4,746 research outputs found
The Degrees of Freedom of Partial Least Squares Regression
The derivation of statistical properties for Partial Least Squares regression
can be a challenging task. The reason is that the construction of latent
components from the predictor variables also depends on the response variable.
While this typically leads to good performance and interpretable models in
practice, it makes the statistical analysis more involved. In this work, we
study the intrinsic complexity of Partial Least Squares Regression. Our
contribution is an unbiased estimate of its Degrees of Freedom. It is defined
as the trace of the first derivative of the fitted values, seen as a function
of the response. We establish two equivalent representations that rely on the
close connection of Partial Least Squares to matrix decompositions and Krylov
subspace techniques. We show that the Degrees of Freedom depend on the
collinearity of the predictor variables: The lower the collinearity is, the
higher the Degrees of Freedom are. In particular, they are typically higher
than the naive approach that defines the Degrees of Freedom as the number of
components. Further, we illustrate how the Degrees of Freedom approach can be
used for the comparison of different regression methods. In the experimental
section, we show that our Degrees of Freedom estimate in combination with
information criteria is useful for model selection.Comment: to appear in the Journal of the American Statistical Associatio
Can effects of quantum gravity be observed in the cosmic microwave background?
We investigate the question whether small quantum-gravitational effects can
be observed in the anisotropy spectrum of the cosmic microwave background
radiation. An observation of such an effect is needed in order to discriminate
between different approaches to quantum gravity. Using canonical quantum
gravity with the Wheeler-DeWitt equation, we find a suppression of power at
large scales. Current observations only lead to an upper bound on the energy
scale of inflation, but the framework is general enough to study other
situations in which such effects might indeed be seen.Comment: 5 pages, 1 figure, essay awarded first prize in the Gravity Research
Foundation essay competition 201
Parametric excitation of a Bose-Einstein condensate in a 1D optical lattice
We study the response of a Bose-Einstein condensate to a periodic modulation
of the depth of an optical lattice. Using Gross-Pitaevskii theory, we show that
a modulation at frequency Omega drives the parametric excitation of Bogoliubov
modes with frequency Omega/2. The ensuing nonlinear dynamics leads to a rapid
broadening of the momentum distribution and a consequent large increase of the
condensate size after free expansion. We show that this process does not
require the presence of a large condensate depletion. Our results reproduce the
main features of the spectrum measured in the superfluid phase by Stoeferle et
al., Phys. Rev. Lett. 92, 130403 (2004).Comment: 4 pages, 4 figures, more results added, to appear in PRA Rapid
Communication
Quantum Gravitational Contributions to the CMB Anisotropy Spectrum
We derive the primordial power spectrum of density fluctuations in the
framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer
approximation to the Wheeler-DeWitt equation for an inflationary universe with
a scalar field. In this way we first recover the scale-invariant power spectrum
that is found as an approximation in the simplest inflationary models. We then
obtain quantum gravitational corrections to this spectrum and discuss whether
they lead to measurable signatures in the CMB anisotropy spectrum. The
non-observation so far of such corrections translates into an upper bound on
the energy scale of inflation.Comment: 4 pages, v3: sign error in Eq. (5) and its consequences correcte
Spin Configuration in the 1/3 Magnetization Plateau of Azurite Determined by NMR
High magnetic field Cu NMR spectra were used to determine the local
spin polarization in the 1/3 magnetization plateau of azurite,
Cu(CO)(OH), which is a model system for the distorted diamond
antiferromagnetic spin-1/2 chain. The spin part of the hyperfine field of the
Cu2 (dimer) sites is found to be field independent, negative and strongly
anisotropic, corresponding to 10 % of fully polarized spin in a
-orbital. This is close to the expected configuration of the "quantum"
plateau, where a singlet state is stabilized on the dimer. However, the
observed non-zero spin polarization points to some triplet admixture, induced
by strong asymmetry of the diamond bonds and .Comment: Phys. Rev. Lett. 102, in press (2009
Hysteresis effects in rotating Bose-Einstein condensates
We study the formation of vortices in a dilute Bose-Einstein condensate
confined in a rotating anisotropic trap. We find that the number of vortices
and angular momentum attained by the condensate depends upon the rotation
history of the trap and on the number of vortices present in the condensate
initially. A simplified model based on hydrodynamic equations is developed, and
used to explain this effect in terms of a shift in the resonance frequency of
the quadrupole mode of the condensate in the presence of a vortex lattice.
Differences between the spin-up and spin-down response of the condensate are
found, demonstrating hysteresis phenomena in this system.Comment: 16 pages, 7 figures; revised after referees' report
Dimensional reduction by pressure in the magnetic framework material CuF(DO)pyz: from spin-wave to spinon excitations
Metal organic magnets have enormous potential to host a variety of electronic
and magnetic phases that originate from a strong interplay between the spin,
orbital and lattice degrees of freedom. We control this interplay in the
quantum magnet CuF(DO)pyz by using high pressure to drive the
system through a structural and magnetic phase transition. Using neutron
scattering, we show that the low pressure state, which hosts a two-dimensional
square lattice with spin-wave excitations and a dominant exchange coupling of
0.89 meV, transforms at high pressure into a one-dimensional spin-chain
hallmarked by a spinon continuum and a reduced exchange interaction of 0.43
meV. This direct microscopic observation of a magnetic dimensional crossover as
a function of pressure opens up new possibilities for studying the evolution of
fractionalised excitations in low dimensional quantum magnets and eventually
pressure-controlled metal--insulator transitions
Spatially Resolved Magnetization in the Bose-Einstein Condensed State of BaCuSi2O6: Evidence for Imperfect Frustration
In order to understand the nature of the two-dimensional Bose-Einstein
condensed (BEC) phase in BaCuSi2O6, we performed detailed 63Cu and 29Si NMR
above the critical magnetic field, Hc1= 23.4 T. The two different alternating
layers present in the system have very different local magnetizations close to
Hc1; one is very weak, and its size and field dependence are highly sensitive
to the nature of inter-layer coupling. Its precise value could only be
determined by "on-site" 63Cu NMR, and the data are fully reproduced by a model
of interacting hard-core bosons in which the perfect frustration associated to
tetragonal symmetry is slightly lifted, leading to the conclusion that the
population of the less populated layers is not fully incoherent but must be
partially condensed
TMDlib and TMDplotter: library and plotting tools for transverse-momentum-dependent parton distributions
Transverse-momentum-dependent distributions (TMDs) are central in high-energy
physics from both theoretical and phenomenological points of view. In this
manual we introduce the library, TMDlib, of fits and parameterisations for
transverse-momentum-dependent parton distribution functions (TMD PDFs) and
fragmentation functions (TMD FFs) together with an online plotting tool,
TMDplotter. We provide a description of the program components and of the
different physical frameworks the user can access via the available
parameterisations.Comment: version 2, referring to TMDlib 1.0.2 - comments and references adde
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