Translation from Classical Two-Way Automata to Pebble Two-Way Automata

We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it is not known whether there exists a polynomial trade-off, in the number of states, between the nondeterministic and deterministic pebble two-way automata. However, we show that these two machine models are not independent: if there exists a polynomial trade-off for the classical two-way automata, then there must also exist a polynomial trade-off for the pebble two-way automata. Thus, we have an upward collapse (or a downward separation) from the classical two-way automata to more powerful pebble automata, still staying within the class of regular languages. The same upward collapse holds for complementation of nondeterministic two-way machines. These results are obtained by showing that each pebble machine can be, by using suitable inputs, simulated by a classical two-way automaton with a linear number of states (and vice versa), despite the existing exponential blow-up between the classical and pebble two-way machines

Abundances in Stars from the Red Giant Branch Tip to the Near the Main Sequence in M71: I. Sample Selection, Observing Strategy and Stellar Parameters

We present the sample for an abundance analysis of 25 members of M71 with luminosities ranging from the red giant branch tip to the upper main sequence. The spectra are of high dispersion and of high precision. We describe the observing strategy and determine the stellar parameters for the sample stars using both broad band colors and fits of H$\alpha$ profiles. The derived stellar parameters agree with those from the Yale$^2$ stellar evolutionary tracks to within 50 -- 100K for a fixed log g, which is within the level of the uncertainties.Comment: Minor changes to conform to version accepted for publication, with several new figures (Paper 1 of a pair

Astrometry with "Carte du Ciel" plates, San Fernando zone. I. Digitization and measurement using a flatbed scanner

We present an original method of digitizing and astrometrically reducing "Carte du Ciel" plate material using an inexpensive flatbed scanner, to demonstrate that for this material there is an alternative to more specialized measuring machines that are very few in number and thus not readily available. The sample of plates chosen to develop this method are original "Carte du Ciel" plates of the San Fernando zone, photographic material with a mean epoch 1903.6, and a limiting photographic magnitude ~14.5, covering the declination range of -10 < dec < -2. Digitization has been made using a commercial flatbed scanner, demonstrating the internal precision that can be attained with such a device. A variety of post-scan corrections are shown to be necessary. In particular, the large distortion introduced by the non-uniform action of the scanner is modelled using multiple scans of each plate. We also tackle the specific problems associated with the triple-exposure images on some plates and the grid lines present on all. The final measures are reduced to celestial coordinates using the Tycho-2 Catalogue. The internal precision obtained over a single plate, 3microns ~ 0.18" in each axis, is comparable to what is realized with similar plate material using slower, less affordable, and less widely available conventional measuring machines, such as a PDS microdensitometer. The accuracy attained over large multi-plate areas, employing an overlapping plate technique, is estimated at 0.2".Comment: 16 pages, 19 figures and 3 tables. Accepted for publication in A&

Coherence resonance in a network of FitzHugh-Nagumo systems: interplay of noise, time-delay and topology

We systematically investigate the phenomena of coherence resonance in time-delay coupled networks of FitzHugh-Nagumo elements in the excitable regime. Using numerical simulations, we examine the interplay of noise, time-delayed coupling and network topology in the generation of coherence resonance. In the deterministic case, we show that the delay-induced dynamics is independent of the number of nearest neighbors and the system size. In the presence of noise, we demonstrate the possibility of controlling coherence resonance by varying the time-delay and the number of nearest neighbors. For a locally coupled ring, we show that the time-delay weakens coherence resonance. For nonlocal coupling with appropriate time-delays, both enhancement and weakening of coherence resonance are possible

Unary probabilistic and quantum automata on promise problems

We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs can be exponentially more succinct than DFAs.Comment: Minor correction

