1,797 research outputs found
Phase transitions in optimal unsupervised learning
We determine the optimal performance of learning the orientation of the
symmetry axis of a set of P = alpha N points that are uniformly distributed in
all the directions but one on the N-dimensional sphere. The components along
the symmetry breaking direction, of unitary vector B, are sampled from a
mixture of two gaussians of variable separation and width. The typical optimal
performance is measured through the overlap Ropt=B.J* where J* is the optimal
guess of the symmetry breaking direction. Within this general scenario, the
learning curves Ropt(alpha) may present first order transitions if the clusters
are narrow enough. Close to these transitions, high performance states can be
obtained through the minimization of the corresponding optimal potential,
although these solutions are metastable, and therefore not learnable, within
the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper
contains one new section, Bayesian versus optimal solutions, where we explain
in detail the results supporting our claim that bayesian learning may not be
optimal. Figures 4 of the first submission was difficult to understand. We
replaced it by two new figures (Figs. 4 and 5 in this new version) containing
more detail
Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions
When a Bose-Einstein condensed cloud of atoms is given some angular momentum,
it forms vortices arranged in structures with a discrete rotational symmetry.
For these vortex states, the Hilbert space of the exact solution separates into
a "primary" space related to the mean-field Gross-Pitaevskii solution and a
"complementary" space including the corrections beyond mean-field. Considering
a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we
demonstrate how this separation can be used to close the conceptual gap between
exact solutions for systems with only a few atoms and the thermodynamic limit
for which the mean-field is the correct leading-order approximation. Although
we illustrate this approach for the case of weak interactions, it is expected
to be more generally valid.Comment: 8 pages, 5 figure
Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: a mean field approach
We address a recently introduced model describing a system of periodically
coupled nonlinear phase oscillators submitted to multiplicative white noises,
wherein a ratchet-like transport mechanism arises through a symmetry-breaking
noise-induced nonequilibrium phase transition. Numerical simulations of this
system reveal amazing novel features such as negative zero-bias conductance and
anomalous hysteresis, explained resorting to a strong-coupling analysis in the
thermodynamic limit. Using an explicit mean-field approximation we explore the
whole ordered phase finding a transition from anomalous to normal hysteresis
inside this phase, estimating its locus and identifying (within this scheme) a
mechanism whereby it takes place.Comment: RevTex, 21 pgs, 15 figures. Submited to Physical Review E (2000
Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases
We introduce a density functional formalism to study the ground-state
properties of strongly-correlated dipolar and ionic ultracold bosonic and
fermionic gases, based on the self-consistent combination of the weak and the
strong coupling limits. Contrary to conventional density functional approaches,
our formalism does not require a previous calculation of the interacting
homogeneous gas, and it is thus very suitable to treat systems with tunable
long-range interactions. Due to its asymptotic exactness in the regime of
strong correlation, the formalism works for systems in which standard
mean-field theories fail.Comment: 5 pages, 2 figure
Ferromagnetic coupling and magnetic anisotropy in molecular Ni(II) squares
We investigated the magnetic properties of two isostructural Ni(II) metal
complexes [Ni4Lb8] and [Ni4Lc8]. In each molecule the four Ni(II) centers form
almost perfect regular squares. Magnetic coupling and anisotropy of single
crystals were examined by magnetization measurements and in particular by
high-field torque magnetometry at low temperatures. The data were analyzed in
terms of an effective spin Hamiltonian appropriate for Ni(II) centers. For both
compounds, we found a weak intramolecular ferromagnetic coupling of the four
Ni(II) spins and sizable single-ion anisotropies of the easy-axis type. The
coupling strengths are roughly identical for both compounds, whereas the
zero-field-splitting parameters are significantly different. Possible reasons
for this observation are discussed.Comment: 7 pages, 7 figure
Equilibration of isolated macroscopic quantum systems
We investigate the equilibration of an isolated macroscopic quantum system in
the sense that deviations from a steady state become unmeasurably small for the
overwhelming majority of times within any sufficiently large time interval. The
