Vector bundles on the projective line and finite domination of chain complexes

Finitely dominated chain complexes over a Laurent polynomial ring in one indeterminate are characterised by vanishing of their Novikov homology. We present an algebro-geometric approach to this result, based on extension of chain complexes to sheaves on the projective line. We also discuss the K-theoretical obstruction to extension.Comment: v1: 11 page

Extremal Optimization at the Phase Transition of the 3-Coloring Problem

We investigate the phase transition of the 3-coloring problem on random graphs, using the extremal optimization heuristic. 3-coloring is among the hardest combinatorial optimization problems and is closely related to a 3-state anti-ferromagnetic Potts model. Like many other such optimization problems, it has been shown to exhibit a phase transition in its ground state behavior under variation of a system parameter: the graph's mean vertex degree. This phase transition is often associated with the instances of highest complexity. We use extremal optimization to measure the ground state cost and the ``backbone'', an order parameter related to ground state overlap, averaged over a large number of instances near the transition for random graphs of size $n$ up to 512. For graphs up to this size, benchmarks show that extremal optimization reaches ground states and explores a sufficient number of them to give the correct backbone value after about $O(n^{3.5})$ update steps. Finite size scaling gives a critical mean degree value $\alpha_{\rm c}=4.703(28)$. Furthermore, the exploration of the degenerate ground states indicates that the backbone order parameter, measuring the constrainedness of the problem, exhibits a first-order phase transition.Comment: RevTex4, 8 pages, 4 postscript figures, related information available at http://www.physics.emory.edu/faculty/boettcher

Detection of Harmful Algal Blooms Using Photopigments and Absorption Signatures: A Case Study of the Florida Red Tide Dinoflagellate, Gymnodinium breve

The utility of photopigments and absorption signatures to detect and enumerate the red tide dinoflagellate, Gymnodinium breve, was evaluated in laboratory cultures and in natural assemblages. The carotenoid, gyroxanthindiester, was an adequate biomarker for G. breve biomass; water‐column concentrations corresponded with cell standing crops and chlorophyll a concentrations during bloom events in Sarasota Bay, Florida. Unlike other carotenoids, the relative abundance of gyroxanthin‐diester did not change throughout a range of physiological states in culture and the gyroxanthin‐diester: chlorophyll a ratio exhibited little variability in a natural assemblage during bloom senescence. Stepwise discriminant analysis indicated that wavelengths indicative of in vivo absorption by accessory chlorophylls and carotenoids could correctly discern spectra of the fucoxanthin‐containing G. breve from spectra of peridinin‐containing dinoflagellates, a diatom, a haptophyte, and a prasinophyte. With the use of a similarity algorithm, the increasing contribution of G. breve was discerned in absorption spectra (and corresponding fourth‐derivative plots) for hypothetical mixed assemblages. However, the absorption properties of chlorophyll c‐containing algae vary little among taxa and it is difficult to discern the contribution of accessory chlorophylls and carotenoids caused by cell packaging. Therefore, the use of absorption spectra alone may not identify the contribution of a chlorophyll c‐containing taxon to the composite spectrum of a mixed assemblage. This difficulty in distinguishing among spectra can be minimized by using the similarity algorithm in conjunction with fourth‐derivative analysis

The Shapes of Cooperatively Rearranging Regions in Glass Forming Liquids

The shapes of cooperatively rearranging regions in glassy liquids change from being compact at low temperatures to fractal or ``stringy'' as the dynamical crossover temperature from activated to collisional transport is approached from below. We present a quantitative microscopic treatment of this change of morphology within the framework of the random first order transition theory of glasses. We predict a correlation of the ratio of the dynamical crossover temperature to the laboratory glass transition temperature, and the heat capacity discontinuity at the glass transition, Delta C_p. The predicted correlation agrees with experimental results for the 21 materials compiled by Novikov and Sokolov.Comment: 9 pages, 6 figure

A catalogue of bright (K <9) M dwarfs

Using the Position and Proper Motion Extended-L (PPMXL) catalogue, we have used optical and near-infrared colour cuts together with a reduced proper motion cut to find bright M dwarfs for future exoplanet transit studies. PPMXL's low proper motion uncertainties allow us to probe down to smaller proper motions than previous similar studies. We have combined unique objects found with this method to that of previous work to produce 8479 K <9 M dwarfs. Low-resolution spectroscopy was obtained of a sample of the objects found using this selection method to gain statistics on their spectral type and physical properties. Results show a spectral-type range of K7-M4V. This catalogue is the most complete collection of K <9 M dwarfs currently available and is made available here.Peer reviewe