Sublogarithmic bounds on space and reversals

The complexity measure under consideration is SPACE x REVERSALS for Turing machines that are able to branch both existentially and universally. We show that, for any function h(n) between log log n and log n, Pi(1) SPACE x REVERSALS(h(n)) is separated from Sigma(1)SPACE x REVERSALS(h(n)) as well as from co Sigma(1)SPACE x REVERSALS(h(n)), for middle, accept, and weak modes of this complexity measure. This also separates determinism from the higher levels of the alternating hierarchy. For "well-behaved" functions h(n) between log log n and log n, almost all of the above separations can be obtained by using unary witness languages. In addition, the construction of separating languages contributes to the research on minimal resource requirements for computational devices capable of recognizing nonregular languages. For any (arbitrarily slow growing) unbounded monotone recursive function f(n), a nonregular unary language is presented that can be accepted by a middle Pi(1) alternating Turing machine in s(n) space and i(n) input head reversals, with s(n) . i(n) is an element of O(log log n . f(n)). Thus, there is no exponential gap for the optimal lower bound on the product s(n) . i(n) between unary and general nonregular language acceptance-in sharp contrast with the one-way case

A Far-Ultraviolet Survey of 47 Tucanae.II The Long-Period Cataclysmic Variable AKO 9

We present time-resolved, far-ultraviolet (FUV) spectroscopy and photometry of the 1.1 day eclipsing binary system AKO 9 in the globular cluster 47 Tucanae. The FUV spectrum of AKO 9 is blue and exhibits prominent C IV and He II emission lines. The spectrum broadly resembles that of long-period, cataclysmic variables in the galactic field. Combining our time-resolved FUV data with archival optical photometry of 47 Tuc, we refine the orbital period of AKO 9 and define an accurate ephemeris for the system. We also place constraints on several other system parameters, using a variety of observational constraints. We find that all of the empirical evidence is consistent with AKO 9 being a long-period dwarf nova in which mass transfer is driven by the nuclear expansion of a sub-giant donor star. We therefore conclude that AKO 9 is the first spectroscopically confirmed cataclysmic variable in 47 Tuc. We also briefly consider AKO 9's likely formation and ultimate evolution. Regarding the former, we find that the system was almost certainly formed dynamically, either via tidal capture or in a 3-body encounter. Regarding the latter, we show that AKO 9 will probably end its CV phase by becoming a detached, double WD system or by exploding in a Type Ia supernova.Comment: 40 pages, 11 figures, to appear in the Dec 20 issue of ApJ; minor changes to match final published versio

Far-Ultraviolet Surveys of Globular Clusters: Hunting for the Products of Stellar Collisions and Near Misses

Globular clusters are gravitationally bound stellar systems containing on the order of 100,000 stars. Due to the high stellar densities in the cores of these clusters, close encounters and even physical collisions between stars are inevitable. These dynamical interactions can produce exotic types of single and binary stars that are extremely rare in the galactic field, but which may be important to the dynamical evolution of their host clusters. A common feature of these dynamically-formed stellar populations is that many of their members are relatively hot, and thus bright in the far-ultraviolet (FUV) waveband. In this short review, I describe how space-based FUV observations are being used to find and study these populations.Comment: 15 pages, 6 figures; invited "Brief Review" for Modern Physics Letters

Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation

Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept and generate, respectively, type-3 (regular) languages. Based on our previous work, this paper analyzes effects of graph manipulations on corresponding RE. In this present, starting stage we assume that the DG under consideration contains no cycles. Graph manipulation is performed by deleting or inserting of nodes or arcs. Combined and/or multiple application of these basic operators enable a great variety of transformations of DG (and corresponding RE) that can be seen as mutants of the original DG (and corresponding RE). DG are popular for modeling complex systems; however they easily become intractable if the system under consideration is complex and/or large. In such situations, we propose to switch to corresponding RE in order to benefit from their compact format for modeling and algebraic operations for analysis. The results of the study are of great potential interest to mutation testing

Graph-Controlled Insertion-Deletion Systems

In this article, we consider the operations of insertion and deletion working in a graph-controlled manner. We show that like in the case of context-free productions, the computational power is strictly increased when using a control graph: computational completeness can be obtained by systems with insertion or deletion rules involving at most two symbols in a contextual or in a context-free manner and with the control graph having only four nodes.Comment: In Proceedings DCFS 2010, arXiv:1008.127