Nonextensive distributions of rotation periods and diameters of asteroids

Context. To investigate the distribution of rotation periods of asteroids from different regions of the Solar System and distribution of diameters of near-Earth asteroids (NEAs). Aims. Verify if nonextensive statistics satisfactorily describes the data. Methods. Light curve data was taken from Planetary Database System (PDS) with Rel $\ge 2$. Taxonomic class and region of the Solar System was also considered. Data of NEA were taken from Minor Planet Center. Results. The rotation periods of asteroids follow a $q$-Gaussian with $q=2.6$ regardless of taxonomy, diameter or region of the Solar System of the object. The distribution of rotation periods is influenced by observational bias. The diameters of NEAs are described by a $q$-exponential with $q=1.3$. According to this distribution, there are expected to be $994 \pm 30$ NEAs with diameters greater than 1 km.Comment: 5 pages, 4 figures; observational bias taken into account in the new versio

Swap Bribery

In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that the voter is asked to implement. Specifically, in our model the briber can change a voter's preference list by paying for a sequence of swaps of consecutive candidates. Each swap may have a different price; the price of a bribery is the sum of the prices of all swaps that it involves. We prove complexity results for this model, which we call swap bribery, for a broad class of election systems, including variants of approval and k-approval, Borda, Copeland, and maximin.Comment: 17 page

Hitting forbidden subgraphs in graphs of bounded treewidth

We study the complexity of a generic hitting problem H-Subgraph Hitting, where given a fixed pattern graph $H$ and an input graph $G$, the task is to find a set $X \subseteq V(G)$ of minimum size that hits all subgraphs of $G$ isomorphic to $H$. In the colorful variant of the problem, each vertex of $G$ is precolored with some color from $V(H)$ and we require to hit only $H$-subgraphs with matching colors. Standard techniques shows that for every fixed $H$, the problem is fixed-parameter tractable parameterized by the treewidth of $G$; however, it is not clear how exactly the running time should depend on treewidth. For the colorful variant, we demonstrate matching upper and lower bounds showing that the dependence of the running time on treewidth of $G$ is tightly governed by $\mu(H)$, the maximum size of a minimal vertex separator in $H$. That is, we show for every fixed $H$ that, on a graph of treewidth $t$, the colorful problem can be solved in time $2^{\mathcal{O}(t^{\mu(H)})}\cdot|V(G)|$, but cannot be solved in time $2^{o(t^{\mu(H)})}\cdot |V(G)|^{O(1)}$, assuming the Exponential Time Hypothesis (ETH). Furthermore, we give some preliminary results showing that, in the absence of colors, the parameterized complexity landscape of H-Subgraph Hitting is much richer.Comment: A full version of a paper presented at MFCS 201

Finding and counting vertex-colored subtrees

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors $M$. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis et al., we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.Comment: Conference version in International Symposium on Mathematical Foundations of Computer Science (MFCS), Brno : Czech Republic (2010) Journal Version in Algorithmic

A Fast Counting Method for 6-motifs with Low Connectivity

A $k$-motif (or graphlet) is a subgraph on $k$ nodes in a graph or network. Counting of motifs in complex networks has been a well-studied problem in network analysis of various real-word graphs arising from the study of social networks and bioinformatics. In particular, the triangle counting problem has received much attention due to its significance in understanding the behavior of social networks. Similarly, subgraphs with more than 3 nodes have received much attention recently. While there have been successful methods developed on this problem, most of the existing algorithms are not scalable to large networks with millions of nodes and edges. The main contribution of this paper is a preliminary study that genaralizes the exact counting algorithm provided by Pinar, Seshadhri and Vishal to a collection of 6-motifs. This method uses the counts of motifs with smaller size to obtain the counts of 6-motifs with low connecivity, that is, containing a cut-vertex or a cut-edge. Therefore, it circumvents the combinatorial explosion that naturally arises when counting subgraphs in large networks

Assessing the impact of diagenesis on foraminiferal geochemistry from a low latitude, shallow-water drift deposit

Due to their large heat and moisture storage capabilities, the tropics are fundamental in modulating both regional and global climate. Furthermore, their thermal response during past extreme warming periods, such as super interglacials, is not fully resolved. In this regard, we present high-resolution (analytical) foraminiferal geochemical (δ18O and Mg/Ca) records for the last 1800 kyr from the shallow (487 m) Inner Sea drift deposits of the Maldives archipelago in the equatorial Indian Ocean. Considering the diagenetic susceptibility of these proxies, in carbonate-rich environments, we assess the integrity of a suite of commonly used planktonic and benthic foraminifera geochemical datasets (Globigerinoides ruber (white), Globigerinita glutinata (with bulla), Pulleniatina obliquiloculata (with cortex) and Cibicides mabahethi) and their use for future paleoceanographic reconstructions. Using a combination of spot Secondary Ion Mass Spectrometer, Electron Probe Micro-Analyzer and Scanning Electron Microscope image data, it is evident that authigenic overgrowths are present on both the external and internal test (shell) surfaces, yet the degree down-core as well as the associated bias is shown to be variable across the investigated species and proxies. Given the elevated authigenic overgrowth Mg/Ca (∼12–22 mmol/mol) and δ18O values (closer to the benthic isotopic compositions) the whole-test planktonic G. ruber (w) geochemical records are notably impacted beyond ∼627.4 ka (24.7 mcd). Yet, considering the setting (i.e. bottom water location) for overgrowth formation, the benthic foraminifera δ18O record is markedly less impacted with only minor diagenetic bias beyond ∼790.0 ka (28.7 mcd). Even though only the top of the G. ruber (w) and C. mabahethi records (whole-test data) would be suitable for paleo-reconstructions of absolute values (i.e. sea surface temperature, salinity, seawater δ18O), the long-term cycles, while dampened, appear to be preserved. Furthermore, planktonic species with thicker-tests (i.e. P. obliquiloculata (w/c)) might be better suited, in comparison to thinner-test counter-parts (i.e. G. glutinata (w/b), G. ruber (w)), for traditional whole- test geochemical studies in shallow, carbonate-rich environments. A thicker test equates to a smaller overall bias from the authigenic overgrowth. Overall, if the diagenetic impact is constrained, as done in this study, these types of diagenetically altered geochemical records can still significantly contribute to studies relating to past tropical seawater temperatures, latitudinal scale ocean current shifts and South Asian Monsoon dynamics