Case studies and mathematical models of ecological speciation. 1. Cichlids in a crater lake.

A recent study of a pair of sympatric species of cichlids in Lake Apoyo in Nicaragua is viewed as providing probably one of the most convincing examples of sympatric speciation to date. Here, we describe and study a stochastic, individual-based, explicit genetic model tailored for this cichlid system. Our results show that relatively rapid (<20,000 generations) colonization of a new ecological niche and (sympatric or parapatric) speciation via local adaptation and divergence in habitat and mating preferences are theoretically plausible if: (i) the number of loci underlying the traits controlling local adaptation, and habitat and mating preferences is small; (ii) the strength of selection for local adaptation is intermediate; (iii) the carrying capacity of the population is intermediate; and (iv) the effects of the loci influencing nonrandom mating are strong. We discuss patterns and timescales of ecological speciation identified by our model, and we highlight important parameters and features that need to be studied empirically to provide information that can be used to improve the biological realism and power of mathematical models of ecological speciation.

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Estimation of the noisy component of anatomical backgrounds.

The knowledge of the relationship that links radiation dose and image quality is a prerequisite to any optimization of medical diagnostic radiology. Image quality depends, on the one hand, on the physical parameters such as contrast, resolution, and noise, and on the other hand, on characteristics of the observer that assesses the image. While the role of contrast and resolution is precisely defined and recognized, the influence of image noise is not yet fully understood. Its measurement is often based on imaging uniform test objects, even though real images contain anatomical backgrounds whose statistical nature is much different from test objects used to assess system noise. The goal of this study was to demonstrate the importance of variations in background anatomy by quantifying its effect on a series of detection tasks. Several types of mammographic backgrounds and signals were examined by psychophysical experiments in a two-alternative forced-choice detection task. According to hypotheses concerning the strategy used by the human observers, their signal to noise ratio was determined. This variable was also computed for a mathematical model based on the statistical decision theory. By comparing theoretical model and experimental results, the way that anatomical structure is perceived has been analyzed. Experiments showed that the observer's behavior was highly dependent upon both system noise and the anatomical background. The anatomy partly acts as a signal recognizable as such and partly as a pure noise that disturbs the detection process. This dual nature of the anatomy is quantified. It is shown that its effect varies according to its amplitude and the profile of the object being detected. The importance of the noisy part of the anatomy is, in some situations, much greater than the system noise. Hence, reducing the system noise by increasing the dose will not improve task performance. This observation indicates that the tradeoff between dose and image quality might be optimized by accepting a higher system noise. This could lead to a better resolution, more contrast, or less dose.

IMRT credentialing for prospective trials using institutional virtual phantoms: results of a joint European Organization for the Research and Treatment of Cancer and Radiological Physics Center project.

BACKGROUND AND PURPOSE: Intensity-modulated radiotherapy (IMRT) credentialing for a EORTC study was performed using an anthropomorphic head phantom from the Radiological Physics Center (RPC; RPCPH). Institutions were retrospectively requested to irradiate their institutional phantom (INSTPH) using the same treatment plan in the framework of a Virtual Phantom Project (VPP) for IMRT credentialing. MATERIALS AND METHODS: CT data set of the institutional phantom and measured 2D dose matrices were requested from centers and sent to a dedicated secure EORTC uploader. Data from the RPCPH and INSTPH were thereafter centrally analyzed and inter-compared by the QA team using commercially available software (RIT; ver.5.2; Colorado Springs, USA). RESULTS: Eighteen institutions participated to the VPP. The measurements of 6 (33%) institutions could not be analyzed centrally. All other centers passed both the VPP and the RPC ±7%/4 mm credentialing criteria. At the 5%/5 mm gamma criteria (90% of pixels passing), 11(92%) as compared to 12 (100%) centers pass the credentialing process with RPCPH and INSTPH (p = 0.29), respectively. The corresponding pass rate for the 3%/3 mm gamma criteria (90% of pixels passing) was 2 (17%) and 9 (75%; p = 0.01), respectively. CONCLUSIONS: IMRT dosimetry gamma evaluations in a single plane for a H&N prospective trial using the INSTPH measurements showed agreement at the gamma index criteria of ±5%/5 mm (90% of pixels passing) for a small number of VPP measurements. Using more stringent, criteria, the RPCPH and INSTPH comparison showed disagreement. More data is warranted and urgently required within the framework of prospective studies.

