Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Machine learning applied to neuroimaging for diagnosis of adult classic Chiari malformation: role of the basion as a key morphometric indicator.

OBJECTIVE The current diagnostic criterion for Chiari malformation Type I (CM-I), based on tonsillar herniation (TH), includes a diversity of patients with amygdalar descent that may be caused by a variety of factors. In contrast, patients presenting with an overcrowded posterior cranial fossa, a key characteristic of the disease, may remain misdiagnosed if they have little or no TH. The objective of the present study was to use machine-learning classification methods to identify morphometric measures that help discern patients with classic CM-I to improve diagnosis and treatment and provide insight into the etiology of the disease. METHODS Fifteen morphometric measurements of the posterior cranial fossa were performed on midsagittal T1-weighted MR images obtained in 195 adult patients diagnosed with CM. Seven different machine-learning classification methods were applied to images from 117 patients with classic CM-I and 50 controls matched by age and sex to identify the best classifiers discriminating the 2 cohorts with the minimum number of parameters. These classifiers were then tested using independent CM cohorts representing different entities of the disease. RESULTS Machine learning identified combinations of 2 and 3 morphometric measurements that were able to discern not only classic CM-I (with more than 5 mm TH) but also other entities such as classic CM-I with moderate TH and CM Type 1.5 (CM-1.5), with high accuracy (> 87%) and independent of the TH criterion. In contrast, lower accuracy was obtained in patients with CM Type 0. The distances from the lower aspect of the corpus callosum, pons, and fastigium to the foramen magnum and the basal and Wackenheim angles were identified as the most relevant morphometric traits to differentiate these patients. The stronger significance (p < 0.01) of the correlations with the clivus length, compared with the supraoccipital length, suggests that these 5 relevant traits would be affected more by the relative position of the basion than the opisthion. CONCLUSIONS Tonsillar herniation as a unique criterion is insufficient for radiographic diagnosis of CM-I, which can be improved by considering the basion position. The position of the basion was altered in different entities of CM, including classic CM-I, classic CM-I with moderate TH, and CM-1.5. The authors propose a predictive model based on 3 parameters, all related to the basion location, to discern classic CM-I with 90% accuracy and suggest considering the anterior alterations in the evaluation of surgical procedures and outcomes.

Discrete-to-continuum modeling of weakly interacting incommensurate chains.

In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains represent a cross section of a three-dimensional system consisting of a graphene sheet suspended over a substrate. The continuum model recovers both qualitatively and quantitatively the behavior observed in the corresponding discrete model. The numerical solutions for both models demonstrate the presence of large commensurate regions separated by localized incommensurate domain walls.

Complex mixed-mode oscillatory patterns in a periodically forced excitable Belousov-Zhabotinsky reaction model.

The Oregonator is the simplest chemically plausible model for the Belousov-Zhabotinsky reaction. We investigate the response of the Oregonator to sinusoidal inputs with amplitudes and frequencies within plausible ranges. We focus on a regime where the unforced Oregonator is excitable (with no sustained oscillations). We use numerical simulations and dynamical systems tools to both characterize the response patterns and explain the underlying dynamic mechanisms.