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The Homotopy Exponent Problem For Certain Classes Of Polyhedral Products
Get PDFGiven a sequence of n topological pairs, and a simplicial complex on n vertices, there is a topological space by a construction of Buchstaber and Panov. Such spaces are called polyhedral products and they generalize the central notion of the moment-angle complex in toric topology. In this thesis we study certain classes of polyhedral products from a homotopy theoretic point of view
An algebraic approach to time borrowing
Get PDFThis paper is about a novel application of linear algebra to the timing of digital hardware. In particular we describe a rigorous, algorithmic approach to �time borrowing�. Time borrowing is a technique whereby the use of a multiphase
clock can allow for a more flexible, efficient use of time. In this approach the system is clocked periodically, but within each clock cycle processes are allowed to interact
asynchronously allowing longer processes to be juxtaposed with shorter processes. We show that this problem can be solved completely using linear algebra defined over the max-plus semi-ring, and that the method so obtained conforms with an earlier, heuristic approach to the problem
Maximising the Size of Non-Redundant Protein Datasets Using Graph Theory
Get PDFAnalysis of protein data sets often requires prior removal of redundancy, so that data is not biased by having multiple copies of similar proteins. This is usually achieved by pairwise comparison of sequences, followed by purging so that no two pairs have similarities above a chosen threshold. From a starting set, such as the PDB or a genome, one should remove as few sequences as possible, to give the largest possible non-redundant set for subsequent analysis. Protein redundancy can be represented as a graph, with proteins as nodes connected by undirected edges, if they have a pairwise similarity above the chosen threshold. The problem is then equivalent to finding the maximum independent set (MIS), where as few nodes are removed as possible to remove all edges. We tested seven MIS algorithms, three of which are new. We applied the methods to the PDB, subsets of the PDB, various genomes and the BHOLSIB benchmark datasets. For PDB subsets of up to 1000 proteins, we could compare to the exact MIS, found by the Cliquer algorithm.
The best algorithm was the new method, Leaf. This works by adding clique members that have no edges to nodes outside the clique to the MIS, starting with the smallest cliques. For PDB subsets of up to 1000 members, it usually finds the MIS and is fast enough to apply to data sets of tens of thousands of proteins. It gives sets that are around 10% larger than the commonly used PISCES algorithm, that are of identical quality. We therefore suggest that Leaf should be the method of choice for generating non-redundant protein data sets, though it is ineffective on dense graphs, such as the BHOLSIB benchmarks. The Leaf algorithm and sets from genomes and the PDB are available at: http://www.bioinf.manchester.ac.uk/leaf/
A Frequency domain approach for the estimation of parameters of spatio-temporal stationary random processes
Get PDFIn this paper we consider the estimation of the parameters of the spatio-temporal covariances of spatio-temporal stationary random processes. We define Finite Fourier Transforms of the processes at each location and based on joint distribution of these complex valued random
variables we define an approximate likelihood function and consider the maximization. Ideas are similar to Whittle likelihood function considered in time series. The sampling properties of the estimators are investigated. The method is applied to simulated data and also to pacific wind
speed data considered earlier by Cressie and Huang
A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions
Get PDFRational Arnoldi is a powerful method for approximating functions of large sparse matrices times a vector. The selection of asymptotically optimal parameters for this method is crucial for its fast convergence. We present and investigate a novel strategy for the automated parameter selection when the function to be approximated is of Cauchy-Stieltjes (or Markov) type, such as the matrix square root or the logarithm. The performance of this approach is demonstrated by numerical examples involving symmetric and nonsymmetric matrices. These examples suggest that our black-box method performs at least as well, and typically better, as the standard rational Arnoldi method with parameters being manually optimized for a given matrix
The hyperbolic Schur decomposition
Get PDFWe propose a hyperbolic counterpart of the Schur decomposition, with the emphasis on the preservation of structures related to some given hyperbolic scalar product. We give results regarding the existence of such a decomposition and research the properties of its block triangular factor for various structured matrices
Exponential sensitivity to symmetry imperfections in an exact Navier–Stokes solution.
No full textWe consider the (radial) stretching flow of an incompressible viscous fluid between two parallel plates.
For infinite plates, a well-known self-similar solution reduces the Navier�Stokes equations to a simple nonlinear boundary-value problem. We demonstrate that, for large Reynolds numbers, a naïve matched asymptotic description of the self-similar flow yields a continuum of solutions. To describe which of the continuum of states is realised requires the inclusion of terms that are beyond all orders in the asymptotic description. Sensitivity to exponentially small terms in the asymptotic description has practical significance in that (i) exponentially small symmetry imperfections in the boundary conditions have a leading-order effect, and (ii) linearised perturbations are seen to decay only on exponentially long space/time scales owing to the presence of eigenmodes that are exponentially near neutral. The results of axisymmetric Navier�Stokes computations are presented to show that the asymptotic description of the self-similar states (and their stability) is of practical relevance to finite-domain solutions
High-speed Dynamic Imaging with a Real Time Tomography System
Get PDFThe Real Time Tomography (RTT) system is a new type of fast cone beam CT scanner, using fixed rings of multiple sources and detectors in an offset geometry. We demonstrate the potential of this system for use in the imaging of high speed dynamic processes, such as moving fluid flows. Through the use of a simple temporal regularisation term, we show that temporal resolution can be further increased, at the expense of a slight loss in spatial resolution
Letting the flux define the kinetics: using a single steady state to predict network behaviour under diverse stress conditions
No full textMotivation
The understanding of metabolic interactions has grown rapidly in recent years with metabolic network reconstructions constantly increasing in scope and quality. These networks can be manipulated into models which allow for fluxes to be estimated using methods such as flux balance analysis. However, the solution space of fluxes is large, and the inability to provide dynamic behaviour of the system can make understanding it under changing conditions difficult. It is under these circumstances where kinetic models can prove more valuable. However, collecting kinetic information for large scale networks is time consuming and expensive, and existing data is difficult to find and collate.
Results
We develop and validate a novel methodology which uses the flux information of one steady state to define the kinetics of the system and produce a reasonable approximation of the steady state behaviour of the real system. We show that first approximation models, in the first instance, show a poor ability to extrapolate beyond the initial conditions. However, metabolic control analysis directs our attention towards the most important reactions of the network. When experimentally-elucidated kinetics are used for those reactions, and the remainder of the network modelled using empirical rate laws that are inspired in enzyme kinetics, predictability improves dramatically
Unstructured finite element method for the solution of the Boussinesq problem in 3D
Get PDFWe present a numerical method for the monolithic discretisation of the Boussinesq system in three spatial dimensions. The key ingredients of the proposed methodology are the finite element discretisation of the spatial
part of the problem using unstructured tetrahedral meshes, an implicit time integrator, based on adaptive predictor-corrector scheme (the explicit AB2 method with the implicit stabilised trapezoid rule), and a new preconditioned
Krylov subspace solver for the rersulting linearised discrete problem. We test the proposed methodology on a number of physically relevant cases, including laterally heated cavities and the Rayleigh-B\'enard convection, and
compare the obtained results with other numerical methods and the experiments