Local optima networks of hard combinatorial landscapes

Combinatorial optimization involves finding an optimal solution in a finite set of options; many everyday life problems are of this kind. However, the number of options grows exponentially with the size of the problem, such that an exhaustive search for the best solution is practically infeasible beyond a certain problem size. When efficient algorithms are not available, a practical approach to obtain an approximate solution to the problem at hand, is to start with an educated guess and gradually refine it until we have a good-enough solution. Roughly speaking, this is how local search heuristics work. These stochastic algorithms navigate the problem search space by iteratively turning the current solution into new candidate solutions, guiding the search towards better solutions. The search performance, therefore, depends on structural aspects of the search space, which in turn depend on the move operator being used to modify solutions. A common way to characterize the search space of a problem is through the study of its fitness landscape, a mathematical object comprising the space of all possible solutions, their value with respect to the optimization objective, and a relationship of neighborhood defined by the move operator. The landscape metaphor is used to explain the search dynamics as a sort of potential function. The concept is indeed similar to that of potential energy surfaces in physical chemistry. Borrowing ideas from that field, we propose to extend to combinatorial landscapes the notion of the inherent network formed by energy minima in energy landscapes. In our case, energy minima are the local optima of the combinatorial problem, and we explore several definitions for the network edges. At first, we perform an exhaustive sampling of local optima basins of attraction, and define weighted transitions between basins by accounting for all the possible ways of crossing the basins frontier via one random move. Then, we reduce the computational burden by only counting the chances of escaping a given basin via random kick moves that start at the local optimum. Finally, we approximate network edges from the search trajectory of simple search heuristics, mining the frequency and inter-arrival time with which the heuristic visits local optima. Through these methodologies, we build a weighted directed graph that provides a synthetic view of the whole landscape, and that we can characterize using the tools of complex networks science. We argue that the network characterization can advance our understanding of the structural and dynamical properties of hard combinatorial landscapes. We apply our approach to prototypical problems such as the Quadratic Assignment Problem, the NK model of rugged landscapes, and the Permutation Flow-shop Scheduling Problem. We show that some network metrics can differentiate problem classes, correlate with problem non-linearity, and predict problem hardness as measured from the performances of trajectory-based local search heuristics.

The Crocidura fuliginosa species complex (Mammalia, Insectivora) in Peninsular Malaya: biological, karyological and genetical evidence

Four West Malaysian shrew populations of the genus Crocidura were investigated through their karyotype and allozyme variations, and, in part, by interfertility experiments. Two different karyotypes characterize these shrews. The first, restricted to the Cameron Highlands (Peninsular Malaysia), invariably has 2n = 40 chromosomes but a varying fundamental number (FN = 54-58). The second karyotype shows a fundamental number of 62-68 and a polymorphic chromosomal number of 2n = 38, 39 or 40, a rare event in the genus Crocidura. Thus both can be distinguished by either a low or a higher number of meta- and submetacentric elements. In heterospecific breeding experiments, mutual avoidance was observed suggesting prezygotic barriers, whereas intraspecific pairs produced 13 liters (mean 2.1 young). Furthermore, our biochemical results indicate that both karyotypes correspond to a relatively ancient separation (Nei's D = 0.354), an amount of genetic differentiation comparable to the distance separating them from the West Palearctic C. russula (D = 0.429-0.583). In contrast, conspecific island and mainland Malaysian shrews possessing the second karyotype had only one fixed allelic difference over the 35 loci surveyed. The problem of naming the two biological species remains unsolved and requires further comparative investigations.

Rapid, combinatorial analysis of membrane compartments in intact plants with a multicolor marker set.

