Improved Montgomery modular inverse algorithm

A new, single and unified Montgomery modular inverse algorithm, which performs both classical and Montgomery modular inversion, is proposed. This reduces the number of Montgomery multiplication operations required by 33% when compared with previous algorithms reported in the literature. The use of this in practice has been investigated by implementation of the improved unified algorithm and the previous algorithms on FPGA devices. The unified algorithm implementation shows a significant speed-up and a reduction in silicon area usage.

An inverse method for determining source characteristics for emergency response applications

Following a malicious or accidental atmospheric release in an outdoor environment it is essential for first responders to ensure safety by identifying areas where human life may be in danger. For this to happen quickly, reliable information is needed on the source strength and location, and the type of chemical agent released. We present here an inverse modelling technique that estimates the source strength and location of such a release, together with the uncertainty in those estimates, using a limited number of measurements of concentration from a network of chemical sensors considering a single, steady, ground-level source. The technique is evaluated using data from a set of dispersion experiments conducted in a meteorological wind tunnel, where simultaneous measurements of concentration time series were obtained in the plume from a ground-level point-source emission of a passive tracer. In particular, we analyze the response to the number of sensors deployed and their arrangement, and to sampling and model errors. We find that the inverse algorithm can generate acceptable estimates of the source characteristics with as few as four sensors, providing these are well-placed and that the sampling error is controlled. Configurations with at least three sensors in a profile across the plume were found to be superior to other arrangements examined. Analysis of the influence of sampling error due to the use of short averaging times showed that the uncertainty in the source estimates grew as the sampling time decreased. This demonstrated that averaging times greater than about 5min (full scale time) lead to acceptable accuracy.

Fluorescence-enhanced optical imaging on three-dimensional phantoms using a hand-held probe based frequency-domain intensified charge coupled device (ICCD) optical imager

Fluorescence-enhanced optical imaging is an emerging non-invasive and non-ionizing modality towards breast cancer diagnosis. Various optical imaging systems are currently available, although most of them are limited by bulky instrumentation, or their inability to flexibly image different tissue volumes and shapes. Hand-held based optical imaging systems are a recent development for its improved portability, but are currently limited only to surface mapping. Herein, a novel optical imager, consisting primarily of a hand-held probe and a gain-modulated intensified charge coupled device (ICCD) detector, is developed towards both surface and tomographic breast imaging. The unique features of this hand-held probe based optical imager are its ability to; (i) image large tissue areas (5×10 sq. cm) in a single scan, (ii) reduce overall imaging time using a unique measurement geometry, and (iii) perform tomographic imaging for tumor three-dimensional (3-D) localization. Frequency-domain based experimental phantom studies have been performed on slab geometries (650 ml) under different target depths (1-2.5 cm), target volumes (0.45, 0.23 and 0.10 cc), fluorescence absorption contrast ratios (1:0, 1000:1 to 5:1), and number of targets (up to 3), using Indocyanine Green (ICG) as fluorescence contrast agents. An approximate extended Kalman filter based inverse algorithm has been adapted towards 3-D tomographic reconstructions. Single fluorescence target(s) was reconstructed when located: (i) up to 2.5 cm deep (at 1:0 contrast ratio) and 1.5 cm deep (up to 10:1 contrast ratio) for 0.45 cc-target; and (ii) 1.5 cm deep for target as small as 0.10 cc at 1:0 contrast ratio. In the case of multiple targets, two targets as close as 0.7 cm were tomographically resolved when located 1.5 cm deep. It was observed that performing multi-projection (here dual) based tomographic imaging using a priori target information from surface images, improved the target depth recovery over using single projection based imaging. From a total of 98 experimental phantom studies, the sensitivity and specificity of the imager was estimated as 81-86% and 43-50%, respectively. With 3-D tomographic imaging successfully demonstrated for the first time using a hand-held based optical imager, the clinical translation of this technology is promising upon further experimental validation from in-vitro and in-vivo studies.

