Neural Network Methods for Boundary Value Problems Defined in Arbitrarily Shaped Domains

Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the satisfaction of the boundary conditions. The method has been successfuly tested on two-dimensional and three-dimensional PDEs and has yielded accurate solutions

ExoSim: the Exoplanet Observation Simulator

A new generation of exoplanet research beckons and with it the need for simulation tools that accurately predict signal and noise in transit spectroscopy observations. We developed ExoSim: an end-to-end simulator that models noise and systematics in a dynamical simulation. ExoSim improves on previous simulators in the complexity of its simulation, versatility of use and its ability to be generically applied to different instruments. It performs a dynamical simulation that can capture temporal effects such as correlated noise and systematics on the light curve. It has also been extensively validated, including against real results from the Hubble WFC3 instrument. We find ExoSim is accurate to within 5% in most comparisons. ExoSim can interact with other models which simulate specific time-dependent processes. A dedicated star spot simulator allows ExoSim to produce simulated observations that include spot and facula contamination. ExoSim has been used extensively in the Phase A and B design studies of the ARIEL mission, and has many potential applications in the field of transit spectroscopy

Adaptive Memetic Particle Swarm Optimization with Variable Local Search Pool Size

We propose an adaptive Memetic Particle Swarm Optimization algorithm where local search is selected from a pool of different algorithms. The choice of local search is based on a probabilistic strategy that uses a simple metric to score the efficiency of local search. Our study investigates whether the pool size affects the memetic algorithm’s performance, as well as the possible benefit of using the adaptive strategy against a baseline static one. For this purpose, we employed the memetic algorithms framework provided in the recent MEMPSODE optimization software, and tested the proposed algorithms on the Benchmarking Black Box Optimization (BBOB 2012) test suite. The obtained results lead to a series of useful conclusions

Benjamin-Ono Kadomtsev-Petviashvili’s models in interfacial electro-hydrodynamics

Three-dimensional nonlinear potential free surface flows in the presence of vertical electric fields are considered. Both the effects of gravity and surface tension are included in the dynamic boundary condition. An asymptotic analysis (based on the assumptions of small depth and small free surface displacements) is presented. It is shown that the problem can be modelled by a Benjamin-Ono Kadomtsev-Petviashvili equation. Furthermore a fifth order Benjamin-Ono Kadomtsev-Petviashvili equation is derived to describe the flows in the particular case of values of the Bond number close to 1/3

The effect of a mixture of herbal essential oils or á-tocopheryl acetate on performance parameters and oxidation of body lipid in broilers

No Abstract. South African Journal of Animal Science Vol. 34 (1) 2004: pp.52-6

Solutions of Adler's lattice equation associated with 2-cycles of the Backlund transformation

The BT of Adler's lattice equation is inherent in the equation itself by virtue of its multidimensional consistency. We refer to a solution of the equation that is related to itself by the composition of two BTs (with different Backlund parameters) as a 2-cycle of the BT. In this article we will show that such solutions are associated with a commuting one-parameter family of rank-2 (i.e., 2-variable), 2-valued mappings. We will construct the explicit solution of the mappings within this family and hence give the solutions of Adler's equation that are 2-cycles of the BT.Comment: 10 pages, contribution to the NEEDS 2007 proceeding

Computation of an MRI brain atlas from a population of Parkinson’s disease patients

Abstract Parkinson’s Disease (PD) is a degenerative disorder of the brain. This study presents an MRI-based brain atlas of PD to characterize associated alterations for diagnostic and interventional purposes. The atlas standardizes primarily the implicated subcortical regions such as the globus pallidus (GP), substantia nigra (SN), subthalamic nucleus (STN), caudate nucleus (CN), thalamus (TH), putamen (PUT), and red nucleus (RN). The data were 3.0 T MRI brain images from 16 PD patients and 10 matched controls. The images used were T1-weighted ( T 1 w ), T2-weighted ( T 2 w ) images, and Susceptibility Weighted Images (SWI). The T1w images were the reference for the inter-subject non-rigid registration available from 3DSlicer. Anatomic labeling was achieved with BrainSuite and regions were refined with the level sets segmentation of ITK-Snap. The subcortical centers were analyzed for their volume and signal intensity. Comparison with an age-matched control group unravels a significant PD-related T1w signal loss in the striatum (CN and PUT) centers, but approximately a constant volume. The results in this study improve MRI based PD localization and can lead to the development of novel biomarkers

EChOSim: The Exoplanet Characterisation Observatory software simulator

EChOSim is the end-to-end time-domain simulator of the Exoplanet Characterisation Observatory (EChO) space mission. EChOSim has been developed to assess the capability EChO has to detect and characterize the atmospheres of transiting exoplanets, and through this revolutionize the knowledge we have of the Milky Way and of our place in the Galaxy. Here we discuss the details of the EChOSim implementation and describe the models used to represent the instrument and to simulate the detection. Software simulators have assumed a central role in the design of new instrumentation and in assessing the level of systematics affecting the measurements of existing experiments. Thanks to its high modularity, EChOSim can simulate basic aspects of several existing and proposed spectrometers for exoplanet transits, including instruments on the Hubble Space Telescope and Spitzer, or ground-based and balloon borne experiments. A discussion of different uses of EChOSim is given, including examples of simulations performed to assess the EChO mission

Cauchy problem for integrable discrete equations on quad-graphs

Initial value problems for the integrable discrete equations on quad-graphs are investigated. A geometric criterion of the well-posedness of such a problem is found. The effects of the interaction of the solutions with the localized defects in the regular square lattice are discussed for the discrete potential KdV and linear wave equations. The examples of kinks and solitons on various quad-graphs, including quasiperiodic tilings, are presented.Comment: Corrected version with the assumption of nonsingularity of solutions explicitly state