Plant membrane compartments and trafficking pathways are highly complex, and are often distinct from those of animals and fungi. Progress has been made in defining trafficking in plants using transient expression systems. However, many processes require a precise understanding of plant membrane trafficking in a developmental context, and in diverse, specialized cell types. These include defense responses to pathogens, regulation of transporter accumulation in plant nutrition or polar auxin transport in development. In all of these cases a central role is played by the endosomal membrane system, which, however, is the most divergent and ill-defined aspect of plant cell compartmentation. We have designed a new vector series, and have generated a large number of stably transformed plants expressing membrane protein fusions to spectrally distinct, fluorescent tags. We selected lines with distinct subcellular localization patterns, and stable, non-toxic expression. We demonstrate the power of this multicolor 'Wave' marker set for rapid, combinatorial analysis of plant cell membrane compartments, both in live-imaging and immunoelectron microscopy. Among other findings, our systematic co-localization analysis revealed that a class of plant Rab1-homologs has a much more extended localization than was previously assumed, and also localizes to trans-Golgi/endosomal compartments. Constructs that can be transformed into any genetic background or species, as well as seeds from transgenic Arabidopsis plants, will be freely available, and will promote rapid progress in diverse areas of plant cell biology.

A pseudo-spectral method for simulating of poro-elastic seismic wave propagation in complex borehole environments

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in cylindrical coordinates. An important application of this method is the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the center, the borehole casing and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction, Fourier expansions in the other directions, and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method based on the method of characteristics is used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces. The viability and accuracy of the proposed method has been tested and verified in 2D polar coordinates through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. The proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is handled adequately.

Metal concentrations in soils around the copper smelter and surrounding industrial complex of Port Kembla, NSW, Australia

Anthropogenic emissions of metals from sources such as smelters are an international problem, but there is limited published information on emissions from Australian smelters. The objective of this study was to investigate the regional distribution of heavy metals in soils in the vicinity of the industrial complex of Port Kembla, NSW, Australia, which comprises a copper smelter, steelworks and associated industries. Soil samples (n=25) were collected at the depths of 0-5 and 5-20 cm, air dried and sieved to < 2 mm. Aqua regia extractable amounts of As, Cr, Cu, Ph and Zn were analysed by inductively coupled plasma mass spectrometry (lCP-MS) and inductively coupled plasma atomic emission spectrometry (ICP-AES). Outliers were identified from background levels by statistical methods. Mean background levels at a depth of 0-5 cm were estimated at 3.2 mg/kg As, 12 mg/kg Cr, 49 mg/kg Cu, 20 mg/kg Ph and 42 mg/kg Zn. Outliers for elevated As and Cu values were mainly present within 4 km from the Port Kembla industrial complex, but high Ph at two sites and high Zn concentrations were found at six sites up to 23 km from Port Kembla. Chromium concentrations were not anomalous close to the industrial complex. There was no significant difference of metal concentrations at depths of 0-5 and 5-20 cm, except for Ph and Zn. Copper and As concentrations in the soils are probably related to the concentrations in the parent rock. From this investigation, the extent of the contamination emanating from the Port Kembla industrial complex is limited to 1-13 km, but most likely <4 km, depending on the element; the contamination at the greater distance may not originate from the industrial complex. (C) 2003 Elsevier B.V. All rights reserved.

