Chandra X-ray observation of the HII region Gum 31 in the Carina Nebula complex

(abridged) We used the Chandra observatory to perform a deep (70 ksec) X-ray observation of the Gum 31 region and detected 679 X-ray point sources. This extends and complements the X-ray survey of the central Carina nebula regions performed in the Chandra Carina Complex Project. Using deep near-infrared images from our recent VISTA survey of the Carina nebula complex, our Spitzer point-source catalog, and optical archive data, we identify counterparts for 75% of these X-ray sources. Their spatial distribution shows two major concentrations, the central cluster NGC 3324 and a partly embedded cluster in the southern rim of the HII region, but majority of X-ray sources constitute a rather homogeneously distributed population of young stars. Our color-magnitude diagram analysis suggests ages of ~1-2 Myr for the two clusters, whereas the distributed population shows a wider age range up to ~10 Myr. We also identify previously unknown companions to two of the three O-type members of NGC 3324 and detect diffuse X-ray emission in the region. Our results suggests that the observed region contains about 4000 young stars in total. The distributed population is probably part of the widely distributed population of ~ 1-10 Myr old stars, that was identified in the CCCP area. This implies that the global stellar configuration of the Carina nebula complex is a very extended stellar association, in which the (optically prominent) clusters contain only a minority of the stellar population.Comment: Accepted for publication in Astronomy & Astrophysics. A high quality preprint is available at http://www.usm.uni-muenchen.de/people/preibisch/publications.htm

Maximum weight cycle packing in directed graphs, with application to kidney exchange programs

Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration

The Landscape of Bounds for Binary Search Trees

Binary search trees (BSTs) with rotations can adapt to various kinds of structure in search sequences, achieving amortized access times substantially better than the Theta(log n) worst-case guarantee. Classical examples of structural properties include static optimality, sequential access, working set, key-independent optimality, and dynamic finger, all of which are now known to be achieved by the two famous online BST algorithms (Splay and Greedy). (...) In this paper, we introduce novel properties that explain the efficiency of sequences not captured by any of the previously known properties, and which provide new barriers to the dynamic optimality conjecture. We also establish connections between various properties, old and new. For instance, we show the following. (i) A tight bound of O(n log d) on the cost of Greedy for d-decomposable sequences. The result builds on the recent lazy finger result of Iacono and Langerman (SODA 2016). On the other hand, we show that lazy finger alone cannot explain the efficiency of pattern avoiding sequences even in some of the simplest cases. (ii) A hierarchy of bounds using multiple lazy fingers, addressing a recent question of Iacono and Langerman. (iii) The optimality of the Move-to-root heuristic in the key-independent setting introduced by Iacono (Algorithmica 2005). (iv) A new tool that allows combining any finite number of sound structural properties. As an application, we show an upper bound on the cost of a class of sequences that all known properties fail to capture. (v) The equivalence between two families of BST properties. The observation on which this connection is based was known before - we make it explicit, and apply it to classical BST properties. (...

Photon and neutron production as in-situ diagnostics of proton-boron fusion

Short-pulse, ultra high-intensity lasers have opened new regimes for studying fusion plasmas and creating novel ultra-short ion beams and neutron sources. Diagnosing the plasma in these experiments is important for optimizing the fusion yield but difficult due to the picosecond time scales, 10s of micron-cubed volumes and high densities. We propose to use the yields of photons and neutrons produced by parallel reactions involving the same reactants to diagnose the plasma conditions and predict the yields of specific reactions of interest. In this work, we focus on verifying the yield of the high-interest aneutronic proton-boron fusion reaction $^{11}{B}(p,2\alpha){}^4{He}$, which is difficult to measure directly due to the short stopping range of the produced $\alpha$s in most materials. We identify promising photon-producing reactions for this purpose and compute the ratios of the photon yield to the $\alpha$ yield as a function of plasma parameters. In beam fusion experiments, the ${}^{11}{C}$ yield is an easily-measurable observable to verify the $\alpha$ yield. In light of our results, improving and extending measurements of the cross sections for these parallel reactions are important steps to gaining greater control over these laser-driven fusion plasmas.Comment: 23 pages, 7 figures, revtex forma

Locally Chain-Parsable Languages

If a context-free language enjoys the local parsability property then, no matter how the source string is segmented, each segment can be parsed in- dependently, and an efficient parallel parsing algorithm becomes possible. The new class of locally chain-parsable languages (LCPL), included in deterministic context-free languages, is here defined by means of the chain-driven automa- ton and characterized by decidable properties of grammar derivations. Such au- tomaton decides to reduce or not a factor in a way purely driven by the terminal characters, thus extending the well-known concept of Input-Driven (ID) (visibly) pushdown machines. LCPL extend and improve the practically relevant operator- precedence languages (Floyd), which are known to strictly include the ID lan- guages, and for which a parallel-parser generator exists. Consistently with the classical results for ID, chain-compatible LCPL are closed under reversal and Boolean operations, and language inclusion is decidable

A transfer matrix approach to the enumeration of plane meanders

A closed plane meander of order $n$ is a closed self-avoiding curve intersecting an infinite line $2n$ times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on transfer matrix methods, for the enumeration of plane meanders. While the algorithm has exponential complexity, its rate of growth is much smaller than that of previous algorithms. The algorithm is easily modified to enumerate various systems of closed meanders, semi-meanders, open meanders and many other geometries.Comment: 13 pages, 9 eps figures, to appear in J. Phys.

Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified network for rate $r$ and \Copt(r) denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201

Hot dense capsule implosion cores produced by z-pinch dynamic hohlraum radiation

Hot dense capsule implosions driven by z-pinch x-rays have been measured for the first time. A ~220 eV dynamic hohlraum imploded 1.7-2.1 mm diameter gas-filled CH capsules which absorbed up to ~20 kJ of x-rays. Argon tracer atom spectra were used to measure the Te~ 1keV electron temperature and the ne ~ 1-4 x10^23 cm-3 electron density. Spectra from multiple directions provide core symmetry estimates. Computer simulations agree well with the peak compression values of Te, ne, and symmetry, indicating reasonable understanding of the hohlraum and implosion physics.Comment: submitted to Phys. Rev. Let