly around a finite set. This belief is supported by simulations, but so far not by analytical investigations. We study the stationary distribution of this model in one dimension, for several values of $a$ and $b$. When there is only one site, exact computations are possible. Our main result concerns the limit as the number of sites tends to infinity, in the one-dimensional case. We find that the stationary distribution, in the case $a \geq E_c/2$, indeed tends to that of the ASM (up to a scaling factor), in agreement with Zhang's conjecture. For the case $a=0$, $b=1$ we provide strong evidence that the stationary expectation tends to $\sqrt{1/2}$.Comment: 47 pages, 3 figure

Driving sandpiles to criticality and beyond

A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the abelian sandpile model equals the threshold density of the fixed-energy sandpile. We refute this prediction for a wide variety of underlying graphs, including the square grid. Driven dissipative sandpiles continue to evolve even after reaching criticality. This result casts doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the abelian sandpile model at stationarity.Comment: v4 adds referenc

The relationship between motor competence and health-related fitness in children and adolescents

Background and aims : In the last twenty years, there has been increasing evidence that Motor Competence (MC) is vital for developing an active and healthy lifestyle. This study analyses the associations between motor competence and its components, with health-related fitness (HRF). Methods : A random sample of 546 children (278 males, mean = 10.77 years) divided into four age groups (7-8; 9-10; 11-12; 13-14 years old) was evaluated. A quantitative MC instrument (evaluating stability, locomotor and manipulative skills), a maximal multistage 20-m shuttle-run test and the handgrip test, height and BMI were used in the analyses. Pearson correlations and standard regression modelling were performed to explore the associations between variables. Results : Moderate to strong significant correlations (0.49 < r < 0.73) were found between MC and HRF, for both sexes, and correlation values were stable across the age groups. The MC model explained 74% of the HRF variance, with the locomotor component being the highest predictor for the entire sample (beta =.302; p < .001). Gender-related differences were found when boys and girls were analysed at each age group. Locomotor MC for girls was the most consistent significant predictor of HRF across all age groups (0.47 < beta < 0.65; all p <=.001). For boys, significant predictors were locomotor and manipulative MC (0.21 <beta< 0.49; all p < .05) in the two younger age groups (7-8 and 9-10 years) and stability (0.50 <beta< 0.54; all p <=.001) for the older two age groups (11-12 and 13-14 years). Conclusion : These results support the idea that: (1) the relationship between overall MC and HRF is strong and stable across childhood and early adolescence; (2) when accounting for the different MC components, boys and girls show different relationship patterns with HFR across age