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

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 $\Pi_2 \mathrm P$-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply $\Pi_2 \mathrm P$-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