1,886 research outputs found
Computational Aspects of the Hausdorff Distance in Unbounded Dimension
We study the computational complexity of determining the Hausdorff distance
of two polytopes given in halfspace- or vertex-presentation in arbitrary
dimension. Subsequently, a matching problem is investigated where a convex body
is allowed to be homothetically transformed in order to minimize its Hausdorff
distance to another one. For this problem, we characterize optimal solutions,
deduce a Helly-type theorem and give polynomial time (approximation) algorithms
for polytopes
Sharpening Geometric Inequalities using Computable Symmetry Measures
Many classical geometric inequalities on functionals of convex bodies depend
on the dimension of the ambient space. We show that this dimension dependence
may often be replaced (totally or partially) by different symmetry measures of
the convex body. Since these coefficients are bounded by the dimension but
possibly smaller, our inequalities sharpen the original ones. Since they can
often be computed efficiently, the improved bounds may also be used to obtain
better bounds in approximation algorithms.Comment: This is a preprint. The proper publication in final form is available
at journals.cambridge.org, DOI 10.1112/S002557931400029
Reputation in multi agent systems and the incentives to provide feedback
The emergence of the Internet leads to a vast increase in the number of interactions between parties that are completely alien to each other. In general, such transactions are likely to be subject to fraud and cheating. If such systems use computerized rational agents to negotiate and execute transactions, mechanisms that lead to favorable outcomes for all parties instead of giving rise to defective behavior are necessary to make the system work: trust and reputation mechanisms. This paper examines different incentive mechanisms helping these trust and reputation mechanisms in eliciting users to report own experiences honestly. --Trust,Reputation
Consistent Searches for SMEFT Effects in Non-Resonant Dijet Events
We investigate the bounds which can be placed on generic new-physics
contributions to dijet production at the LHC using the framework of the
Standard Model Effective Field Theory, deriving the first consistently-treated
EFT bounds from non-resonant high-energy data. We recast an analysis searching
for quark compositeness, equivalent to treating the SM with one
higher-dimensional operator as a complete UV model. In order to reach
consistent, model-independent EFT conclusions, it is necessary to truncate the
EFT effects consistently at order and to include the possibility
of multiple operators simultaneously contributing to the observables, neither
of which has been done in previous searches of this nature. Furthermore, it is
important to give consistent error estimates for the theoretical predictions of
the signal model, particularly in the region of phase space where the probed
energy is approaching the cutoff scale of the EFT. There are two linear
combinations of operators which contribute to dijet production in the SMEFT
with distinct angular behavior; we identify those linear combinations and
determine the ability of LHC searches to constrain them simultaneously.
Consistently treating the EFT generically leads to weakened bounds on
new-physics parameters. These constraints will be a useful input to future
global analyses in the SMEFT framework, and the techniques used here to
consistently search for EFT effects are directly applicable to other
off-resonance signals.Comment: v1: 23 pages, 9 figures, 3 tables; v2: references added, typos
corrected, matches version published in JHE
Large deviations for trapped interacting Brownian particles and paths
We introduce two probabilistic models for interacting Brownian motions
moving in a trap in under mutually repellent forces. The two
models are defined in terms of transformed path measures on finite time
intervals under a trap Hamiltonian and two respective pair-interaction
Hamiltonians. The first pair interaction exhibits a particle repellency, while
the second one imposes a path repellency. We analyze both models in the limit
of diverging time with fixed number of Brownian motions. In particular, we
prove large deviations principles for the normalized occupation measures. The
minimizers of the rate functions are related to a certain associated operator,
the Hamilton operator for a system of interacting trapped particles. More
precisely, in the particle-repellency model, the minimizer is its ground state,
and in the path-repellency model, the minimizers are its ground product-states.
In the case of path-repellency, we also discuss the case of a Dirac-type
interaction, which is rigorously defined in terms of Brownian intersection
local times. We prove a large-deviation result for a discrete variant of the
model. This study is a contribution to the search for a mathematical
formulation of the quantum system of trapped interacting bosons as a model
for Bose--Einstein condensation, motivated by the success of the famous 1995
experiments. Recently, Lieb et al. described the large-N behavior of the ground
state in terms of the well-known Gross--Pitaevskii formula, involving the
scattering length of the pair potential. We prove that the large-N behavior of
the ground product-states is also described by the Gross--Pitaevskii formula,
however, with the scattering length of the pair potential replaced by its
integral.Comment: Published at http://dx.doi.org/10.1214/009117906000000214 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Generation of Spin Entanglement in Nonequilibrium Quantum Dots
We propose schemes for generating spatially-separated spin entanglement in
systems of two quantum dots with onsite Coulomb repulsion weakly coupled to a
joint electron reservoir. An enhanced probability for the formation of spin
entanglement is found in nonequilibrium situations with one extra electron on
each dot, either in the transient state after rapid changes of the gate
voltage, or in the steady state with applied bias voltage. In both cases
so-called Werner states with spin singlet fidelity exceeding 1/2 are generated,
which indicates entanglement.Comment: 6 pages, 4 figures, replaced with version to be published in PR
Exclusive Radiative Decays of Z Bosons in QCD Factorization
We discuss the very rare, exclusive hadronic decays of a Z boson into a meson
and a photon. The QCD factorization approach allows to organize the decay
amplitude as an expansion in powers of , where the
leading terms contain convolutions of perturbatively calculable hard functions
with the leading-twist light-cone distribution amplitudes of the meson. We find
that power corrections to these leading terms are negligible since they are
suppressed by the small ratio .
Renormalization-group effects play a crucial role as they render our
theoretical predictions less sensitive to the hadronic input parameters which
are currently not known very precisely. Thus, measurements of the decays at the LHC or a future lepton collider provide a theoretically very
clean way to test the QCD factorization approach. The special case where
is complicated by the fact that the decay amplitude receives
an additional contribution where the meson is formed from a two-gluon state.
The corresponding branching ratios are very sensitive to the hadronic
parameters describing the system. Future measurements of these
decays could yield interesting information about these parameters and the gluon
distribution amplitude.Comment: 6 pages, 3 figures, 1 table, contribution to the proceedings of the
38th International Conference on High Energy Physics, 3-10 August 2016,
Chicago, US
Optimal Opinion Control: The Campaign Problem
Opinion dynamics is nowadays a very common field of research. In this article
we formulate and then study a novel, namely strategic perspective on such
dynamics: There are the usual normal agents that update their opinions, for
instance according the well-known bounded confidence mechanism. But,
additionally, there is at least one strategic agent. That agent uses opinions
as freely selectable strategies to get control on the dynamics: The strategic
agent of our benchmark problem tries, during a campaign of a certain length, to
influence the ongoing dynamics among normal agents with strategically placed
opinions (one per period) in such a way, that, by the end of the campaign, as
much as possible normals end up with opinions in a certain interval of the
opinion space. Structurally, such a problem is an optimal control problem. That
type of problem is ubiquitous. Resorting to advanced and partly non-standard
methods for computing optimal controls, we solve some instances of the campaign
problem. But even for a very small number of normal agents, just one strategic
agent, and a ten-period campaign length, the problem turns out to be extremely
difficult. Explicitly we discuss moral and political concerns that immediately
arise, if someone starts to analyze the possibilities of an optimal opinion
control.Comment: 47 pages, 12 figures, and 11 table
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