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Added by
Daniel Lemire
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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Bitmap indexes are frequently used to index multidimensional data. They rely mostly on sequential input/output. Bitmaps can be compressed to reduce input/output costs and minimize CPU usage. The most efficient compression techniques are based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH) compression. This type of compression accelerates logical operations (AND, OR) over the bitmaps. However, run-length encoding is sensitive to the order of the facts. Thus, we propose to sort the fact tables. We review lexicographic, Gray-code, and block-wise sorting. We found that a lexicographic sort improves compression--sometimes generating indexes twice as small--and make indexes several times faster. While sorting takes time, this is partially offset by the fact that it is faster to index a sorted table. Column order is significant: it is generally preferable to put the columns having more distinct values at the beginning. A block-wise sort is much less efficient than a full sort. Moreover, we found that Gray-code sorting is not better than lexicographic sorting when using word-aligned compression.
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This paper contains results concerning a conjecture made by Lang and Silverman predicting a lower bound for the canonical height on abelian varieties of dimension 2 over number fields. The method used here is a local height decomposition. We derive as corollaries uniform bounds on the number of torsion points on families of abelian surfaces and on the number of rational points on families of genus 2 curves.
The first parts of the thesis recalls the main features of the large MACRO experiment at the underground Gran Sasso Laboratory. It then describes the atmospheric muons measured by the experiment and the selection criteria to obtain and analyze a large sample of cosmic muons. The time series of MACRO muons was analyzed with two complementary approaches: search for the occurrence of bursts of muon events and search for periodicities in the muon time distribution. The Scan Statistics method was used in the first case and the Lomb-Scargle spectral analysis in the second case. The two techniques complete early analyses performed with folding methods. It is confirmed that the seasonal variation is the dominant periodic variation, and one also confirms the solar diurnal and sidereal modulations. A separate study concerns the analysis of the energy losses of the hypothetical Nuclearites in different materials and detectors; their importance for the searches performed by the MACRO and the SLIM experiments is discussed.
Let X_d be the p-adic analytic space classifying the d-dimensional (semisimple) p-adic Galois representations of the absolute Galois group of Q_p. We show that the crystalline representations are Zarski-dense in many irreducible components of X_d, including the components made of residually irreducible representations. This extends to any dimension d previous results of Colmez and Kisin for d = 2. For this we construct an analogue of the infinite fern of Gouv^ea-Mazur in this context, based on a study of analytic families of trianguline (phi,Gamma)-modules over the Robba ring. We show in particular the existence of a universal family of (framed, regular) trianguline (phi,Gamma)-modules, as well as the density of the crystalline (phi,Gamma)-modules in this family. These results may be viewed as a local analogue of the theory of p-adic families of finite slope automorphic forms, they are new already in dimension 2. The technical heart of the paper is a collection of results about the Fontaine-Herr cohomology of families of trianguline (phi,Gamma)-modules.
We give a new definition, simpler but equivalent, of the abelian category of Banach-Colmez spaces introduced by Colmez, and we explain the precise relationship with the category of coherent sheaves on the Fargues-Fontaine curve. One goes from one category to the other by changing the t-structure on the derived category. Along the way, we obtain a description of the pro-etale cohomology of the open disk and the affine space, of independent interest.
Let X be a complex analytic manifold and D subset X a free divisor. Integrable logarithmic connections along D can be seen as locally free {cal O}_X-modules endowed with a (left) module structure over the ring of logarithmic differential operators {cal D}_X(log D). In this paper we study two related results: the relationship between the duals of any integrable logarithmic connection over the base rings {cal D}_X and {cal D}_X(log D), and a differential criterion for the logarithmic comparison theorem. We also generalize a formula of Esnault-Viehweg in the normal crossing case for the Verdier dual of a logarithmic de Rham complex.
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