An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

A near real-time water surface detection method based on HSV transformation of MODIS multi-Spectral time series data

In the face of global population growth and the uneven distribution of water supply, a better knowledge of the spatial and temporal distribution of surface water resources is critical. Remote sensing provides a synoptic view of ongoing processes, which addresses the intricate nature of water surfaces and allows an assessment of the pressures placed on aquatic ecosystems. However, the main challenge in identifying water surfaces from remotely sensed data is the high variability of spectral signatures, both in space and time. In the last 10 years only a few operational methods have been proposed to map or monitor surface water at continental or global scale, and each of them show limitations. The objective of this study is to develop and demonstrate the adequacy of a generic multi-temporal and multi-spectral image analysis method to detect water surfaces automatically, and to monitor them in near-real-time. The proposed approach, based on a transformation of the RGB color space into HSV, provides dynamic information at the continental scale. The validation of the algorithm showed very few omission errors and no commission errors. It demonstrates the ability of the proposed algorithm to perform as effectively as human interpretation of the images. The validation of the permanent water surface product with an independent dataset derived from high resolution imagery, showed an accuracy of 91.5% and few commission errors. Potential applications of the proposed method have been identified and discussed. The methodology that has been developed 27 is generic: it can be applied to sensors with similar bands with good reliability, and minimal effort. Moreover, this experiment at continental scale showed that the methodology is efficient for a large range of environmental conditions. Additional preliminary tests over other continents indicate that the proposed methodology could also be applied at the global scale without too many difficulties

Universality in the merging dynamics of parametric active contours:a study in MRI based lung segmentation

Measurement of lung ventilation is one of the most reliable techniques in diagnosing pulmonary diseases. The time-consuming and bias-prone traditional methods using hyperpolarized H 3He and 1H magnetic resonance imageries have recently been improved by an automated technique based on 'multiple active contour evolution'. This method involves a simultaneous evolution of multiple initial conditions, called 'snakes', eventually leading to their 'merging' and is entirely independent of the shapes and sizes of snakes or other parametric details. The objective of this paper is to show, through a theoretical analysis, that the functional dynamics of merging as depicted in the active contour method has a direct analogue in statistical physics and this explains its 'universality'. We show that the multiple active contour method has an universal scaling behaviour akin to that of classical nucleation in two spatial dimensions. We prove our point by comparing the numerically evaluated exponents with an equivalent thermodynamic model. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80.

A New Class of Processes for Formalizing and Generalizing Individual-Based Models: The Semi-Semi-Markov Processes

2000 Mathematics Subject Classification: 60K15, 60K20, 60G20,60J75, 60J80, 60J85, 60-08, 90B15.

In God we trust: Faith-based development, spiritual transformation, and economic change in southern Andean indigenous communities

In communities throughout the developing world, faith-based organizations (FBOs) focus on goals such as eradicating poverty, bolstering local economies, and fostering community development, while premising their activities and interaction with local communities on theological and religious understandings. Due to their pervasive interaction with participants, the religious ideologies of these FBOs impact the religious, economic, and social realities of communities. This study investigates the relationship between the international FBO, World Vision International (WVI), and changes to religious, economic, and social ideologies and practices in Andean indigenous communities in southern Peruvian. This study aims to contribute to the greater knowledge and understanding of (1) institutionalized development strategies, (2) faith-based development, and (3) how institutionalized development interacts with processes of socio-cultural change. Based on fifteen months of field research, this study involved qualitative and quantitative methods of participant-observation, interviews, surveys, and document analysis. Data were primarily collected from households from a sample of eight communities in the Pitumarca and Combapata districts, department of Canchis, province of Cusco, Peru where two WVI Area Development Programs were operating. Research findings reveal that there is a relationship between WVI’s intervention and some changes to religious, economic, and social structure (values, ideologies, and norms) and practices, demonstrating that structure and practices change when social systems are altered by new social actors. Findings also revealed that the impacts of WVI’s intervention greatly increased over the course of several years, demonstrating that changes in structure and practice occur gradually and need a period of time to take root. Finally, results showed that the impacts of WVI’s intervention were primarily limited to those most closely involved with the organization, revealing that the ability of one social actor to incite changes in the structure and practice of another actor is associated with the intensity of the relationship between the social actors. The findings of this study should be useful in ascertaining deductions and strengthening understandings of how faith-based development organizations impact aspects of religious, economic, and social life in the areas where they work.

