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Evolutionary Inference for Functional Data: Using Gaussian Processes on Phylogenies to Study Shape Evolution
Get PDFThis paper uses the interface between two disciplines�phylogenetics and functional data
analysis�to aid the analysis of rich ancestral data like continuous curves. We place Gaus-
sian processes on phylogenies in order to perform evolutionary inference on such functional
data objects. Unlike morphological summaries, which reduce data dimension, this approach
allows one to make inferential statements about curves themselves. We provide a modified
covariance function that corrects for the relationships between states at different points on
a phylogeny and discuss its use in inference. In general, this covariance is expressed as the
solution of an integral equation and we note that, for a given Gaussian process, a set of
solutions sufficient for all phylogenies may be precomputed as a library which, for station-
ary processes, is one dimensional. This work has relevance for those wanting to perform
inference on functional data objects related by an evolutionary process; it also specifies a
class of hierarchical clustering algorithms for functional data objects and can be used for
multivariate time series forecasting
An interview with Paul Van Dooren
Get PDFInterviews and dialogues have been a special way to transmit science since Socrates. They are maybe the only way to get the stories behind most discoveries. I was so positively impressed by the interview of Gene Golub by
Nicholas J. Higham [1] that the idea of doing one with Paul Van Dooren obsessed me for a while. After a few attempts to arrange a meeting, I finally got an occasion during the Householder Symposium at Tahoe City. On June 15, 2011, when most participants were on an excursion (Paul did have a kind of cold), we sat in a corner of the Granhall of the Granlibakken Conference Center and we did the interview. This document provides an edited transcript of that dialogue. The bibliography contains some refernces in the
interview
dqds with aggressive early deflation
Get PDFThe dqds algorithm computes all the singular values of an -by- bidiagonal matrix to high relative accuracy in cost. Its efficient implementation is now available as a LAPACK subroutine and is the preferred algorithm for this purpose. In this paper we incorporate into dqds a technique called aggressive early deflation, which has been applied successfully to the Hessenberg QR algorithm. Extensive numerical experiments show that aggressive early deflation often reduces the dqds runtime significantly. In addition, our theoretical analysis suggests that with aggressive early deflation, the performance of dqds is largely independent of the shift strategy. We confirm through experiments that the zero-shift version is often as fast as the shifted version.
We give a detailed error analysis to prove that with our proposed deflation strategy, dqds computes all the singular values to high relative accuracy
Analysis of Structured Polynomial Eigenvalue Problems
Get PDFThis thesis considers Hermitian/symmetric, alternating and palindromic matrix polynomials which all arise frequently in a variety of applications, such as vibration analysis of dynamical systems and optimal control problems. A classication of Hermitian matrix polynomials whose eigenvalues belong to the extended real line, with each eigenvalue being of denite type, is provided rst. We call such polynomials quasidenite. Denite pencils, denitizable pencils, overdamped quadratics, gyroscopically stabilized quadratics, (quasi)hyperbolic and denite matrix polynomials
are all quasidenite. We show, using homogeneous rotations, special Hermitian linearizations and a new characterization of hyperbolic matrix polynomials, that the main common thread between these many subclasses is the distribution of their eigenvalue types. We also identify, amongst all quasihyperbolic matrix polynomials, those that can be diagonalized by a congruence transformation applied to a Hermitian linearization of the matrix polynomial while maintaining the structure of the linearization.
Secondly, we generalize the notion of self-adjoint standard triples associated with Hermitian matrix polynomials in Gohberg, Lancaster and Rodman's theory of matrix
polynomials to present spectral decompositions of structured matrix polynomials in terms of standard pairs (X,T), which are either real or complex, plus a parameter
matrix S that acquires particular properties depending on the structure under investigation.
