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Investment Lags: A Numerical Approach
No full textIn this paper we use a mixture of numerical methods including finite difference and body fitted co-ordinates
to form a robust stable numerical scheme to solve the investment lag model presented in the paper by Bar-Ilan
and Strange (1996). This allows us to apply our methodology to models with different stochastic processes
that does not have analytic solutions
Hecke algebras for inner forms of p-adic special linear groups
Get PDFLet F be a non-archimedean local field and let G^# be the group of F-rational
points of an inner form of SL_n. We study Hecke algebras for all Bernstein components
of G^#, via restriction from an inner form G of GL_n (F).
For any packet of L-indistinguishable Bernstein components, we exhibit an explicit
algebra whose module category is equivalent to the associated category of complex smooth
G^#-representations. This algebra comes from an idempotent in the full Hecke
algebra of G^#, and the idempotent is derived from a type for G. We show that the
Hecke algebras for Bernstein components of G^# are similar to affine Hecke algebras
of type A, yet in many cases are not Morita equivalent to any crossed product of an
affine Hecke algebra with a finite group
Zolotarev quadrature rules and load balancing for the FEAST eigensolver
Get PDFThe FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function. We propose improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximants based on the work of Zolotarev. Numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues. The new approach improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel
Mutual information as a measure of image quality for 3D dynamic lung imaging with EIT
Get PDFWe report on a pilot study of dynamic lung electrical impedance tomography (EIT) at the University of Manchester. Low-noise EIT data at 100 frames per second were obtained from healthy male subjects during controlled breathing, followed by magnetic resonance imaging (MRI) subsequently used for spatial validation of the EIT reconstruction. The torso surface in the MR image and electrode positions obtained using MRI fiducial markers informed the construction of a 3D finite element model extruded along the caudal-distal axis of the subject. Small changes in the boundary that occur during respiration were accounted for by incorporating the sensitivity with respect to boundary
shape into a robust temporal difference reconstruction algorithm. EIT and MRI images were co-registered using the open source medical imaging software, 3D Slicer. A quantitative comparison of quality of different EIT reconstructions was achieved through calculation of the mutual information with a lung-segmented MR image. EIT reconstructions using a linear shape correction algorithm
reduced boundary image artefacts, yielding better contrast of the lungs, and had 10% greater mutual information compared with a standard linear EIT reconstruction
A Rational Krylov Toolbox for MATLAB
Get PDFThe Rational Krylov Toolbox contains MATLAB implementations of Ruhe's rational Krylov sequence method, algorithms for the implicit and explicit relocation of the poles of a rational Krylov space, an implementation of RKFIT, a robust algorithm for rational least squares fitting, and the RKFUN and RKFUNM classes for numerical computations with rational functions
Playing off the curve - testing quantitative predictions of skill acquisition theories in development of chess performance
Get PDFLearning curves have been proposed as an adequate description of learning processes, no matter whether the processes manifest within minutes or across years. Different mechanisms underlying skill acquisition can lead to differences in the shape of learning curves. In the current study, we analyze the tournament performance data of 1383 chess players who begin competing at young age and play tournaments for at least 10 years. We analyze the performance development with the goal to test the adequacy of learning curves, and the skill acquisition theories they are based on, for describing and predicting expertise acquisition. On the one hand, we show that the skill acquisition theories implying a negative exponential learning curve do a better job in both describing early performance gains and predicting later trajectories of chess performance than those theories implying a power function learning curve. On the other hand, the learning curves of a large proportion of players show systematic qualitative deviations from the predictions of either type of skill acquisition theory. While skill acquisition theories predict larger performance gains in early years and smaller gains in later years, a substantial number of players begin to show substantial improvements with a delay of several years (and no improvement in the first years), deviations not fully accounted for by quantity of practice. The current work adds to the debate on how learning processes on a small time scale combine to large-scale changes
L-packets and depth for SL_2(K) with K a local function field of characteristic 2
No full textLet G = SL_2(K) with K a local function field of characteristic 2. We review Artin-Schreier theory for the field K, and show that this leads to a parametrization of certain L-packets in the smooth dual of G. We relate this to a recent geometric conjecture. The L-packets in the principal series are parametrized by quadratic extensions, and the supercuspidal L-packets of cardinality 4 are parametrized by biquadratic extensions. Each supercuspidal packet of cardinality 4 is accompanied by a singleton packet for SL_1(D). We compute the depths of the irreducible constituents of all these L-packets for SL_2(K) and its inner form SL_1(D)
Fast solvers for discretized Navier-Stokes problems using vector extrapolation
No full textWe discuss the design and implementation of a vector extrapolation method for computing numerical solutions of the steady-state Navier-Stokes equation system. We describe a “proof of concept” implementation of vector extrapolation, and we illustrate its effectiveness when integrated into the Incompressible Flow Iterative Solution Software (IFISS) package
CICADA Collection
No full textThis volume is CICADA Collection which contains contributions developed by researches working on
CICADA Project, The University of Manchester. CICADA Project creates a warm and fruitful atmosphere
for research collaboration in many aries of Mathematics, Computer Science, Engineering including hybrid
and dynamical systems, verification of safety critical systems, human robotics, model reduction and high
dimensional systems, max-pus algebra, stochastic hybrid systems, analysis of adaptive systems and control.
This volume presents examples and software which have been developed and used by CICADA community
Convergence of restarted Krylov subspace methods for Stieltjes functions of matrices
Get PDFTo approximate f(A)b---the action of a matrix function on a vector---by a Krylov subspace method, restarts may become mandatory due to storage requirements for the Arnoldi basis or due to the growing computational complexity of evaluating f on a Hessenberg matrix of growing size. A number of restarting methods have been proposed in the literature in recent years and there has been substantial algorithmic advancement concerning their stability and computational efficiency. However, the question under which circumstances convergence of these methods can be guaranteed has remained largely unanswered. In this paper we consider the class of Stieltjes functions and a related class, which contains important functions like the (inverse) square root and the matrix logarithm. For these classes of functions we present new theoretical results which prove convergence for Hermitian positive definite matrices A and arbitrary restart lengths. We also propose a modification of the Arnoldi approximation which guarantees convergence for the same classes of functions and any restart length if A is not necessarily Hermitian but positive real