8,335 research outputs found
On the second order derivatives of convex functions on the Heisenberg group
In the Euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem
states that convex functions are a.e. twice differentiable. In this paper we
prove that a similar result holds in the Heisenberg group, by showing that
every continuous H-convex function belongs to the class of functions whose
second order horizontal distributional derivatives are Radon measures. Together
with a recent result by Ambrosio and Magnani, this proves the existence a.e. of
second order horizontal derivatives for the class of continuous H-convex
functions in the Heisenberg group
Maximum and comparison principles for convex functions on the Heisenberg group
We prove estimates, similar in form to the classical Aleksandrov estimates,
for a Monge-Ampere type operator on the Heisenberg group. A notion of normal
mapping does not seem to be available in this context and the method of proof
uses integration by parts and oscillation estimates that lead to the
construction of an analogue of Monge-Ampere measures for convex functions in
the Heisenberg group.Comment: The results in this paper and the ideas of their proofs have been
presented in the following talks: Analysis Seminar, Temple U., October 2002;
Fabes--Chiarenza Lectures at Siracusa, December 2002; Pan-American
Conference, Santiago de Chile, January 2003; Analysis Seminar, U. of Bologna,
March 2003; and Analysis Seminar, U. Texas at Austin, March 200
Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes
Performance evaluation of nursing homes is usually accomplished by the
repeated administration of questionnaires aimed at measuring the health status
of the patients during their period of residence in the nursing home. We
illustrate how a latent Markov model with covariates may effectively be used
for the analysis of data collected in this way. This model relies on a not
directly observable Markov process, whose states represent different levels of
the health status. For the maximum likelihood estimation of the model we apply
an EM algorithm implemented by means of certain recursions taken from the
literature on hidden Markov chains. Of particular interest is the estimation of
the effect of each nursing home on the probability of transition between the
latent states. We show how the estimates of these effects may be used to
construct a set of scores which allows us to rank these facilities in terms of
their efficacy in taking care of the health conditions of their patients. The
method is used within an application based on data concerning a set of nursing
homes located in the Region of Umbria, Italy, which were followed for the
period 2003--2005.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS230 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Item selection by Latent Class-based methods
The evaluation of nursing homes is usually based on the administration of
questionnaires made of a large number of polytomous items. In such a context,
the Latent Class (LC) model represents a useful tool for clustering subjects in
homogenous groups corresponding to different degrees of impairment of the
health conditions. It is known that the performance of model-based clustering
and the accuracy of the choice of the number of latent classes may be affected
by the presence of irrelevant or noise variables. In this paper, we show the
application of an item selection algorithm to real data collected within a
project, named ULISSE, on the quality-of-life of elderly patients hosted in
italian nursing homes. This algorithm, which is closely related to that
proposed by Dean and Raftery in 2010, is aimed at finding the subset of items
which provides the best clustering according to the Bayesian Information
Criterion. At the same time, it allows us to select the optimal number of
latent classes. Given the complexity of the ULISSE study, we perform a
validation of the results by means of a sensitivity analysis to different
specifications of the initial subset of items and of a resampling procedure
SN/GRB connection: a statistical approach with BATSE and Asiago Catalogues
Recent observations suggest that some types of GRB are physically connected
with SNe of type Ib/c. However, it has been pointed out by several authors that
some GRBs could be associated also with other types of core-collapse SNe (type
IIdw/IIn). On the basis of a comphrensive statistical study, which has made use
of the BATSE and Asiago catalogues, we have found that: i) the temporal and
spacial distribution of SNe-Ib/c is marginally correlated with that of the
BATSE GRBs; ii) we do not confirm the existence of an association between GRBs
and SNe-IIdw/IIn.Comment: Proceeding of the 4th workshop on Gamma Ray Bursts in the Afterglow
Era, Rome, 2004; 4 page
Ethical and medico-legal remarks on uterus transplantation: may it solve uterine factor infertility?
Uterus transplantation was firstly tested with animal trials sixty-five years ago. Despite several successful attempts in human subjects, the different procedures still lay at the experimental stage, in need of further studies and investigations before they can be considered as standard clinical practices. Uterus transplant cannot be regarded as a life-saving procedure, but rather a method to restore woman ability to procreate, when lost, thus improving her quality of life. Uterus transplant is a complex surgical procedure and presents significant health threats. Medical staff should therefore always obtain informed consent from patients, emphasizing such risks. Before that, women undergoing uterine transplants should be thoroughly informed about the hazards inherent to the procedure and especially about the dangers of immunosuppressant drugs, administered after the surgery which may injure the fetus, eventually formed in the restored organ and even lead to its death, thus nullifying the purpose of the transplant itself. Therefore, the risk-benefit ratio of uterus transplantation needs to be carefully assessed and described
Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality
We consider a family of vector fields defined in some bounded domain of R^p,
and we assume that they satisfy Hormander's rank condition of some step r, and
that their coefficients have r-1 continuous derivatives. We extend to this
nonsmooth context some results which are well-known for smooth Hormander's
vector fields, namely: some basic properties of the distance induced by the
vector fields, the doubling condition, Chow's connectivity theorem, and, under
the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's
inequality. By known results, these facts also imply a Sobolev embedding. All
these tools allow to draw some consequences about second order differential
operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous
version) changed. Some references adde
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