35,059 research outputs found
Existence results for mean field equations
Let be an annulus. We prove that the mean field equation
-\Delta\psi=\frac{e\sp{-\beta\psi}}{\int\sb{\Omega}e\sp{-\beta\psi}} admits
a solution with zero boundary for . This is a
supercritical case for the Moser-Trudinger inequality.Comment: Filling a gap in the argument and adding 2 referrence
Emergent O(n) Symmetry in a series of three-dimensional Potts Models
We study the q-state Potts model on the simple cubic lattice with
ferromagnetic interactions in one lattice direction, and antiferromagnetic
interactions in the two other directions. As the temperature T decreases, the
system undergoes a second-order phase transition that fits in the universality
class of the 3D O(n) model with n=q-1. This conclusion is based on the
estimated critical exponents, and histograms of the order parameter. At even
smaller T we find, for q=4 and 5, a first-order transition to a phase with a
different type of long-range order. This long-range order dissolves at T=0, and
the system effectively reduces to a disordered two-dimensional Potts
antiferromagnet. These results are obtained by means of Monte Carlo simulations
and finite-size scaling.Comment: 5 pages, 7 figures, accepted by Physical Review
Variational Derivation of Relativistic Fermion-Antifermion Wave Equations in QED
We present a variational method for deriving relativistic two-fermion wave
equations in a Hamiltonian formulation of QED. A reformulation of QED is
performed, in which covariant Green functions are used to solve for the
electromagnetic field in terms of the fermion fields. The resulting modified
Hamiltonian contains the photon propagator directly. The reformulation permits
one to use a simple Fock-space variational trial state to derive relativistic
fermion-antifermion wave equations from the corresponding quantum field theory.
We verify that the energy eigenvalues obtained from the wave equation agree
with known results for positronium.Comment: 25 pages, accepted in Journal of Mathematical Physics (2004
Generalized reflection symmetry and leptonic CP violation
We propose a generalized reflection symmetry to constrain the
lepton flavor mixing parameters. We obtain a new correlation between the
atmospheric mixing angle and the "Dirac" CP violation phase
. Only in a specific limit our proposed CP transformation
reduces to standard reflection, for which and
are both maximal. The "Majorana" phases are predicted to lie at
their CP-conserving values with important implications for the neutrinoless
double beta decay rates. We also study the phenomenological implications of our
scheme for present and future neutrino oscillation experiments including T2K,
NOA and DUNE.Comment: 14 pages, 9 figures, latex, Final version to appear in Physics
Letters
A blind deconvolution approach to recover effective connectivity brain networks from resting state fMRI data
A great improvement to the insight on brain function that we can get from
fMRI data can come from effective connectivity analysis, in which the flow of
information between even remote brain regions is inferred by the parameters of
a predictive dynamical model. As opposed to biologically inspired models, some
techniques as Granger causality (GC) are purely data-driven and rely on
statistical prediction and temporal precedence. While powerful and widely
applicable, this approach could suffer from two main limitations when applied
to BOLD fMRI data: confounding effect of hemodynamic response function (HRF)
and conditioning to a large number of variables in presence of short time
series. For task-related fMRI, neural population dynamics can be captured by
modeling signal dynamics with explicit exogenous inputs; for resting-state fMRI
on the other hand, the absence of explicit inputs makes this task more
difficult, unless relying on some specific prior physiological hypothesis. In
order to overcome these issues and to allow a more general approach, here we
present a simple and novel blind-deconvolution technique for BOLD-fMRI signal.
Coming to the second limitation, a fully multivariate conditioning with short
and noisy data leads to computational problems due to overfitting. Furthermore,
conceptual issues arise in presence of redundancy. We thus apply partial
conditioning to a limited subset of variables in the framework of information
theory, as recently proposed. Mixing these two improvements we compare the
differences between BOLD and deconvolved BOLD level effective networks and draw
some conclusions
- …