A Robust Classification of Galaxy Spectra: Dealing with Noisy and Incomplete Data

Over the next few years new spectroscopic surveys (from the optical surveys of the Sloan Digital Sky Survey and the 2 degree Field survey through to space-based ultraviolet satellites such as GALEX) will provide the opportunity and challenge of understanding how galaxies of different spectral type evolve with redshift. Techniques have been developed to classify galaxies based on their continuum and line spectra. Some of the most promising of these have used the Karhunen and Loeve transform (or Principal Component Analysis) to separate galaxies into distinct classes. Their limitation has been that they assume that the spectral coverage and quality of the spectra are constant for all galaxies within a given sample. In this paper we develop a general formalism that accounts for the missing data within the observed spectra (such as the removal of sky lines or the effect of sampling different intrinsic rest wavelength ranges due to the redshift of a galaxy). We demonstrate that by correcting for these gaps we can recover an almost redshift independent classification scheme. From this classification we can derive an optimal interpolation that reconstructs the underlying galaxy spectral energy distributions in the regions of missing data. This provides a simple and effective mechanism for building galaxy spectral energy distributions directly from data that may be noisy, incomplete or drawn from a number of different sources.Comment: 20 pages, 8 figures. Accepted for publication in A

How clumpy is my image? Evaluating crowdsourced annotation tasks

13th UK Workshop on Computational Intelligence (UKCI), Guildford, UK, 9-11 September 2013This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.The use of citizen science to obtain annotations from multiple annotators has been shown to be an effective method for annotating datasets in which computational methods alone are not feasible. The way in which the annotations are obtained is an important consideration which affects the quality of the resulting consensus estimates. In this paper, we examine three separate approaches to obtaining scores for instances rather than merely classifications. To obtain a consensus score annotators were asked to make annotations in one of three paradigms: classification, scoring and ranking. A web-based citizen science experiment is described which implements the three approaches as crowdsourced annotation tasks. The tasks are evaluated in relation to the accuracy and agreement among the participants using both simulated and real-world data from the experiment. The results show a clear difference in performance between the three tasks, with the ranking task obtaining the highest accuracy and agreement among the participants. We show how a simple evolutionary optimiser may be used to improve the performance by reweighting the importance of annotators

Shape optimisation using Computational Fluid Dynamics and Evolutionary Algorithms

This is the author accepted manuscript.Optimisation of designs using Computational Fluid Dynamics (CFD) are frequently performed across many fields of research, such as the optimisation of an aircraft wing to reduce drag, or to increase the efficiency of a heat exchanger. General optimisation strategies involves altering design variables with a view to improve appropriate objective function(s). Often the objective function(s) are non-linear and multi-modal, and thus polynomial time algorithms for solving such problems may not be available. In such cases, applying Evolutionary Algorithms (EAs - a class of stochastic global optimisation techniques inspired from natural evolution) may locate good solutions within a practical time frame. The traditional CFD design optimisation process is often based on a ‘trial-and-error type approach. Starting from an initial geometry, Computational Aided Design changes are introduced manually based on results from a limited number of design iterations and CFD analyses. The process is usually complex, time-consuming and relies heavily on engineering experience, thus making the overall design procedure inconsistent, i.e. different ‘best’ solutions are obtained from different designers. [...]This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant (reference number: EP/M017915/1) for the University of Exeter’s College of Engineering, Mathematics, and Physical Sciences

Automatic shape optimisation of the turbine-99 draft tube

This is the author accepted manuscript.INTRODUCTION The performance of a hydraulic reaction turbine is significantly affected by the efficiency of its draft tube. Factors which impede the tube’s performance include the geometrical shape (profile), and velocity distribution at the inflow. So far, the design of draft tubes has been improved through experimental observations resulting in empirical formulae or ‘rules of thumb’. The use of Computational Fluid Dynamics (CFD) in this design process has only been a recent addition due to its robustness and cost-effectivenesses with increasing availability to computational power. The flexibility of CFD, allowing for comprehensive analysis of complex profiles, is especially appealing for optimising the design. Hence, there is a need for developing an accurate and reliable CFD approach together with an efficient optimisation strategy. Flows through a turbine draft tube are characterised as turbulent with a range of flow phenomena, e.g. unsteadiness, flow separation, and swirling flow. With the aim of improving the techniques for analysing such flows, the turbomachinery community have proposed a standard test case in the form of the Turbine-99 draft tube [1]. Along with this standard geometry, with the aim of simulating the swirling inflow, an additional runner proposed by Cervantes [2] is included in the present work. The draft tube geometry is shown in Fig.1. The purpose of this abstract is to outline the framework developed to achieve the automated shape optimisation of this draft tube.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant (reference number: EP/M017915/1) for the University of Exeters College of Engineering, Mathematics, and Physical Sciences

Coexistence and critical behaviour in a lattice model of competing species

In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of resources is on an intermediate level, the species with slower metabolism becomes extinct. On the other hand, when resources are scarce it is the species with faster metabolism that becomes extinct. The range of coexistence of the two species increases with dimension. We suggest that our model might describe some aspects of the competition between normal and tumor cells. With such an interpretation, examples of tumor remission, recurrence and of different morphologies are presented. In the d=1 and d=2 models, we analyse the nature of phase transitions: they are either discontinuous or belong to the directed-percolation universality class, and in some cases they have an active subcritical phase. In the d=2 case, one of the transitions seems to be characterized by critical exponents different than directed-percolation ones, but this transition could be also weakly discontinuous. In the d=3 version, Monte Carlo simulations are in a good agreement with the solution of the mean-field approximation. This approximation predicts that oscillatory behaviour occurs in the present model, but only for d>2. For d>=2, a steady state depends on the initial configuration in some cases.Comment: 11 pages, 14 figure

