6,104 research outputs found
Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs
Physicists have argued that periodic orbit bunching leads to universal
spectral fluctuations for chaotic quantum systems. To establish a more detailed
mathematical understanding of this fact, it is first necessary to look more
closely at the classical side of the problem and determine orbit pairs
consisting of orbits which have similar actions. In this paper we specialize to
the geodesic flow on compact factors of the hyperbolic plane as a classical
chaotic system. We prove the existence of a periodic partner orbit for a given
periodic orbit which has a small-angle self-crossing in configuration space
which is a `2-encounter'; such configurations are called `Sieber-Richter pairs'
in the physics literature. Furthermore, we derive an estimate for the action
difference of the partners. In the second part of this paper [13], an inductive
argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit
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Complete Genomic Sequences of Three Salmonella enterica subsp. enterica Serovar Muenchen Strains from an Orchard in San Joaquin County, California.
We present here the complete genome sequences of three Salmonella enterica subsp. enterica serovar Muenchen strains, LG24, LG25, and LG26. All three strains were isolated from almond drupes grown in an orchard in San Joaquin County, California, in 2016. These genomic sequences are nonidentical and will contribute to our understanding of S. enterica genomics
Integer Vector Addition Systems with States
This paper studies reachability, coverability and inclusion problems for
Integer Vector Addition Systems with States (ZVASS) and extensions and
restrictions thereof. A ZVASS comprises a finite-state controller with a finite
number of counters ranging over the integers. Although it is folklore that
reachability in ZVASS is NP-complete, it turns out that despite their
naturalness, from a complexity point of view this class has received little
attention in the literature. We fill this gap by providing an in-depth analysis
of the computational complexity of the aforementioned decision problems. Most
interestingly, it turns out that while the addition of reset operations to
ordinary VASS leads to undecidability and Ackermann-hardness of reachability
and coverability, respectively, they can be added to ZVASS while retaining
NP-completness of both coverability and reachability.Comment: 17 pages, 2 figure
Unary Pushdown Automata and Straight-Line Programs
We consider decision problems for deterministic pushdown automata over a
unary alphabet (udpda, for short). Udpda are a simple computation model that
accept exactly the unary regular languages, but can be exponentially more
succinct than finite-state automata. We complete the complexity landscape for
udpda by showing that emptiness (and thus universality) is P-hard, equivalence
and compressed membership problems are P-complete, and inclusion is
coNP-complete. Our upper bounds are based on a translation theorem between
udpda and straight-line programs over the binary alphabet (SLPs). We show that
the characteristic sequence of any udpda can be represented as a pair of
SLPs---one for the prefix, one for the lasso---that have size linear in the
size of the udpda and can be computed in polynomial time. Hence, decision
problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP
can be converted in logarithmic space into a udpda, and this forms the basis
for our lower bound proofs. We show coNP-hardness of the ordered matching
problem for SLPs, from which we derive coNP-hardness for inclusion. In
addition, we complete the complexity landscape for unary nondeterministic
pushdown automata by showing that the universality problem is -hard, using a new class of integer expressions. Our techniques have
applications beyond udpda. We show that our results imply -completeness for a natural fragment of Presburger arithmetic and coNP lower
bounds for compressed matching problems with one-character wildcards
Radio Observations of the Hubble Deep Field South Region III: The 2.5, 5.2 and 8.7 GHz Catalogues and Radio Source Properties
Deep radio observations of a wide region centred on the Hubble Deep Field
South have been performed, providing one of the most sensitive set of radio
observations acquired on the Australia Telescope Compact Array to date. A
central rms of ~10 microJy is reached at four frequencies (1.4, 2.5, 5.2 and
8.7 GHz). In this paper the full source catalogues from the 2.5, 5.2 and 8.7
GHz observations are presented to complement Paper II, along with a detailed
analysis of image quality and noise. We produce a consolidated catalogue by
matching sources across all four frequencies of our survey. Radio spectral
indices are used to investigate the nature of the radio sources and identify a
number of sources with flat or inverted radio spectra, which indicates AGN
activity. We also find several other interesting sources, including a broadline
emitting radio galaxy, a giant radio galaxy and three Gigahertz Peaked Spectrum
sources.Comment: Accepted by AJ. 13 figures and 13 table
Conservative self-organized extremal model for wealth distribution
We present a detailed numerical analysis of the modified version of a
conservative self-organized extremal model introduced by Pianegonda et. al. for
the distribution of wealth of the people in a society. Here the trading process
has been modified by the stochastic bipartite trading rule. More specifically
in a trade one of the agents is necessarily the one with the globally minimal
value of wealth, the other one being selected randomly from the neighbors of
the first agent. The pair of agents then randomly re-shuffle their entire
amount of wealth without saving. This model has most of the characteristics
similar to the self-organized critical Bak-Sneppen model of evolutionary
dynamics. Numerical estimates of a number of critical exponents indicate this
model is likely to belong to a new universality class different from the well
known models in the literature. In addition the persistence time, which is the
time interval between two successive updates of wealth of an agent has been
observed to have a non-trivial power law distribution. An opposite version of
the model has also been studied where the agent with maximal wealth is selected
instead of the one with minimal wealth, which however, exhibits similar
behavior as the Minimal Wealth model.Comment: 11 pages, 16 figure
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