5,109 research outputs found
Cohomogeneity one manifolds with positive euler characteristic
We classify those manifolds of positive euler characteristic on which a lie
group G acts with cohomogeneity one, where G is classical simpl
DeepOBS: A Deep Learning Optimizer Benchmark Suite
Because the choice and tuning of the optimizer affects the speed, and
ultimately the performance of deep learning, there is significant past and
recent research in this area. Yet, perhaps surprisingly, there is no generally
agreed-upon protocol for the quantitative and reproducible evaluation of
optimization strategies for deep learning. We suggest routines and benchmarks
for stochastic optimization, with special focus on the unique aspects of deep
learning, such as stochasticity, tunability and generalization. As the primary
contribution, we present DeepOBS, a Python package of deep learning
optimization benchmarks. The package addresses key challenges in the
quantitative assessment of stochastic optimizers, and automates most steps of
benchmarking. The library includes a wide and extensible set of ready-to-use
realistic optimization problems, such as training Residual Networks for image
classification on ImageNet or character-level language prediction models, as
well as popular classics like MNIST and CIFAR-10. The package also provides
realistic baseline results for the most popular optimizers on these test
problems, ensuring a fair comparison to the competition when benchmarking new
optimizers, and without having to run costly experiments. It comes with output
back-ends that directly produce LaTeX code for inclusion in academic
publications. It supports TensorFlow and is available open source.Comment: Accepted at ICLR 2019. 9 pages, 3 figures, 2 table
Do risk attitudes differ within the group of entrepreneurs?
The notion of risk and entrepreneurship has been widely discussed in the entrepreneurship literature. Starting a business involves risk and requires a risk-taking attitude. Most studies have com-pared entrepreneurs with non-entrepreneurs such as managers or bankers. So far, little research exists on the risk attitudes of different types of entrepreneurs. This study aims to fill this gap. Our particular focus is on the entrepreneurs’ motivations to start their business. The results show that opportunity entrepreneurs are more willing to take risks than necessity entrepreneurs. In addition, entrepreneurs who are motivated by creativity are more risk-tolerant than other entrepreneurs. The study contributes to the literature about risk attitudes of entrepreneurs and to the literature about necessity and opportunity entrepreneurship.Entrepreneurship; Self-employment; Risk attitude; Necessity entrepreneurship; Creativity entrepreneurship
The isomorphism problem for tree-automatic ordinals with addition
This paper studies tree-automatic ordinals (or equivalently, well-founded
linearly ordered sets) together with the ordinal addition operation +.
Informally, these are ordinals such that their elements are coded by finite
trees for which the linear order relation of the ordinal and the ordinal
addition operation can be determined by tree automata. We describe an algorithm
that, given two tree-automatic ordinals with the ordinal addition operation,
decides if the ordinals are isomorphic
Higher-dimensional Wannier interpolation for the modern theory of the Dzyaloshinskii-Moriya interaction: Application to Co-based trilayers
We present an advanced first-principles formalism to evaluate the
Dzyaloshinskii-Moriya interaction (DMI) in its modern theory as well as Berry
curvatures in complex spaces based on a higher-dimensional Wannier
interpolation. Our method is applied to the Co-based trilayer systems
IrPt/Co/Pt and AuPt/Co/Pt, where we
gain insights into the correlations between the electronic structure and the
DMI, and we uncover prominent sign changes of the chiral interaction with the
overlayer composition. Beyond the discussed phenomena, the scope of
applications of our Wannier-based scheme is particularly broad as it is ideally
suited to study efficiently the Hamiltonian evolution under the slow variation
of very general parameters.Comment: 8 pages, 3 figures, contribution to Special Topics "New ab initio
approaches to explore emergent phenomena in quantum matters" in J. Phys. Soc.
Jp
Higher dimensional Wannier functions of multi-parameter Hamiltonians
When using Wannier functions to study the electronic structure of
multi-parameter Hamiltonians carrying a
dependence on crystal momentum and an additional periodic
parameter , one usually constructs several sets of Wannier
functions for a set of values of . We present the concept of higher
dimensional Wannier functions (HDWFs), which provide a minimal and accurate
description of the electronic structure of multi-parameter Hamiltonians based
on a single set of HDWFs. The obstacle of non-orthogonality of Bloch functions
at different is overcome by introducing an auxiliary real space,
which is reciprocal to the parameter . We derive a generalized
interpolation scheme and emphasize the essential conceptual and computational
simplifications in using the formalism, for instance, in the evaluation of
linear response coefficients. We further implement the necessary machinery to
construct HDWFs from ab initio within the full-potential linearized augmented
plane-wave method (FLAPW). We apply our implementation to accurately
interpolate the Hamiltonian of a one-dimensional magnetic chain of Mn atoms in
two important cases of : (i) the spin-spiral vector , and (ii) the direction of the ferromagnetic magnetization . Using the generalized interpolation of the energy, we extract the
corresponding values of magneto-crystalline anisotropy energy, Heisenberg
exchange constants, and spin stiffness, which compare very well with the values
obtained from direct first principles calculations. For toy models we
demonstrate that the method of HDWFs can also be used in applications such as
the virtual crystal approximation, ferroelectric polarization and spin torques.Comment: 23 pages, 11 figure
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