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.

Three essays on liquidity risk

Preface In this thesis we study several questions related to transaction data measured at an individual level. The questions are addressed in three essays that will constitute this thesis. In the first essay we use tick-by-tick data to estimate non-parametrically the jump process of 37 big stocks traded on the Paris Stock Exchange, and of the CAC 40 index. We separate the total daily returns in three components (trading continuous, trading jump, and overnight), and we characterize each one of them. We estimate at the individual and index levels the contribution of each return component to the total daily variability. For the index, the contribution of jumps is smaller and it is compensated by the larger contribution of overnight returns. We test formally that individual stocks jump more frequently than the index, and that they do not respond independently to the arrive of news. Finally, we find that daily jumps are larger when their arrival rates are larger. At the contemporaneous level there is a strong negative correlation between the jump frequency and the trading activity measures. The second essay study the general properties of the trade- and volume-duration processes for two stocks traded on the Paris Stock Exchange. These two stocks correspond to a very illiquid stock and to a relatively liquid stock. We estimate a class of autoregressive gamma process with conditional distribution from the family of non-central gamma (up to a scale factor). This process was introduced by Gouriéroux and Jasiak and it is known as Autoregressive gamma process. We also evaluate the ability of the process to fit the data. For this purpose we use the Diebold, Gunther and Tay (1998) test; and the capacity of the model to reproduce the moments of the observed data, and the empirical serial correlation and the partial serial correlation functions. We establish that the model describes correctly the trade duration process of illiquid stocks, but have problems to adjust correctly the trade duration process of liquid stocks which present long-memory characteristics. When the model is adjusted to volume duration, it successfully fit the data. In the third essay we study the economic relevance of optimal liquidation strategies by calibrating a recent and realistic microstructure model with data from the Paris Stock Exchange. We distinguish the case of parameters which are constant through the day from time-varying ones. An optimization problem incorporating this realistic microstructure model is presented and solved. Our model endogenizes the number of trades required before the position is liquidated. A comparative static exercise demonstrates the realism of our model. We find that a sell decision taken in the morning will be liquidated by the early afternoon. If price impacts increase over the day, the liquidation will take place more rapidly.

Large-scale clustering through functional embedding

We present a new framework for large-scale data clustering. The main idea is to modify functional dimensionality reduction techniques to directly optimize over discrete labels using stochastic gradient descent. Compared to methods like spectral clustering our approach solves a single optimization problem, rather than an ad-hoc two-stage optimization approach, does not require a matrix inversion, can easily encode prior knowledge in the set of implementable functions, and does not have an ?out-of-sample? problem. Experimental results on both artificial and real-world datasets show the usefulness of our approach.

Surface reconstruction from microscopic images in optical lithography.

This paper presents a method to reconstruct 3D surfaces of silicon wafers from 2D images of printed circuits taken with a scanning electron microscope. Our reconstruction method combines the physical model of the optical acquisition system with prior knowledge about the shapes of the patterns in the circuit; the result is a shape-from-shading technique with a shape prior. The reconstruction of the surface is formulated as an optimization problem with an objective functional that combines a data-fidelity term on the microscopic image with two prior terms on the surface. The data term models the acquisition system through the irradiance equation characteristic of the microscope; the first prior is a smoothness penalty on the reconstructed surface, and the second prior constrains the shape of the surface to agree with the expected shape of the pattern in the circuit. In order to account for the variability of the manufacturing process, this second prior includes a deformation field that allows a nonlinear elastic deformation between the expected pattern and the reconstructed surface. As a result, the minimization problem has two unknowns, and the reconstruction method provides two outputs: 1) a reconstructed surface and 2) a deformation field. The reconstructed surface is derived from the shading observed in the image and the prior knowledge about the pattern in the circuit, while the deformation field produces a mapping between the expected shape and the reconstructed surface that provides a measure of deviation between the circuit design models and the real manufacturing process.

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.

Combination of enteral and parenteral nutrition in intensive care patients: A new concept of optimization

Undernutrition is a widespread problem in intensive care unit and is associated with a worse clinical outcome. A state of negative energy balance increases stress catabolism and is associated with increased morbidity and mortality in ICU patients. Undernutrition-related increased morbidity is correlated with an increase in the length of hospital stay and health care costs. Enteral nutrition is the recommended feeding route in critically ill patients, but it is often insufficient to cover the nutritional needs. The initiation of supplemental parenteral nutrition, when enteral nutrition is insufficient, could optimize the nutritional therapy by preventing the onset of early energy deficiency, and thus, could allow to reduce morbidity, length of stay and costs, shorten recovery period and, finally, improve quality of life. (C) 2009 Elsevier Masson SAS. All rights reserved.