Numerical Modelling of Eddy Current Probes for CANDU® Fuel Channel Inspection

Multi-frequency Eddy Current (EC) inspection with a transmit-receive probe (two horizontally offset coils) is used to monitor the Pressure Tube (PT) to Calandria Tube (CT) gap of CANDU® fuel channels. Accurate gap measurements are crucial to ensure fitness of service; however, variations in probe liftoff, PT electrical resistivity, and PT wall thickness can generate systematic measurement errors. Validated mathematical models of the EC probe are very useful for data interpretation, and may improve the gap measurement under inspection conditions where these parameters vary. As a first step, exact solutions for the electromagnetic response of a transmit-receive coil pair situated above two parallel plates separated by an air gap were developed. This model was validated against experimental data with flat-plate samples. Finite element method models revealed that this geometrical approximation could not accurately match experimental data with real tubes, so analytical solutions for the probe in a double-walled pipe (the CANDU® fuel channel geometry) were generated using the Second-Order Vector Potential (SOVP) formalism. All electromagnetic coupling coefficients arising from the probe, and the layered conductors were determined and substituted into Kirchhoff’s circuit equations for the calculation of the pickup coil signal. The flat-plate model was used as a basis for an Inverse Algorithm (IA) to simultaneously extract the relevant experimental parameters from EC data. The IA was validated over a large range of second layer plate resistivities (1.7 to 174 µΩ∙cm), plate wall thickness (~1 to 4.9 mm), probe liftoff (~2 mm to 8 mm), and plate-to plate gap (~0 mm to 13 mm). The IA achieved a relative error of less than 6% for the extracted FP resistivity and an accuracy of ±0.1 mm for the LO measurement. The IA was able to achieve a plate gap measurement with an accuracy of less than ±0.7 mm error over a ~2.4 mm to 7.5 mm probe liftoff and ±0.3 mm at nominal liftoff (2.42±0.05 mm), providing confidence in the general validity of the algorithm. This demonstrates the potential of using an analytical model to extract variable parameters that may affect the gap measurement accuracy.

A Reactive Inverse PN Algorithm for Collision Avoidance among Multiple Unmanned Aerial Vehicles

While performing a mission, multiple Unmanned Aerial Vehicles (UAVs) need to avoid each other to prevent collisions among them. In this paper, we design a collision avoidance algorithm to resolve the conflict among UAVs that are on a collision course while flying to heir respective destinations. The collision avoidance algorithm consist of each UAV that is on a collision course reactively executing a maneuver that will, as in `inverse' Proportional Navigation (PN), increase Line of Sight (LOS) rate between them, resulting in a `pulling out' of collision course. The algorithm is tested for high density traffic scenarios as well as for robustness in the presence of noise.

A regularized iterative algorithm for limited-angle inverse Radon transform

The tomography problem is investigated when the available projections are restricted to a limited angular domain. It is shown that a previous algorithm proposed for extrapolating the data to the missing cone in Fourier space is unstable in the presence of noise because of the ill-posedness of the problem. A regularized algorithm is proposed, which converges to stable solutions. The efficiency of both algorithms is tested by means of numerical simulations. © 1983 Taylor and Francis Group, LLC.

Performance evaluation of a distributed algorithm for an inverse heat conduction problem

Numerical solutions of realistic 2-D and 3-D inverse problems may require a very large amount of computation. A two-level concept on parallelism is often used to solve such problems. The primary level uses the problem partitioning concept which is a decomposition based on the mathematical/physical problem. The secondary level utilizes the widely used data partitioning concept. A theoretical performance model is built based on the two-level parallelism. The observed performance results obtained from a network of general purpose Sun Sparc stations are compared with the theoretical values. Restrictions of the theoretical model are also discussed.

A domain decomposition algorithm for inverse welding problems

A mathematical model and a numerical scheme for the inverse determination of heat sources generated by means of a welding process is presented in this paper. The accuracy of the heat source retrieval is discussed.

