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.

Analysis and optimization of the satellite-to-plane link of an aeronautical global system

En aquest projecte s’ha analitzat i optimitzat l’enllaç satèl·lit amb avió per a un sistema aeronàutic global. Aquest nou sistema anomenat ANTARES està dissenyat per a comunicar avions amb estacions base mitjançant un satèl·lit. Aquesta és una iniciativa on hi participen institucions oficials en l’aviació com ara l’ECAC i que és desenvolupat en una col·laboració europea d’universitats i empreses. El treball dut a terme en el projecte compren bàsicament tres aspectes. El disseny i anàlisi de la gestió de recursos. La idoneïtat d’utilitzar correcció d’errors en la capa d’enllaç i en cas que sigui necessària dissenyar una opció de codificació preliminar. Finalment, estudiar i analitzar l’efecte de la interferència co-canal en sistemes multifeix. Tots aquests temes són considerats només per al “forward link”. L’estructura que segueix el projecte és primer presentar les característiques globals del sistema, després centrar-se i analitzar els temes mencionats per a poder donar resultats i extreure conclusions.

Line search multilevel optimization as computational methods for dense optical flow

We evaluate the performance of different optimization techniques developed in the context of optical flowcomputation with different variational models. In particular, based on truncated Newton methods (TN) that have been an effective approach for large-scale unconstrained optimization, we develop the use of efficient multilevel schemes for computing the optical flow. More precisely, we evaluate the performance of a standard unidirectional multilevel algorithm - called multiresolution optimization (MR/OPT), to a bidrectional multilevel algorithm - called full multigrid optimization (FMG/OPT). The FMG/OPT algorithm treats the coarse grid correction as an optimization search direction and eventually scales it using a line search. Experimental results on different image sequences using four models of optical flow computation show that the FMG/OPT algorithm outperforms both the TN and MR/OPT algorithms in terms of the computational work and the quality of the optical flow estimation.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

An algorithm for semi-infinite polynomial optimization

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

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

Artificial Snow Optimization in Winter Sport Destinations Using a Multi-agent Simulation

This paper presents the Juste-Neige system for predicting the snow height on the ski runs of a resort using a multi-agent simulation software. Its aim is to facilitate snow cover management in order to i) reduce the production cost of artificial snow and to improve the profit margin for the companies managing the ski resorts; and ii) to reduce the water and energy consumption, and thus to reduce the environmental impact, by producing only the snow needed for a good skiing experience. The software provides maps with the predicted snow heights for up to 13 days. On these maps, the areas most exposed to snow erosion are highlighted. The software proceeds in three steps: i) interpolation of snow height measurements with a neural network; ii) local meteorological forecasts for every ski resort; iii) simulation of the impact caused by skiers using a multi-agent system. The software has been evaluated in the Swiss ski resort of Verbier and provides useful predictions.

Optimization of spatial resolution for peripheral magnetic resonance angiography.

RATIONALE AND OBJECTIVES: To determine optimum spatial resolution when imaging peripheral arteries with magnetic resonance angiography (MRA). MATERIALS AND METHODS: Eight vessel diameters ranging from 1.0 to 8.0 mm were simulated in a vascular phantom. A total of 40 three-dimensional flash MRA sequences were acquired with incremental variations of fields of view, matrix size, and slice thickness. The accurately known eight diameters were combined pairwise to generate 22 "exact" degrees of stenosis ranging from 42% to 87%. Then, the diameters were measured in the MRA images by three independent observers and with quantitative angiography (QA) software and used to compute the degrees of stenosis corresponding to the 22 "exact" ones. The accuracy and reproducibility of vessel diameter measurements and stenosis calculations were assessed for vessel size ranging from 6 to 8 mm (iliac artery), 4 to 5 mm (femoro-popliteal arteries), and 1 to 3 mm (infrapopliteal arteries). Maximum pixel dimension and slice thickness to obtain a mean error in stenosis evaluation of less than 10% were determined by linear regression analysis. RESULTS: Mean errors on stenosis quantification were 8.8% +/- 6.3% for 6- to 8-mm vessels, 15.5% +/- 8.2% for 4- to 5-mm vessels, and 18.9% +/- 7.5% for 1- to 3-mm vessels. Mean errors on stenosis calculation were 12.3% +/- 8.2% for observers and 11.4% +/- 15.1% for QA software (P = .0342). To evaluate stenosis with a mean error of less than 10%, maximum pixel surface, the pixel size in the phase direction, and the slice thickness should be less than 1.56 mm2, 1.34 mm, 1.70 mm, respectively (voxel size 2.65 mm3) for 6- to 8-mm vessels; 1.31 mm2, 1.10 mm, 1.34 mm (voxel size 1.76 mm3), for 4- to 5-mm vessels; and 1.17 mm2, 0.90 mm, 0.9 mm (voxel size 1.05 mm3) for 1- to 3-mm vessels. CONCLUSION: Higher spatial resolution than currently used should be selected for imaging peripheral vessels.