Parametric, Optimization-Based Study on the Feasibility of a Multisegment Antisolvent Crystallizer for in Situ Fines Removal and Matching of Target Size Distribution

Peer reviewed

Parametric CAD model based shape optimization using adjoint functions

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.

Clustering-based Query Routing in Cooperative Semi-structured Peer to Peer Networks

We consider the problem of resource selection in clustered Peer-to-Peer Information Retrieval (P2P IR) networks with cooperative peers. The clustered P2P IR framework presents a significant departure from general P2P IR architectures by employing clustering to ensure content coherence between resources at the resource selection layer, without disturbing document allocation. We propose that such a property could be leveraged in resource selection by adapting well-studied and popular inverted lists for centralized document retrieval. Accordingly, we propose the Inverted PeerCluster Index (IPI), an approach that adapts the inverted lists, in a straightforward manner, for resource selection in clustered P2P IR. IPI also encompasses a strikingly simple peer-specific scoring mechanism that exploits the said index for resource selection. Through an extensive empirical analysis on P2P IR testbeds, we establish that IPI competes well with the sophisticated state-of-the-art methods in virtually every parameter of interest for the resource selection task, in the context of clustered P2P IR.

A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

Spectral-based mesh segmentation

In design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (BRep), which in turn is central for featurebased design, machining, parametric CAD and reverse engineering, among others -- Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (graph spectrum), as we consider that this tool has not been fully exploited -- We preprocess the mesh to obtain a edgelength homogeneous triangle set and its Graph Laplacian is calculated -- We then produce a monotonically increasing permutation of the Fiedler vector (2nd eigenvector of Graph Laplacian) for encoding the connectivity among part feature submeshes -- Within the mutated vector, discontinuities larger than a threshold (interactively set by a human) determine the partition of the original mesh -- We present tests of our method on large complex meshes, which show results which mostly adjust to BRep FACE partition -- The achieved segmentations properly locate most manufacturing features, although it requires human interaction to avoid over segmentation -- Future work includes an iterative application of this algorithm to progressively sever features of the mesh left from previous submesh removals

A multi-method study of the transformation of the carbonaceous skeleton of a polymer-based nanoporous carbon along the activation pathway

The change in the carbonaceous skeleton of nanoporous carbons during their activation has received limited attention, unlike its counterpart process in the presence of an inert atmosphere. Here we adopt a multi-method approach to elucidate this change in a poly(furfuryl alcohol)-derived carbon activated using cyclic application of oxygen saturation at 250 °C before its removal (with carbon) at 800 °C in argon. The methods used include helium pycnometry, synchrotron-based X-ray diffraction (XRD) and associated radial distribution function (RDF) analysis, transmission electron microscopy (TEM) and, uniquely, electron energy-loss spectroscopy spectrum-imaging (EELS-SI), electron nanodiffraction and fluctuation electron microscopy (FEM). Helium pycnometry indicates the solid skeleton of the carbon densifies during activation from 78% to 93% of graphite. RDF analysis, EELS-SI, and FEM all suggest this densification comes through an in-plane growth of sp2 carbon out to the medium range without commensurate increase in order normal to the plane. This process could be termed ‘graphenization’. The exact way in which this process occurs is not clear, but TEM images of the carbon before and after activation suggest it may come through removal of the more reactive carbon, breaking constraining cross-links and creating space that allows the remaining carbon material to migrate in an annealing-like process.