Basin structure in the two-dimensional dissipative circle map

Fractal basin structure in the two-dimensional dissipative circle map is examined in detail. Numerically obtained basin appears to be riddling in the parameter region where two periodic orbits co-exist near a boundary crisis, but it is shown to consist of layers of thin bands.Comment: published in J. Phys. Soc. Jpn., 72, 1943-1947 (2003

Riddled-like Basin in Two-Dimensional Map for Bouncing Motion of an Inelastic Particle on a Vibrating Board

Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling bifurcation, we found peculiar behavior in the parameter region where two stable periodic attractors coexist. A typical orbit in the region goes through chaotic motion for an extended transient period before it converges into one of the two periodic attractors. The basin structure in this parameter region is almost riddling and the fractal dimension of the basin boundary is close to two, {\it i.e.}, the dimension of the phase space.Comment: 4 pages, 5 figures. to be published in J. Phys. Soc. Jpn. (2002

Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn't yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative Marketing and Economics vol 4 (2006), no. 2, 173--20

Extending periodic eddy covariance latent heat fluxes through tree sap-flow measurements to estimate long-term total evaporation in a peat swamp forest

A combination of measurement and modelling was used to find a pragmatic solution to estimate the annual total evaporation from the rare and indigenous Nkazana Peat Swamp Forest (PSF) on the east coast of Southern Africa to improve the water balance estimates within the area. Actual total evaporation (ETa) was measured during three window periods (between 7 and 9 days each) using an eddy covariance (EC) system on a telescopic mast above the forest canopy. Sap flows of an understory tree and an emergent tree were measured using a low-maintenance heat pulse velocity system for an entire hydrological year (October 2009 to September 2010). An empirical model was derived, describing the relationship between ETa from the Nkazana PSF and sap-flow measurements. These overlapped during two of the window periods (R2 = 0.92 and 0.90), providing hourly estimates of ETa from the Nkazana PSF for a year, totalling 1125 mm (while rainfall was 650 mm). In building the empirical model, it was found that to include the understory tree sap flow provided no benefit to the model performance. In addition, the relationship between the emergent tree sap flow with ETa between the two field campaigns was consistent and could be represented by a single empirical model (R2 = 0.90; RMSE = 0.08 mm h−1). During the window periods of EC measurement, no single meteorological variable was found to describe the Nkazana PSF ETa satisfactorily. However, in terms of evaporation models, the hourly FAO Penman–Monteith reference evaporation (ETo) best described ETa during the August 2009 (R2 = 0.75), November 2009 (R2 = 0.85) and March 2010 (R2 = 0.76) field campaigns, compared to the Priestley–Taylor potential evaporation (ETp) model (R2 = 0.54, 0.74 and 0.62 during the respective field campaigns). From the extended record of ETa (derived in this study from sap flow) and ETo, a monthly crop factor (Kc) was derived for the Nkazana PSF, providing a method of estimating long-term swamp forest water-use from meteorological data. The monthly Kc indicated two distinct periods. From February to May, it was between 1.2 and 1.4 compared with June to January, when the crop factor was 0.8 to 1.0. The derived monthly Kc values were verified as accurate (to one significant digit) using historical data measured at the same site, also using EC, from a previous study. The measurements provided insights into the microclimate within a subtropical peat swamp forest and the contrasting sap flow of emergent and understory trees. They showed that expensive, high-maintenance equipment can be used during manageable window periods in conjunction with low-maintenance systems, dedicated to individual trees, to derive a model to estimate long-term ETa over remote heterogeneous forests. In addition, the contrast in annual ETa and rainfall emphasised the reliance of the Nkazana PSF on groundwater

A new method to measure Bowen ratios using high-resolution vertical dry and wet bulb temperature profiles

The Bowen ratio surface energy balance method is a relatively simple method to determine the latent heat flux and the actual land surface evaporation. The Bowen ratio method is based on the measurement of air temperature and vapour pressure gradients. If these measurements are performed at only two heights, correctness of data becomes critical. In this paper we present the concept of a new measurement method to estimate the Bowen ratio based on vertical dry and wet bulb temperature profiles with high spatial resolution. A short field experiment with distributed temperature sensing (DTS) in a fibre optic cable with 13 measurement points in the vertical was undertaken. A dry and a wetted section of a fibre optic cable were suspended on a 6 m high tower installed over a sugar beet trial plot near Pietermaritzburg (South Africa). Using the DTS cable as a psychrometer, a near continuous observation of vapour pressure and air temperature at 0.20 m intervals was established. These data allowed the computation of the Bowen ratio with a high spatial and temporal precision. The daytime latent and sensible heat fluxes were estimated by combining the Bowen ratio values from the DTS-based system with independent measurements of net radiation and soil heat flux. The sensible heat flux, which is the relevant term to evaluate, derived from the DTS-based Bowen ratio (BR-DTS) was compared with that derived from co-located eddy covariance (<i>R</i>² = 0.91), surface layer scintillometer (<i>R</i>² = 0.81) and surface renewal (<i>R</i>² = 0.86) systems. By using multiple measurement points instead of two, more confidence in the derived Bowen ratio values is obtained