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

A Static Optimality Transformation with Applications to Planar Point Location

Over the last decade, there have been several data structures that, given a planar subdivision and a probability distribution over the plane, provide a way for answering point location queries that is fine-tuned for the distribution. All these methods suffer from the requirement that the query distribution must be known in advance. We present a new data structure for point location queries in planar triangulations. Our structure is asymptotically as fast as the optimal structures, but it requires no prior information about the queries. This is a 2D analogue of the jump from Knuth's optimum binary search trees (discovered in 1971) to the splay trees of Sleator and Tarjan in 1985. While the former need to know the query distribution, the latter are statically optimal. This means that we can adapt to the query sequence and achieve the same asymptotic performance as an optimum static structure, without needing any additional information.Comment: 13 pages, 1 figure, a preliminary version appeared at SoCG 201

Fractal dimension of domain walls in two-dimensional Ising spin glasses

We study domain walls in 2d Ising spin glasses in terms of a minimum-weight path problem. Using this approach, large systems can be treated exactly. Our focus is on the fractal dimension $d_f$ of domain walls, which describes via \simL^{d_f} the growth of the average domain-wall length with %% systems size $L\times L$. %% 20.07.07 OM %% Exploring systems up to L=320 we yield $d_f=1.274(2)$ for the case of Gaussian disorder, i.e. a much higher accuracy compared to previous studies. For the case of bimodal disorder, where many equivalent domain walls exist due to the degeneracy of this model, we obtain a true lower bound $d_f=1.095(2)$ and a (lower) estimate $d_f=1.395(3)$ as upper bound. Furthermore, we study the distributions of the domain-wall lengths. Their scaling with system size can be described also only by the exponent $d_f$, i.e. the distributions are monofractal. Finally, we investigate the growth of the domain-wall width with system size (``roughness'') and find a linear behavior.Comment: 8 pages, 8 figures, submitted to Phys. Rev. B; v2: shortened versio

Computing Real Roots of Real Polynomials -- An Efficient Method Based on Descartes' Rule of Signs and Newton Iteration

Computing the real roots of a polynomial is a fundamental problem of computational algebra. We describe a variant of the Descartes method that isolates the real roots of any real square-free polynomial given through coefficient oracles. A coefficient oracle provides arbitrarily good approximations of the coefficients. The bit complexity of the algorithm matches the complexity of the best algorithm known, and the algorithm is simpler than this algorithm. The algorithm derives its speed from the combination of Descartes method with Newton iteration. Our algorithm can also be used to further refine the isolating intervals to an arbitrary small size. The complexity of root refinement is nearly optimal

Approximating the {Nash} Social Welfare with Budget-Additive Valuations

We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and $1/\varepsilon$. Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties. Although the existence of equilibria is not guaranteed, we show that the market instances arising from the Nash social welfare problem always have an equilibrium. Further, we show that the set of equilibria is not convex, answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an approximate equilibrium, a result that may be of independent interest

Critical behavior of the Random-Field Ising Magnet with long range correlated disorder

We study the correlated-disorder driven zero-temperature phase transition of the Random-Field Ising Magnet using exact numerical ground-state calculations for cubic lattices. We consider correlations of the quenched disorder decaying proportional to r^a, where r is the distance between two lattice sites and a<0. To obtain exact ground states, we use a well established mapping to the graph-theoretical maximum-flow problem, which allows us to study large system sizes of more than two million spins. We use finite-size scaling analyses for values a={-1,-2,-3,-7} to calculate the critical point and the critical exponents characterizing the behavior of the specific heat, magnetization, susceptibility and of the correlation length close to the critical point. We find basically the same critical behavior as for the RFIM with delta-correlated disorder, except for the finite-size exponent of the susceptibility and for the case a=-1, where the results are also compatible with a phase transition at infinitesimal disorder strength. A summary of this work can be found at the papercore database at www.papercore.org.Comment: 9 pages, 13 figure

Local investigation of femtosecond laser induced dynamics of water nanoclusters on Cu(111)

We explore the dynamics of low temperature interfacial water nanoclusters on Cu(111) by femtosecond-laser excitation, scanning tunneling microscopy and density functional theory. Laser illumination can be used to induce single molecules to diffuse within water clusters and across the surface, breaking and reforming hydrogen bonds. A linear diffusion probability with laser fluence is observed up to 0.6 J/m2 and we suggest that diffusion is initiated by hot electron attachment and detachment processes. The density functional calculations shed light on the detailed molecular mechanism for water diffusion that is determined by the local structure of the water clusters

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. (...

One-variable word equations in linear time

In this paper we consider word equations with one variable (and arbitrary many appearances of it). A recent technique of recompression, which is applicable to general word equations, is shown to be suitable also in this case. While in general case it is non-deterministic, it determinises in case of one variable and the obtained running time is O(n + #_X log n), where #_X is the number of appearances of the variable in the equation. This matches the previously-best algorithm due to D\k{a}browski and Plandowski. Then, using a couple of heuristics as well as more detailed time analysis the running time is lowered to O(n) in RAM model. Unfortunately no new properties of solutions are shown.Comment: submitted to a journal, general overhaul over the previous versio