Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

Unconstrained optimization with MINTOOLKIT for GNU octave

The paper documents MINTOOLKIT for GNU Octave. MINTOOLKIT provides functions for minimization and numeric differentiation. The main algorithms are BFGS, LBFGS, and simulated annealing. Examples are given.

Strong exceptional sequences of vector bundles on certain Fano varieties

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

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.

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).

Textural classification of land cover using support vector machines: an empirical comparison with parametric, non parametric and hybrid classifiers in the Bolivian Amazon

Land cover classification is a key research field in remote sensing and land change science as thematic maps derived from remotely sensed data have become the basis for analyzing many socio-ecological issues. However, land cover classification remains a difficult task and it is especially challenging in heterogeneous tropical landscapes where nonetheless such maps are of great importance. The present study aims to establish an efficient classification approach to accurately map all broad land cover classes in a large, heterogeneous tropical area of Bolivia, as a basis for further studies (e.g., land cover-land use change). Specifically, we compare the performance of parametric (maximum likelihood), non-parametric (k-nearest neighbour and four different support vector machines - SVM), and hybrid classifiers, using both hard and soft (fuzzy) accuracy assessments. In addition, we test whether the inclusion of a textural index (homogeneity) in the classifications improves their performance. We classified Landsat imagery for two dates corresponding to dry and wet seasons and found that non-parametric, and particularly SVM classifiers, outperformed both parametric and hybrid classifiers. We also found that the use of the homogeneity index along with reflectance bands significantly increased the overall accuracy of all the classifications, but particularly of SVM algorithms. We observed that improvements in producer’s and user’s accuracies through the inclusion of the homogeneity index were different depending on land cover classes. Earlygrowth/degraded forests, pastures, grasslands and savanna were the classes most improved, especially with the SVM radial basis function and SVM sigmoid classifiers, though with both classifiers all land cover classes were mapped with producer’s and user’s accuracies of around 90%. Our approach seems very well suited to accurately map land cover in tropical regions, thus having the potential to contribute to conservation initiatives, climate change mitigation schemes such as REDD+, and rural development policies.

Route optimization and customization using real geographical data in Android mobile devices

Nowadays, there are several services and applications that allow users to locate and move to different tourist areas using a mobile device. These systems can be used either by internet or downloading an application in concrete places like a visitors centre. Although such applications are able to facilitate the location and the search for points of interest, in most cases, these services and applications do not meet the needs of each user. This paper aims to provide a solution by studying the main projects, services and applications, their routing algorithms and their treatment of the real geographical data in Android mobile devices, focusing on the data acquisition and treatment to improve the routing searches in off-line environments.

Desenvolupament d'algorismes biològicament inspirats basats en Support Vector Machines

L'objectiu d'aquest projecte ha estat el desenvolupament d'algorismes biològicament inspirats per a l'olfacció artificial. Per a assolir-lo ens hem basat en el paradigma de les màquines amb suport vectorial. Hem construit algoritmes que imitaven els processos computacionals dels diferents sistemes que formen el sistema olfactiu dels insectes, especialment de la llagosta Schistocerca gregaria. Ens hem centrat en el lòbuls de les antenes, i en el cos fungiforme. El primer està considerat un dispositiu de codificació de les olors, que a partir de la resposta temporal dels receptors olfactius a les antenes genera un patró d'activació espaial i temporal. Quant al cos fungiforme es considera que la seva funció és la d'una memòria per als olors, així com un centre per a la integració multi-sensorial. El primer pas ha estat la construcció de models detallats dels dos sistemes. A continuació, hem utilitzat aquests models per a processar diferents tipus de senyals amb l'objectiu de abstraure els principis computacionals subjacents. Finalment, hem avaluat les capacitats d'aquests models abstractes, i els hem utilitzat per al processat de dades provinents de sensors de gasos. Els resultats mostren que el models abstractes tenen millor comportament front el soroll i més capacitat d'emmagatzematge de records que altres models més clàssics, com ara les memòries associatives de Hopfield o fins i tot en determinades circumstàncies que les mateixes Support Vector Machines.

Algorithm creation and optimization for the crew pairing problem

Algoritmo que optimiza y crea pairings para tripulaciones de líneas aéreas mediante la posterior programación en Java.

Optimization of floor cleaning coverage performance of a random path-planning mobile robot

Floor cleaning is a typical robot application. There are several mobile robots aviable in the market for domestic applications most of them with random path-planning algorithms. In this paper we study the cleaning coverage performances of a random path-planning mobile robot and propose an optimized control algorithm, some methods to estimate the are of the room, the evolution of the cleaning and the time needed for complete coverage.

Algorithm optimization for solving crew scheduling problems

In this paper, we are proposing a methodology to determine the most efficient and least costly way of crew pairing optimization. We are developing a methodology based on algorithm optimization on Eclipse opensource IDE using the Java programming language to solve the crew scheduling problems.