Extreme Precipitation Modelling Using Geostatistics and Machine Learning Algorithms

The paper presents an approach for mapping of precipitation data. The main goal is to perform spatial predictions and simulations of precipitation fields using geostatistical methods (ordinary kriging, kriging with external drift) as well as machine learning algorithms (neural networks). More practically, the objective is to reproduce simultaneously both the spatial patterns and the extreme values. This objective is best reached by models integrating geostatistics and machine learning algorithms. To demonstrate how such models work, two case studies have been considered: first, a 2-day accumulation of heavy precipitation and second, a 6-day accumulation of extreme orographic precipitation. The first example is used to compare the performance of two optimization algorithms (conjugate gradients and Levenberg-Marquardt) of a neural network for the reproduction of extreme values. Hybrid models, which combine geostatistical and machine learning algorithms, are also treated in this context. The second dataset is used to analyze the contribution of radar Doppler imagery when used as external drift or as input in the models (kriging with external drift and neural networks). Model assessment is carried out by comparing independent validation errors as well as analyzing data patterns.

Geological realism in hydrogeological and geophysical inverse modeling: A review

Scientific curiosity, exploration of georesources and environmental concerns are pushing the geoscientific research community toward subsurface investigations of ever-increasing complexity. This review explores various approaches to formulate and solve inverse problems in ways that effectively integrate geological concepts with geophysical and hydrogeological data. Modern geostatistical simulation algorithms can produce multiple subsurface realizations that are in agreement with conceptual geological models and statistical rock physics can be used to map these realizations into physical properties that are sensed by the geophysical or hydrogeological data. The inverse problem consists of finding one or an ensemble of such subsurface realizations that are in agreement with the data. The most general inversion frameworks are presently often computationally intractable when applied to large-scale problems and it is necessary to better understand the implications of simplifying (1) the conceptual geological model (e.g., using model compression); (2) the physical forward problem (e.g., using proxy models); and (3) the algorithm used to solve the inverse problem (e.g., Markov chain Monte Carlo or local optimization methods) to reach practical and robust solutions given today's computer resources and knowledge. We also highlight the need to not only use geophysical and hydrogeological data for parameter estimation purposes, but also to use them to falsify or corroborate alternative geological scenarios.

New considerations on the management of osteoporosis in Central and Eastern Europe (CEE): summary of the "3rd Summit on Osteoporosis-CEE", November 2009, Budapest, Hungary.

INTRODUCTION: In November 2009, the "3rd Summit on Osteoporosis-Central and Eastern Europe (CEE)" was held in Budapest, Hungary. The conference aimed to tackle issues regarding osteoporosis management in CEE identified during the second CEE summit in 2008 and to agree on approaches that allow most efficient and cost-effective diagnosis and therapy of osteoporosis in CEE countries in the future. DISCUSSION: The following topics were covered: past year experience from FRAX® implementation into local diagnostic algorithms; causes of secondary osteoporosis as a FRAX® risk factor; bone turnover markers to estimate bone loss, fracture risk, or monitor therapies; role of quantitative ultrasound in osteoporosis management; compliance and economical aspects of osteoporosis; and osteoporosis and genetics. Consensus and recommendations developed on these topics are summarised in the present progress report. CONCLUSION: Lectures on up-to-date data of topical interest, the distinct regional provenances of the participants, a special focus on practical aspects, intense mutual exchange of individual experiences, strong interest in cross-border cooperations, as well as the readiness to learn from each other considerably contributed to the establishment of these recommendations. The "4th Summit on Osteoporosis-CEE" held in Prague, Czech Republic, in December 2010 will reveal whether these recommendations prove of value when implemented in the clinical routine or whether further improvements are still required.

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.

