16,188 research outputs found
Non-renormalization for the Liouville wave function
Using an exact functional method, within the framework of the gradient
expansion for the Liouville effective action, we show that the kinetic term for
the Liouville field is not renormalized.Comment: 13 pages Latex, no figure
Quasi-isometries Between Groups with Two-Ended Splittings
We construct `structure invariants' of a one-ended, finitely presented group
that describe the way in which the factors of its JSJ decomposition over
two-ended subgroups fit together.
For groups satisfying two technical conditions, these invariants reduce the
problem of quasi-isometry classification of such groups to the problem of
relative quasi-isometry classification of the factors of their JSJ
decompositions. The first condition is that their JSJ decompositions have
two-ended cylinder stabilizers. The second is that every factor in their JSJ
decompositions is either `relatively rigid' or `hanging'. Hyperbolic groups
always satisfy the first condition, and it is an open question whether they
always satisfy the second.
The same methods also produce invariants that reduce the problem of
classification of one-ended hyperbolic groups up to homeomorphism of their
Gromov boundaries to the problem of classification of the factors of their JSJ
decompositions up to relative boundary homeomorphism type.Comment: 61pages, 6 figure
Control of quantum fluctuations for a Yukawa interaction in the Kaluza Klein picture
We study a system of fermions interacting with a scalar field, in 4+1
dimensions where the 5th dimension is compactified, using an exact functional
method, where quantum fluctuations are controlled by the amplitude of the bare
fermion mass. The integration of our equationsleads to the properties of the
dressed Yukawa coupling, that we study at one-loop so as to show the
consistency of the approach. Beyond one loop, the non-perturbative aspect of
the method gives us the possibility to derive the dynamical fermion mass. The
result obtained is cut off independent and this derivation proposes an
alternative to the Schwinger-Dyson approach.Comment: extended discussion on the scalar effective potentia
Aggregation for Gaussian regression
This paper studies statistical aggregation procedures in the regression
setting. A motivating factor is the existence of many different methods of
estimation, leading to possibly competing estimators. We consider here three
different types of aggregation: model selection (MS) aggregation, convex (C)
aggregation and linear (L) aggregation. The objective of (MS) is to select the
optimal single estimator from the list; that of (C) is to select the optimal
convex combination of the given estimators; and that of (L) is to select the
optimal linear combination of the given estimators. We are interested in
evaluating the rates of convergence of the excess risks of the estimators
obtained by these procedures. Our approach is motivated by recently published
minimax results [Nemirovski, A. (2000). Topics in non-parametric statistics.
Lectures on Probability Theory and Statistics (Saint-Flour, 1998). Lecture
Notes in Math. 1738 85--277. Springer, Berlin; Tsybakov, A. B. (2003). Optimal
rates of aggregation. Learning Theory and Kernel Machines. Lecture Notes in
Artificial Intelligence 2777 303--313. Springer, Heidelberg]. There exist
competing aggregation procedures achieving optimal convergence rates for each
of the (MS), (C) and (L) cases separately. Since these procedures are not
directly comparable with each other, we suggest an alternative solution. We
prove that all three optimal rates, as well as those for the newly introduced
(S) aggregation (subset selection), are nearly achieved via a single
``universal'' aggregation procedure. The procedure consists of mixing the
initial estimators with weights obtained by penalized least squares. Two
different penalties are considered: one of them is of the BIC type, the second
one is a data-dependent -type penalty.Comment: Published in at http://dx.doi.org/10.1214/009053606000001587 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Coherent Diffractive Imaging Using Randomly Coded Masks
Coherent diffractive imaging (CDI) provides new opportunities for high
resolution X-ray imaging with simultaneous amplitude and phase contrast.
Extensions to CDI broaden the scope of the technique for use in a wide variety
of experimental geometries and physical systems. Here, we experimentally
demonstrate a new extension to CDI that encodes additional information through
the use of a series of randomly coded masks. The information gained from the
few additional diffraction measurements removes the need for typical
object-domain constraints; the algorithm uses prior information about the masks
instead. The experiment is performed using a laser diode at 532.2 nm, enabling
rapid prototyping for future X-ray synchrotron and even free electron laser
experiments. Diffraction patterns are collected with up to 15 different masks
placed between a CCD detector and a single sample. Phase retrieval is performed
using a convex relaxation routine known as "PhaseCut" followed by a variation
on Fienup's input-output algorithm. The reconstruction quality is judged via
calculation of phase retrieval transfer functions as well as by an object-space
comparison between reconstructions and a lens-based image of the sample. The
results of this analysis indicate that with enough masks (in this case 3 or 4)
the diffraction phases converge reliably, implying stability and uniqueness of
the retrieved solution
The performance of modularity maximization in practical contexts
Although widely used in practice, the behavior and accuracy of the popular
module identification technique called modularity maximization is not well
understood in practical contexts. Here, we present a broad characterization of
its performance in such situations. First, we revisit and clarify the
resolution limit phenomenon for modularity maximization. Second, we show that
the modularity function Q exhibits extreme degeneracies: it typically admits an
exponential number of distinct high-scoring solutions and typically lacks a
clear global maximum. Third, we derive the limiting behavior of the maximum
modularity Q_max for one model of infinitely modular networks, showing that it
depends strongly both on the size of the network and on the number of modules
it contains. Finally, using three real-world metabolic networks as examples, we
show that the degenerate solutions can fundamentally disagree on many, but not
all, partition properties such as the composition of the largest modules and
the distribution of module sizes. These results imply that the output of any
modularity maximization procedure should be interpreted cautiously in
scientific contexts. They also explain why many heuristics are often successful
at finding high-scoring partitions in practice and why different heuristics can
disagree on the modular structure of the same network. We conclude by
discussing avenues for mitigating some of these behaviors, such as combining
information from many degenerate solutions or using generative models.Comment: 20 pages, 14 figures, 6 appendices; code available at
http://www.santafe.edu/~aaronc/modularity
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