1,990 research outputs found
Metabelian groups with quadratic Dehn function and Baumslag-Solitar groups
We prove that groups in a certain class of metabelian locally compact groups,
have quadratic Dehn function. As an application, we embed the solvable
Baumslag-Solitar groups into finitely presented metabelian groups with
quadratic Dehn function. Also, we prove that Baumslag's finitely presented
metabelian groups, in which the lamplighter groups embed, have quadratic Dehn
function.Comment: 13 pages, one figure. v1->v2: title has been changed; added
application to Baumslag's group v2->v3 numerous correction
Quasi-friendly sup-interpretations
In a previous paper, the sup-interpretation method was proposed as a new tool
to control memory resources of first order functional programs with pattern
matching by static analysis. Basically, a sup-interpretation provides an upper
bound on the size of function outputs. In this former work, a criterion, which
can be applied to terminating as well as non-terminating programs, was
developed in order to bound polynomially the stack frame size. In this paper,
we suggest a new criterion which captures more algorithms computing values
polynomially bounded in the size of the inputs. Since this work is related to
quasi-interpretations, we compare the two notions obtaining two main features.
The first one is that, given a program, we have heuristics for finding a
sup-interpretation when we consider polynomials of bounded degree. The other
one consists in the characterizations of the set of function computable in
polynomial time and in polynomial space
Resource control of object-oriented programs
A sup-interpretation is a tool which provides an upper bound on the size of a
value computed by some symbol of a program. Sup-interpretations have shown
their interest to deal with the complexity of first order functional programs.
For instance, they allow to characterize all the functions bitwise computable
in Alogtime. This paper is an attempt to adapt the framework of
sup-interpretations to a fragment of oriented-object programs, including
distinct encodings of numbers through the use of constructor symbols, loop and
while constructs and non recursive methods with side effects. We give a
criterion, called brotherly criterion, which ensures that each brotherly
program computes objects whose size is polynomially bounded by the inputs
sizes
Complexity Information Flow in a Multi-threaded Imperative Language
We propose a type system to analyze the time consumed by multi-threaded
imperative programs with a shared global memory, which delineates a class of
safe multi-threaded programs. We demonstrate that a safe multi-threaded program
runs in polynomial time if (i) it is strongly terminating wrt a
non-deterministic scheduling policy or (ii) it terminates wrt a deterministic
and quiet scheduling policy. As a consequence, we also characterize the set of
polynomial time functions. The type system presented is based on the
fundamental notion of data tiering, which is central in implicit computational
complexity. It regulates the information flow in a computation. This aspect is
interesting in that the type system bears a resemblance to typed based
information flow analysis and notions of non-interference. As far as we know,
this is the first characterization by a type system of polynomial time
multi-threaded programs
Classification and Anomaly Detection for Astronomical Datasets
This work develops two new statistical techniques for astronomical problems: a star /
galaxy separator for the UKIRT Infrared Deep Sky Survey (UKIDSS) and a novel anomaly
detection method for cross-matched astronomical datasets.
The star / galaxy separator is a statistical classification method which outputs class
membership probabilities rather than class labels and allows the use of prior knowledge
about the source populations. Deep Sloan Digital Sky Survey (SDSS) data from the multiply
imaged Stripe 82 region is used to check the results from our classifier, which compares
favourably with the UKIDSS pipeline classification algorithm.
The anomaly detection method addresses the problem posed by objects having different
sets of recorded variables in cross-matched datasets. This prevents the use of methods
unable to handle missing values and makes direct comparison between objects difficult.
For each source, our method computes anomaly scores in subspaces of the observed feature
space and combines them to an overall anomaly score. The proposed technique is very
general and can easily be used in applications other than astronomy. The properties and
performance of our method are investigated using both real and simulated datasets
Isometric group actions on Hilbert spaces: growth of cocycles
We study growth of 1-cocycles of locally compact groups, with values in
unitary representations. Discussing the existence of 1-cocycles with linear
growth, we obtain the following alternative for a class of amenable groups G
containing polycyclic groups and connected amenable Lie groups: either G has no
quasi-isometric embedding into Hilbert space, or G admits a proper cocompact
action on some Euclidean space.
On the other hand, noting that almost coboundaries (i.e. 1-cocycles
approximable by bounded 1-cocycles) have sublinear growth, we discuss the
converse, which turns out to hold for amenable groups with "controlled" Folner
sequences; for general amenable groups we prove the weaker result that
1-cocycles with sufficiently small growth are almost coboundaries. Besides, we
show that there exist, on a-T-menable groups, proper cocycles with arbitrary
small growth.Comment: 26 pages, no figure. To appear in Geom. Funct. Ana
The Howe-Moore property for real and p-adic groups
We consider in this paper a relative version of the Howe-Moore Property,
about vanishing at infinity of coefficients of unitary representations. We
characterize this property in terms of ergodic measure-preserving actions. We
also characterize, for linear Lie groups or p-adic Lie groups, the pairs with
the relative Howe-Moore Property with respect to a closed, normal subgroup.
This involves, in one direction, structural results on locally compact groups
all of whose proper closed characteristic subgroups are compact, and, in the
other direction, some results about the vanishing at infinity of oscillatory
integrals.Comment: 25 pages, no figur
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are
non-elementary Gromov-hyperbolic and amenable. They coincide with the class of
mapping tori of discrete or continuous one-parameter groups of compacting
automorphisms. We moreover give a description of all Gromov-hyperbolic locally
compact groups with a cocompact amenable subgroup: modulo a compact normal
subgroup, these turn out to be either rank one simple Lie groups, or
automorphism groups of semi-regular trees acting doubly transitively on the set
of ends. As an application, we show that the class of hyperbolic locally
compact groups with a cusp-uniform non-uniform lattice, is very restricted.Comment: 41 pages, no figure. v2: revised version (minor changes
Isometric group actions on Hilbert spaces: structure of orbits
Our main result is that a finitely generated nilpotent group has no isometric
action on an infinite-dimensional Hilbert space with dense orbits. In contrast,
we construct such an action with a finitely generated metabelian group.Comment: 12 pages, to appear in Canadian Math.
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