Multi-scale support vector algorithms for hot spot detection and modelling

The algorithmic approach to data modelling has developed rapidly these last years, in particular methods based on data mining and machine learning have been used in a growing number of applications. These methods follow a data-driven methodology, aiming at providing the best possible generalization and predictive abilities instead of concentrating on the properties of the data model. One of the most successful groups of such methods is known as Support Vector algorithms. Following the fruitful developments in applying Support Vector algorithms to spatial data, this paper introduces a new extension of the traditional support vector regression (SVR) algorithm. This extension allows for the simultaneous modelling of environmental data at several spatial scales. The joint influence of environmental processes presenting different patterns at different scales is here learned automatically from data, providing the optimum mixture of short and large-scale models. The method is adaptive to the spatial scale of the data. With this advantage, it can provide efficient means to model local anomalies that may typically arise in situations at an early phase of an environmental emergency. However, the proposed approach still requires some prior knowledge on the possible existence of such short-scale patterns. This is a possible limitation of the method for its implementation in early warning systems. The purpose of this paper is to present the multi-scale SVR model and to illustrate its use with an application to the mapping of Cs137 activity given the measurements taken in the region of Briansk following the Chernobyl accident.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Artificial Snow Optimization in Winter Sport Destinations Using a Multi-agent Simulation

This paper presents the Juste-Neige system for predicting the snow height on the ski runs of a resort using a multi-agent simulation software. Its aim is to facilitate snow cover management in order to i) reduce the production cost of artificial snow and to improve the profit margin for the companies managing the ski resorts; and ii) to reduce the water and energy consumption, and thus to reduce the environmental impact, by producing only the snow needed for a good skiing experience. The software provides maps with the predicted snow heights for up to 13 days. On these maps, the areas most exposed to snow erosion are highlighted. The software proceeds in three steps: i) interpolation of snow height measurements with a neural network; ii) local meteorological forecasts for every ski resort; iii) simulation of the impact caused by skiers using a multi-agent system. The software has been evaluated in the Swiss ski resort of Verbier and provides useful predictions.

COMMIT: Convex Optimization Modeling for Microstructure Informed Tractography.

Tractography is a class of algorithms aiming at in vivo mapping the major neuronal pathways in the white matter from diffusion magnetic resonance imaging (MRI) data. These techniques offer a powerful tool to noninvasively investigate at the macroscopic scale the architecture of the neuronal connections of the brain. However, unfortunately, the reconstructions recovered with existing tractography algorithms are not really quantitative even though diffusion MRI is a quantitative modality by nature. As a matter of fact, several techniques have been proposed in recent years to estimate, at the voxel level, intrinsic microstructural features of the tissue, such as axonal density and diameter, by using multicompartment models. In this paper, we present a novel framework to reestablish the link between tractography and tissue microstructure. Starting from an input set of candidate fiber-tracts, which are estimated from the data using standard fiber-tracking techniques, we model the diffusion MRI signal in each voxel of the image as a linear combination of the restricted and hindered contributions generated in every location of the brain by these candidate tracts. Then, we seek for the global weight of each of them, i.e., the effective contribution or volume, such that they globally fit the measured signal at best. We demonstrate that these weights can be easily recovered by solving a global convex optimization problem and using efficient algorithms. The effectiveness of our approach has been evaluated both on a realistic phantom with known ground-truth and in vivo brain data. Results clearly demonstrate the benefits of the proposed formulation, opening new perspectives for a more quantitative and biologically plausible assessment of the structural connectivity of the brain.

A hierarchical approach to model parameter optimization for developmental systems.

In the context of Systems Biology, computer simulations of gene regulatory networks provide a powerful tool to validate hypotheses and to explore possible system behaviors. Nevertheless, modeling a system poses some challenges of its own: especially the step of model calibration is often difficult due to insufficient data. For example when considering developmental systems, mostly qualitative data describing the developmental trajectory is available while common calibration techniques rely on high-resolution quantitative data. Focusing on the calibration of differential equation models for developmental systems, this study investigates different approaches to utilize the available data to overcome these difficulties. More specifically, the fact that developmental processes are hierarchically organized is exploited to increase convergence rates of the calibration process as well as to save computation time. Using a gene regulatory network model for stem cell homeostasis in Arabidopsis thaliana the performance of the different investigated approaches is evaluated, documenting considerable gains provided by the proposed hierarchical approach.

A surface-based approach to quantify local cortical gyrification.

