3,117 research outputs found
The Fenchel-type inequality in the 3-dimensional Lorentz space and a Crofton formula
We generalize the Fenchel theorem to strong spacelike (which means that the
tangent vector and the curvature vector span a spacelike 2-plane at each point)
closed curves with index 1 in the 3-dimensional Lorentz space, showing that the
total curvatures must be less than or equal to . A similar generalization
of the Fary-Milnor theorem is also obtained. We establish the Crofton formula
on the de Sitter 2-sphere which implies the above results.Comment: 9 pages, 4 figures. Comments are welcom
Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
Robustness of Bayesian Pool-based Active Learning Against Prior Misspecification
We study the robustness of active learning (AL) algorithms against prior
misspecification: whether an algorithm achieves similar performance using a
perturbed prior as compared to using the true prior. In both the average and
worst cases of the maximum coverage setting, we prove that all
-approximate algorithms are robust (i.e., near -approximate) if
the utility is Lipschitz continuous in the prior. We further show that
robustness may not be achieved if the utility is non-Lipschitz. This suggests
we should use a Lipschitz utility for AL if robustness is required. For the
minimum cost setting, we can also obtain a robustness result for approximate AL
algorithms. Our results imply that many commonly used AL algorithms are robust
against perturbed priors. We then propose the use of a mixture prior to
alleviate the problem of prior misspecification. We analyze the robustness of
the uniform mixture prior and show experimentally that it performs reasonably
well in practice.Comment: This paper is published at AAAI Conference on Artificial Intelligence
(AAAI 2016
Band structure reconstruction across nematic order in high quality FeSe single crystal as revealed by optical spectroscopy study
We perform an in-plane optical spectroscopy measurement on high quality FeSe
single crystals grown by a vapor transport technique. Below the structural
transition at 90 K, the reflectivity spectrum clearly shows a
gradual suppression around 400 cm and the conductivity spectrum shows a
peak at higher frequency. The energy scale of this gap-like feature is
comparable to the width of the band splitting observed by ARPES. The
low-frequency conductivity consists of two Drude components and the overall
plasma frequency is smaller than that of the FeAs based compounds, suggesting a
lower carrier density or stronger correlation effect. The plasma frequency
becomes even smaller below which agrees with the very small Fermi
energy estimated by other experiments. Similar to iron pnictides, a clear
temperature-induced spectral weight transfer is observed for FeSe, being
indicative of strong correlation effect.Comment: 6 page
High strain rate and quasi-static compression behavior and energy absorption characteristic of PVC foam
The mechanical properties at room temperature of two densities PVC foams have been experimentally evaluated in both quasi-static and dynamic compression loading conditions. The strain rate effect have been evaluated by comparing the constant strength during plateau region. Energy absorption efficiency of PVC foam is investigated, and it shows that in certain density range, the efficiency of lighter PVC foam is larger than that of heavier PVC foam, but the efficiency stress of lighter PVC foam is smaller than that of heavier PVC foam. While the lighter PVC foam has been compressed more than heavier PVC foam when they reach their peak efficiency. Therefore, for a certain density of PVC foam itself, when the loading rates increase, the PVC foam will absorb more energy more efficiently
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