Chemical Oscillations out of Chemical Noise

The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally introduced, which allows developing a Hamiltonian dynamical system able to describe the system dynamics. Using this technique we are able to show that the intrinsic fluctuations, originated in the discrete character of the reagents, may sustain oscillations and chaotic trajectories which are impossible when these fluctuations are disregarded. An important point is that oscillations and chaos appear in systems whose mean-field dynamics has too low a dimensionality for showing such a behavior. In this sense these phenomena are purely induced by noise, which does not limit itself to shifting a bifurcation threshold. On the other hand, they are large deviations of a short transient nature which typically only appear after long waiting times. We also discuss the implications of our results in understanding extinction events in population dynamics models expressed by means of stoichiometric relations

Commensurate-Incommensurate Magnetic Phase Transition in Magnetoelectric Single Crystal LiNiPO4_4

Neutron scattering studies of single-crystal LiNiPO$_4$ reveal a spontaneous first-order commensurate-incommensurate magnetic phase transition. Short- and long-range incommensurate phases are intermediate between the high temperature paramagnetic and the low temperature antiferromagnetic phases. The modulated structure has a predominant antiferromagnetic component, giving rise to satellite peaks in the vicinity of the fundamental antiferromagnetic Bragg reflection, and a ferromagnetic component giving rise to peaks at small momentum-transfers around the origin at $(0,\pm Q,0)$. The wavelength of the modulated magnetic structure varies continuously with temperature. It is argued that the incommensurate short- and long-range phases are due to spin-dimensionality crossover from a continuous to the discrete Ising state. These observations explain the anomalous first-order transition seen in the magnetoelectric effect of this system

Remarks on the representation theory of the Moyal plane

We present an explicit construction of a unitary representation of the commutator algebra satisfied by position and momentum operators on the Moyal plane.Comment: 10 pages, minor changes, refs. adde

Robust Machine Learning-Based Correction on Automatic Segmentation of the Cerebellum and Brainstem.

Automated segmentation is a useful method for studying large brain structures such as the cerebellum and brainstem. However, automated segmentation may lead to inaccuracy and/or undesirable boundary. The goal of the present study was to investigate whether SegAdapter, a machine learning-based method, is useful for automatically correcting large segmentation errors and disagreement in anatomical definition. We further assessed the robustness of the method in handling size of training set, differences in head coil usage, and amount of brain atrophy. High resolution T1-weighted images were acquired from 30 healthy controls scanned with either an 8-channel or 32-channel head coil. Ten patients, who suffered from brain atrophy because of fragile X-associated tremor/ataxia syndrome, were scanned using the 32-channel head coil. The initial segmentations of the cerebellum and brainstem were generated automatically using Freesurfer. Subsequently, Freesurfer's segmentations were both manually corrected to serve as the gold standard and automatically corrected by SegAdapter. Using only 5 scans in the training set, spatial overlap with manual segmentation in Dice coefficient improved significantly from 0.956 (for Freesurfer segmentation) to 0.978 (for SegAdapter-corrected segmentation) for the cerebellum and from 0.821 to 0.954 for the brainstem. Reducing the training set size to 2 scans only decreased the Dice coefficient ≤0.002 for the cerebellum and ≤ 0.005 for the brainstem compared to the use of training set size of 5 scans in corrective learning. The method was also robust in handling differences between the training set and the test set in head coil usage and the amount of brain atrophy, which reduced spatial overlap only by <0.01. These results suggest that the combination of automated segmentation and corrective learning provides a valuable method for accurate and efficient segmentation of the cerebellum and brainstem, particularly in large-scale neuroimaging studies, and potentially for segmenting other neural regions as well

On the noncommutative eikonal

We study the eikonal approximation to quantum mechanics on the Moyal plane. Instead of using a star product, the analysis is carried out in terms of operator-valued wavefunctions depending on noncommuting, operator-valued coordinates.Comment: 18 page

The Adapted Ordering Method for Lie Algebras and Superalgebras and their Generalizations

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras in two dimensions. It allows: to determine maximal dimensions for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this article we present the Adapted Ordering Method for general Lie algebras and superalgebras, and their generalizations, provided they can be triangulated. We also review briefly the results obtained for the Virasoro algebra and for the N=2 and Ramond N=1 superconformal algebras.Comment: Many improvements in the redaction for pedagogical purposes. Latex, 11 page