Extremal Optimization for Graph Partitioning

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of runtime and system size. The method has a single free parameter, which we determine numerically and justify using a simple argument. Our numerical results demonstrate that on random graphs, extremal optimization maintains consistent accuracy for increasing system sizes, with an approximation error decreasing over runtime roughly as a power law t^(-0.4). On geometrically structured graphs, the scaling of results from the average run suggests that these are far from optimal, with large fluctuations between individual trials. But when only the best runs are considered, results consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher

Near-infrared spectra of ISO selected Chamaeleon I young stellar objects

We present 0.95--2.5 micron moderate (R = 500) resolution spectra of 19 ISOCAM detected sources in the Chamaeleon I dark cloud. Thirteen of these stars are candidate very low mass members of the cloud proposed by Persi et al. (2000 A&A 357:219) on basis of the mid-IR color excess. The sample also includes a bona-fide young brown dwarf (Cha Halpha 1), a transition --stellar/sub-stellar-- object (Cha Halpha 2), one previously known T Tauri star (Sz 33) and three ISOCAM sources with no mid-IR excess. The spectra of the mid-IR color excess sources are relatively flat and featureless in this wavelength range. Both atomic and molecular lines (when in absorption) are partially veiled suggesting the presence of continuum emission from circumstellar dust. In addition some of the sources show Paschen and Brackett lines in emission. We apply the 2 micron water vapor index defined by Wilking et al. (1999 AJ 117:469) to estimate spectral types. These stars have spectral types M0--8. We use Persi et al.'s stellar luminosity determinations, in combination with D'Antona & Mazzitelli latest pre-main sequence evolutionary tracks, to estimate masses and ages. The ISOCAM detected mid-IR excess sources have sub-solar masses down to the H-burning limit and a median age of few x 10^6 yr, in good agreement with the higher mass members of this cloud.Comment: Preprint in Manuscript format; 30 pages including 10 figure

Transitioning to adulthood with a mild intellectual disability: Young people's experiences, expectations, and aspirations

Aim: Very little attention has been paid to the views and experiences of young people with mild intellectual disabilities on the broad topics of adulthood and adult identity. The following study was undertaken to explore how young adults with mild intellectual disabilities conceptualize, relate to, and experience the process of transition. Method: Eight young adults with mild to borderline intellectual disabilities participated in semi‐structured interviews. Results were analysed using interpretive thematic analysis. Results: Two umbrella themes were identified: “On a developmental pathway” and “Negotiations in the environment”. Conclusions: The participants concerns were surprisingly similar to those commonly expressed by young adults without disabilities. Self‐perceived adult identity appeared to be affected by the participants' personal definitions of adulthood, as well as by social comparisons with both peers and adults. Finally, while concerns were expressed about their capacity to cope with responsibility, most felt optimistic about adopting full adult status in the future

Extremal Optimization of Graph Partitioning at the Percolation Threshold

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in extensive numerical simulations. While generally a complex (NP-hard) problem, the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivities near the percolation threshold. At this threshold, the relative error of Simulated Annealing for large graphs is found to diverge relative to Extremal Optimization at equalized runtime. On the other hand, Extremal Optimization, based on the extremal dynamics of self-organized critical systems, reproduces known results about optimal partitions at this critical point quite well.Comment: 7 pages, RevTex, 9 ps-figures included, as to appear in Journal of Physics

Testing "microscopic" theories of glass-forming liquids

We assess the validity of "microscopic" approaches of glass-forming liquids based on the sole k nowledge of the static pair density correlations. To do so we apply them to a benchmark provided by two liquid models that share very similar static pair density correlation functions while disp laying distinct temperature evolutions of their relaxation times. We find that the approaches are unsuccessful in describing the difference in the dynamical behavior of the two models. Our study is not exhausti ve, and we have not tested the effect of adding corrections by including for instance three-body density correlations. Yet, our results appear strong enough to challenge the claim that the slowd own of relaxation in glass-forming liquids, for which it is well established that the changes of the static structure factor with temperature are small, can be explained by "microscopic" appr oaches only requiring the static pair density correlations as nontrivial input.Comment: 10 pages, 7 figs; Accepted to EPJE Special Issue on The Physics of Glasses. Arxiv version contains an addendum to the appendix which does not appear in published versio