15,018 research outputs found
Parameter-Independent Strategies for pMDPs via POMDPs
Markov Decision Processes (MDPs) are a popular class of models suitable for
solving control decision problems in probabilistic reactive systems. We
consider parametric MDPs (pMDPs) that include parameters in some of the
transition probabilities to account for stochastic uncertainties of the
environment such as noise or input disturbances.
We study pMDPs with reachability objectives where the parameter values are
unknown and impossible to measure directly during execution, but there is a
probability distribution known over the parameter values. We study for the
first time computing parameter-independent strategies that are expectation
optimal, i.e., optimize the expected reachability probability under the
probability distribution over the parameters. We present an encoding of our
problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem
to computing optimal strategies in POMDPs.
We evaluate our method experimentally on several benchmarks: a motivating
(repeated) learner model; a series of benchmarks of varying configurations of a
robot moving on a grid; and a consensus protocol.Comment: Extended version of a QEST 2018 pape
Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions
The occupation of more than one single-particle state and hence the emergence
of fragmentation is a many-body phenomenon universal to systems of spatially
confined interacting bosons. In the present study, we investigate the effect of
the range of the interparticle interactions on the fragmentation degree of one-
and two-dimensional systems. We solve the full many-body Schr\"odinger equation
of the system using the recursive implementation of the multiconfigurational
time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the
degree of fragmentation on dimensionality, particle number, areal or line
density and interaction strength is assessed. It is found that for contact
interactions, the fragmentation is essentially density independent in two
dimensions. However, fragmentation increasingly depends on density the more
long-ranged the interactions become. The degree of fragmentation is increasing,
keeping the particle number fixed, when the density is decreasing as
expected in one spatial dimension. We demonstrate that this remains,
nontrivially, true also for long-range interactions in two spatial dimensions.
We, finally, find that within our fully self-consistent approach, the
fragmentation degree, to a good approximation, decreases universally as
when only is varied.Comment: 8 pages of RevTex4-1, 5 figure
Computer aided synthesis: a game theoretic approach
In this invited contribution, we propose a comprehensive introduction to game
theory applied in computer aided synthesis. In this context, we give some
classical results on two-player zero-sum games and then on multi-player non
zero-sum games. The simple case of one-player games is strongly related to
automata theory on infinite words. All along the article, we focus on general
approaches to solve the studied problems, and we provide several illustrative
examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language
Theory" (DLT 2017
Parallel Transport over Path Spaces
We develop a differential geometric framework for parallel transport over
path spaces and a corresponding discrete theory, an integrated version of the
continuum theory, using a category-theoretic framework.Comment: 27pp 3fig pdflatex only; v2: rewritten with several clarifications;
v3: minor changes, added references. Version to be published, 30p
Achieving sub-diffraction imaging through bound surface states in negative-refracting photonic crystals at the near-infrared
We report the observation of imaging beyond the diffraction limit due to
bound surface states in negative refraction photonic crystals. We achieve an
effective negative index figure-of-merit [-Re(n)/Im(n)] of at least 380, ~125x
improvement over recent efforts in the near-infrared, with a 0.4 THz bandwidth.
Supported by numerical and theoretical analyses, the observed near-field
resolution is 0.47 lambda, clearly smaller than the diffraction limit of 0.61
lambda. Importantly, we show this sub-diffraction imaging is due to the
resonant excitation of surface slab modes, allowing refocusing of
non-propagating evanescent waves
Dynamics of Shock Probes in Driven Diffusive Systems
We study the dynamics of shock-tracking probe particles in driven diffusive
systems and also in equilibrium systems. In a driven system, they induce a
diverging timescale that marks the crossover between a passive scalar regime at
early times and a diffusive regime at late times; a scaling form characterises
this crossover. Introduction of probes into an equilibrium system gives rise to
a system-wide density gradient, and the presence of even a single probe can be
felt across the entire system.Comment: Accepted in Journal of Statistical Mechanics: Theory and Experimen
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