2,277 research outputs found
Second-order Shape Optimization for Geometric Inverse Problems in Vision
We develop a method for optimization in shape spaces, i.e., sets of surfaces
modulo re-parametrization. Unlike previously proposed gradient flows, we
achieve superlinear convergence rates through a subtle approximation of the
shape Hessian, which is generally hard to compute and suffers from a series of
degeneracies. Our analysis highlights the role of mean curvature motion in
comparison with first-order schemes: instead of surface area, our approach
penalizes deformation, either by its Dirichlet energy or total variation.
Latter regularizer sparks the development of an alternating direction method of
multipliers on triangular meshes. Therein, a conjugate-gradients solver enables
us to bypass formation of the Gaussian normal equations appearing in the course
of the overall optimization. We combine all of the aforementioned ideas in a
versatile geometric variation-regularized Levenberg-Marquardt-type method
applicable to a variety of shape functionals, depending on intrinsic properties
of the surface such as normal field and curvature as well as its embedding into
space. Promising experimental results are reported
Ultrafast and reversible control of the exchange interaction in Mott insulators
The strongest interaction between microscopic spins in magnetic materials is
the exchange interaction . Therefore, ultrafast control of
holds the promise to control spins on ultimately fast timescales.
We demonstrate that time-periodic modulation of the electronic structure by
electric fields can be used to reversibly control on ultrafast
timescales in extended antiferromagnetic Mott insulators. In the regime of weak
driving strength, we find that can be enhanced and reduced for
frequencies below and above the Mott gap, respectively. Moreover, for strong
driving strength, even the sign of can be reversed and we show
that this causes time reversal of the associated quantum spin dynamics. These
results suggest wide applications, not only to control magnetism in condensed
matter systems, for example, via the excitation of spin resonances, but also to
assess fundamental questions concerning the reversibility of the quantum
many-body dynamics in cold atom systems.Comment: 9 pages, 4 figure
Electronic correlations in double ionization of atoms in pump-probe experiments
The ionization dynamics of a two-electron atom in an attosecond XUV-infrared
pump-probe experiment is simulated by solving the time-dependent two-electron
Schr\"odinger equation. A dramatic change of the double ionization (DI) yield
with variation of the pump-probe delay is reported and the governing role of
electron-electron correlations is shown. The results allow for a direct control
of the DI yield and of the relative strength of double and single ionization
A new approach to hierarchical data analysis: Targeted maximum likelihood estimation for the causal effect of a cluster-level exposure
We often seek to estimate the impact of an exposure naturally occurring or
randomly assigned at the cluster-level. For example, the literature on
neighborhood determinants of health continues to grow. Likewise, community
randomized trials are applied to learn about real-world implementation,
sustainability, and population effects of interventions with proven
individual-level efficacy. In these settings, individual-level outcomes are
correlated due to shared cluster-level factors, including the exposure, as well
as social or biological interactions between individuals. To flexibly and
efficiently estimate the effect of a cluster-level exposure, we present two
targeted maximum likelihood estimators (TMLEs). The first TMLE is developed
under a non-parametric causal model, which allows for arbitrary interactions
between individuals within a cluster. These interactions include direct
transmission of the outcome (i.e. contagion) and influence of one individual's
covariates on another's outcome (i.e. covariate interference). The second TMLE
is developed under a causal sub-model assuming the cluster-level and
individual-specific covariates are sufficient to control for confounding.
Simulations compare the alternative estimators and illustrate the potential
gains from pairing individual-level risk factors and outcomes during
estimation, while avoiding unwarranted assumptions. Our results suggest that
estimation under the sub-model can result in bias and misleading inference in
an observational setting. Incorporating working assumptions during estimation
is more robust than assuming they hold in the underlying causal model. We
illustrate our approach with an application to HIV prevention and treatment
On the Coulomb-dipole transition in mesoscopic classical and quantum electron-hole bilayers
We study the Coulomb-to-dipole transition which occurs when the separation
of an electron-hole bilayer system is varied with respect to the
characteristic in-layer distances. An analysis of the classical ground state
configurations for harmonically confined clusters with reveals that
the energetically most favorable state can differ from that of two-dimensional
pure dipole or Coulomb systems. Performing a normal mode analysis for the N=19
cluster it is found that the lowest mode frequencies exhibit drastic changes
when is varied. Furthermore, we present quantum-mechanical ground states
for N=6, 10 and 12 spin-polarized electrons and holes. We compute the
single-particle energies and orbitals in self-consistent Hartree-Fock
approximation over a broad range of layer separations and coupling strengths
between the limits of the ideal Fermi gas and the Wigner crystal
Estimating Effects on Rare Outcomes: Knowledge is Power
Many of the secondary outcomes in observational studies and randomized trials are rare. Methods for estimating causal effects and associations with rare outcomes, however, are limited, and this represents a missed opportunity for investigation. In this article, we construct a new targeted minimum loss-based estimator (TMLE) for the effect of an exposure or treatment on a rare outcome. We focus on the causal risk difference and statistical models incorporating bounds on the conditional risk of the outcome, given the exposure and covariates. By construction, the proposed estimator constrains the predicted outcomes to respect this model knowledge. Theoretically, this bounding provides stability and power to estimate the exposure effect. In finite sample simulations, the proposed estimator performed as well, if not better, than alternative estimators, including the propensity score matching estimator, inverse probability of treatment weighted (IPTW) estimator, augmented-IPTW and the standard TMLE algorithm. The new estimator remained unbiased if either the conditional mean outcome or the propensity score were consistently estimated. As a substitution estimator, TMLE guaranteed the point estimates were within the parameter range. Our results highlight the potential for double robust, semiparametric efficient estimation with rare event
Role of material properties and mesostructure on dynamic deformation and shear instability in Al-W granular composites
Dynamic experiments with Al-W granular/porous composites revealed
qualitatively different behavior with respect to shear localization depending
on bonding between Al particles. Two-dimensional numerical modeling was used to
explore the mesomechanics of the large strain dynamic deformation in Al-W
granular/porous composites and explain the experimentally observed differences
in shear localization between composites with various mesostructures.
Specifically, the bonding between the Al particles, the porosity, the roles of
the relative particle sizes of Al and W, the arrangements of the W particles,
and the material properties of Al were investigated using numerical
calculations. It was demonstrated in simulations that the bonding between the
"soft" Al particles facilitated shear localization as seen in the experiments.
Numerical calculations and experiments revealed that the mechanism of the shear
localization in granular composites is mainly due to the local high strain flow
of "soft" Al around the "rigid" W particles causing localized damage
accumulation and subsequent growth of the meso/macro shear bands/cracks. The
"rigid" W particles were the major geometrical factor determining the
initiation and propagation of "kinked" shear bands in the matrix of "soft" Al
particles, leaving some areas free of extensive plastic deformation as observed
in experiments and numerical calculations.Comment: 10 pages, 14 figures, submitted to Journal of Applied Physic
Influence of spin fluctuations near the Mott transition: a DMFT study
Dynamics of magnetic moments near the Mott metal-insulator transition is
investigated by a combined slave-rotor and Dynamical Mean-Field Theory solution
of the Hubbard model with additional fully-frustrated random Heisenberg
couplings. In the paramagnetic Mott state, the spinon decomposition allows to
generate a Sachdev-Ye spin liquid in place of the collection of independent
local moments that typically occurs in the absence of magnetic correlations.
Cooling down into the spin-liquid phase, the onset of deviations from pure
Curie behavior in the spin susceptibility is found to be correlated to the
temperature scale at which the Mott transition lines experience a marked
bending. We also demonstrate a weakening of the effective exchange energy upon
approaching the Mott boundary from the Heisenberg limit, due to quantum
fluctuations associated to zero and doubly occupied sites.Comment: 6 pages, 3 figures. V3 was largely expande
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