Greedy Algorithms for Steiner Forest

In the Steiner Forest problem, we are given terminal pairs $\{s_i, t_i\}$, and need to find the cheapest subgraph which connects each of the terminal pairs together. In 1991, Agrawal, Klein, and Ravi, and Goemans and Williamson gave primal-dual constant-factor approximation algorithms for this problem; until now, the only constant-factor approximations we know are via linear programming relaxations. We consider the following greedy algorithm: Given terminal pairs in a metric space, call a terminal "active" if its distance to its partner is non-zero. Pick the two closest active terminals (say $s_i, t_j$), set the distance between them to zero, and buy a path connecting them. Recompute the metric, and repeat. Our main result is that this algorithm is a constant-factor approximation. We also use this algorithm to give new, simpler constructions of cost-sharing schemes for Steiner forest. In particular, the first "group-strict" cost-shares for this problem implies a very simple combinatorial sampling-based algorithm for stochastic Steiner forest

Multisetting Bell-type inequalities for detecting genuine tripartite entanglement

In a recent paper, Bancal et al. put forward the concept of device-independent witnesses of genuine multipartite entanglement. These witnesses are capable of verifying genuine multipartite entanglement produced in a lab without resorting to any knowledge of the dimension of the state space or of the specific form of the measurement operators. As a by-product they found a three-party three-setting Bell inequality which enables to detect genuine tripartite entanglement in a noisy 3-qubit Greenberger-Horne-Zeilinger (GHZ) state for visibilities as low as 2/3 in a device-independent way. In this paper, we generalize this inequality to an arbitrary number of settings, demonstrating a threshold visibility of 2/pi~0.6366 for number of settings going to infinity. We also present a pseudo-telepathy Bell inequality achieving the same threshold value. We argue that our device-independent witnesses are optimal in the sense that the above value cannot be beaten with three-party-correlation Bell inequalities.Comment: 7 page

A közoktatási típusú sportiskolai kerettantervek tantervelméleti vonatkozásai

A Kormány 202/2007. (VII. 31.) rendelete részeként kihirdetésre kerülő Nemzeti alaptanterv 2007. évi változatának egyik pozitív eleme a közoktatási típusú sportiskolai nevelés és oktatás megjelenése volt. A rendelet értelmében számos iskola láthat el sportiskolai feladatot meghatározott sportágak körében, a helyi közoktatási típusú sportiskolai kerettanterve alapján. Ezeknek az iskoláknak biztosítaniuk kell a testnevelés tantárgy emelt szintű oktatását az elsőtől a tizenkettedik osztályig. A tanintézetek több sportág közül választhatnak a helyi sajátosságaiknak, létesítményeiknek, igényeiknek megfelelően. Az iskolák órarendbe iktatva, egy vagy több kiválasztott sportágra szakosodva, sportági képzést végezhetnek az alkalmazásukban lévő szakedzőkkel

Evidence for fresh frost layer on the bare nucleus of comet Hale--Bopp at 32 AU distance

Here we report that the activity of comet Hale--Bopp ceased between late 2007 and March, 2009, at about 28 AU distance from the Sun. At that time the comet resided at a distance from the Sun that exceeded the freeze-out distance of regular comets by an order of magnitude. A Herschel Space Observatory PACS scan was taken in mid-2010, in the already inactive state of the nucleus. The albedo has been found to be surprisingly large (8.1$\pm$0.9%{}), which exceeds the value known for any other comets. With re-reduction of archive HST images from 1995 and 1996, we confirm that the pre-perihelion albedo resembled that of an ordinary comet, and was smaller by a factor of two than the post-activity albedo. Our further observations with the Very Large Telescope (VLT) also confirmed that the albedo increased significantly by the end of the activity. We explain these observations by proposing gravitational redeposition of icy grains towards the end of the activity. This is plausible for such a massive body in a cold environment, where gas velocity is lowered to the range of the escape velocity. These observations also show that giant comets are not just the upscaled versions of the comets we know but can be affected by processes that are yet to be fully identified.Comment: 7 pages, 6 figures, accepted for publication in Ap

Molecular dynamics simulations of the water adsorption around malonic acid aerosol models

Water nucleation around a malonic acid aggregate has been studied by means of molecular dynamics simulations in the temperature and pressure range relevant for atmospheric conditions. Systems of different water contents have been considered and a large number of simulations have allowed us to determine the phase diagram of the corresponding binary malonic acid–water systems. Two phases have been evidenced in the phase diagrams corresponding either to water adsorption on a large malonic acid grain at low temperatures, or to the formation of a liquid-like mixed aggregate of the two types of molecules, at higher temperatures. Finally, the comparison between the phase diagrams simulated for malonic acid–water and oxalic acid–water mixtures emphasizes the influence of the O : C ratio on the hydrophilic behavior of the aerosol, and thus on its ability to act as a cloud condensation nucleus, in accordance with recent experimental conclusions

Antitumor effect of lysine-isopeptides

Isopeptides (ε-peptides) of lysine, with a given Mw and low polydispersity (10–400 units), were synthesized to study the relationship between their chemical structure and biological effect. The designed compounds were of high purity, low polydispersity and high stereochemical purity. The effect of the compounds was tested on a human erythroleukemia cell line (K-562) and on four transplantable mouse tumors (L1210 lymphoid leukemia, P38 macrophage derived tumor, Ehrlich ascites carcinoma, Lewis lung tumor /LLT/). In case of the L1210 and P388 tumors and the Ehrlich carcinoma, survival of the animals was used as an indicator of the effect. In case of the Lewis lung tumor, the number and size of metastases in the lung and/or liver of treated and untreated mice were used as indicators. The polymers of polymerisation degree 80–120 (Mw 10.2–15.4 KD) showed the strongest antiproliferative effect both on K562 cells and the tumors growing in vivo. This effect was manifest with a significantly higher survival rate as compared to the control (L1210, P38, Ehrlich ascites), furthermore, by a decrease in the number and size of liver and lung metastases (LLT)

Pushing the limits, episode 2: K2 observations of extragalactic RR Lyrae stars in the dwarf galaxy Leo IV

We present the first observations of extragalactic pulsating stars in the K2 ecliptic survey of the Kepler space telescope. Variability of all three RR Lyrae stars in the dwarf spheroidal galaxy Leo IV were successfully detected, at a brightness of Kp~21.5 mag, from data collected during Campaign 1. We identified one modulated star and another likely Blazhko candidate with periods of 29.8+-0.9 d and more than 80 d, respectively. EPIC 210282473 represents the first star beyond the Magellanic Clouds for which the Blazhko period and cycle-to-cycle variations in the modulation were unambiguously measured.The photometric [Fe/H] indices of the stars agree with earlier results that Leo IV is a very metal-poor galaxy. Two out of three stars blend with brighter background galaxies in the K2 frames. We demonstrate that image subtraction can be reliably used to extract photometry from faint confused sources that will be crucial not only for the K2 mission but for future space photometric missions as well.Comment: 8 pages, 6 figures, accepted for publication in the Astrophysical Journal. Light curves can be downloaded from http://konkoly.hu/KIK/data.htm