2,599 research outputs found
Deformations of Lie brackets and representations up to homotopy
We show that representations up to homotopy can be differentiated in a
functorial way. A van Est type isomorphism theorem is established and used to
prove a conjecture of Crainic and Moerdijk on deformations of Lie brackets.Comment: 28 page
Conservation of geometric structures for non-homogeneous inviscid incompressible fluids
We obtain a result about propagation of geometric properties for solutions of
the non-homogeneous incompressible Euler system in any dimension . In
particular, we investigate conservation of striated and conormal regularity,
which is a natural way of generalizing the 2-D structure of vortex patches. The
results we get are only local in time, even in the dimension N=2; however, we
provide an explicit lower bound for the lifespan of the solution. In the case
of physical dimension N=2 or 3, we investigate also propagation of H\"older
regularity in the interior of a bounded domain
A continuum-tree-valued Markov process
We present a construction of a L\'evy continuum random tree (CRT) associated
with a super-critical continuous state branching process using the so-called
exploration process and a Girsanov's theorem. We also extend the pruning
procedure to this super-critical case. Let be a critical branching
mechanism. We set . Let
or be the set
of values of for which is a branching mechanism. The
pruning procedure allows to construct a decreasing L\'evy-CRT-valued Markov
process (\ct_\theta,\theta\in\Theta), such that has
branching mechanism . It is sub-critical if and
super-critical if . We then consider the explosion time of the
CRT: the smaller (negative) time for which has
finite mass. We describe the law of as well as the distribution of the CRT
just after this explosion time. The CRT just after explosion can be seen as a
CRT conditioned not to be extinct which is pruned with an independent intensity
related to . We also study the evolution of the CRT-valued process after the
explosion time. This extends results from Aldous and Pitman on Galton-Watson
trees. For the particular case of the quadratic branching mechanism, we show
that after explosion the total mass of the CRT behaves like the inverse of a
stable subordinator with index 1/2. This result is related to the size of the
tagged fragment for the fragmentation of Aldous' CRT
Fast learning rates in statistical inference through aggregation
We develop minimax optimal risk bounds for the general learning task
consisting in predicting as well as the best function in a reference set
up to the smallest possible additive term, called the convergence
rate. When the reference set is finite and when denotes the size of the
training data, we provide minimax convergence rates of the form
with tight evaluation of the positive
constant and with exact , the latter value depending on the
convexity of the loss function and on the level of noise in the output
distribution. The risk upper bounds are based on a sequential randomized
algorithm, which at each step concentrates on functions having both low risk
and low variance with respect to the previous step prediction function. Our
analysis puts forward the links between the probabilistic and worst-case
viewpoints, and allows to obtain risk bounds unachievable with the standard
statistical learning approach. One of the key ideas of this work is to use
probabilistic inequalities with respect to appropriate (Gibbs) distributions on
the prediction function space instead of using them with respect to the
distribution generating the data. The risk lower bounds are based on
refinements of the Assouad lemma taking particularly into account the
properties of the loss function. Our key example to illustrate the upper and
lower bounds is to consider the -regression setting for which an
exhaustive analysis of the convergence rates is given while ranges in
.Comment: Published in at http://dx.doi.org/10.1214/08-AOS623 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Convergence in law in the second Wiener/Wigner chaos
Let L be the class of limiting laws associated with sequences in the second
Wiener chaos. We exhibit a large subset L_0 of L satisfying that, for any
F_infinity in L_0, the convergence of only a finite number of cumulants
suffices to imply the convergence in law of any sequence in the second Wiener
chaos to F_infinity. This result is in the spirit of the seminal paper by
Nualart and Peccati, in which the authors discovered the surprising fact that
convergence in law for sequences of multiple Wiener-It\^o integrals to the
Gaussian is equivalent to convergence of just the fourth cumulant. Also, we
offer analogues of this result in the case of free Brownian motion and double
Wigner integrals, in the context of free probability.Comment: 14 pages. This version corrects an error which, unfortunately,
appears in the published version in EC
Land Tenure System: Women’s Access to Land in a Cosmopolitan Context
Land tenure is a concept that looks at how people gain access to land and how they make use of it. In various African societies, there are cases where women's land ownership is complicated by the gender ideology that women should not own property, particularly land and housing. Women who own property tend to be stereotyped as self-assertive and unruly, and therefore not marriage worthy. This study utilized primary data and combined quantitative and qualitative methods in analyzing the data collected. Focused group discussions (FGDs) were also organized as a source of qualitative information to support the quantitative data. Findings from the research are that there is an increase in net registration of titles to land by males over the period, compared to a reduction in females registering titles. There is a gender difference in the number of plots owned by males and females. Males owned more plots of land as compared to females. While the majority of male respondents directly negotiated for their land purchases, it was more usual for females to use male intermediaries in an effort to prevent being duped by predominantly male land sellers. Recommendation from the study is that equal inheritance rights to land should be guaranteed to both men and women
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