552 research outputs found
Revisiting the Equivalence Problem for Finite Multitape Automata
The decidability of determining equivalence of deterministic multitape
automata (or transducers) was a longstanding open problem until it was resolved
by Harju and Karhum\"{a}ki in the early 1990s. Their proof of decidability
yields a co_NP upper bound, but apparently not much more is known about the
complexity of the problem. In this paper we give an alternative proof of
decidability, which follows the basic strategy of Harju and Karhumaki but
replaces their use of group theory with results on matrix algebras. From our
proof we obtain a simple randomised algorithm for deciding language equivalence
of deterministic multitape automata and, more generally, multiplicity
equivalence of nondeterministic multitape automata. The algorithm involves only
matrix exponentiation and runs in polynomial time for each fixed number of
tapes. If the two input automata are inequivalent then the algorithm outputs a
word on which they differ
Inference for SDE models via Approximate Bayesian Computation
Models defined by stochastic differential equations (SDEs) allow for the
representation of random variability in dynamical systems. The relevance of
this class of models is growing in many applied research areas and is already a
standard tool to model e.g. financial, neuronal and population growth dynamics.
However inference for multidimensional SDE models is still very challenging,
both computationally and theoretically. Approximate Bayesian computation (ABC)
allow to perform Bayesian inference for models which are sufficiently complex
that the likelihood function is either analytically unavailable or
computationally prohibitive to evaluate. A computationally efficient ABC-MCMC
algorithm is proposed, halving the running time in our simulations. Focus is on
the case where the SDE describes latent dynamics in state-space models; however
the methodology is not limited to the state-space framework. Simulation studies
for a pharmacokinetics/pharmacodynamics model and for stochastic chemical
reactions are considered and a MATLAB package implementing our ABC-MCMC
algorithm is provided.Comment: Version accepted for publication in Journal of Computational &
Graphical Statistic
Unitarity of Quantum Theory and Closed Time-Like Curves
Interacting quantum fields on spacetimes containing regions of closed
timelike curves (CTCs) are subject to a non-unitary evolution . Recently, a
prescription has been proposed, which restores unitarity of the evolution by
modifying the inner product on the final Hilbert space. We give a rigorous
description of this proposal and note an operational problem which arises when
one considers the composition of two or more non-unitary evolutions. We propose
an alternative method by which unitarity of the evolution may be regained, by
extending to a unitary evolution on a larger (possibly indefinite) inner
product space. The proposal removes the ambiguity noted by Jacobson in
assigning expectation values to observables localised in regions spacelike
separated from the CTC region. We comment on the physical significance of the
possible indefiniteness of the inner product introduced in our proposal.Comment: 13 pages, LaTeX. Final revised paper to be published in Phys Rev D.
Some changes are made to expand our discussion of Anderson's Proposal for
restoring unitarit
Macroscopic resonant tunneling of magnetic flux
We have developed a quantitative theory of resonant tunneling of magnetic
flux between discrete macroscopically distinct quantum states in SQUID systems.
The theory is based on the standard density-matrix approach. Its new elements
include the discussion of the two different relaxation mechanisms that exist
for the double-well potential, and description of the ``photon-assisted''
tunneling driven by external rf radiation. It is shown that in the case of
coherent flux dynamics, rf radiation should lead to splitting of the peaks of
resonant flux tunneling, indicating that the resonant tunneling is a convenient
tool for studying macroscopic quantum coherence of flux.Comment: 11 pages, 8 figure
Uniform random generation of large acyclic digraphs
Directed acyclic graphs are the basic representation of the structure
underlying Bayesian networks, which represent multivariate probability
distributions. In many practical applications, such as the reverse engineering
of gene regulatory networks, not only the estimation of model parameters but
the reconstruction of the structure itself is of great interest. As well as for
the assessment of different structure learning algorithms in simulation
studies, a uniform sample from the space of directed acyclic graphs is required
to evaluate the prevalence of certain structural features. Here we analyse how
to sample acyclic digraphs uniformly at random through recursive enumeration,
an approach previously thought too computationally involved. Based on
complexity considerations, we discuss in particular how the enumeration
directly provides an exact method, which avoids the convergence issues of the
alternative Markov chain methods and is actually computationally much faster.
The limiting behaviour of the distribution of acyclic digraphs then allows us
to sample arbitrarily large graphs. Building on the ideas of recursive
enumeration based sampling we also introduce a novel hybrid Markov chain with
much faster convergence than current alternatives while still being easy to
adapt to various restrictions. Finally we discuss how to include such
restrictions in the combinatorial enumeration and the new hybrid Markov chain
method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin
Topological Charged Black Holes in High Dimensional Spacetimes and Their Formation from Gravitational Collapse of a Type II Fluid
Topological charged black holes coupled with a cosmological constant in
spacetimes are studied, where is an Einstein
space of the form . The global structure for
the four-dimensional spacetimes with is investigated systematically.
The most general solutions that represent a Type fluid in such a high
dimensional spacetime are found, and showed that topological charged black
holes can be formed from the gravitational collapse of such a fluid. When the
spacetime is (asymptotically) self-similar, the collapse always forms black
holes for , in contrast to the case , where it can form
either balck holes or naked singularities.Comment: 14 figures, to appear in Phys. Rev.
Entanglement of solid-state qubits by measurement
We show that two identical solid-state qubits can be made fully entangled
(starting from completely mixed state) with probability 1/4 just measuring them
by a detector, equally coupled to the qubits. This happens in the case of
repeated strong (projective) measurements as well as in a more realistic case
of weak continuous measurement. In the latter case the entangled state can be
identified by a flat spectrum of the detector shot noise, while the
non-entangled state (probability 3/4) leads to a spectral peak at the Rabi
frequency with the maximum peak-to-pedestal ratio of 32/3.Comment: 5 pages, 2 figure
Neutron star properties in the quark-meson coupling model
The effects of internal quark structure of baryons on the composition and
structure of neutron star matter with hyperons are investigated in the
quark-meson coupling (QMC) model. The QMC model is based on mean-field
description of nonoverlapping spherical bags bound by self-consistent exchange
of scalar and vector mesons. The predictions of this model are compared with
quantum hadrodynamic (QHD) model calibrated to reproduce identical nuclear
matter saturation properties. By employing a density dependent bag constant
through direct coupling to the scalar field, the QMC model is found to exhibit
identical properties as QHD near saturation density. Furthermore, this modified
QMC model provides well-behaved and continuous solutions at high densities
relevant to the core of neutron stars. Two additional strange mesons are
introduced which couple only to the strange quark in the QMC model and to the
hyperons in the QHD model. The constitution and structure of stars with
hyperons in the QMC and QHD models reveal interesting differences. This
suggests the importance of quark structure effects in the baryons at high
densities.Comment: 28 pages, 10 figures, to appear in Physical Review
Spin Transport in Two Dimensional Hopping Systems
A two dimensional hopping system with Rashba spin-orbit interaction is
considered. Our main interest is concerned with the evolution of the spin
degree of freedom of the electrons. We derive the rate equations governing the
evolution of the charge density and spin polarization of this system in the
Markovian limit in one-particle approximation. If only two-site hopping events
are taken into account, the evolution of the charge density and of the spin
polarization is found to be decoupled. A critical electric field is found,
above which oscillations are superimposed on the temporal decay of the total
polarization. A coupling between charge density and spin polarization occurs on
the level of three-site hopping events. The coupling terms are identified as
the anomalous Hall effect and the recently proposed spin Hall effect. Thus, an
unpolarized charge current through a sheet of finite width leads to a
transversal spin accumulation in our model system.Comment: 15 pages, 3 figure
Antiflow of kaons in relativistic heavy ion collisions
We compare relativistic transport model calculations to recent data on the
sideward flow of neutral strange K^0_s mesons for Au+Au collisions at 6 AGeV. A
soft nuclear equation of state is found to describe very well the positive
proton flow data measured in the same experiment. In the absence of kaon
potential, the K^0 flow pattern is similar to that of protons. The kaon flow
becomes negative if a repulsive kaon potential determined from the impulse
approximation is introduced. However, this potential underestimates the data
which exhibits larger antiflow. An excellent agreement with the data is
obtained when a relativistic scalar-vector kaon potential, that has stronger
density dependence, is used. We further find that the transverse momentum
dependence of directed and elliptic flow is quite sensitive to the kaon
potential in dense matter.Comment: 5 pages, Revtex, 4 figure
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