23,347 research outputs found
Characterising Probabilistic Processes Logically
In this paper we work on (bi)simulation semantics of processes that exhibit
both nondeterministic and probabilistic behaviour. We propose a probabilistic
extension of the modal mu-calculus and show how to derive characteristic
formulae for various simulation-like preorders over finite-state processes
without divergence. In addition, we show that even without the fixpoint
operators this probabilistic mu-calculus can be used to characterise these
behavioural relations in the sense that two states are equivalent if and only
if they satisfy the same set of formulae.Comment: 18 page
Time Resolution Dependence of Information Measures for Spiking Neurons: Atoms, Scaling, and Universality
The mutual information between stimulus and spike-train response is commonly
used to monitor neural coding efficiency, but neuronal computation broadly
conceived requires more refined and targeted information measures of
input-output joint processes. A first step towards that larger goal is to
develop information measures for individual output processes, including
information generation (entropy rate), stored information (statistical
complexity), predictable information (excess entropy), and active information
accumulation (bound information rate). We calculate these for spike trains
generated by a variety of noise-driven integrate-and-fire neurons as a function
of time resolution and for alternating renewal processes. We show that their
time-resolution dependence reveals coarse-grained structural properties of
interspike interval statistics; e.g., -entropy rates that diverge less
quickly than the firing rate indicate interspike interval correlations. We also
find evidence that the excess entropy and regularized statistical complexity of
different types of integrate-and-fire neurons are universal in the
continuous-time limit in the sense that they do not depend on mechanism
details. This suggests a surprising simplicity in the spike trains generated by
these model neurons. Interestingly, neurons with gamma-distributed ISIs and
neurons whose spike trains are alternating renewal processes do not fall into
the same universality class. These results lead to two conclusions. First, the
dependence of information measures on time resolution reveals mechanistic
details about spike train generation. Second, information measures can be used
as model selection tools for analyzing spike train processes.Comment: 20 pages, 6 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/trdctim.ht
Contributions to the relativistic mechanics of continuous media
This is a translation from German of an article originally published inProceedings of the Mathematical-Natural Science Section of the Mainz Academy of Science and Literature, Nr. 11, 1961 (pp. 792–837) (printed by Franz Steiner and Co, Wiesbaden), which is Paper IV in the series ldquoExact Solutions of the Field Equations of General Relativity Theoryrdquo by Pascual Jordan, Jürgen Ehlers, Wolfgang Kundt and Rainer K. Sachs. The translation has been carried out by G. F. R. Ellis (Department of Applied Mathematics, University of Cape Town), assisted by P. K. S. Dunsby, so that this outstanding review paper can be readily accessible to workers in the field today. As far as possible, the translation has preserved both the spirit and the form of the original paper. Despite its age, it remains one of the best reviews available in this area
Final state interaction in the production of heavy unstable particles
We make an attempt to discuss in detail the effects originating from the
final state interaction in the processes involving production of unstable
elementary particles and their subsequent decay. Two complementary scenarios
are considered: the single resonance production and the production of two
resonances. We argue that part of the corrections due to the final state
interaction can be connected with the Coulomb phases of the involved charge
particles; the presence of the unstable particle in the problem makes the
Coulomb phase ``visible''. It is shown how corrections due to the final state
interaction disappear when one proceeds to the total cross-sections. We derive
one-loop non-factorizable radiative corrections to the lowest order matrix
element of both single and double resonance production. We discuss how the
infrared limit of the theories with the unstable particles is modified. In
conclusion we briefly discuss our results in the context of the forthcoming
experiments on the and the production at LEP and NLC.Comment: 33 pages, latex, 6 figures (added), version accepted for publication
in Nuc. Phys. B, substantial revisio
Divergence theorems in path space III: hypoelliptic diffusions and beyond
Let denote a diffusion process defined on a closed compact manifold. In
an earlier article, the author introduced a new approach to constructing
admissible vector fields on the associated space of paths, under the assumption
of ellipticity of . In this article, this method is extended to yield
similar results for degenerate diffusion processes. In particular, these
results apply to non-elliptic diffusions satisfying H\"ormander's condition
Large distance behaviour of light cone operator product in perturbative and nonperturbative QCD regimes
We evaluate the coordinate space dependence of the matrix elements of the
commutator of the electromagnetic and gluon currents in the vicinity of the
light-cone but at large distances within the parton model, DGLAP, the
resummation approaches to the small x behaviour of DIS processes, and for the
Unitarity Bound. We find that an increase of the commutator with relative
distance as is the generic property of QCD
at small but fixed space-time interval in perturbative and
nonperturbative QCD regimes. We explain that the factor follows within the
dipole model (QCD factorization theorem) from the properties of Lorents
transformation. The increase of disappeares at central impact parameters
if cross section of DIS may achieve the Unitarity Limit. We argue that such
long range forces are hardly consistent with thermodynamic equilibrium while a
Unitarity Limit may signal equilibration. Possible implications of this new
long range interaction are briefly discussed.Comment: 23 page
The Athena Astrophysical MHD Code in Cylindrical Geometry
A method for implementing cylindrical coordinates in the Athena
magnetohydrodynamics (MHD) code is described. The extension follows the
approach of Athena's original developers and has been designed to alter the
existing Cartesian-coordinates code as minimally and transparently as possible.
The numerical equations in cylindrical coordinates are formulated to maintain
consistency with constrained transport, a central feature of the Athena
algorithm, while making use of previously implemented code modules such as the
Riemann solvers. Angular-momentum transport, which is critical in astrophysical
disk systems dominated by rotation, is treated carefully. We describe
modifications for cylindrical coordinates of the higher-order spatial
reconstruction and characteristic evolution steps as well as the finite-volume
and constrained transport updates. Finally, we present a test suite of standard
and novel problems in one-, two-, and three-dimensions designed to validate our
algorithms and implementation and to be of use to other code developers. The
code is suitable for use in a wide variety of astrophysical applications and is
freely available for download on the web
Astrophysical Weighted Particle Magnetohydrodynamics
This paper presents applications of weighted meshless scheme for conservation
laws to the Euler equations and the equations of ideal magnetohydrodynamics.
The divergence constraint of the latter is maintained to the truncation error
by a new meshless divergence cleaning procedure. The physics of the interaction
between the particles is described by an one-dimensional Riemann problem in a
moving frame. As a result, necessary diffusion which is required to treat
dissipative processes is added automatically. As a result, our scheme has no
free parameters that controls the physics of inter-particle interaction, with
the exception of the number of the interacting neighbours which control the
resolution and accuracy. The resulting equations have the form similar to SPH
equations, and therefore existing SPH codes can be used to implement the
weighed particle scheme. The scheme is validated in several hydrodynamic and
MHD test cases. In particular, we demonstrate for the first time the ability of
a meshless MHD scheme to model magneto-rotational instability in accretion
disks.Comment: 27 pages, 24 figures, 1 column, submitted to MNRAS, hi-res version
can be obtained at http://www.strw.leidenuniv.nl/~egaburov/wpmhd.pd
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)
- …