2,425 research outputs found
Distinguishing Hidden Markov Chains
Hidden Markov Chains (HMCs) are commonly used mathematical models of
probabilistic systems. They are employed in various fields such as speech
recognition, signal processing, and biological sequence analysis. We consider
the problem of distinguishing two given HMCs based on an observation sequence
that one of the HMCs generates. More precisely, given two HMCs and an
observation sequence, a distinguishing algorithm is expected to identify the
HMC that generates the observation sequence. Two HMCs are called
distinguishable if for every there is a distinguishing
algorithm whose error probability is less than . We show that one
can decide in polynomial time whether two HMCs are distinguishable. Further, we
present and analyze two distinguishing algorithms for distinguishable HMCs. The
first algorithm makes a decision after processing a fixed number of
observations, and it exhibits two-sided error. The second algorithm processes
an unbounded number of observations, but the algorithm has only one-sided
error. The error probability, for both algorithms, decays exponentially with
the number of processed observations. We also provide an algorithm for
distinguishing multiple HMCs. Finally, we discuss an application in stochastic
runtime verification.Comment: This is the full version of a LICS'16 pape
Fractional Energy Loss and Centrality Scaling
The phenomenon of centrality scaling in the high-\pt spectra of
produced in Au-Au collisions at GeV is examined in the framework
of relating fractional energy loss to fractional centrality increase. A new
scaling behavior is found where the scaling variable is given a power-law
dependence on . The exponent specifies the fractional
proportionality relationship between energy loss and centrality, and is a
phenomenologically determined number that characterizes the nuclear suppression
effect. The implication on the parton energy loss in the context of
recombination is discussed.Comment: 4 pages in RevTe
Laser-dressed vacuum polarization in a Coulomb field
We investigate quantum electrodynamic effects under the influence of an
external, time-dependent electromagnetic field, which mediates dynamic
modifications of the radiative corrections. Specifically, we consider the
quantum electrodynamic vacuum-polarization tensor under the influence of two
external background fields: a strong laser field and a nuclear Coulomb field.
We calculate the charge and current densities induced by a nuclear Coulomb
field in the presence of a laser field. We find the corresponding induced
scalar and vector potentials. The induced potential, in first-order
perturbation theory, leads to a correction to atomic energy levels. The
external laser field breaks the rotational symmetry of the system.
Consequently, the induced charge density is not spherically symmetric, and the
energy correction therefore leads to a "polarized Lamb shift." In particular,
the laser generates an additional potential with a quadrupole moment. The
corresponding laser-dressed vacuum-polarization potential behaves like 1/r**3
at large distances, unlike the Uehling potential that vanishes exponentially
for large r. Our investigation might be useful for other situations where
quantum field theoretic phenomena are subjected to external fields of a rather
involved structure.Comment: 13 pages, RevTe
Photon splitting in a laser field
Photon splitting due to vacuum polarization in a laser field is considered.
Using an operator technique, we derive the amplitudes for arbitrary strength,
spectral content and polarization of the laser field. The case of a
monochromatic circularly polarized laser field is studied in detail and the
amplitudes are obtained as three-fold integrals. The asymptotic behavior of the
amplitudes for various limits of interest are investigated also in the case of
a linearly polarized laser field. Using the obtained results, the possibility
of experimental observation of the process is discussed.Comment: 31 pages, 4 figure
Quantitative Analysis of DoS Attacks and Client Puzzles in IoT Systems
Denial of Service (DoS) attacks constitute a major security threat to today's
Internet. This challenge is especially pertinent to the Internet of Things
(IoT) as devices have less computing power, memory and security mechanisms to
mitigate DoS attacks. This paper presents a model that mimics the unique
characteristics of a network of IoT devices, including components of the system
implementing `Crypto Puzzles' - a DoS mitigation technique. We created an
imitation of a DoS attack on the system, and conducted a quantitative analysis
to simulate the impact such an attack may potentially exert upon the system,
assessing the trade off between security and throughput in the IoT system. We
model this through stochastic model checking in PRISM and provide evidence that
supports this as a valuable method to compare the efficiency of different
implementations of IoT systems, exemplified by a case study
Tricritical structure in the adjoint Higgs model?