Modelling hydrodynamics in the Rio Parana, Argentina : an evaluation and inter-comparison of reduced-complexity and physics based models applied to a large sand-bed river

Depth-averaged velocities and unit discharges within a 30 km reach of one of the world's largest rivers, the Rio Parana, Argentina, were simulated using three hydrodynamic models with different process representations: a reduced complexity (RC) model that neglects most of the physics governing fluid flow, a two-dimensional model based on the shallow water equations, and a three-dimensional model based on the Reynolds-averaged Navier-Stokes equations. Row characteristics simulated using all three models were compared with data obtained by acoustic Doppler current profiler surveys at four cross sections within the study reach. This analysis demonstrates that, surprisingly, the performance of the RC model is generally equal to, and in some instances better than, that of the physics based models in terms of the statistical agreement between simulated and measured flow properties. In addition, in contrast to previous applications of RC models, the present study demonstrates that the RC model can successfully predict measured flow velocities. The strong performance of the RC model reflects, in part, the simplicity of the depth-averaged mean flow patterns within the study reach and the dominant role of channel-scale topographic features in controlling the flow dynamics. Moreover, the very low water surface slopes that typify large sand-bed rivers enable flow depths to be estimated reliably in the RC model using a simple fixed-lid planar water surface approximation. This approach overcomes a major problem encountered in the application of RC models in environments characterised by shallow flows and steep bed gradients. The RC model is four orders of magnitude faster than the physics based models when performing steady-state hydrodynamic calculations. However, the iterative nature of the RC model calculations implies a reduction in computational efficiency relative to some other RC models. A further implication of this is that, if used to simulate channel morphodynamics, the present RC model may offer only a marginal advantage in terms of computational efficiency over approaches based on the shallow water equations. These observations illustrate the trade off between model realism and efficiency that is a key consideration in RC modelling. Moreover, this outcome highlights a need to rethink the use of RC morphodynamic models in fluvial geomorphology and to move away from existing grid-based approaches, such as the popular cellular automata (CA) models, that remain essentially reductionist in nature. In the case of the world's largest sand-bed rivers, this might be achieved by implementing the RC model outlined here as one element within a hierarchical modelling framework that would enable computationally efficient simulation of the morphodynamics of large rivers over millennial time scales. (C) 2012 Elsevier B.V. All rights reserved.

Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined

Update on the non-prewhitening model observer in computed tomography for the assessment of the adaptive statistical and model-based iterative reconstruction algorithms.

The state of the art to describe image quality in medical imaging is to assess the performance of an observer conducting a task of clinical interest. This can be done by using a model observer leading to a figure of merit such as the signal-to-noise ratio (SNR). Using the non-prewhitening (NPW) model observer, we objectively characterised the evolution of its figure of merit in various acquisition conditions. The NPW model observer usually requires the use of the modulation transfer function (MTF) as well as noise power spectra. However, although the computation of the MTF poses no problem when dealing with the traditional filtered back-projection (FBP) algorithm, this is not the case when using iterative reconstruction (IR) algorithms, such as adaptive statistical iterative reconstruction (ASIR) or model-based iterative reconstruction (MBIR). Given that the target transfer function (TTF) had already shown it could accurately express the system resolution even with non-linear algorithms, we decided to tune the NPW model observer, replacing the standard MTF by the TTF. It was estimated using a custom-made phantom containing cylindrical inserts surrounded by water. The contrast differences between the inserts and water were plotted for each acquisition condition. Then, mathematical transformations were performed leading to the TTF. As expected, the first results showed a dependency of the image contrast and noise levels on the TTF for both ASIR and MBIR. Moreover, FBP also proved to be dependent of the contrast and noise when using the lung kernel. Those results were then introduced in the NPW model observer. We observed an enhancement of SNR every time we switched from FBP to ASIR to MBIR. IR algorithms greatly improve image quality, especially in low-dose conditions. Based on our results, the use of MBIR could lead to further dose reduction in several clinical applications.

Classification of very high spatial resolution imagery using mathematical morphology and support vector machines

We investigate the relevance of morphological operators for the classification of land use in urban scenes using submetric panchromatic imagery. A support vector machine is used for the classification. Six types of filters have been employed: opening and closing, opening and closing by reconstruction, and opening and closing top hat. The type and scale of the filters are discussed, and a feature selection algorithm called recursive feature elimination is applied to decrease the dimensionality of the input data. The analysis performed on two QuickBird panchromatic images showed that simple opening and closing operators are the most relevant for classification at such a high spatial resolution. Moreover, mixed sets combining simple and reconstruction filters provided the best performance. Tests performed on both images, having areas characterized by different architectural styles, yielded similar results for both feature selection and classification accuracy, suggesting the generalization of the feature sets highlighted.

First-passage and escape problems in the Feller process

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.

Three mathematical models for bucking-to-order

Abstract

Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined