669 research outputs found
A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces
A Wasserstein spaces is a metric space of sufficiently concentrated
probability measures over a general metric space. The main goal of this paper
is to estimate the largeness of Wasserstein spaces, in a sense to be precised.
In a first part, we generalize the Hausdorff dimension by defining a family of
bi-Lipschitz invariants, called critical parameters, that measure largeness for
infinite-dimensional metric spaces. Basic properties of these invariants are
given, and they are estimated for a naturel set of spaces generalizing the
usual Hilbert cube. In a second part, we estimate the value of these new
invariants in the case of some Wasserstein spaces, as well as the dynamical
complexity of push-forward maps. The lower bounds rely on several embedding
results; for example we provide bi-Lipschitz embeddings of all powers of any
space inside its Wasserstein space, with uniform bound and we prove that the
Wasserstein space of a d-manifold has "power-exponential" critical parameter
equal to d.Comment: v2 Largely expanded version, as reflected by the change of title; all
part I on generalized Hausdorff dimension is new, as well as the embedding of
Hilbert cubes into Wasserstein spaces. v3 modified according to the referee
final remarks ; to appear in Journal of Topology and Analysi
Resilience of Supervised Learning Algorithms to Discriminatory Data Perturbations
Discrimination is a focal concern in supervised learning algorithms
augmenting human decision-making. These systems are trained using historical
data, which may have been tainted by discrimination, and may learn biases
against the protected groups. An important question is how to train models
without propagating discrimination. In this study, we i) define and model
discrimination as perturbations of a data-generating process and show how
discrimination can be induced via attributes correlated with the protected
attributes; ii) introduce a measure of resilience of a supervised learning
algorithm to potentially discriminatory data perturbations, iii) propose a
novel supervised learning algorithm that inhibits discrimination, and iv) show
that it is more resilient to discriminatory perturbations in synthetic and
real-world datasets than state-of-the-art learning algorithms. The proposed
method can be used with general supervised learning algorithms and avoids
inducement of discrimination, while maximizing model accuracy.Comment: 17 pages, 10 figures, 1 tabl
Proton radiography to improve proton radiotherapy: Simulation study at different proton beam energies
To improve the quality of cancer treatment with protons, a translation of
X-ray Computed Tomography (CT) images into a map of the proton stopping powers
needs to be more accurate. Proton stopping powers determined from CT images
have systematic uncertainties in the calculated proton range in a patient of
typically 3-4\% and even up to 10\% in region containing
bone~\cite{USchneider1995,USchneider1996,WSchneider2000,GCirrone2007,HPaganetti2012,TPlautz2014,GLandry2013,JSchuemann2014}.
As a consequence, part of a tumor may receive no dose, or a very high dose can
be delivered in healthy ti\-ssues and organs at risks~(e.g. brain
stem)~\cite{ACKnopf2013}. A transmission radiograph of high-energy protons
measuring proton stopping powers directly will allow to reduce these
uncertainties, and thus improve the quality of treatment.
The best way to obtain a sufficiently accurate radiograph is by tracking
individual protons traversing the phantom
(patient)~\cite{GCirrone2007,TPlautz2014,VSipala2013}. In our simulations we
have used an ideal position sensitive detectors measuring a single proton
before and after a phantom, while the residual energy of a proton was detected
by a BaF crystal. To obtain transmission radiographs, diffe\-rent phantom
materials have been irradiated with a 3x3~cm scattered proton beam, with
various beam energies. The simulations were done using the Geant4 simulation
package~\cite{SAgostinelli2003}.
In this study we focus on the simulations of the energy loss radiographs for
various proton beam energies that are clinically available in proton
radiotherapy.Comment: 6 pages, 6 figures, Presented at Jagiellonian Symposium on
Fundamental and Applied Subatomic Physics, 7-12 June, 2015, Krak\'ow, Polan
Critical behavior of the metallic triangular-lattice Heisenberg antiferromagnet PdCrO2
We report physical properties of the conductive magnet PdCrO2 consisting of a
layered structure with a triangular lattice of Cr3+ ions (S=3/2). We confirmed
an antiferromagnetic transition at TN=37.5K by means of specific heat,
electrical resistivity, magnetic susceptibility, and neutron scattering
measurements. The critical behavior in the specific heat persists in an
unusually wide temperature range above TN. This fact implies that spin
correlations develop even at much higher temperature than TN. The observed
sub-linear temperature dependence of the resistivity above TN is also
attributed to the short-range correlations among the frustrated spins. While
the critical exponent for the magnetization agrees reasonably with the
prediction of the relevant model, that for the specific heat evaluated in the
wide temperature range differs substantially from the prediction.Comment: 7 pages, 6 figure
Doenças de hortaliças no Amapá.
Em inspeções feitas nos núcleos rurais do Estado do Amapá e nas bases fÃsicas da UEPAE de Macapá/Embrapa, constataram-se sintomas de doenças fúngicas e bacterianas em hortaliças. Exames microscópicos, cultura pura, testes de patogenicidade e bioquÃmicos confirmaram a diagnose visual das doenças
Observation of Field-Induced Transverse N\'{e}el Ordering in the Spin Gap System TlCuCl
Neutron elastic scattering experiments have been performed on the spin gap
system TlCuCl in magnetic fields parallel to the -axis. The magnetic
Bragg peaks which indicate the field-induced N\'{e}el ordering were observed
for magnetic field higher than the gap field T at with odd in the plane. The spin structure in the ordered
phase was determined. The temperature and field dependence of the Bragg peak
intensities and the phase boundary obtained were discussed in connection with a
recent theory which describes the field-induced N\'{e}el ordering as a
Bose-Einstein condensation of magnons.Comment: 4 pages, 5 eps figures, jpsj styl
Drastic Change of Magnetic Phase Diagram in Doped Quantum Antiferromagnet TlCuMgCl
TlCuCl is a coupled spin dimer system, which has a singlet ground state
with an excitation gap of = 5.5 T.
TlCuMgCl doped with nonmagnetic Mg ions undergoes
impurity-induced magnetic ordering. Because triplet excitation with a finite
gap still remains, this doped system can also undergo magnetic-field-induced
magnetic ordering. By specific heat measurements and neutron scattering
experiments under a magnetic field, we investigated the phase diagram in
TlCuMgCl with , and found that impurity- and
field-induced ordered phases are the same. The gapped spin liquid state
observed in pure TlCuCl is completely wiped out by the small amount of
doping.Comment: 9 pages, 5 figures, jpsj2 class file, to be published in J. Phy. Soc.
Jpn. Vol.75 No.3 (2006); layout changed, unrelated figure remove
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