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Making big steps in trajectories
Get PDFWe consider the solution of initial value problems within the context of hybrid systems and emphasise use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a prototypical implementation illustrate that the algorithm might provide results with higher precision than well-known ODE solvers at a
similar computation time
Scatter in an uncollimated x-ray CT machine based on a Geant4 Monte Carlo simulation
Get PDFA high-speed motionless-gantry x-ray CT machine has been designed to allow for 3D images to be collected in real time. By using multiple, switched x-ray sources and fixed detector rings, the time consuming mechanical rotation of conventional CT machines can be removed. However, the nature of this design limits the possibility of detector collimation since each detector must now be able to record the energy of x-ray beams from a number of different directions. The lack of collimation has implications in the reconstructed image due to an increase in the number of scattered photons recorded. A Monte Carlo computer simulation of the x-ray machine has been developed, using the Geant4 software toolkit, to analyse the behaviour of both Rayleigh and Compton scattered photons when considering airport baggage and medical applications. Four different scattering objects were analysed based on 50kVp, 100kVp and 150kVp spectra for a tungsten target. Two suitcase objects, a body and a brain phantom were chosen as objects typical of airport baggage and medical CT. The results indicate that the level of scatter is negligible for a typical airport baggage application, since the majority of space in a suitcase consists of clothing, which has a low density. Scatter contributes to less than 1% of the image in the 100kVp and 150kVp instances. However, due to the large amounts of water found in the human body, the level of scatter in the medical instances are significantly higher, reaching 37% when the body phantom is analysed at 50kVp
THE MILSTEIN SCHEME FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITHOUT ANTICIPATIVE CALCULUS
Get PDFThe Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential
equations with a strong order of convergence one. The scheme has been extended to the
stochastic delay dierential equations but the analysis of the convergence is technically complicated
due to anticipative integrals in the remainder terms. This paper employs an elementary method
to derive the Milstein scheme and its rst order strong rate of convergence for stochastic delay
dierential equations
SOURCE FIRING PATTERNS AND RECONSTRUCTION ALGORITHMS FOR A SWITCHED SOURCE, OFFSET DETECTOR CT MACHINE
Get PDFWe present a new theoretical model and reconstruction results for a new class of fast
x-ray CT machine, the Real Time Tomography (RTT) system, which uses switched
sources and an offset detector array. We begin by reviewing elementary properties
of the Radon and x-ray transforms, and limited angle tomography. Through the
introduction of a new continuum model, that of sources covering the surface of a
cylinder in R 3 , we show that the problem of three-dimensional reconstruction from
RTT data reduces to inversion of the three-dimensional Radon transform with limited
angle data. Using the Paley-Wiener theorem, we then prove the existence of a unique
solution and give comments on stability and singularity detection.
We show, first in the two-dimensional case, that the conjugate gradient least
squares algorithm is suitable for CT reconstruction. By exploiting symmetries in
the system, we then derive a method of applying CGLS to the three-dimensional
inversion problem using stored matrix coefficients.
The new concept of source firing order is introduced and formalised, and some
novel visualisations are used to show how this affects aspects of the geometry of the
system. We then perform a detailed numerical analysis using the condition number
and SVD of the reconstruction matrix A, to show that the choice of firing order
affects the conditioning of the problem. Finally, we give reconstruction results using
phantom data that support the numerical analysis
Hermitian Matrix Polynomials with Real Eigenvalues of Definite Type. Part I: Classification
No full textThe spectral properties of Hermitian matrix polynomials with real eigenvalues
have been extensively studied, through classes such as the definite or
definitizable pencils, definite, hyperbolic, or quasihyperbolic matrix
polynomials, and overdamped or gyroscopically stabilized quadratics.
We give a unified treatment of these and related classes that uses the
eigenvalue type (or sign characteristic) as a common thread. Equivalent
conditions are given for each class in a consistent format. We show that these
classes form a hierarchy, all of which are contained in the new class of
quasidefinite matrix polynomials. As well as collecting and unifying existing
results, we make several new contributions.
