Low rank subspace clustering (LRSC)

We consider the problem of fitting a union of subspaces to a collection of data points drawn from one or more subspaces and corrupted by noise and/or gross errors. We pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise and/or gross errors. By self-expressive we mean a dictionary whose atoms can be expressed as linear combinations of themselves with low-rank coefficients. In the case of noisy data, our key contribution is to show that this non-convex matrix decomposition problem can be solved in closed form from the SVD of the noisy data matrix. The solution involves a novel polynomial thresholding operator on the singular values of the data matrix, which requires minimal shrinkage. For one subspace, a particular case of our framework leads to classical PCA, which requires no shrinkage. For multiple subspaces, the low-rank coefficients obtained by our framework can be used to construct a data affinity matrix from which the clustering of the data according to the subspaces can be obtained by spectral clustering. In the case of data corrupted by gross errors, we solve the problem using an alternating minimization approach, which combines our polynomial thresholding operator with the more traditional shrinkage-thresholding operator. Experiments on motion segmentation and face clustering show that our framework performs on par with state-of-the-art techniques at a reduced computational cost.

Distributed Rate Allocation in Inter-Session Network Coding

In this work, we propose a distributed rate allocation algorithm that minimizes the average decoding delay for multimedia clients in inter-session network coding systems. We consider a scenario where the users are organized in a mesh network and each user requests the content of one of the available sources. We propose a novel distributed algorithm where network users determine the coding operations and the packet rates to be requested from the parent nodes, such that the decoding delay is minimized for all clients. A rate allocation problem is solved by every user, which seeks the rates that minimize the average decoding delay for its children and for itself. Since this optimization problem is a priori non-convex, we introduce the concept of equivalent packet flows, which permits to estimate the expected number of packets that every user needs to collect for decoding. We then decompose our original rate allocation problem into a set of convex subproblems, which are eventually combined to obtain an effective approximate solution to the delay minimization problem. The results demonstrate that the proposed scheme eliminates the bottlenecks and reduces the decoding delay experienced by users with limited bandwidth resources. We validate the performance of our distributed rate allocation algorithm in different video streaming scenarios using the NS-3 network simulator. We show that our system is able to take benefit of inter-session network coding for simultaneous delivery of video sessions in networks with path diversity.

Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.

Automatic X-ray landmark detection and shape segmentation via data-driven joint estimation of image displacements

In this paper, we propose a new method for fully-automatic landmark detection and shape segmentation in X-ray images. To detect landmarks, we estimate the displacements from some randomly sampled image patches to the (unknown) landmark positions, and then we integrate these predictions via a voting scheme. Our key contribution is a new algorithm for estimating these displacements. Different from other methods where each image patch independently predicts its displacement, we jointly estimate the displacements from all patches together in a data driven way, by considering not only the training data but also geometric constraints on the test image. The displacements estimation is formulated as a convex optimization problem that can be solved efficiently. Finally, we use the sparse shape composition model as the a priori information to regularize the landmark positions and thus generate the segmented shape contour. We validate our method on X-ray image datasets of three different anatomical structures: complete femur, proximal femur and pelvis. Experiments show that our method is accurate and robust in landmark detection, and, combined with the shape model, gives a better or comparable performance in shape segmentation compared to state-of-the art methods. Finally, a preliminary study using CT data shows the extensibility of our method to 3D data.

Block of the hERG channel by bupivacaine: Electrophysiological and modeling insights towards stereochemical optimization

The hERG voltage-gated potassium channel mediates the cardiac I(Kr) current, which is crucial for the duration of the cardiac action potential. Undesired block of the channel by certain drugs may prolong the QT interval and increase the risk of malignant ventricular arrhythmias. Although the molecular determinants of hERG block have been intensively studied, not much is known about its stereoselectivity. Levo-(S)-bupivacaine was the first drug reported to have a higher affinity to block hERG than its enantiomer. This study strives to understand the principles underlying the stereoselectivity of bupivacaine block with the help of mutagenesis analyses and molecular modeling simulations. Electrophysiological measurements of mutated hERG channels allowed for the identification of residues involved in bupivacaine binding and stereoselectivity. Docking and molecular mechanics simulations for both enantiomers of bupivacaine and terfenadine (a non-stereoselective blocker) were performed inside an open-state model of the hERG channel. The predicted binding modes enabled a clear depiction of ligand-protein interactions. Estimated binding affinities for both enantiomers were consistent with electrophysiological measurements. A similar computational procedure was applied to bupivacaine enantiomers towards two mutated hERG channels (Tyr652Ala and Phe656Ala). This study confirmed, at the molecular level, that bupivacaine stereoselectively binds the hERG channel. These results help to lay the foundation for structural guidelines to optimize the cardiotoxic profile of drug candidates in silico.

Initial cord blood unit volume affects mononuclear cell and CD34+ cell-processing efficiency in a non-linear fashion

Umbilical cord blood (UCB) is a source of hematopoietic stem cells that initially was used exclusively for the hematopoietic reconstitution of pediatric patients. It is now suggested for use for adults as well, a fact that increases the pressure to obtain units with high cellularity. Therefore, the optimization of UCB processing is a priority.

Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).

Vitamin D time profile based on the contribution of non-genetic and genetic factors in HIV-infected individuals of European ancestry

BACKGROUND Vitamin D deficiency is prevalent in HIV-infected individuals and vitamin D supplementation is proposed according to standard care. This study aimed at characterizing the kinetics of 25(OH)D in a cohort of HIV-infected individuals of European ancestry to better define the influence of genetic and non-genetic factors on 25(OH)D levels. These data were used for the optimization of vitamin D supplementation in order to reach therapeutic targets. METHODS 1,397 25(OH)D plasma levels and relevant clinical information were collected in 664 participants during medical routine follow up visits. They were genotyped for 7 SNPs in 4 genes known to be associated with 25(OH)D levels. 25(OH)D concentrations were analyzed using a population pharmacokinetic approach. The percentage of individuals with 25(OH)D concentrations within the recommended range of 20-40ng/ml during 12 months of follow up and several dosage regimens were evaluated by simulation. RESULTS A one-compartment model with linear absorption and elimination was used to describe 25(OH)D pharmacokinetics, while integrating endogenous baseline plasma concentrations. Covariate analyses confirmed the effect of seasonality, body mass index, smoking habits, the analytical method, darunavir/r and the genetic variant in GC (rs2282679) on 25(OH)D concentrations. 11% of the interindividual variability in 25(OH)D levels was explained by seasonality and other non-genetic covariates and 1% by genetics. The optimal supplementation for severe vitamin D deficient patients was 300000 IU two times per year. CONCLUSIONS This analysis allowed identifying factors associated with 25(OH)D plasma levels in HIV-infected individuals. Improvement of dosage regimen and timing of vitamin D supplementation is proposed based on those results.

A generalisation of the fractional Brownian field based on non-Euclidean norms

We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.