Ratio selection for classification models

This paper is concerned with the selection of inputs for classification models based on ratios of measured quantities. For this purpose, all possible ratios are built from the quantities involved and variable selection techniques are used to choose a convenient subset of ratios. In this context, two selection techniques are proposed: one based on a pre-selection procedure and another based on a genetic algorithm. In an example involving the financial distress prediction of companies, the models obtained from ratios selected by the proposed techniques compare favorably to a model using ratios usually found in the financial distress literature.

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.

An efficient shock capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.

Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces.

A generalised background correction algorithm for a Halo Doppler lidar and its application to data from Finland

Current commercially available Doppler lidars provide an economical and robust solution for measuring vertical and horizontal wind velocities, together with the ability to provide co- and cross-polarised backscatter profiles. The high temporal resolution of these instruments allows turbulent properties to be obtained from studying the variation in radial velocities. However, the instrument specifications mean that certain characteristics, especially the background noise behaviour, become a limiting factor for the instrument sensitivity in regions where the aerosol load is low. Turbulent calculations require an accurate estimate of the contribution from velocity uncertainty estimates, which are directly related to the signal-to-noise ratio. Any bias in the signal-to-noise ratio will propagate through as a bias in turbulent properties. In this paper we present a method to correct for artefacts in the background noise behaviour of commercially available Doppler lidars and reduce the signal-to-noise ratio threshold used to discriminate between noise, and cloud or aerosol signals. We show that, for Doppler lidars operating continuously at a number of locations in Finland, the data availability can be increased by as much as 50 % after performing this background correction and subsequent reduction in the threshold. The reduction in bias also greatly improves subsequent calculations of turbulent properties in weak signal regimes.

An improved algorithm for generating global window brightness temperatures from multiple satellite infrared imagery

An improved algorithm for the generation of gridded window brightness temperatures is presented. The primary data source is the International Satellite Cloud Climatology Project, level B3 data, covering the period from July 1983 to the present. The algorithm rakes window brightness, temperatures from multiple satellites, both geostationary and polar orbiting, which have already been navigated and normalized radiometrically to the National Oceanic and Atmospheric Administration's Advanced Very High Resolution Radiometer, and generates 3-hourly global images on a 0.5 degrees by 0.5 degrees latitude-longitude grid. The gridding uses a hierarchical scheme based on spherical kernel estimators. As part of the gridding procedure, the geostationary data are corrected for limb effects using a simple empirical correction to the radiances, from which the corrected temperatures are computed. This is in addition to the application of satellite zenith angle weighting to downweight limb pixels in preference to nearer-nadir pixels. The polar orbiter data are windowed on the target time with temporal weighting to account for the noncontemporaneous nature of the data. Large regions of missing data are interpolated from adjacent processed images using a form of motion compensated interpolation based on the estimation of motion vectors using an hierarchical block matching scheme. Examples are shown of the various stages in the process. Also shown are examples of the usefulness of this type of data in GCM validation.

Land/sea warming ratio in response to climate change: IPCC AR4 model results and comparison with observations

Climate model simulations consistently show that in response to greenhouse gas forcing surface temperatures over land increase more rapidly than over sea. The enhanced warming over land is not simply a transient effect, since it is also present in equilibrium conditions. We examine 20 models from the IPCC AR4 database. The global land/sea warming ratio varies in the range 1.36–1.84, independent of global mean temperature change. In the presence of increasing radiative forcing, the warming ratio for a single model is fairly constant in time, implying that the land/sea temperature difference increases with time. The warming ratio varies with latitude, with a minimum in equatorial latitudes, and maxima in the subtropics. A simple explanation for these findings is provided, and comparisons are made with observations. For the low-latitude (40°S–40°N) mean, the models suggest a warming ratio of 1.51 ± 0.13, while recent observations suggest a ratio of 1.54 ± 0.09.

Classifying dynamical forcing mechanisms using a climatology of extratropical cyclones

A climatology of almost 700 extratropical cyclones is compiled by applying an automated feature tracking algorithm to a database of objectively identified cyclonic features. Cyclones are classified according to the relative contributions to the midlevel vertical motion of the forcing from upper and lower levels averaged over the cyclone intensification period (average U/L ratio) and also by the horizontal separation between their upper-level trough and low-level cyclone (tilt). The frequency distribution of the average U/L ratio of the cyclones contains two significant peaks and a long tail at high U/L ratio. Although discrete categories of cyclones have not been identified, the cyclones comprising the peaks and tail have characteristics that have been shown to be consistent with the type A, B, and C cyclones of the threefold classification scheme. Using the thresholds in average U/L ratio determined from the frequency distribution, type A, B, and C cyclones account for 30\%, 38\%, and 32\% of the total number of cyclones respectively. Cyclones with small average U/L ratio are more likely to be developing cyclones (attain a relative vorticity $\ge 1.2 \times 10^{-4} \mbox{s}^{-1}$) whereas cyclones with large average U/L ratio are more likely to be nondeveloping cyclones (60\% of type A cyclones develop whereas 31\% of type C cyclones develop). Type A cyclogenesis dominates in the development region East of the Rockies and over the gulf stream, type B cyclogenesis dominates in the region off the East coast of the USA, and type C cyclogenesis is more common over the oceans in regions of weaker low-level baroclinicity.

