Provenance Circuits for Trees and Treelike Instances (Extended Version)

Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such as counting query results [3] or performing query evaluation on probabilistic trees [10]. These are two examples of the more general problem of computing augmented query output, that is referred to as provenance. This article presents a provenance framework for trees and treelike instances, by describing a linear-time construction of a circuit provenance representation for MSO queries. We show how this provenance can be connected to the usual definitions of semiring provenance on relational instances [20], even though we compute it in an unusual way, using tree automata; we do so via intrinsic definitions of provenance for general semirings, independent of the operational details of query evaluation. We show applications of this provenance to capture existing counting and probabilistic results on trees and treelike instances, and give novel consequences for probability evaluation.Comment: 48 pages. Presented at ICALP'1

Structurally Parameterized d-Scattered Set

In $d$-Scattered Set we are given an (edge-weighted) graph and are asked to select at least $k$ vertices, so that the distance between any pair is at least $d$, thus generalizing Independent Set. We provide upper and lower bounds on the complexity of this problem with respect to various standard graph parameters. In particular, we show the following: - For any $d\ge2$, an $O^*(d^{\textrm{tw}})$-time algorithm, where $\textrm{tw}$ is the treewidth of the input graph. - A tight SETH-based lower bound matching this algorithm's performance. These generalize known results for Independent Set. - $d$-Scattered Set is W[1]-hard parameterized by vertex cover (for edge-weighted graphs), or feedback vertex set (for unweighted graphs), even if $k$ is an additional parameter. - A single-exponential algorithm parameterized by vertex cover for unweighted graphs, complementing the above-mentioned hardness. - A $2^{O(\textrm{td}^2)}$-time algorithm parameterized by tree-depth ($\textrm{td}$), as well as a matching ETH-based lower bound, both for unweighted graphs. We complement these mostly negative results by providing an FPT approximation scheme parameterized by treewidth. In particular, we give an algorithm which, for any error parameter $\epsilon > 0$, runs in time $O^*((\textrm{tw}/\epsilon)^{O(\textrm{tw})})$ and returns a $d/(1+\epsilon)$-scattered set of size $k$, if a $d$-scattered set of the same size exists

Recognizing hyperelliptic graphs in polynomial time

Recently, a new set of multigraph parameters was defined, called "gonalities". Gonality bears some similarity to treewidth, and is a relevant graph parameter for problems in number theory and multigraph algorithms. Multigraphs of gonality 1 are trees. We consider so-called "hyperelliptic graphs" (multigraphs of gonality 2) and provide a safe and complete sets of reduction rules for such multigraphs, showing that for three of the flavors of gonality, we can recognize hyperelliptic graphs in O(n log n+m) time, where n is the number of vertices and m the number of edges of the multigraph.Comment: 33 pages, 8 figure

Microstructure and mechanical properties of ductile aluminium alloy manufactured by recycled materials

The present paper introduces the microstructure and mechanical properties of the Al-Mg- Si-Mn alloy made by recycled materials, in which the impurity levels of iron are mainly concerned. It is found that the increased Fe content reduces the ductility and yield strength but slightly increases the UTS of the diecast alloy. The tolerable Fe content is 0.45wt.%, at which the recycled alloys are still able to produce castings with the mechanical properties of yield strength over 140MPa, UTS over 280MPa and elongation over 15%.The Fe content is steadily accumulated in the alloy with the increase of recycle times. However, after 13 cycles, the recycled alloys are still able to produce ductile alloys with satisfied mechanical properties.The TSB (UK

Exploiting the Symmetry of the Resonator Mode to Enhance PELDOR Sensitivity.

