229 research outputs found
Mixing properties in the advection of passive tracers via recurrences and extreme value theory
In this paper we characterize the mixing properties in the advection of
passive tracers by exploiting the extreme value theory for dynamical systems.
With respect to classical techniques directly related to the Poincar\'e
recurrences analysis, our method provides reliable estimations of the
characteristic mixing times and distinguishes between barriers and unstable
fixed points. The method is based on a check of convergence for extreme value
laws on finite datasets. We define the mixing times in terms of the shortest
time intervals such that extremes converge to the asymptotic (known) parameters
of the Generalized Extreme Value distribution. Our technique is suitable for
applications in the analysis of other systems where mixing time scales need to
be determined and limited datasets are available.Comment: arXiv admin note: text overlap with arXiv:1107.597
Design and optimisation of scientific programs in a categorical language
This thesis presents an investigation into the use of advanced computer languages for scientific computing, an examination of performance issues that arise from using such languages for such a task, and a step toward achieving portable performance from compilers by attacking these problems in a way that compensates for the complexity of and differences between modern computer architectures. The language employed is Aldor, a functional language from computer algebra, and the scientific computing area is a subset of the family of iterative linear equation solvers applied to sparse systems. The linear equation solvers that are considered have much common structure, and this is factored out and represented explicitly in the lan-guage as a framework, by means of categories and domains. The flexibility introduced by decomposing the algorithms and the objects they act on into separate modules has a strong performance impact due to its negative effect on temporal locality. This necessi-tates breaking the barriers between modules to perform cross-component optimisation. In this instance the task reduces to one of collective loop fusion and array contrac
An experimental exploration of Marsaglia's xorshift generators, scrambled
Marsaglia proposed recently xorshift generators as a class of very fast,
good-quality pseudorandom number generators. Subsequent analysis by Panneton
and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing
several weaknesses of such generators, verified experimentally using the
TestU01 suite. Nonetheless, many of the weaknesses of xorshift generators fade
away if their result is scrambled by a non-linear operation (as originally
suggested by Marsaglia). In this paper we explore the space of possible
generators obtained by multiplying the result of a xorshift generator by a
suitable constant. We sample generators at 100 equispaced points of their state
space and obtain detailed statistics that lead us to choices of parameters that
improve on the current ones. We then explore for the first time the space of
high-dimensional xorshift generators, following another suggestion in
Marsaglia's paper, finding choices of parameters providing periods of length
and . The resulting generators are of extremely
high quality, faster than current similar alternatives, and generate
long-period sequences passing strong statistical tests using only eight logical
operations, one addition and one multiplication by a constant
Continued fractions and orthogonal polynomials in several variables
We extend the close interplay between continued fractions, orthogonal
polynomials, and Gaussian quadrature rules to several variables in a special
but natural setting which we characterize in terms of moment sequences. The
crucial condition for the characterization is the commutativity of the
multiplication operators on finite polynomial subspaces modulo an ideal.
Moreover, starting from the orthogonal polynomials or the three-term
recurrence, our method constructs a sequence of moment sequences that provides
an approximation of the maximal order for recovering the moment sequence that
defines the orthogonality.Comment: 23 page
Acceleration of Profile-HMM Search for Protein Sequences in Reconfigurable Hardware - Master\u27s Thesis, May 2006
Profile Hidden Markov models are highly expressive representations of functional units, or motifs, conserved across protein sequences. Profile-HMM search is a powerful computational technique that is used to annotate new sequences by identifying occurrences of known motifs in them. With the exponential growth of protein databases, there is an increasing demand for acceleration of such techniques. We describe an accelerator for the Viterbi algorithm using a two-stage pipelined design in which the first stage is implemented in parallel reconfigurable hardware for greater speedup. To this end, we identify algorithmic modifications that expose a high level of parallelism and characterize their impact on the accuracy and performance relative to a standard software implementation. We develop a performance model to evaluate any accelerator design and propose two alternative architectures that recover the accuracy lost by a basic architecture. We compare the performance of the two architectures to show that speedups of up to 3 orders of magnitude may be achieved. We also investigate the use of the Forward algorithm in the first pipeline stage of the accelerator using floating-point arithmetic and report its accuracy and performance
