Backward error analysis and the substitution law for Lie group integrators

Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio

Precipitable Water Comparisons Over Ghana using PPP Techniques and Reanalysis Data

Atmospheric Water vapor is an important greenhouse gas and contributes greatly in maintaining the Earth’s energy balance. This critical meteorological parameter is not being sensed by any of the 22 synoptic weather stations in Ghana. This study presents a highly precise tool for water vapor sensing based on the concept Global Navigation Satellite Systems (GNSS) meteorology and tests the computed results against global reanalysis data. Conventional approaches used to sense the atmospheric water vapor or Precipitable Water (PW) such as radiosondes, hygrometers, microwave radiometers or sun photometers are expensive and have coverage and temporal limitations. Whereas GNSS meteorological concept offers an easier, inexpensive and all-weather technique to retrieve PW or Integrated Water Vapor (IWV) from zenith tropospheric delays (ZTD) over a reference station. This study employed precise point positioning (PPP) techniques to quantify the extend of delays on the signal due to the troposphere and stratosphere where atmospheric water vapor resides. Stringent processing criteria were set using an elevation cut-off of 5 degrees, precise orbital and clock products were used as well as nominal tropospheric corrections and mapping functions implemented. The delays which are originally slanted are mapped unto the zenith direction and integrated with surface meteorological parameters to retrieve PW or IWV. The gLAB software, Canadian Spatial Reference System (CSRS) and Automatic Precise Positioning Service (APPS) online PPP services were the approaches used to compute ZTD. PW values obtained were compared with Japanese Metro Agency Reanalysis (JRA), European Centre for Medium-Range Weather Forecasts Reanalysis (ERA-interim) and National Center for Environmental Prediction (NCEP) global reanalysis data. Correlation analysis were run on the logged station data using the three approaches and global reanalysis data. The obtained results show stronger correlation between the retrieved PW values and those provided by the ERA-interim. Finally, the study results indicate that with a more densified network of GNSS base stations the retrieved PW or IWV will greatly improve numerical weather predictions in Ghana.Keywords: GNSS Signals, PPP, Integrated Water vapour, Precipitable Water, Reanalysis Model

Ultra Precise Modular Reaction Wheel Operation for Optical and Radar Satellites

With the new space arena evolving towards serious science and defense missions, the availability of new space avionics with high-end performance is becoming a prerequisite for modern and future satellite missions. This puts requirements for very accurate speed and torque control of modern reaction wheels used to perform attitude control of modern spacecraft. Nearly vibration free operation (optical payloads) Extremely trum of frequencies Modularity Fast delivery Scalabilit

A Rapid and Reliable Method of Counting Neurons and Other Cells in Brain Tissue: A Comparison of Flow Cytometry and Manual Counting Methods

It is of critical importance to understand the numbers and distributions of neurons and non-neurons in the cerebral cortex because cell numbers are reduced with normal aging and by diseases of the CNS. The isotropic fractionator method provides a faster way of estimating numbers of total cells and neurons in whole brains and dissected brain parts. Several comparative studies have illustrated the accuracy and utility of the isotropic fractionator method, yet it is a relatively new methodology, and there is opportunity to adjust procedures to optimize its efficiency and minimize error. In the present study, we use 142 samples from a dissected baboon cortical hemisphere to evaluate if isotropic fractionator counts using a Neubauer counting chamber and fluorescence microscopy could be accurately reproduced using flow cytometry methods. We find greater repeatability in flow cytometry counts, and no evidence of constant or proportional bias when comparing microscopy to flow cytometry counts. We conclude that cell number estimation using a flow cytometer is more efficient and more precise than comparable counts using a Neubauer chamber on a fluorescence microscope. This method for higher throughput, precise estimation of cell numbers has the potential to rapidly advance research in post-mortem human brains and vastly improve our understanding of cortical and subcortical structures in normal, injured, aged, and diseased brains

Managing BRCA Mutation Carriers in China: Reply

published_or_final_versionSpringer Open Choice, 31 May 201

Fingerprint-enhanced capacitive-piezoelectric flexible sensing skin to discriminate static and dynamic tactile stimuli

nspired by the structure and functions of the human skin, a highly sensitive capacitive‐piezoelectric flexible sensing skin with fingerprint‐like patterns to detect and discriminate between spatiotemporal tactile stimuli including static and dynamic pressures and textures is presented. The capacitive‐piezoelectric tandem sensing structure is embedded in the phalange of a 3D‐printed robotic hand, and a tempotron classifier system is used for tactile exploration. The dynamic tactile sensor, interfaced with an extended gate configuration to a common source metal oxide semiconductor field effect transistor (MOSFET), exhibits a sensitivity of 2.28 kPa−1. The capacitive sensing structure has nonlinear characteristics with sensitivity varying from 0.25 kPa−1 in the low‐pressure range (<100 Pa) to 0.002 kPa−1 in high pressure (≈2.5 kPa). The output from the presented sensor under a closed‐loop tactile scan, carried out with an industrial robotic arm, is used as latency‐coded spike trains in a spiking neural network (SNN) tempotron classifier system. With the capability of performing a real‐time binary naturalistic texture classification with a maximum accuracy of 99.45%, the presented bioinspired skin finds applications in robotics, prosthesis, wearable sensors, and medical devices