Kernel-based Mapping of Meteorological Fields in Complex Orography

Due to the advances in sensor networks and remote sensing technologies, the acquisition and storage rates of meteorological and climatological data increases every day and ask for novel and efficient processing algorithms. A fundamental problem of data analysis and modeling is the spatial prediction of meteorological variables in complex orography, which serves among others to extended climatological analyses, for the assimilation of data into numerical weather prediction models, for preparing inputs to hydrological models and for real time monitoring and short-term forecasting of weather.In this thesis, a new framework for spatial estimation is proposed by taking advantage of a class of algorithms emerging from the statistical learning theory. Nonparametric kernel-based methods for nonlinear data classification, regression and target detection, known as support vector machines (SVM), are adapted for mapping of meteorological variables in complex orography.With the advent of high resolution digital elevation models, the field of spatial prediction met new horizons. In fact, by exploiting image processing tools along with physical heuristics, an incredible number of terrain features which account for the topographic conditions at multiple spatial scales can be extracted. Such features are highly relevant for the mapping of meteorological variables because they control a considerable part of the spatial variability of meteorological fields in the complex Alpine orography. For instance, patterns of orographic rainfall, wind speed and cold air pools are known to be correlated with particular terrain forms, e.g. convex/concave surfaces and upwind sides of mountain slopes.Kernel-based methods are employed to learn the nonlinear statistical dependence which links the multidimensional space of geographical and topographic explanatory variables to the variable of interest, that is the wind speed as measured at the weather stations or the occurrence of orographic rainfall patterns as extracted from sequences of radar images. Compared to low dimensional models integrating only the geographical coordinates, the proposed framework opens a way to regionalize meteorological variables which are multidimensional in nature and rarely show spatial auto-correlation in the original space making the use of classical geostatistics tangled.The challenges which are explored during the thesis are manifolds. First, the complexity of models is optimized to impose appropriate smoothness properties and reduce the impact of noisy measurements. Secondly, a multiple kernel extension of SVM is considered to select the multiscale features which explain most of the spatial variability of wind speed. Then, SVM target detection methods are implemented to describe the orographic conditions which cause persistent and stationary rainfall patterns. Finally, the optimal splitting of the data is studied to estimate realistic performances and confidence intervals characterizing the uncertainty of predictions.The resulting maps of average wind speeds find applications within renewable resources assessment and opens a route to decrease the temporal scale of analysis to meet hydrological requirements. Furthermore, the maps depicting the susceptibility to orographic rainfall enhancement can be used to improve current radar-based quantitative precipitation estimation and forecasting systems and to generate stochastic ensembles of precipitation fields conditioned upon the orography.

Bayesian Networks and the Value of the Evidence for the Forensic Two-Trace Transfer Problem

Forensic scientists face increasingly complex inference problems for evaluating likelihood ratios (LRs) for an appropriate pair of propositions. Up to now, scientists and statisticians have derived LR formulae using an algebraic approach. However, this approach reaches its limits when addressing cases with an increasing number of variables and dependence relationships between these variables. In this study, we suggest using a graphical approach, based on the construction of Bayesian networks (BNs). We first construct a BN that captures the problem, and then deduce the expression for calculating the LR from this model to compare it with existing LR formulae. We illustrate this idea by applying it to the evaluation of an activity level LR in the context of the two-trace transfer problem. Our approach allows us to relax assumptions made in previous LR developments, produce a new LR formula for the two-trace transfer problem and generalize this scenario to n traces.

A Monte Carlo approach to the inverse problem of diffuse pollution risk in agricultural catchments

The hydrological and biogeochemical processes that operate in catchments influence the ecological quality of freshwater systems through delivery of fine sediment, nutrients and organic matter. Most models that seek to characterise the delivery of diffuse pollutants from land to water are reductionist. The multitude of processes that are parameterised in such models to ensure generic applicability make them complex and difficult to test on available data. Here, we outline an alternative - data-driven - inverse approach. We apply SCIMAP, a parsimonious risk based model that has an explicit treatment of hydrological connectivity. we take a Bayesian approach to the inverse problem of determining the risk that must be assigned to different land uses in a catchment in order to explain the spatial patterns of measured in-stream nutrient concentrations. We apply the model to identify the key sources of nitrogen (N) and phosphorus (P) diffuse pollution risk in eleven UK catchments covering a range of landscapes. The model results show that: 1) some land use generates a consistently high or low risk of diffuse nutrient pollution; but 2) the risks associated with different land uses vary both between catchments and between nutrients; and 3) that the dominant sources of P and N risk in the catchment are often a function of the spatial configuration of land uses. Taken on a case-by-case basis, this type of inverse approach may be used to help prioritise the focus of interventions to reduce diffuse pollution risk for freshwater ecosystems. (C) 2012 Elsevier B.V. All rights reserved.