Derivative spectroscopy and the continuous relaxation spectrum
Derivative spectroscopy is conventionally understood to be a collection of techniques for extracting fine structure from spectroscopic data by means of numerical differentiation. In this paper we extend the conventional interpretation of derivative spectroscopy with a view to recovering the continuous relaxation spectrum of a viscoelastic material from oscillatory shear data. To achieve this, the term “spectroscopic data” is allowed to include spectral data which have been severely broadened by the action of a strong low-pass filter. Consequently, a higher order of differentiation than is usually encountered in conventional derivative spectroscopy is required. However, by establishing a link between derivative spectroscopy and wavelet decomposition, high-order differentiation of oscillatory shear data can be achieved using specially constructed wavelet smoothing. This method of recovery is justified when the reciprocal of the Fourier transform of the filter function (convolution kernel) is an entire function, and is particularly powerful when the associated Maclaurin series converges rapidly. All derivatives are expressed algebraically in terms of scaling functions and wavelets of different scales, and the recovered relaxation spectrum is expressible in analytic form. An important feature of the method is that it facilitates local recovery of the spectrum, and is therefore appropriate for real scenarios where the oscillatory shear data is only available for a finite range of frequencies. We validate the method using synthetic data, but also demonstrate its use on real experimental data
Essays on the nonlinear and nonstochastic nature of stock market data
The nature and structure of stock-market price dynamics is an area of ongoing and rigourous scientific debate. For almost three decades, most emphasis has been given on upholding the concepts of Market Efficiency and rational investment behaviour. Such an approach has favoured the development of numerous linear and nonlinear models mainly of stochastic foundations. Advances in mathematics have shown that nonlinear deterministic processes i.e. "chaos" can produce sequences that appear random to linear statistical techniques. Till recently, investment finance has been a science based on linearity and stochasticity. Hence it is important that studies of Market Efficiency include investigations of chaotic determinism and power laws. As far as chaos is concerned, there are rather mixed or inconclusive research results, prone with controversy. This inconclusiveness is attributed to two things: the nature of stock market time series, which are highly volatile and contaminated with a substantial amount of noise of largely unknown structure, and the lack of appropriate robust statistical testing procedures. In order to overcome such difficulties, within this thesis it is shown empirically and for the first time how one can combine novel techniques from recent chaotic and signal analysis literature, under a univariate time series analysis framework. Three basic methodologies are investigated: Recurrence analysis, Surrogate Data and Wavelet transforms. Recurrence Analysis is used to reveal qualitative and quantitative evidence of nonlinearity and nonstochasticity for a number of stock markets. It is then demonstrated how Surrogate Data, under a statistical hypothesis testing framework, can be simulated to provide similar evidence. Finally, it is shown how wavelet transforms can be applied in order to reveal various salient features of the market data and provide a platform for nonparametric regression and denoising. The results indicate that without the invocation of any parametric model-based assumptions, one can easily deduce that there is more to linearity and stochastic randomness in the data. Moreover, substantial evidence of recurrent patterns and aperiodicities is discovered which can be attributed to chaotic dynamics. These results are therefore very consistent with existing research indicating some types of nonlinear dependence in financial data. Concluding, the value of this thesis lies in its contribution to the overall evidence on Market Efficiency and chaotic determinism in financial markets. The main implication here is that the theory of equilibrium pricing in financial markets may need reconsideration in order to accommodate for the structures revealed
Quaternion-based complexity study of human postural sway time series
A multidimensional approach for the study of the center of pressure (CoP) was selected. During the work the dataset was characterized recurring to algorithms taken from Chaotic and Stochastic time series analysis. The effects of the visual and cognitive components were addressed to allow a proper modelization of the data in the complex and quaternion domains
Magnetic operations: a little fuzzy physics?
We examine the behaviour of charged particles in homogeneous, constant and/or
oscillating magnetic fields in the non-relativistic approximation. A special
role of the geometric center of the particle trajectory is elucidated. In
quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an
element of non-commutative geometry which enters into the traditional control
problems. We show that its application extends beyond the usually considered
time independent magnetic fields of the quantum Hall effect. Some simple cases
of magnetic control by oscillating fields lead to the stability maps differing
from the traditional Strutt diagram.Comment: 28 pages, 8 figure
- …