Remarks on separating words

The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem, consider some variations, and prove several new results

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

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

Algorithms for Colourful Simplicial Depth and Medians in the Plane

The colourful simplicial depth of a point x in the plane relative to a configuration of n points in k colour classes is exactly the number of closed simplices (triangles) with vertices from 3 different colour classes that contain x in their convex hull. We consider the problems of efficiently computing the colourful simplicial depth of a point x, and of finding a point, called a median, that maximizes colourful simplicial depth. For computing the colourful simplicial depth of x, our algorithm runs in time O(n log(n) + k n) in general, and O(kn) if the points are sorted around x. For finding the colourful median, we get a time of O(n^4). For comparison, the running times of the best known algorithm for the monochrome version of these problems are O(n log(n)) in general, improving to O(n) if the points are sorted around x for monochrome depth, and O(n^4) for finding a monochrome median.Comment: 17 pages, 8 figure

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

Lightweight BWT and LCP merging via the gap algorithm

Recently, Holt and McMillan [Bioinformatics 2014, ACM-BCB 2014] have proposed a simple and elegant algorithm to merge the Burrows-Wheeler transforms of a collection of strings. In this paper we show that their algorithm can be improved so that, in addition to the BWTs, it also merges the Longest Common Prefix (LCP) arrays. Because of its small memory footprint this new algorithm can be used for the final merge of BWT and LCP arrays computed by a faster but memory intensive construction algorithm

Astrometric Control of the Inertiality of the Hipparcos Catalog

Based on the most complete list of the results of an individual comparison of the proper motions for stars of various programs common to the Hipparcos catalog, each of which is an independent realization of the inertial reference frame with regard to stellar proper motions, we redetermined the vector $\omega$ of residual rotation of the ICRS system relative to the extragalactic reference frame. The equatorial components of this vector were found to be the following: $\omega_x = +0.04\pm 0.15$ mas yr$^{-1}$, $\omega_y = +0.18\pm 0.12$ mas yr$^{-1}$, and $\omega_z = -0.35\pm 0.09$ mas yr$^{-1}$.Comment: 8 pages, 1 figur

XMM-Newton X-ray and optical observations of the globular clusters M 55 and NGC 3201

We have observed two low concentration Galactic globular clusters with the X-ray observatory XMM-Newton. We detect 47 faint X-ray sources in the direction of M 55 and 62 in the field of view of NGC 3201. Using the statistical Log N-Log S relationship of extragalactic sources derived from XMM-Newton Lockman Hole observations, to estimate the background source population, we estimate that very few of the sources (1.5+/-1.0) in the field of view of M 55 actually belong to the cluster. These sources are located in the centre of the cluster as we expect if the cluster has undergone mass segregation. NGC 3201 has approximately 15 related sources, which are centrally located but are not constrained to lie within the half mass radius. The sources belonging to this cluster can lie up to 5 core radii from the centre of the cluster which could imply that this cluster has been perturbed. Using X-ray (and optical, in the case of M 55) colours, spectral and timing analysis (where possible) and comparing these observations to previous X-ray observations, we find evidence for sources in each cluster that could be cataclysmic variables, active binaries, millisecond pulsars and possible evidence for a quiescent low mass X-ray binary with a neutron star primary, even though we do not expect any such objects in either of the clusters, due to their low central concentrations. The majority of the other sources are background sources, such as AGN.Comment: 12 pages, 7 figures, accepted to be published in A&

A Deep Chandra Survey of the Globular Cluster 47 Tucanae: Catalog of Point Sources

We have detected 300 X-ray sources within the half-mass radius (2.79') of the globular cluster 47 Tucanae in a deep (281 ks) Chandra exposure. We perform photometry and simple spectral fitting for our detected sources, and construct luminosity functions, X-ray color-magnitude and color-color diagrams. Eighty-seven X-ray sources show variability on timescales from hours to years. Thirty-one of the new X-ray sources are identified with chromospherically active binaries from the catalogs of Albrow et al. The radial distributions of detected sources imply roughly 70 are background sources of some kind. Most source spectra are well-fit by thermal plasma models, except for quiescent low-mass X-ray binaries (qLMXBs, containing accreting neutron stars) and millisecond pulsars (MSPs). We identify three new candidate qLMXBs with relatively low X-ray luminosities. One of the brightest cataclysmic variables (CVs, X10) shows evidence (a 4.7 hour period pulsation and strong soft X-ray emission) for a magnetically dominated accretion flow as in AM Her systems. Most of the bright CVs require intrinsic N_H columns of order 10^{21} cm^-2, suggesting a possible DQ Her nature. A group of X-ray sources associated with bright (sub)giant stars also requires intrinsic absorption. By comparing the X-ray colors, luminosities, variability, and quality of spectral fits of the detected MSPs to those of unidentified sources, we estimate that a total of \~25-30 MSPs exist in 47 Tuc (<60 at 95% confidence), regardless of their radio beaming fraction. We estimate that the total number of neutron stars in 47 Tuc is of order 300, reducing the discrepancy between theoretical neutron star retention rates and observed neutron star populations in globular clusters. (Abstract truncated.)Comment: Accepted by ApJ. 62 pages (18 pp. text, 17 pp. figures, 27 pp. tables), 19 figures (8 color), 8 table

Reconstruction Embedding Spaces of Coupled Dynamical Systems from Multivariate Data

A method for reconstructing dimensions of subspaces for weakly coupled dynamical systems is offered. The tool is able to extrapolate the subspace dimensions from the zero coupling limit, where the division of dimensions as per the algorithm is exact. Implementation of the proposed technique to multivariate data demonstrates its effectiveness in disentangling subspace dimensionalities also in the case of emergent synchronized motions, for both numerical and experimental systems