6,472 research outputs found
The Foster-Hart Measure of Riskiness for General Gambles
Foster and Hart proposed an operational measure of riskiness for discrete
random variables. We show that their defining equation has no solution for many
common continuous distributions including many uniform distributions, e.g. We
show how to extend consistently the definition of riskiness to continuous
random variables. For many continuous random variables, the risk measure is
equal to the worst--case risk measure, i.e. the maximal possible loss incurred
by that gamble. We also extend the Foster--Hart risk measure to dynamic
environments for general distributions and probability spaces, and we show that
the extended measure avoids bankruptcy in infinitely repeated gambles
Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity
We consider positive solutions of the semilinear biharmonic equation
in with non-removable singularities at the origin. Under natural
assumptions on the nonlinearity , we show that is a
periodic function of and we classify all such solutions.Comment: To V. Maz'ya on the occasion of his 80th birthday; references adde
Theory of electronic and spin-orbit proximity effects in graphene on Cu(111)
We study orbital and spin-orbit proximity effects in graphene adsorbed to the
Cu(111) surface by means of density functional theory (DFT). The proximity
effects are caused mainly by the hybridization of graphene and copper d
orbitals. Our electronic structure calculations agree well with the
experimentally observed features. We carry out a graphene-Cu(111) distance
dependent study to obtain proximity orbital and spin-orbit coupling parameters,
by fitting the DFT results to a robust low energy model Hamiltonian. We find a
strong distance dependence of the Rashba and intrinsic proximity induced
spin-orbit coupling parameters, which are in the meV and hundreds of eV
range, respectively, for experimentally relevant distances. The Dirac spectrum
of graphene also exhibits a proximity orbital gap, of about 20 meV.
Furthermore, we find a band inversion within the graphene states accompanied by
a reordering of spin and pseudospin states, when graphene is pressed towards
copper
Multiplicative Approximations, Optimal Hypervolume Distributions, and the Choice of the Reference Point
Many optimization problems arising in applications have to consider several
objective functions at the same time. Evolutionary algorithms seem to be a very
natural choice for dealing with multi-objective problems as the population of
such an algorithm can be used to represent the trade-offs with respect to the
given objective functions. In this paper, we contribute to the theoretical
understanding of evolutionary algorithms for multi-objective problems. We
consider indicator-based algorithms whose goal is to maximize the hypervolume
for a given problem by distributing {\mu} points on the Pareto front. To gain
new theoretical insights into the behavior of hypervolume-based algorithms we
compare their optimization goal to the goal of achieving an optimal
multiplicative approximation ratio. Our studies are carried out for different
Pareto front shapes of bi-objective problems. For the class of linear fronts
and a class of convex fronts, we prove that maximizing the hypervolume gives
the best possible approximation ratio when assuming that the extreme points
have to be included in both distributions of the points on the Pareto front.
Furthermore, we investigate the choice of the reference point on the
approximation behavior of hypervolume-based approaches and examine Pareto
fronts of different shapes by numerical calculations
The spatial component of R&D networks
We study the role of geography in R&D networks by means of a quantitative,
micro-geographic approach. Using a large database that covers international R&D
collaborations from 1984 to 2009, we localize each actor precisely in space
through its latitude and longitude. This allows us to analyze the R&D network
at all geographic scales simultaneously. Our empirical results show that
despite the high importance of the city level, transnational R&D collaborations
at large distances are much more frequent than expected from similar networks.
This provides evidence for the ambiguity of distance in economic cooperation
which is also suggested by the existing literature. In addition we test whether
the hypothesis of local buzz and global pipelines applies to the observed R&D
network by calculating well-defined metrics from network theory.Comment: Working paper, 22 pages, 7 figure
Post-Matrix Product State Methods: To tangent space and beyond
We develop in full detail the formalism of tangent states to the manifold of
matrix product states, and show how they naturally appear in studying
time-evolution, excitations and spectral functions. We focus on the case of
systems with translation invariance in the thermodynamic limit, where momentum
is a well defined quantum number. We present some new illustrative results and
discuss analogous constructions for other variational classes. We also discuss
generalizations and extensions beyond the tangent space, and give a general
outlook towards post matrix product methods.Comment: 40 pages, 8 figure
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