Fitness, inclusive fitness, and optimization

Individual-as-maximizing agent analogies result in a simple understanding of the functioning of the biological world. Identifying the conditions under which individuals can be regarded as fitness maximizing agents is thus of considerable interest to biologists. Here, we compare different concepts of fitness maximization, and discuss within a single framework the relationship between Hamilton's (J Theor Biol 7: 1-16, 1964) model of social interactions, Grafen's (J Evol Biol 20: 1243-1254, 2007a) formal Darwinism project, and the idea of evolutionary stable strategies. We distinguish cases where phenotypic effects are additive separable or not, the latter not being covered by Grafen's analysis. In both cases it is possible to define a maximand, in the form of an objective function phi(z), whose argument is the phenotype of an individual and whose derivative is proportional to Hamilton's inclusive fitness effect. However, this maximand can be identified with the expression for fecundity or fitness only in the case of additive separable phenotypic effects, making individual-as-maximizing agent analogies unattractive (although formally correct) under general situations of social interactions. We also feel that there is an inconsistency in Grafen's characterization of the solution of his maximization program by use of inclusive fitness arguments. His results are in conflict with those on evolutionary stable strategies obtained by applying inclusive fitness theory, and can be repaired only by changing the definition of the problem.

Optimisation des doses en tomographie computérisée pédiatrique [Patient dose optimization in pediatric computerized tomography]

The development of CT applications might become a public health problem if no effort is made on the justification and the optimisation of the examinations. This paper presents some hints to assure that the risk-benefit compromise remains in favour of the patient, especially when one deals with the examinations of young patients. In this context a particular attention has to be made on the justification of the examination. When performing the acquisition one needs to optimise the extension of the volume investigated together with the number of acquisition sequences used. Finally, the use of automatic exposure systems, now available on all the units, and the use of the Diagnostic Reference Levels (DRL) should allow help radiologists to control the exposure of their patients.

Multiparametric brainstem segmentation using a modified multivariate mixture of Gaussians

The human brainstem is a densely packed, complex but highly organised structure. It not only serves as a conduit for long projecting axons conveying motor and sensory information, but also is the location of multiple primary nuclei that control or modulate a vast array of functions, including homeostasis, consciousness, locomotion, and reflexive and emotive behaviours. Despite its importance, both in understanding normal brain function as well as neurodegenerative processes, it remains a sparsely studied structure in the neuroimaging literature. In part, this is due to the difficulties in imaging the internal architecture of the brainstem in vivo in a reliable and repeatable fashion. A modified multivariate mixture of Gaussians (mmMoG) was applied to the problem of multichannel tissue segmentation. By using quantitative magnetisation transfer and proton density maps acquired at 3 T with 0.8 mm isotropic resolution, tissue probability maps for four distinct tissue classes within the human brainstem were created. These were compared against an ex vivo fixated human brain, imaged at 0.5 mm, with excellent anatomical correspondence. These probability maps were used within SPM8 to create accurate individual subject segmentations, which were then used for further quantitative analysis. As an example, brainstem asymmetries were assessed across 34 right-handed individuals using voxel based morphometry (VBM) and tensor based morphometry (TBM), demonstrating highly significant differences within localised regions that corresponded to motor and vocalisation networks. This method may have important implications for future research into MRI biomarkers of pre-clinical neurodegenerative diseases such as Parkinson's disease.

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.

How Much Does It Cost? Optimization of Costs in Sequence Analysis of Social Science Data

One major methodological problem in analysis of sequence data is the determination of costs from which distances between sequences are derived. Although this problem is currently not optimally dealt with in the social sciences, it has some similarity with problems that have been solved in bioinformatics for three decades. In this article, the authors propose an optimization of substitution and deletion/insertion costs based on computational methods. The authors provide an empirical way of determining costs for cases, frequent in the social sciences, in which theory does not clearly promote one cost scheme over another. Using three distinct data sets, the authors tested the distances and cluster solutions produced by the new cost scheme in comparison with solutions based on cost schemes associated with other research strategies. The proposed method performs well compared with other cost-setting strategies, while it alleviates the justification problem of cost schemes.

Ecological-economic optimization of biodiversity conservation under climate change

Substantial investment in climate change research has led to dire predictions of the impacts and risks to biodiversity. The Intergovernmental Panel on Climate Change fourth assessment report(1) cites 28,586 studies demonstrating significant biological changes in terrestrial systems(2). Already high extinction rates, driven primarily by habitat loss, are predicted to increase under climate change(3-6). Yet there is little specific advice or precedent in the literature to guide climate adaptation investment for conserving biodiversity within realistic economic constraints(7). Here we present a systematic ecological and economic analysis of a climate adaptation problem in one of the world's most species-rich and threatened ecosystems: the South African fynbos. We discover a counterintuitive optimal investment strategy that switches twice between options as the available adaptation budget increases. We demonstrate that optimal investment is nonlinearly dependent on available resources, making the choice of how much to invest as important as determining where to invest and what actions to take. Our study emphasizes the importance of a sound analytical framework for prioritizing adaptation investments(4). Integrating ecological predictions in an economic decision framework will help support complex choices between adaptation options under severe uncertainty. Our prioritization method can be applied at any scale to minimize species loss and to evaluate the robustness of decisions to uncertainty about key assumptions.

MBIS: multivariate Bayesian image segmentation tool.

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multichannel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.