19,043 research outputs found
Moduli Spaces and Formal Operads
Let overline{M}_{g,n} be the moduli space of stable algebraic curves of genus
g with n marked points. With the operations which relate the different moduli
spaces identifying marked points, the family (overline{M}_{g,n})_{g,n} is a
modular operad of projective smooth Deligne-Mumford stacks, overline{M}. In
this paper we prove that the modular operad of singular chains
C_*(overline{M};Q) is formal; so it is weakly equivalent to the modular operad
of its homology H_*(overline{M};Q). As a consequence, the "up to homotopy"
algebras of these two operads are the same. To obtain this result we prove a
formality theorem for operads analogous to Deligne-Griffiths-Morgan-Sullivan
formality theorem, the existence of minimal models of modular operads, and a
characterization of formality for operads which shows that formality is
independent of the ground field.Comment: 36 pages (v3: some typographical corrections
A Cartan-Eilenberg approach to Homotopical Algebra
In this paper we propose an approach to homotopical algebra where the basic
ingredient is a category with two classes of distinguished morphisms: strong
and weak equivalences. These data determine the cofibrant objects by an
extension property analogous to the classical lifting property of projective
modules. We define a Cartan-Eilenberg category as a category with strong and
weak equivalences such that there is an equivalence between its localization
with respect to weak equivalences and the localised category of cofibrant
objets with respect to strong equivalences. This equivalence allows us to
extend the classical theory of derived additive functors to this non additive
setting. The main examples include Quillen model categories and functor
categories with a triple, in the last case we find examples in which the class
of strong equivalences is not determined by a homotopy relation. Among other
applications, we prove the existence of filtered minimal models for \emph{cdg}
algebras over a zero-characteristic field and we formulate an acyclic models
theorem for non additive functors
Document Retrieval on Repetitive Collections
Document retrieval aims at finding the most important documents where a
pattern appears in a collection of strings. Traditional pattern-matching
techniques yield brute-force document retrieval solutions, which has motivated
the research on tailored indexes that offer near-optimal performance. However,
an experimental study establishing which alternatives are actually better than
brute force, and which perform best depending on the collection
characteristics, has not been carried out. In this paper we address this
shortcoming by exploring the relationship between the nature of the underlying
collection and the performance of current methods. Via extensive experiments we
show that established solutions are often beaten in practice by brute-force
alternatives. We also design new methods that offer superior time/space
trade-offs, particularly on repetitive collections.Comment: Accepted to ESA 2014. Implementation and experiments at
http://www.cs.helsinki.fi/group/suds/rlcsa
Satellites of Simulated Galaxies: survival, merging, and their relation to the dark and stellar halos
We study the population of satellite galaxies formed in a suite of
N-body/gasdynamical simulations of galaxy formation in a LCDM universe. We find
little spatial or kinematic bias between the dark matter and the satellite
population. The velocity dispersion of the satellites is a good indicator of
the virial velocity of the halo: \sigma_{sat}/V_{vir}=0.9 +/- 0.2. Applied to
the Milky Way and M31 this gives V_{vir}^{MW}=109 +/- 22$ km/s and
V_{vir}^{M31} = 138 +/- 35 km/s, respectively, substantially lower than the
rotation speed of their disk components. The detailed kinematics of simulated
satellites and dark matter are also in good agreement. By contrast, the stellar
halo of the simulated galaxies is kinematically and spatially distinct from the
population of surviving satellites. This is because the survival of a satellite
depends on mass and on time of accretion; surviving satellites are biased
toward low-mass systems that have been recently accreted by the galaxy. Our
results support recent proposals for the origin of the systematic differences
between stars in the Galactic halo and in Galactic satellites: the elusive
``building blocks'' of the Milky Way stellar halo were on average more massive,
and were accreted (and disrupted) earlier than the population of dwarfs that
has survived self-bound until the present.Comment: 13 pages, 11 figures, MNRAS in press. Accepted version with minor
changes. Version with high resolution figures available at:
http://www.astro.uvic.ca/~lsales/SatPapers/SatPapers.htm
Cosmic M\'enage \`a Trois: The Origin of Satellite Galaxies On Extreme Orbits
We examine the orbits of satellite galaxies identified in a suite of
N-body/gasdynamical simulations of the formation of galaxies in a LCDM
universe. Most satellites follow conventional orbits; after turning around,
they accrete into their host halo and settle on orbits whose apocentric radii
are steadily eroded by dynamical friction. However, a number of outliers are
also present, we find that ~1/3 of satellites identified at are on
unorthodox orbits, with apocenters that exceed their turnaround radii. This
population of satellites on extreme orbits consists typically of the faint
member of a satellite pair that has been ejected onto a highly-energetic orbit
during its first approach to the primary. Since the concurrent accretion of
multiple satellite systems is a defining feature of hierarchical models of
galaxy formation, we speculate that this three-body ejection mechanism may be
the origin of (i) some of the newly discovered high-speed satellites around M31
(such as Andromeda XIV); (ii) some of the distant fast-receding Local Group
members, such as Leo I; and (iii) the oddly isolated dwarf spheroidals Cetus
and Tucana in the outskirts of the Local Group. Our results suggest that care
must be exercised when using the orbits of the most weakly bound satellites to
place constraints on the total mass of the Local Group.Comment: 10 pages, 6 figures, MNRAS in press. Accepted version with minor
changes. Version with high resolution figures available at:
http://www.astro.uvic.ca/~lsales/SatPapers/SatPapers.htm
From Theory to Practice: Plug and Play with Succinct Data Structures
Engineering efficient implementations of compact and succinct structures is a
time-consuming and challenging task, since there is no standard library of
easy-to- use, highly optimized, and composable components. One consequence is
that measuring the practical impact of new theoretical proposals is a difficult
task, since older base- line implementations may not rely on the same basic
components, and reimplementing from scratch can be very time-consuming. In this
paper we present a framework for experimentation with succinct data structures,
providing a large set of configurable components, together with tests,
benchmarks, and tools to analyze resource requirements. We demonstrate the
functionality of the framework by recomposing succinct solutions for document
retrieval.Comment: 10 pages, 4 figures, 3 table
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