Baier R, Gavai RV, Lang CB. Tricritical structure in the adjoint Higgs model? Physics letters B. 1986;172(3-4):387-391
Flow Faster: Efficient Decision Algorithms for Probabilistic Simulations
Strong and weak simulation relations have been proposed for Markov chains,
while strong simulation and strong probabilistic simulation relations have been
proposed for probabilistic automata. However, decision algorithms for strong
and weak simulation over Markov chains, and for strong simulation over
probabilistic automata are not efficient, which makes it as yet unclear whether
they can be used as effectively as their non-probabilistic counterparts. This
paper presents drastically improved algorithms to decide whether some
(discrete- or continuous-time) Markov chain strongly or weakly simulates
another, or whether a probabilistic automaton strongly simulates another. The
key innovation is the use of parametric maximum flow techniques to amortize
computations. We also present a novel algorithm for deciding strong
probabilistic simulation preorders on probabilistic automata, which has
polynomial complexity via a reduction to an LP problem. When extending the
algorithms for probabilistic automata to their continuous-time counterpart, we
retain the same complexity for both strong and strong probabilistic
simulations.Comment: LMC
Verification and Control of Partially Observable Probabilistic Real-Time Systems
We propose automated techniques for the verification and control of
probabilistic real-time systems that are only partially observable. To formally
model such systems, we define an extension of probabilistic timed automata in
which local states are partially visible to an observer or controller. We give
a probabilistic temporal logic that can express a range of quantitative
properties of these models, relating to the probability of an event's
occurrence or the expected value of a reward measure. We then propose
techniques to either verify that such a property holds or to synthesise a
controller for the model which makes it true. Our approach is based on an
integer discretisation of the model's dense-time behaviour and a grid-based
abstraction of the uncountable belief space induced by partial observability.
The latter is necessarily approximate since the underlying problem is
undecidable, however we show how both lower and upper bounds on numerical
results can be generated. We illustrate the effectiveness of the approach by
implementing it in the PRISM model checker and applying it to several case
studies, from the domains of computer security and task scheduling
Calculating Quenching Weights
We calculate the probability (``quenching weight'') that a hard parton
radiates an additional energy fraction due to scattering in spatially extended
QCD matter. This study is based on an exact treatment of finite in-medium path
length, it includes the case of a dynamically expanding medium, and it extends
to the angular dependence of the medium-induced gluon radiation pattern. All
calculations are done in the multiple soft scattering approximation
(Baier-Dokshitzer-Mueller-Peign\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and
in the single hard scattering approximation (N=1 opacity approximation). By
comparison, we establish a simple relation between transport coefficient, Debye
screening mass and opacity, for which both approximations lead to comparable
results. Together with this paper, a CPU-inexpensive numerical subroutine for
calculating quenching weights is provided electronically. To illustrate its
applications, we discuss the suppression of hadronic transverse momentum
spectra in nucleus-nucleus collisions. Remarkably, the kinematic constraint
resulting from finite in-medium path length reduces significantly the
transverse momentum dependence of the nuclear modification factor, thus leading
to consistency with the data measured at the Relativistic Heavy Ion Collider
(RHIC).Comment: 45 pages LaTeX, 20 eps-figure
Light diffraction by a strong standing electromagnetic wave
The nonlinear quantum interaction of a linearly polarized x-ray probe beam
with a focused intense standing laser wave is studied theoretically. Because of
the tight focusing of the standing laser pulse, diffraction effects arise for
the probe beam as opposed to the corresponding plane wave scenario. A
quantitative estimate for realistic experimental conditions of the ellipticity
and the rotation of the main polarization plane acquired by the x-ray probe
after the interaction shows that the implementation of such vacuum effects is
feasible with future X-ray Free Electron Laser light.Comment: 5 pages, 2 figures. Published versio
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