Iterative reconstruction methods in two different MDCT scanners: Physical metrics and 4-alternative forced-choice detectability experiments - A phantom approach.

This paper characterizes and evaluates the potential of three commercial CT iterative reconstruction methods (ASIR?, VEO? and iDose(4 ()?())) for dose reduction and image quality improvement. We measured CT number accuracy, standard deviation (SD), noise power spectrum (NPS) and modulation transfer function (MTF) metrics on Catphan phantom images while five human observers performed four-alternative forced-choice (4AFC) experiments to assess the detectability of low- and high-contrast objects embedded in two pediatric phantoms. Results show that 40% and 100% ASIR as well as iDose(4) levels 3 and 6 do not affect CT number and strongly decrease image noise with relative SD constant in a large range of dose. However, while ASIR produces a shift of the NPS curve apex, less change is observed with iDose(4) with respect to FBP methods. With second-generation iterative reconstruction VEO, physical metrics are even further improved: SD decreased to 70.4% at 0.5 mGy and spatial resolution improved to 37% (MTF(50%)). 4AFC experiments show that few improvements in detection task performance are obtained with ASIR and iDose(4), whereas VEO makes excellent detections possible even at an ultra-low-dose (0.3 mGy), leading to a potential dose reduction of a factor 3 to 7 (67%-86%). In spite of its longer reconstruction time and the fact that clinical studies are still required to complete these results, VEO clearly confirms the tremendous potential of iterative reconstructions for dose reduction in CT and appears to be an important tool for patient follow-up, especially for pediatric patients where cumulative lifetime dose still remains high.

How Low Can We Go in Contrast-Enhanced CT Imaging of the Chest?: A Dose-Finding Cadaver Study Using the Model-based Iterative Image Reconstruction Approach.

RATIONALE AND OBJECTIVES: Dose reduction may compromise patients because of a decrease of image quality. Therefore, the amount of dose savings in new dose-reduction techniques needs to be thoroughly assessed. To avoid repeated studies in one patient, chest computed tomography (CT) scans with different dose levels were performed in corpses comparing model-based iterative reconstruction (MBIR) as a tool to enhance image quality with current standard full-dose imaging. MATERIALS AND METHODS: Twenty-five human cadavers were scanned (CT HD750) after contrast medium injection at different, decreasing dose levels D0-D5 and respectively reconstructed with MBIR. The data at full-dose level, D0, have been additionally reconstructed with standard adaptive statistical iterative reconstruction (ASIR), which represented the full-dose baseline reference (FDBR). Two radiologists independently compared image quality (IQ) in 3-mm multiplanar reformations for soft-tissue evaluation of D0-D5 to FDBR (-2, diagnostically inferior; -1, inferior; 0, equal; +1, superior; and +2, diagnostically superior). For statistical analysis, the intraclass correlation coefficient (ICC) and the Wilcoxon test were used. RESULTS: Mean CT dose index values (mGy) were as follows: D0/FDBR = 10.1 ± 1.7, D1 = 6.2 ± 2.8, D2 = 5.7 ± 2.7, D3 = 3.5 ± 1.9, D4 = 1.8 ± 1.0, and D5 = 0.9 ± 0.5. Mean IQ ratings were as follows: D0 = +1.8 ± 0.2, D1 = +1.5 ± 0.3, D2 = +1.1 ± 0.3, D3 = +0.7 ± 0.5, D4 = +0.1 ± 0.5, and D5 = -1.2 ± 0.5. All values demonstrated a significant difference to baseline (P < .05), except mean IQ for D4 (P = .61). ICC was 0.91. CONCLUSIONS: Compared to ASIR, MBIR allowed for a significant dose reduction of 82% without impairment of IQ. This resulted in a calculated mean effective dose below 1 mSv.