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Review: Practical Design and Analysis of 2-Colour cDNA Microarray Experiments
Get PDFThis review paper, is aimed at biological researchers who are interested in or have begun to use cDNA microarrays for their investigations. Large microarray studies typically involve a multi-disciplinary team with various groups performing different aspects of the same experiment. This approach means that microarrays are less accessible to new researchers than more traditional biological techniques. This review aims to make current techniques of statistical design, normalisation and linear analysis of cDNA microarray experiments accessible to a wider community. These methods will be illustrated with examples that use freely-available packages implemented in Bioconductor and R
Does Reaction-diffusion Dynamics on a Fractal Space Imply Power Law Behaviour?
Get PDFIn biological systems, chemical reactions often take place in complex spatial environments. For example, the translation of m-RNA to produce protein within eukaryotic cells takes place within the extremely crowded cytoplasmic environment and appears to require the spatial coordination of many translation factors. It is important, therefore, to understand the transport processes within such an environment. While there is growing interest in both experimental and computational studies of such environments, it is also important to develop suitable mathematical models. Here, as an example of such a model, we study a reaction-diffusion equation defined on the Sierpinski gasket. Both experimental and computational studies of analogous systems have shown power law behaviour and associated deviations from mass action kinetics. The analysis presented here allows us to distinguish the roles of the fractal domain and of the discreteness of molecular interactions in producing this effect. Indeed, we show that the fractal domain alone is insufficient
A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures
Get PDFAs multicore systems continue to gain ground in the High
Performance Computing world, linear algebra algorithms have to be re-
formulated or new algorithms have to be developed in order to take ad-
vantage of the architectural features on these new processors. Fine grain
parallelism becomes a major requirement and introduces the necessity
of loose synchronization in the parallel execution of an operation. This
paper presents an algorithm for the Cholesky, LU and QR factorization
where the operations can be represented as a sequence of small tasks
that operate on square blocks of data. These tasks can be dynamically
scheduled for execution based on the dependencies among them and on
the availability of computational resources. This may result in an out
of order execution of the tasks which will completely hide the presence
of intrinsically sequential tasks in the factorization. Performance com-
parisons are presented with the LAPACK algorithms where parallelism
can only be exploited at the level of the BLAS operations and vendor
implementations
Analysis of a laminar premixed spray flame with modified Zeldovitch-Linan kinetics
Get PDFA new preliminary analysis of a one dimensional laminar lean premixed spray flame
has been performed using a chain branching/chain breaking chemical kinetic scheme
and under the assumption that the fuel droplets evaporate in a sharp front. The
sensitivity of the flame speed and the location of the evaporation front to the initial
droplet load have been demonstrated. A linear stability analysis reveals the way in
which the spray’s presence modifies the neutral stability curves
Critical exponents for groups of isometries
Get PDFLet Γ be a convex co-compact group of isometries of a CAT(−1) space X and let Γ_0 be a normal subgroup of Γ. We show that, provided Γ is a free group, a sufficient condition for Γ and Γ_0 to have the same critical exponent is that Γ / Γ_0 is amenable
Vorticity structuring and velocity rolls triggered by gradient shear bands
Get PDFWe suggest a mechanism by which vorticity structuring and velocity rolls can form in complex fluids, triggered by the linear instability of one-dimensional gradient shear banded flow. We support this with a numerical study of the diffusive Johnson-Segalman model. In the steady vorticity structured state, the thickness of the interface between the bands remains finite in the limit of zero stress diffusivity, presenting a possible challenge to the accepted theory of shear banding
Symplectic group actions and covering spaces
Get PDFFor symplectic group actions which are not Hamiltonian there are two ways to define reduction. Firstly using the cylinder-valued momentum map and secondly lifting the action to any Hamiltonian cover (such as the universal cover), and then performing symplectic reduction in the usual way. We show that provided the action is free and proper, and the Hamiltonian holonomy associated to the action is closed, the natural projection from the latter to the former is a symplectic covering. At the same time we give a classification of all Hamiltonian coverings of a given symplectic group action. The main properties of the lifting of a group action to a cover are studied
Deflating Quadratic Matrix Polynomials
Get PDFIn this thesis we consider algorithms for solving the quadratic eigenvalue problem,
(lambda^2*A_2 + lambda*A_1 + A_0)x=0
when the leading or trailing
coefficient matrices are singular. In a finite element discretization this corresponds to the mass or stiffness matrices
being singular
and reflects modes of vibration (or eigenvalues) at zero or ``infinity''. We are interested in deflation procedures
that enable us to utilize knowledge of the presence of these (or any) eigenvalues to reduce the overall cost in
computing the remaining eigenvalues and eigenvectors of interest.
We first give an introduction to the quadratic eigenvalue problem and explain how it can be solved by a process called linearization.
We present two types of algorithms, firstly a modification of an algorithm published by
Kublanovskaya, Mikhailov, and Khazanov in the 1970s that has recently been translated into English.
Using these ideas we present algorithms that are able to reduce the size of the problem by ``deflating''
infinite and zero eigenvalues that arise when the mass or stiffness matrix (or both) are singular.
Secondly we look at methods that deflate zero and infinite eigenvalues by the use of Householder reflectors;
this requires a basis for the null space of the mass or stiffness matrix (or both), so we also summarize various decompositions
that can be used to give this information.
We consider different applications that yield a quadratic eigenvalue problem
with singular leading and trailing coefficients and after testing the implementations of the algorithms
on some of these problems we comment on their stability
Structured Mapping Problems for Matrices Associated with Scalar Products Part I: Lie and Jordan Algebras
Get PDFGiven a class of structured matrices \Sb, we identify pairs of vectors
for which there exists a matrix A\in\Sb such that , and also
characterize the set of all matrices A\in\Sb mapping to . The
structured classes we consider are the Lie and Jordan algebras associated with
orthosymmetric scalar products. These include (skew-)symmetric,
(skew-)Hamiltonian, pseudo (skew-)Hermitian, persymmetric and perskew-symmetric
matrices. Structured mappings with extremal properties are also investigated. In
particular, structured mappings of minimal rank are identified and shown to be
unique when rank-1 is achieved. The structured mapping of minimal Frobenius norm
is always unique and explicit formulas for it and its norm are obtained. Finally
the set of all structured mappings of minimal 2-norm is characterized. Our
results generalize and unify existing work, answer a number of open questions,
and provide useful tools for structured backward error investigations
