Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

A Survey of Active Learning Algorithms for Supervised Remote Sensing Image Classification

Defining an efficient training set is one of the most delicate phases for the success of remote sensing image classification routines. The complexity of the problem, the limited temporal and financial resources, as well as the high intraclass variance can make an algorithm fail if it is trained with a suboptimal dataset. Active learning aims at building efficient training sets by iteratively improving the model performance through sampling. A user-defined heuristic ranks the unlabeled pixels according to a function of the uncertainty of their class membership and then the user is asked to provide labels for the most uncertain pixels. This paper reviews and tests the main families of active learning algorithms: committee, large margin, and posterior probability-based. For each of them, the most recent advances in the remote sensing community are discussed and some heuristics are detailed and tested. Several challenging remote sensing scenarios are considered, including very high spatial resolution and hyperspectral image classification. Finally, guidelines for choosing the good architecture are provided for new and/or unexperienced user.

Neural Wiskott-Aldrich syndrome protein modulates Wnt signaling and is required for hair follicle cycling in mice.

The Rho family GTPases Cdc42 and Rac1 are critical regulators of the actin cytoskeleton and are essential for skin and hair function. Wiskott-Aldrich syndrome family proteins act downstream of these GTPases, controlling actin assembly and cytoskeletal reorganization, but their role in epithelial cells has not been characterized in vivo. Here, we used a conditional knockout approach to assess the role of neural Wiskott-Aldrich syndrome protein (N-WASP), the ubiquitously expressed Wiskott-Aldrich syndrome-like (WASL) protein, in mouse skin. We found that N-WASP deficiency in mouse skin led to severe alopecia, epidermal hyperproliferation, and ulceration, without obvious effects on epidermal differentiation and wound healing. Further analysis revealed that the observed alopecia was likely the result of a progressive and ultimately nearly complete block in hair follicle (HF) cycling by 5 months of age. N-WASP deficiency also led to abnormal proliferation of skin progenitor cells, resulting in their depletion over time. Furthermore, N-WASP deficiency in vitro and in vivo correlated with decreased GSK-3beta phosphorylation, decreased nuclear localization of beta-catenin in follicular keratinocytes, and decreased Wnt-dependent transcription. Our results indicate a critical role for N-WASP in skin function and HF cycling and identify a link between N-WASP and Wnt signaling. We therefore propose that N-WASP acts as a positive regulator of beta-catenin-dependent transcription, modulating differentiation of HF progenitor cells.

Advanced mapping of environmental data: Geostatistics, Machine Learning and Bayesian Maximum Entropy

This book combines geostatistics and global mapping systems to present an up-to-the-minute study of environmental data. Featuring numerous case studies, the reference covers model dependent (geostatistics) and data driven (machine learning algorithms) analysis techniques such as risk mapping, conditional stochastic simulations, descriptions of spatial uncertainty and variability, artificial neural networks (ANN) for spatial data, Bayesian maximum entropy (BME), and more.

Neural activity of the anterior insula in emotional processing depends on the individuals' emotional susceptibility

Differences in personality factors between individuals may manifest themselves with different patterns of neural activity while individuals process stimuli with emotional content. We attempted to verify this hypothesis by investigating emotional susceptibility (ES), a specific emotional trait of the human personality defined as the tendency to "experience feelings of discomfort, helplessness, inadequacy and vulnerability" after exposure to stimuli with emotional valence. By administering a questionnaire evaluating the individuals' ES, we selected two groups of participants with high and low ES respectively. Then, we used functional magnetic resonance imaging to investigate differences between the groups in the neural activity involved while they were processing emotional stimuli in an explicit (focusing on the content of the stimuli) or an incidental (focusing on spatial features of the stimuli, irrespectively of their content) way. The results showed a selective difference in brain activity between groups only in the explicit processing of the emotional stimuli: bilateral activity of the anterior insula was present in subjects with high ES but not in subjects with low ES. This difference in neural activity within the anterior insula proved to be purely functional since no brain morphological differences were found between groups, as assessed by a voxel-based morphometry analysis. Although the role of the anterior insula in the processing of contexts perceived as emotionally salient is well established, the present study provides the first evidence of a modulation of the insular activity depending on the individuals' ES trait of personality.

Hard instances of algorithms and proof systems

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

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Expression of the gene encoding the high-Km glucose transporter 2 by the early postimplantation mouse embryo is essential for neural tube defects associated with diabetic embryopathy.

AIMS/HYPOTHESIS: Excess glucose transport to embryos during diabetic pregnancy causes congenital malformations. The early postimplantation embryo expresses the gene encoding the high-Km GLUT2 (also known as SLC2A2) glucose transporter. The hypothesis tested here is that high-Km glucose transport by GLUT2 causes malformations resulting from maternal hyperglycaemia during diabetic pregnancy. MATERIALS AND METHODS: Glut2 mRNA was assayed by RT-PCR. The Km of embryo glucose transport was determined by measuring 0.5-20 mmol/l 2-deoxy[3H]glucose transport. To test whether the GLUT2 transporter is required for neural tube defects resulting from maternal hyperglycaemia, Glut2+/- mice were crossed and transient hyperglycaemia was induced by glucose injection on day 7.5 of pregnancy. Embryos were recovered on day 10.5, and the incidence of neural tube defects in wild-type, Glut2+/- and Glut2-/- embryos was scored. RESULTS: Early postimplantation embryos expressed Glut2, and expression was unaffected by maternal diabetes. Moreover, glucose transport by these embryos showed Michaelis-Menten kinetics of 16.19 mmol/l, consistent with transport mediated by GLUT2. In pregnancies made hyperglycaemic on day 7.5, neural tube defects were significantly increased in wild-type embryos, but Glut2+/- embryos were partially protected from neural tube defects, and Glut2-/- embryos were completely protected from these defects. The frequency of occurrence of wild-type, Glut2+/- and Glut2-/- embryos suggests that the presence of Glut2 alleles confers a survival advantage in embryos before day 10.5. CONCLUSIONS/INTERPRETATIONS: High-Km glucose transport by the GLUT2 glucose transporter during organogenesis is responsible for the embryopathic effects of maternal diabetes.

Distinction of males of the Lutzomyia intermedia (Lutz & Neiva, 1912) species complex by ratios between dimensions and by an artificial neural network (Diptera: Psychodidae, Phlebotominae)

The females of the two species of the Lutzomyia intermedia complex can be easily distinguished, but the males of each species are quite similar. The ratios between the extra-genital and the genital structures of L. neivai are larger than those of L. intermedia s. s., according to ANOVA. An artificial neural network was trained with a set of 300 examples, randomly taken from a sample of 358 individuals. The input vectors consisted of several ratios between some structures of each insect. The model was tested on the remaining 58 insects, 56 of which (96.6%) were correctly identified. This ratio of success can be considered remarkable if one takes into account the difficulty of attaining comparable results using traditional statistical techniques.