319 research outputs found
On isoperimetric inequalities with respect to infinite measures
We study isoperimetric problems with respect to infinite measures on .
In the case of the measure defined by , ,
we prove that, among all sets with given measure, the ball centered at
the origin has the smallest (weighted) perimeter. Our results are then
applied to obtain Polya-Szego-type inequalities, Sobolev embeddings theorems
and a comparison result for elliptic boundary value problems.Comment: 25 page
Critical and tricritical singularities of the three-dimensional random-bond Potts model for large
We study the effect of varying strength, , of bond randomness on the
phase transition of the three-dimensional Potts model for large . The
cooperative behavior of the system is determined by large correlated domains in
which the spins points into the same direction. These domains have a finite
extent in the disordered phase. In the ordered phase there is a percolating
cluster of correlated spins. For a sufficiently large disorder
this percolating cluster coexists with a percolating cluster
of non-correlated spins. Such a co-existence is only possible in more than two
dimensions. We argue and check numerically that is the tricritical
disorder, which separates the first- and second-order transition regimes. The
tricritical exponents are estimated as and
. We claim these exponents are independent, for sufficiently
large . In the second-order transition regime the critical exponents
and are independent of the strength of
disorder.Comment: 12 pages, 11 figure
Neural networks for driver behavior analysis
The proliferation of info-entertainment systems in nowadays vehicles has provided a really cheap and easy-to-deploy platform with the ability to gather information about the vehicle under analysis. With the purpose to provide an architecture to increase safety and security in automotive context, in this paper we propose a fully connected neural network architecture considering positionbased features aimed to detect in real-time: (i) the driver, (ii) the driving style and (iii) the path. The experimental analysis performed on real-world data shows that the proposed method obtains encouraging results
Finsler Hardy inequalities
In this paper we present a unified simple approach to anisotropic Hardy
inequalities in various settings. We consider Hardy inequalities which involve
a Finsler distance from a point or from the boundary of a domain. The sharpness
and the non-attainability of the constants in the inequalities are also proved.Comment: 31 pages. We add "Note added to Proof" in Introduction and several
reference
The isoperimetric problem for a class of non-radial weights and applications
We study a class of isoperimetric problems on R+ N where the densities of the weighted volume and weighted perimeter are given by two different non-radial functions of the type |x|kxN α. Our results imply some sharp functional inequalities, like for instance, Caffarelli-Kohn-Nirenberg type inequalities
Confidence Intervals for Predictive Values Using Data from a Case Control Study
The accuracy of a binary-scale diagnostic test can be represented by sensitivity (Se), specificity (Sp) and positive and negative predictive values (PPV and NPV). Although Se and Sp measure the intrinsic accuracy of a diagnostic test that does not depend on the prevalence rate, they do not provide information on the diagnostic accuracy of a particular patient. To obtain this information we need to use PPV and NPV. Since PPV and NPV are functions of both the intrinsic accuracy and the prevalence of the disease, constructing confidence intervals for PPV and NPV for a particular patient in a population with a given prevalence of disease using data from a case-control study is not straightforward. In this paper, a novel method for the estimation of PPV and NPV is developed using estimates of sensitivity and specificity in a case-control study. For PPV and NPV, standard, adjusted and their logit transformed based confidence intervals are compared using coverage probabilities and interval lengths in a simulation study. These methods are then applied to two examples: a diagnostic test assessing the ability of the ApoE4 allele on distinguishing patients with late-onset Alzheimer\u27s disease and a prognostic test assessing the predictive ability of a 70-gene signature on breast cancer metastasis
Disorder induced rounding of the phase transition in the large q-state Potts model
The phase transition in the q-state Potts model with homogeneous
ferromagnetic couplings is strongly first order for large q, while is rounded
in the presence of quenched disorder. Here we study this phenomenon on
different two-dimensional lattices by using the fact that the partition
function of the model is dominated by a single diagram of the high-temperature
expansion, which is calculated by an efficient combinatorial optimization
algorithm. For a given finite sample with discrete randomness the free energy
is a pice-wise linear function of the temperature, which is rounded after
averaging, however the discontinuity of the internal energy at the transition
point (i.e. the latent heat) stays finite even in the thermodynamic limit. For
a continuous disorder, instead, the latent heat vanishes. At the phase
transition point the dominant diagram percolates and the total magnetic moment
is related to the size of the percolating cluster. Its fractal dimension is
found d_f=(5+\sqrt{5})/4 and it is independent of the type of the lattice and
the form of disorder. We argue that the critical behavior is exclusively
determined by disorder and the corresponding fixed point is the isotropic
version of the so called infinite randomness fixed point, which is realized in
random quantum spin chains. From this mapping we conjecture the values of the
critical exponents as \beta=2-d_f, \beta_s=1/2 and \nu=1.Comment: 12 pages, 12 figures, version as publishe
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