The high complexity of cortical convolutions in humans is very challenging both for engineers to measure and compare it, and for biologists and physicians to understand it. In this paper, we propose a surface-based method for the quantification of cortical gyrification. Our method uses accurate 3-D cortical reconstruction and computes local measurements of gyrification at thousands of points over the whole cortical surface. The potential of our method to identify and localize precisely gyral abnormalities is illustrated by a clinical study on a group of children affected by 22q11 Deletion Syndrome, compared to control individuals.

Global tractography with embedded anatomical priors for quantitative connectivity analysis.

Tractography algorithms provide us with the ability to non-invasively reconstruct fiber pathways in the white matter (WM) by exploiting the directional information described with diffusion magnetic resonance. These methods could be divided into two major classes, local and global. Local methods reconstruct each fiber tract iteratively by considering only directional information at the voxel level and its neighborhood. Global methods, on the other hand, reconstruct all the fiber tracts of the whole brain simultaneously by solving a global energy minimization problem. The latter have shown improvements compared to previous techniques but these algorithms still suffer from an important shortcoming that is crucial in the context of brain connectivity analyses. As no anatomical priors are usually considered during the reconstruction process, the recovered fiber tracts are not guaranteed to connect cortical regions and, as a matter of fact, most of them stop prematurely in the WM; this violates important properties of neural connections, which are known to originate in the gray matter (GM) and develop in the WM. Hence, this shortcoming poses serious limitations for the use of these techniques for the assessment of the structural connectivity between brain regions and, de facto, it can potentially bias any subsequent analysis. Moreover, the estimated tracts are not quantitative, every fiber contributes with the same weight toward the predicted diffusion signal. In this work, we propose a novel approach for global tractography that is specifically designed for connectivity analysis applications which: (i) explicitly enforces anatomical priors of the tracts in the optimization and (ii) considers the effective contribution of each of them, i.e., volume, to the acquired diffusion magnetic resonance imaging (MRI) image. We evaluated our approach on both a realistic diffusion MRI phantom and in vivo data, and also compared its performance to existing tractography algorithms.

Quantification of the local heartwall motion by magnetic resonance myocardial tagging.

Sophisticated magnetic resonance tagging techniques provide powerful tools for the non-invasive assessment of the local heartwall motion towards a deeper fundamental understanding of local heart function. For the extraction of motion data from the time series of magnetic resonance tagged images and for the visualization of the local heartwall motion a new image analysis procedure has been developed. New parameters have been derived which allows quantification of the motion patterns and are highly sensitive to any changes in these patterns. The new procedure has been applied for heart motion analysis in healthy volunteers and in patient collectives with different heart diseases. The achieved results are summarized and discussed.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

EADock: docking of small molecules into protein active sites with a multiobjective evolutionary optimization.

In recent years, protein-ligand docking has become a powerful tool for drug development. Although several approaches suitable for high throughput screening are available, there is a need for methods able to identify binding modes with high accuracy. This accuracy is essential to reliably compute the binding free energy of the ligand. Such methods are needed when the binding mode of lead compounds is not determined experimentally but is needed for structure-based lead optimization. We present here a new docking software, called EADock, that aims at this goal. It uses an hybrid evolutionary algorithm with two fitness functions, in combination with a sophisticated management of the diversity. EADock is interfaced with the CHARMM package for energy calculations and coordinate handling. A validation was carried out on 37 crystallized protein-ligand complexes featuring 11 different proteins. The search space was defined as a sphere of 15 A around the center of mass of the ligand position in the crystal structure, and on the contrary to other benchmarks, our algorithm was fed with optimized ligand positions up to 10 A root mean square deviation (RMSD) from the crystal structure, excluding the latter. This validation illustrates the efficiency of our sampling strategy, as correct binding modes, defined by a RMSD to the crystal structure lower than 2 A, were identified and ranked first for 68% of the complexes. The success rate increases to 78% when considering the five best ranked clusters, and 92% when all clusters present in the last generation are taken into account. Most failures could be explained by the presence of crystal contacts in the experimental structure. Finally, the ability of EADock to accurately predict binding modes on a real application was illustrated by the successful docking of the RGD cyclic pentapeptide on the alphaVbeta3 integrin, starting far away from the binding pocket.