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.

B-spline neural network based digital baseband predistorter solution using the inverse of De Boor algorithm

In this paper a new nonlinear digital baseband predistorter design is introduced based on direct learning, together with a new Wiener system modeling approach for the high power amplifiers (HPA) based on the B-spline neural network. The contribution is twofold. Firstly, by assuming that the nonlinearity in the HPA is mainly dependent on the input signal amplitude the complex valued nonlinear static function is represented by two real valued B-spline neural networks, one for the amplitude distortion and another for the phase shift. The Gauss-Newton algorithm is applied for the parameter estimation, in which the De Boor recursion is employed to calculate both the B-spline curve and the first order derivatives. Secondly, we derive the predistorter algorithm calculating the inverse of the complex valued nonlinear static function according to B-spline neural network based Wiener models. The inverse of the amplitude and phase shift distortion are then computed and compensated using the identified phase shift model. Numerical examples have been employed to demonstrate the efficacy of the proposed approaches.

Digital predistorter design using B-Spline neural network and inverse of De Boor algorithm

This contribution introduces a new digital predistorter to compensate serious distortions caused by memory high power amplifiers (HPAs) which exhibit output saturation characteristics. The proposed design is based on direct learning using a data-driven B-spline Wiener system modeling approach. The nonlinear HPA with memory is first identified based on the B-spline neural network model using the Gauss-Newton algorithm, which incorporates the efficient De Boor algorithm with both B-spline curve and first derivative recursions. The estimated Wiener HPA model is then used to design the Hammerstein predistorter. In particular, the inverse of the amplitude distortion of the HPA's static nonlinearity can be calculated effectively using the Newton-Raphson formula based on the inverse of De Boor algorithm. A major advantage of this approach is that both the Wiener HPA identification and the Hammerstein predistorter inverse can be achieved very efficiently and accurately. Simulation results obtained are presented to demonstrate the effectiveness of this novel digital predistorter design.

Inverse kinematics of a humanoid robot with non-spherical hip: a hybrid algorithm approach

This paper describes an approach to solve the inverse kinematics problem of humanoid robots whose construction shows a small but non negligible offset at the hip which prevents any purely analytical solution to be developed. Knowing that a purely numerical solution is not feasible due to variable efficiency problems, the proposed one first neglects the offset presence in order to obtain an approximate “solution” by means of an analytical algorithm based on screw theory, and then uses it as the initial condition of a numerical refining procedure based on the Levenberg‐Marquardt algorithm. In this way, few iterations are needed for any specified attitude, making it possible to implement the algorithm for real‐time applications. As a way to show the algorithm’s implementation, one case of study is considered throughout the paper, represented by the SILO2 humanoid robot.

Three-dimensional inverse modelling of magnetic anomaly sources based on a genetic algorithm.

We present a modelling method to estimate the 3-D geometry and location of homogeneously magnetized sources from magnetic anomaly data. As input information, the procedure needs the parameters defining the magnetization vector (intensity, inclination and declination) and the Earth's magnetic field direction. When these two vectors are expected to be different in direction, we propose to estimate the magnetization direction from the magnetic map. Then, using this information, we apply an inversion approach based on a genetic algorithm which finds the geometry of the sources by seeking the optimum solution from an initial population of models in successive iterations through an evolutionary process. The evolution consists of three genetic operators (selection, crossover and mutation), which act on each generation, and a smoothing operator, which looks for the best fit to the observed data and a solution consisting of plausible compact sources. The method allows the use of non-gridded, non-planar and inaccurate anomaly data and non-regular subsurface partitions. In addition, neither constraints for the depth to the top of the sources nor an initial model are necessary, although previous models can be incorporated into the process. We show the results of a test using two complex synthetic anomalies to demonstrate the efficiency of our inversion method. The application to real data is illustrated with aeromagnetic data of the volcanic island of Gran Canaria (Canary Islands).