Piecewise Convex Curves and their Integral Representation

2000 Mathematics Subject Classification: 52A10.

Using sentinels to detect intersections of convex and nonconvex polygons

We describe finite sets of points, called sentinels, which allow us to decide if isometric copies of polygons, convex or not, intersect. As an example of the applicability of the concept of sentinel, we explain how they can be used to formulate an algorithm based on the optimization of differentiable models to pack polygons in convex sets. Mathematical subject classification: 90C53, 65K05.

THE SLOAN BRIGHT ARCS SURVEY: DISCOVERY OF SEVEN NEW STRONGLY LENSED GALAXIES FROM z=0.66-2.94

We report the discovery of seven new, very bright gravitational lens systems from our ongoing gravitational lens search, the Sloan Bright Arcs Survey (SBAS). Two of the systems are confirmed to have high source redshifts z = 2.19 and z = 2.94. Three other systems lie at intermediate redshift with z = 1.33, 1.82, 1.93 and two systems are at low redshift z = 0.66, 0.86. The lensed source galaxies in all of these systems are bright, with i-band magnitudes ranging from 19.73 to 22.06. We present the spectrum of each of the source galaxies in these systems along with estimates of the Einstein radius for each system. The foreground lens in most systems is identified by a red sequence based cluster finder as a galaxy group; one system is identified as a moderately rich cluster. In total, SBAS has now discovered 19 strong lens systems in the SDSS imaging data, 8 of which are among the highest surface brightness z similar or equal to 2-3 galaxies known.

Improving the tracking capability of adaptive filters via convex combination

As is well known, Hessian-based adaptive filters (such as the recursive-least squares algorithm (RLS) for supervised adaptive filtering, or the Shalvi-Weinstein algorithm (SWA) for blind equalization) converge much faster than gradient-based algorithms [such as the least-mean-squares algorithm (LMS) or the constant-modulus algorithm (CMA)]. However, when the problem is tracking a time-variant filter, the issue is not so clear-cut: there are environments for which each family presents better performance. Given this, we propose the use of a convex combination of algorithms of different families to obtain an algorithm with superior tracking capability. We show the potential of this combination and provide a unified theoretical model for the steady-state excess mean-square error for convex combinations of gradient- and Hessian-based algorithms, assuming a random-walk model for the parameter variations. The proposed model is valid for algorithms of the same or different families, and for supervised (LMS and RLS) or blind (CMA and SWA) algorithms.

Convex Total Variation Denoising of Poisson Fluorescence Confocal Images With Anisotropic Filtering

Fluorescence confocal microscopy (FCM) is now one of the most important tools in biomedicine research. In fact, it makes it possible to accurately study the dynamic processes occurring inside the cell and its nucleus by following the motion of fluorescent molecules over time. Due to the small amount of acquired radiation and the huge optical and electronics amplification, the FCM images are usually corrupted by a severe type of Poisson noise. This noise may be even more damaging when very low intensity incident radiation is used to avoid phototoxicity. In this paper, a Bayesian algorithm is proposed to remove the Poisson intensity dependent noise corrupting the FCM image sequences. The observations are organized in a 3-D tensor where each plane is one of the images acquired along the time of a cell nucleus using the fluorescence loss in photobleaching (FLIP) technique. The method removes simultaneously the noise by considering different spatial and temporal correlations. This is accomplished by using an anisotropic 3-D filter that may be separately tuned in space and in time dimensions. Tests using synthetic and real data are described and presented to illustrate the application of the algorithm. A comparison with several state-of-the-art algorithms is also presented.

Sensing Cloud Optimization applied to a non-convex constrained economical dispatch

Conferência: 39th Annual Conference of the IEEE Industrial-Electronics-Society (IECON) - NOV 10-14, 2013

Convex optimization framework for intermediate deadline assignment in soft and hard real-time distributed systems

It is generally challenging to determine end-to-end delays of applications for maximizing the aggregate system utility subject to timing constraints. Many practical approaches suggest the use of intermediate deadline of tasks in order to control and upper-bound their end-to-end delays. This paper proposes a unified framework for different time-sensitive, global optimization problems, and solves them in a distributed manner using Lagrangian duality. The framework uses global viewpoints to assign intermediate deadlines, taking resource contention among tasks into consideration. For soft real-time tasks, the proposed framework effectively addresses the deadline assignment problem while maximizing the aggregate quality of service. For hard real-time tasks, we show that existing heuristic solutions to the deadline assignment problem can be incorporated into the proposed framework, enriching their mathematical interpretation.

Convex and toric geometry to analyze complex dynamics in chemical reaction systems

Convex cone, toric variety, graph theory, electrochemical catalysis, oxidation of formic acid, feedback-loopsbifurcations, enzymatic catalysis, Peroxidase reaction, Shil'nikov chaos

Adelic convex geometry of numbers

Magdeburg, Univ., Fak. für Mathematik, Diss., 2014

Permutations defining convex permutominoes

"Vegeu el resum a l'inici del document del fitxer adjunt."

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

On stability of solutions to systems of convex inequalities

"Vegeu el resum a l'inici del document del fitxer adjunt."

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.