These decompositions are mainly an extension of the Jordan canonical form for a matrix over the real or complex eld so we investigate the important special case of structured Jordan triples. Finally, we use the concept of structured Jordan triples to solve a structured inverse
polynomial eigenvalue problem. As a consequence, we can enlarge the collection of nonlinear eigenvalue problems by generating quadratic and cubic quasidenite matrix polynomials in dierent subclasses from some given spectral
data by solving an appropriate inverse eigenvalue problem. For the quadratic case, we employ available algorithms to provide tridiagonal denite matrix polynomials
Identification of amino acid substitutions associated with neutralization phenotype in the human immunodeficiency virus type-1 subtype C gp120
No full textNeutralizing antibodies (Nabs) are thought to play an important role in prevention and control of HIV-1 infection and should be targeted by an AIDS vaccine. It is critical to understand how HIV-1 induces Nabs by analyzing viral sequences in both tested viruses and sera. Neutralization susceptibility to antibodies in autologous and heterologous plasma was determined for multiple Envs (3�6) from each of 15 subtype-C- infected individuals. Heterologous neutralization was divided into two distinct groups: plasma with strong, cross-reactive neutralization (n = 9) and plasma with weak neutralization (n = 6). Plasma with cross-reactive heterologous Nabs also more potently neutralized contemporaneous autologous viruses. Analysis of Env sequences in plasma from both groups revealed a three-amino-acid substitution pattern in the V4 region that was associated with greater neutralization potency and breadth. Identification of such potential neutralization signatures may have important implications for the development of HIV-1 vaccines capable of inducing Nabs to subtype C HIV-1
Commuting Involution Graphs of Certain Finite Simple Classical Groups
No full textFor a group G and X a subset of G, the commuting graph of G on X, denoted by C(G,X), is the graph whose vertex set is X with x, y in X joined by an edge if x is not equal to y and x and y commute. If the elements in X are involutions, then C(G,X) is called a commuting involution graph. This thesis studies C(G,X) when G is either a 4-dimensional projective symplectic group; a 3-dimensional unitary group; 4-dimensional unitary group over a field of characteristic 2; a 2-dimensional projective general linear group; or a 4-dimensional affine orthogonal group, and X a G-conjugacy class of involutions. We determine the diameters and structure of the discs of these graphs
Fast iterative solvers for buoyancy driven flow problems
No full textWe outline a new class of robust and efficient methods for solving the Navier-Stokes equations with a Boussinesq model for buoyancy driven flow. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the efficiency of the chosen preconditioning schemes with respect to the discretization parameters
Standard Triples of Structured Matrix Polynomials
No full textThe notion of standard triples plays a central role in the theory of matrix polynomials.
We study such triples for matrix polynomials
with structure , where is the
Hermitian, symmetric, -even, -odd,
-palindromic or -antipalindromic structure (with ).
We introduce the notion of -structured standard triple. With the exception of -(anti)palindromic matrix polynomials of even degree
with both and as eigenvalues,
we show that has structure if and only if
admits an -structured standard triple,
and moreover that every standard triple of a matrix polynomial with
structure is -structured.
We investigate the important special case of -structured
Jordan triples
The Resource Valuation and Optimisation Model: Real Impact from Real Options
Get PDFThis paper presents the scientific framework underpinning the resource valuation and optimisation
model (RVOM). The RVOM is a partial differential equation based real options software package,
which helps mine owners optimally plan their operations, understand their project risks, and make
defensible valuations. This is achieved in the presence of both financial and physical uncertainty, as
well as processing capacity constraints. The RVOM can be applied to any multi-ore mine, open pit or
otherwise, where the block-order of extraction has already been planned using existing software tools
such as the Gemcom Whittle™ strategic mine planning package. The RVOM can also take account
of multiple commodities within a single mine, and multiple forms of price behaviour. The three key
outputs from the RVOM are: valuation, optimal decision and probability of decision. A decision
takes account of upfront costs, and can include an unlimited number of transitions between: normal
operation, expanded operation, care and maintenance and abandonment (and variants thereof).
The RVOM then employs stochastic process theory to determine the probability of reaching these
decisions. This gives the mine operators clear indications as to where their risks lie, aiding their mine
planning. A clear example of the RVOMs usage to a case-study gold mine is presented, demonstrating
its broad applicability, the added value it can create and how users can easily make use of the RVOM’s
state-of-the-art algorithmic engine
On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem
Get PDFFor standard eigenvalue problems, closed-form expressions for the condition numbers of a multiple eigenvalue are known. In particular, they are uniformly 1 in the Hermitian case and generally take di�erent values in the non-Hermitian case. We consider the generalized eigenvalue problem and identify the condition numbers. Our main result is that a multiple eigenvalue generally has multiple condition numbers, even in the Hermitian de�nite case.
The condition numbers are characterized in terms of the singular values of the outer product of the corresponding left and right eigenvectors