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A Stochastic Model for Wind Turbine Power Quality using a Levy Index Analysis of Wind Velocity Data (2011)

Blackledge, Jonathan; Coyle, Eugene; Kearney, Derek

A Stochastic Model for Wind Turbine Power Quality using a Levy Index Analysis of Wind Velocity Data (2011)

Blackledge, Jonathan; Coyle, Eugene; Kearney, Derek

Abstract:

The power quality of a wind turbine is determined by many factors but time-dependent variation in the wind velocity are arguably the most important. After a brief review of the statistics of typical wind speed data, a non- Gaussian model for the wind velocity is introduced that is based on a Levy distribution. It is shown how this distribution can be used to derive a stochastic fractional diusion equation for the wind velocity as a function of time whose solution is characterised by the Levy index. A Levy index numerical analysis is then performed on wind velocity data for both rural and urban areas where, in the latter case, the index has a larger value. Finally, an empirical relationship is derived for the power output from a wind turbine in terms of the Levy index using Betz law.

https://arrow.dit.ie/engscheleart/146

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Application of the Fractal Market Hypothesis for Modelling Macroeconomic Time Series (2008)

Blackledge, Jonathan

Application of the Fractal Market Hypothesis for Modelling Macroeconomic Time Series (2008)

Blackledge, Jonathan

Abstract:

This paper explores the conceptual background to ﬁnancial time series analysis and ﬁnancial signal processing in terms of the Efﬁcient Market Hypothesis. By revisiting the principal conventional approaches to market analysis and the reasoning associated with them, we develop a Fractal Market Hypothesis that is based on the application of non-stationary fractional dynamics using an operator of the type ∂2 / ∂x2 − σq(t) * ∂ q(t)/ ∂tq(t) where σ−1 is the fractional diffusivity and q is the Fourier dimension which, for the topology considered, (i.e. the one-dimensional case) is related to the Fractal Dimension 1 < DF < 2 by q = 1 − DF + 3/2. We consider an approach that is based on the signal q(t) and its interpretation, including its use as a macroeconomic volatility index. In practice, this is based on the application of a moving window data processor that utilises Orthogonal Linear Regression to compute q from the power spectrum of the windowed data. This is applied to FTSE...

https://arrow.dit.ie/engscheleart2/28

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Bayesian exponential random graph modelling of interhospital patient referral networks (2017)

Caimo, Alberto; Pallotti, Francesca; Lomi, Alessandro

Bayesian exponential random graph modelling of interhospital patient referral networks (2017)

Caimo, Alberto; Pallotti, Francesca; Lomi, Alessandro

Abstract:

Using original data that we have collected on referral relations between 110 hospitals serving a large regional community, we show how recently derived Bayesian exponential random graph models may be adopted to illuminate core empirical issues in research on relational coordination among healthcare organisations. We show how a rigorous Bayesian computation approach supports a fully probabilistic analytical framework that alleviates well-known problems in the estimation of model parameters of exponential random graph models. We also show how the main structural features of interhospital patient referral networks that prior studies have described can be reproduced with accuracy by specifying the system of local dependencies that produce – but at the same time are induced by – decentralised collaborative arrangements between hospitals.

https://arrow.dit.ie/scschmatart/233

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Covariate models for accident data (1986)

MacKenzie, Gilbert

Covariate models for accident data (1986)

MacKenzie, Gilbert

Abstract:

The statistical analysis of accident data has historically relied on the mathematical precepts of classical discrete distribution theory Since the first test of the standard null ("pure chance") hypothesis on accident mortality data, relating to horse-kicks in ten Prussian Army Corps during 1875-1894 (von Bortkiewicz, 1898), various models have been advanced to explain departure from Poisson's (1837) law. The ostensibly separate hypotheses of "proneness" (termed "unequal liability" Greenwood and Yule (1920) and "false contagion" by others Bates, et al , (1952), and "contagion" have received extensive attention in the literature (Newbold, 1927, Anscombe, 1950, Bliss and Fisher, 1953, Neyman, 1939, Cresswell and Froggatt, 1963, Kemp and Kemp, 1965 and Kemp, 19670). However, despite considerable development of the associated statistical models, formidable problems of interpretation remain (Froggatt, 1968a).

http://hdl.handle.net/2262/7219

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Diffusion and Fractional Diffusion Based Models for Multiple Light Scattering and Image Analysis (2007)

Blackledge, Jonathan

Diffusion and Fractional Diffusion Based Models for Multiple Light Scattering and Image Analysis (2007)

