Homologia de Lawson i descens

La meva recerca en els tres anys de gaudiment de beca s'ha centrat en l'estudi de teories semitopològiques definides a través d'espais de cicles algebraics, introduïts per Friedlander i Lawson. Hem estudiat propietats de descens d'aquestes teories i hem construït una successió espectral que calcula explícitament la cohomologia mòrfica d'una varietat tòrica. D'altra banda, estem treballant en l'estudi de propietats d'invariància homotòpica per la cohomologia mòrfica, així com en l'estructura algebraica dels grups d'homologia de Lawson.

$E_{1}$-Formality of complex algebraic varieties

Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent complex algebraic varieties (possibly singular and/or non-compact) and to algebraic morphisms between them. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.

On spectral approximation, Folner sequences and crossed products

In this article we review first some of the possibilities in which the notions of Fo lner sequences and quasidiagonality have been applied to spectral approximation problems. We construct then a canonical Fo lner sequence for the crossed product of a concrete C* -algebra and a discrete amenable group. We apply our results to the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schrödinger operators on graphs) and the C* -algebra generated by bounded Jacobi operators.

On the homotopy theory of spectral categories

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Spectral analysis of random sparse matrices

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Multilocus sequence analysis reveals the genetic diversity of European fruit tree phytoplasmas and supports the existence of inter-species recombination

The genetic diversity of three temperate fruit tree phytoplasmas ‘Candidatus Phytoplasma prunorum’, ‘Ca. P. mali’ and ‘Ca. P. pyri’ has been established by multilocus sequence analysis. Among the four genetic loci used, the genes imp and aceF distinguished 30 and 24 genotypes, respectively, and showed the highest variability. Percentage of substitution for imp ranged from 50 to 68% according to species. Percentage of substitution varied between 9 and 12% for aceF, whereas it was between 5 and 6% for pnp and secY. In the case of ‘Ca P. prunorum’ the three most prevalent aceF genotypes were detected in both plants and insect vectors, confirming that the prevalent isolates are propagated by insects. The four isolates known to be hypo-virulent had the same aceF sequence, indicating a possible monophyletic origin. Haplotype network reconstructed by eBURST revealed that among the 34 haplotypes of ‘Ca. P. prunorum’, the four hypo-virulent isolates also grouped together in the same clade. Genotyping of some Spanish and Azerbaijanese ‘Ca. P. pyri’ isolates showed that they shared some alleles with ‘Ca. P. prunorum’, supporting for the first time to our knowledge, the existence of inter-species recombination between these two species.

On spectral properties of the modified convolution operator

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Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

Estimating the motion of an underwater robot from a monocular image sequence

When underwater vehicles perform navigation close to the ocean floor, computer vision techniques can be applied to obtain quite accurate motion estimates. The most crucial step in the vision-based estimation of the vehicle motion consists on detecting matchings between image pairs. Here we propose the extensive use of texture analysis as a tool to ameliorate the correspondence problem in underwater images. Once a robust set of correspondences has been found, the three-dimensional motion of the vehicle can be computed with respect to the bed of the sea. Finally, motion estimates allow the construction of a map that could aid to the navigation of the robot

Detection of matchings in a sequence of underwater images through texture analysis

This paper presents an approach to ameliorate the reliability of the correspondence points relating two consecutive images of a sequence. The images are especially difficult to handle, since they have been acquired by a camera looking at the sea floor while carried by an underwater robot. Underwater images are usually difficult to process due to light absorption, changing image radiance and lack of well-defined features. A new approach based on gray-level region matching and selective texture analysis significantly improves the matching reliability

Parametrization of spectral surfaces of a class of periodic 5-diagonal matrices

The main result of this work is a parametric description of the spectral surfaces of a class of periodic 5-diagonal matrices, related to the strong moment problem. This class is a self-adjoint twin of the class of CMV matrices. Jointly they form the simplest possible classes of 5-diagonal matrices.

Estimation of zero-sequence impedance of undergrounds cables for single-phase fault location in distribution systems with electric arc

This paper focus on the problem of locating single-phase faults in mixed distribution electric systems, with overhead lines and underground cables, using voltage and current measurements at the sending-end and sequence model of the network. Since calculating series impedance for underground cables is not as simple as in the case of overhead lines, the paper proposes a methodology to obtain an estimation of zero-sequence impedance of underground cables starting from previous single-faults occurred in the system, in which an electric arc occurred at the fault location. For this reason, the signal is previously pretreated to eliminate its peaks voltage and the analysis can be done working with a signal as close as a sinus wave as possible

SGP-1: prediction and validation of homologous genes based on sequence alignments

Conventional methods of gene prediction rely on the recognition of DNA-sequence signals, the coding potential or the comparison of a genomic sequence with a cDNA, EST, or protein database. Reasons for limited accuracy in many circumstances are species-specific training and the incompleteness of reference databases. Lately, comparative genome analysis has attracted increasing attention. Several analysis tools that are based on human/mouse comparisons are already available. Here, we present a program for the prediction of protein-coding genes, termed SGP-1 (Syntenic Gene Prediction), which is based on the similarity of homologous genomic sequences. In contrast to most existing tools, the accuracy of SGP-1 depends little on species-specific properties such as codon usage or the nucleotide distribution. SGP-1 may therefore be applied to nonstandard model organisms in vertebrates as well as in plants, without the need for extensive parameter training. In addition to predicting genes in large-scale genomic sequences, the program may be useful to validate gene structure annotations from databases. To this end, SGP-1 output also contains comparisons between predicted and annotated gene structures in HTML format. The program can be accessed via a Web server at http://soft.ice.mpg.de/sgp-1. The source code, written in ANSI C, is available on request from the authors.