main requirements are that the initial state, possibly far from equilibrium,
exhibits a macroscopic population of at most one energy level and that
degeneracies of energy eigenvalues and of energy gaps (differences of energy
eigenvalues) are not of exceedingly large multiplicities. Our approach closely
follows and extends recent works by Short and Farrelly [2012 New J. Phys. 14
013063], in particular going beyond the realm of finite-dimensional systems and
large effective dimensions.Comment: 19 page
Glucose stimulates somatostatin secretion in pancreatic δ-cells by cAMP-dependent intracellular Ca2+ release
© 2019 Denwood et al.Somatostatin secretion from pancreatic islet δ-cells is stimulated by elevated glucose levels, but the underlying mechanisms have only partially been elucidated. Here we show that glucose-induced somatostatin secretion (GISS) involves both membrane potential-dependent and -independent pathways. Although glucose-induced electrical activity triggers somatostatin release, the sugar also stimulates GISS via a cAMP-dependent stimulation of CICR and exocytosis of somatostatin. The latter effect is more quantitatively important and in mouse islets depolarized by 70 mM extracellular K+, increasing glucose from 1 mM to 20 mM produced an ∼3.5-fold stimulation of somatostatin secretion, an effect that was mimicked by the application of the adenylyl cyclase activator forskolin. Inhibiting cAMP-dependent pathways with PKI or ESI-05, which inhibit PKA and exchange protein directly activated by cAMP 2 (Epac2), respectively, reduced glucose/forskolin-induced somatostatin secretion. Ryanodine produced a similar effect that was not additive to that of the PKA or Epac2 inhibitors. Intracellular application of cAMP produced a concentration-dependent stimulation of somatostatin exocytosis and elevation of cytoplasmic Ca2+ ([Ca2+]i). Both effects were inhibited by ESI-05 and thapsigargin (an inhibitor of SERCA). By contrast, inhibition of PKA suppressed δ-cell exocytosis without affecting [Ca2+]i Simultaneous recordings of electrical activity and [Ca2+]i in δ-cells expressing the genetically encoded Ca2+ indicator GCaMP3 revealed that the majority of glucose-induced [Ca2+]i spikes did not correlate with δ-cell electrical activity but instead reflected Ca2+ release from the ER. These spontaneous [Ca2+]i spikes are resistant to PKI but sensitive to ESI-05 or thapsigargin. We propose that cAMP links an increase in plasma glucose to stimulation of somatostatin secretion by promoting CICR, thus evoking exocytosis of somatostatin-containing secretory vesicles in the δ-cell.Peer reviewedFinal Published versio
Current-spin-density functional study of persistent currents in quantum rings
We present a numerical study of persistent currents in quantum rings using
current spin density functional theory (CSDFT). This formalism allows for a
systematic study of the joint effects of both spin, interactions and impurities
for realistic systems. It is illustrated that CSDFT is suitable for describing
the physical effects related to Aharonov-Bohm phases by comparing energy
spectra of impurity-free rings to existing exact diagonalization and
experimental results. Further, we examine the effects of a symmetry-breaking
impurity potential on the density and current characteristics of the system and
propose that narrowing the confining potential at fixed impurity potential will
suppress the persistent current in a characteristic way.Comment: 7 pages REVTeX, including 8 postscript figure
Foundation of Statistical Mechanics under experimentally realistic conditions
We demonstrate the equilibration of isolated macroscopic quantum systems,
prepared in non-equilibrium mixed states with significant population of many
energy levels, and observed by instruments with a reasonably bound working
range compared to the resolution limit. Both properties are fulfilled under
many, if not all, experimentally realistic conditions. At equilibrium, the
predictions and limitations of Statistical Mechanics are recovered.Comment: Accepted in Phys. Rev. Let
Spectral properties of rotating electrons in quantum dots and their relation to quantum Hall liquids
The exact diagonalization technique is used to study many-particle properties
of interacting electrons with spin, confined in a two-dimensional harmonic
potential. The single-particle basis is limited to the lowest Landau level. The
results are analyzed as a function of the total angular momentum of the system.
Only at angular momenta corresponding to the filling factors 1, 1/3, 1/5 etc.
the system is fully polarized. The lowest energy states exhibit spin-waves,
domains, and localization, depending on the angular momentum. Vortices exist
only at excited polarized states. The high angular momentum limit shows
localization of electrons and separation of the charge and spin excitations.Comment: 14 pages 18 figure
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