Blackledge, Jonathan

Abstract:

This paper considers a fractional light diffusion model as an approach to characterizing the case when intermediate scattering processes are present, i.e. the scattering regime is neither strong nor weak. In order to introduce the basis for this approach, we revisit the elements of formal scattering theory and the classical diffusion problem in terms of solutions to the inhomogeneous wave and diffusion equations respectively. We then address the significance of these equations in terms of a random walk model for multiple scattering. This leads to the proposition of a fractional diffusion equation for modelling intermediate strength scattering that is based on a generalization of the diffusion equation to fractional form. It is shown how, by induction, the fractional diffusion equation can be justified in terms of the generalization of a random walk model to fractional form as characterized by the Hurst exponent. Image processing and analysis methods are proposed that are based on di...

https://arrow.dit.ie/engscheleart2/37

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Economic Risk Assessment using the Fractal Market Hypothesis (2010)

Blackledge, Jonathan; Rebow, Marek

Economic Risk Assessment using the Fractal Market Hypothesis (2010)

Blackledge, Jonathan; Rebow, Marek

Abstract:

This paper considers the Fractal Market Hypothesi (FMH) for assessing the risk(s) in developing a financial portfolio based on data that is available through the Internet from an increasing number of sources. Most financial risk management systems are still based on the Efficient Market Hypothesis which often fails due to the inaccuracies of the statistical models that underpin the hypothesis, in particular, that financial data are based on stationary Gaussian processes. The FMH considered in this paper assumes that financial data are non-stationary and statistically self-affine so that a risk analysis can, in principal, be applied at any time scale provided there is sufficient data to make the output of a FMH analysis statistically significant.

https://arrow.dit.ie/engscheleart/151

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Encryption using Deterministic Chaos (2010)

Blackledge, Jonathan; Ptitsyn, Nikolai

Encryption using Deterministic Chaos (2010)

Blackledge, Jonathan; Ptitsyn, Nikolai

Abstract:

The concepts of randomness, unpredictability, complexity and entropy form the basis of modern cryptography and a cryptosystem can be interpreted as the design of a key-dependent bijective transformation that is unpredictable to an observer for a given computational resource. For any cryptosystem, including a Pseudo-Random Number Generator (PRNG), encryption algorithm or a key exchange scheme, for example, a cryptanalyst has access to the time series of a dynamic system and knows the PRNG function (the algorithm that is assumed to be based on some iterative process) which is taken to be in the public domain by virtue of the Kerchhoff-Shannon principal, i.e. the enemy knows the system. However, the time series is not a compact subset of a trajectory (intermediate states are hidden) and the iteration function is taken to include a ‘secret parameter’ - the ‘key’. We can think of the sample as being ‘random’, ‘unpredictable’ and ‘complex’. What do these properties mean mathematically and...

https://arrow.dit.ie/engscheleart2/15

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Models for overdispersed data in entomology (2020)

Demétrio, Clarice G. B.; Hinde, John; Moral, Rafael A.

Models for overdispersed data in entomology (2020)

Demétrio, Clarice G. B.; Hinde, John; Moral, Rafael A.

Abstract:

Entomological data are often overdispersed, characterised by a larger variance than assumed by simple standard models. It is important to model overdispersion properly in order to avoid incorrect and misleading inferences. Outcomes of interest are often in the form of counts or proportions and we present extended models that incorporate overdispersion, methods to assess its impact and model goodness-of-fit, and techniques to test treatment differences in the presence of overdispersion.
Not peer reviewed

http://hdl.handle.net/10379/15790

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Why is an Einstein Ring Blue? (2011)

Blackledge, Jonathan

Why is an Einstein Ring Blue? (2011)

Blackledge, Jonathan

Abstract:

Albert Einstein predicted the existence of `Einstein rings' as a consequence of his general theory of relativity. The phenomenon is a direct result of the idea that if a mass warps space-time then light (and other electromagnetic waves) will be `lensed' by the strong gravitational field produced by a large cosmological body such as a galaxy. Since 1998, when the first complete Einstein ring was observed, many more complete or partially complete Einstein rings have been observed in the radio and infrared spectra, for example, and by the Hubble Space Telescope in the optical spectrum. However, in the latter case, it is observed that the rings are blue providing the light is not red shifted. The gravitational lensing equation does not include dispersion (i.e. wavelength dependent effects) and thus, can not account for this `blue shift' and, to date, there has been no satisfactory explanation for this colour phenomenon. In this paper we provide an explanation for why Eins...

https://arrow.dit.ie/engscheleart2/19