We propose a new characterization of hyperbolicity in terms of the distribution
of the eigenvalue types on the real line. By analyzing their effect on
eigenvalue type, we show that homogeneous rotations allow results for matrix
polynomials with nonsingular or definite leading coefficient to be translated
into results with no such requirement on the leading coefficient, which is
important for treating definite and quasidefinite polynomials. We also give a
sufficient condition for a quasihyperbolic matrix polynomial to be
diagonalizable by structure preserving congruence, and show that this condition
is always satisfied in the quadratic case and for any hyperbolic matrix
polynomial, thereby identifying an important new class of diagonalizable matrix
polynomials
Two efficient SVD/Krylov algorithms for model order reduction of large scale systems
Get PDFWe present two efficient algorithms to produce a reduced order model of a time-invariant linear dynamical system by approximate balanced truncation.
Attention is focused on the use of the structure and the iterative construction via Krylov subspaces of both controllability and observability matrices to compute low-rank approximations of the Gramians or the Hankel operator. This allows us to take advantage of any sparsity in the system matrices and indeed the cost of our two algorithms is only linear in the system dimension. Both algorithms efficiently produce good low-rank approximations (in the least square sense) of the Cholesky factor of each Gramian and the Hankel operator. The second algorithm works directly on the Hankel operator, and it has the advantage that it is independent of the chosen realization. Moreover it is also an approximate Hankel norm method. The two reduced order models produced by our methods are guaranteed to be stable and balanced. We study the convergence of our iterative algorithms and the properties of the fixed point iteration. We also discuss the stopping criteria and the choice of the reduced order
Genetic analysis of wheat landraces enables the location of the first agricultural sites in Italy to be identified
No full textWe typed five microsatellite loci in 52 landraces of Italian emmer wheat to determine if genetic analysis of cereals can provide information relevant to the spread of agriculture. Each of the five loci was polymorphic with 43 allele combinations identified in the 52 landraces. The allele combinations fell into two groups. Group 1 comprised 27 genotypes found in 42 landraces and Group 2 comprised 15 genotypes found in 10 landraces. The landraces with Group 1 genotypes showed a strong correlation between geographical and genetic distances (r = 0.601, p < 0.001) but those with Group 2 genotypes did not (r = 0.116, p = 0.244). We inferred that the Group 1 landraces might therefore retain a phylogeographical structure that reflects ancient events. We present a phylogeographical model for the spread of agriculture that enables the point of origin of crop cultivation to be predicted by comparison between the genetic and geographical distances between landraces. We applied this model to the Group 1 landraces by positioning 131 hypothetical points of origin around the coastline and northern border of Italy. The highest correlation coefficients between genetic and geographical distances were seen for hypothetical points of origin located on the coast of northern Puglia. We repeated the analysis with 1040 hypothetical points of origin located within the Italian peninsula. Again, the highest correlation coefficients were located in northern Puglia. These predicted points of origin correspond with the location of the earliest agricultural sites in Italy. The results show that plant genetics can be used to study the spread of agriculture
Artin-Schreier Theory and L-packets in the principal series of SL_2(F_2((x)))
Get PDFWe survey Artin-Schreier theory, adapted to the local function field F_2((x)). This leads to a neat parametrization of the L-packets in the principal series of SL_2(F_2((x)))
Mosaic HIV-1 vaccines expand the breadth and depth of cellular immune responses in rhesus monkeys
No full textThe worldwide diversity of HIV-1 presents an unprecedented challenge for vaccine development. Antigens derived from natural HIV-1 sequences have elicited only a limited breadth of cellular immune responses in nonhuman primate studies and clinical trials to date. Polyvalent 'mosaic' antigens, in contrast, are designed to optimize cellular immunologic coverage of global HIV-1 sequence diversity. Here we show that mosaic HIV-1 Gag, Pol and Env antigens expressed by recombinant, replication-incompetent adenovirus serotype 26 vectors markedly augmented both the breadth and depth without compromising the magnitude of antigen-specific T lymphocyte responses as compared with consensus or natural sequence HIV-1 antigens in rhesus monkeys. Polyvalent mosaic antigens therefore represent a promising strategy to expand cellular immunologic vaccine coverage for genetically diverse pathogens such as HIV-1
Computing Matrix Functions
Get PDFThe need to evaluate a function of a matrix
arises in a wide and growing number of
applications, ranging from the numerical solution of differential equations to
measures of the complexity of networks.
We give a survey of numerical methods for evaluating matrix functions,
along with a brief treatment of the underlying theory
and a description of two recent applications.
The survey is organized by classes of methods,
which are broadly those based on similarity transformations,
those employing approximation by polynomial or rational functions,
and matrix iterations.
Computation of the Fr\'echet derivative,
which is important for condition number estimation, is also treated,
along with the problem of computing without computing .
A summary of available software completes the survey