A geometric algorithm for an artificial life form based on anachronistic methods

Modern methods of spawning new technological motifs are not appropriate when it is desired to realize artificial life as an actual real world entity unto itself (Pattee 1995; Brooks 2006; Chalmers 1995). Many fundamental aspects of such a machine are absent in common methods, which generally lack methodologies of construction. In this paper we mix classical and modern studies in order to attempt to realize an artificial life form from first principles. A model of an algorithm is introduced, its methodology of construction is presented, and the fundamental source from which it sprang is discussed.

Algorithm for generating defective graphene sheets

An algorithm is presented for the generation of molecular models of defective graphene fragments, containing a majority of 6-membered rings with a small number of 5- and 7-membered rings as defects. The structures are generated from an initial random array of points in 2D space, which are then subject to Delaunay triangulation. The dual of the triangulation forms a Voronoi tessellation of polygons with a range of ring sizes. An iterative cycle of refinement, involving deletion and addition of points followed by further triangulation, is performed until the user-defined criteria for the number of defects are met. The array of points and connectivities are then converted to a molecular structure and subject to geometry optimization using a standard molecular modeling package to generate final atomic coordinates. On the basis of molecular mechanics with minimization, this automated method can generate structures, which conform to user-supplied criteria and avoid the potential bias associated with the manual building of structures. One application of the algorithm is the generation of structures for the evaluation of the reactivity of different defect sites. Ab initio electronic structure calculations on a representative structure indicate preferential fluorination close to 5-ring defects.

Periodic Reordering

For many networks in nature, science and technology, it is possible to order the nodes so that most links are short-range, connecting near-neighbours, and relatively few long-range links, or shortcuts, are present. Given a network as a set of observed links (interactions), the task of finding an ordering of the nodes that reveals such a range-dependent structure is closely related to some sparse matrix reordering problems arising in scientific computation. The spectral, or Fiedler vector, approach for sparse matrix reordering has successfully been applied to biological data sets, revealing useful structures and subpatterns. In this work we argue that a periodic analogue of the standard reordering task is also highly relevant. Here, rather than encouraging nonzeros only to lie close to the diagonal of a suitably ordered adjacency matrix, we also allow them to inhabit the off-diagonal corners. Indeed, for the classic small-world model of Watts & Strogatz (1998, Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442) this type of periodic structure is inherent. We therefore devise and test a new spectral algorithm for periodic reordering. By generalizing the range-dependent random graph class of Grindrod (2002, Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E, 66, 066702-1–066702-7) to the periodic case, we can also construct a computable likelihood ratio that suggests whether a given network is inherently linear or periodic. Tests on synthetic data show that the new algorithm can detect periodic structure, even in the presence of noise. Further experiments on real biological data sets then show that some networks are better regarded as periodic than linear. Hence, we find both qualitative (reordered networks plots) and quantitative (likelihood ratios) evidence of periodicity in biological networks.

A contour-advective semi-lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields

This paper describes a novel numerical algorithm for simulating the evolution of fine-scale conservative fields in layer-wise two-dimensional flows, the most important examples of which are the earth's atmosphere and oceans. the algorithm combines two radically different algorithms, one Lagrangian and the other Eulerian, to achieve an unexpected gain in computational efficiency. The algorithm is demonstrated for multi-layer quasi-geostrophic flow, and results are presented for a simulation of a tilted stratospheric polar vortex and of nearly-inviscid quasi-geostrophic turbulence. the turbulence results contradict previous arguments and simulation results that have suggested an ultimate two-dimensional, vertically-coherent character of the flow. Ongoing extensions of the algorithm to the generally ageostrophic flows characteristic of planetary fluid dynamics are outlined.

A genetic algorithm for the design of a fuzzy controller for active queue management

Active queue management (AQM) policies are those policies of router queue management that allow for the detection of network congestion, the notification of such occurrences to the hosts on the network borders, and the adoption of a suitable control policy. This paper proposes the adoption of a fuzzy proportional integral (FPI) controller as an active queue manager for Internet routers. The analytical design of the proposed FPI controller is carried out in analogy with a proportional integral (PI) controller, which recently has been proposed for AQM. A genetic algorithm is proposed for tuning of the FPI controller parameters with respect to optimal disturbance rejection. In the paper the FPI controller design metodology is described and the results of the comparison with random early detection (RED), tail drop, and PI controller are presented.