Pulsed electron paramagnetic resonance (EPR) spectroscopy using microwaves at two frequencies can be employed to measure distances between pairs of paramagnets separated by up to 10 nm. The method, combined with site-directed mutagenesis, has become increasingly popular in structural biology for both its selectivity and capability of providing information not accessible through more standard methods such as nuclear magnetic resonance and X-ray crystallography. Despite these advantages, EPR distance measurements suffer from poor sensitivity. One contributing factor is technical: since 65 MHz typically separates the pump and detection frequencies, they cannot both be located at the center of the pseudo-Lorentzian microwave resonance of a single-mode resonator. To maximize the inversion efficiency, the pump pulse is usually placed at the center of the resonance, while the observer frequency is placed in the wing, with consequent reduction in sensitivity. Here, we consider an alternative configuration: by spacing pump and observer frequencies symmetrically with respect to the microwave resonance and by increasing the quality factor, valuable improvement in the signal-to-noise ratio can be obtained

Polynomial Kernels for Weighted Problems

Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial kernelizations for Subset Sum and Knapsack when parameterized by the number $n$ of items. We answer both questions affirmatively by using an algorithm for compressing numbers due to Frank and Tardos (Combinatorica 1987). This result had been first used by Marx and V\'egh (ICALP 2013) in the context of kernelization. We further illustrate its applicability by giving polynomial kernels also for weighted versions of several well-studied parameterized problems. Furthermore, when parameterized by the different item sizes we obtain a polynomial kernelization for Subset Sum and an exponential kernelization for Knapsack. Finally, we also obtain kernelization results for polynomial integer programs

An FPT 2-Approximation for Tree-Cut Decomposition

The tree-cut width of a graph is a graph parameter defined by Wollan [J. Comb. Theory, Ser. B, 110:47-66, 2015] with the help of tree-cut decompositions. In certain cases, tree-cut width appears to be more adequate than treewidth as an invariant that, when bounded, can accelerate the resolution of intractable problems. While designing algorithms for problems with bounded tree-cut width, it is important to have a parametrically tractable way to compute the exact value of this parameter or, at least, some constant approximation of it. In this paper we give a parameterized 2-approximation algorithm for the computation of tree-cut width; for an input $n$-vertex graph $G$ and an integer $w$, our algorithm either confirms that the tree-cut width of $G$ is more than $w$ or returns a tree-cut decomposition of $G$ certifying that its tree-cut width is at most $2w$, in time $2^{O(w^2\log w)} \cdot n^2$. Prior to this work, no constructive parameterized algorithms, even approximated ones, existed for computing the tree-cut width of a graph. As a consequence of the Graph Minors series by Robertson and Seymour, only the existence of a decision algorithm was known.Comment: 17 pages, 3 figure

Day use of nest sites by the Tasmanian bettong (Bettongia gaimardz)

A bettong (Bettongia gaimardz) population in the Tom Gibson Reserve, northern Tasmania, was studied for 16 months by trapping and radio-tracking as part of a long-term study of fencing for control of wallabies and the effect on non-target species. Of particular interest was the bettongs' usage of retained bush areas in cultivated paddocks, and the distribution of nest sites. Sixteen of the 26 bettongs trapped were radio-tracked weekly to their daytime nest sites for intervals of nine to 57 weeks. Bettongs occupied between six and 43 different nests; in all, 305 different nests were located. On 23% of occasions, adult females shared nest sites with furred young at heel; however, adults rarely shared a nest. Breeding apparently occurred at any time of the year and all adult females had a pouch young every time they were examined. Estimates based on minimum convex polygon position of nest sites averaged 14.5 ha for females and 27.7 ha for males. All nest sites were accessible ftom low understorey corridors; bettongs did not appear to cross open pasture to access apparently similar habitat to that being used. One young male travelled along a bushland corridor for over 4 km before radio contact was lost

Distributed Approximation of Maximum Independent Set and Maximum Matching

We present a simple distributed $\Delta$-approximation algorithm for maximum weight independent set (MaxIS) in the $\mathsf{CONGEST}$ model which completes in $O(\texttt{MIS}(G)\cdot \log W)$ rounds, where $\Delta$ is the maximum degree, $\texttt{MIS}(G)$ is the number of rounds needed to compute a maximal independent set (MIS) on $G$, and $W$ is the maximum weight of a node. %Whether our algorithm is randomized or deterministic depends on the \texttt{MIS} algorithm used as a black-box. Plugging in the best known algorithm for MIS gives a randomized solution in $O(\log n \log W)$ rounds, where $n$ is the number of nodes. We also present a deterministic $O(\Delta +\log^* n)$-round algorithm based on coloring. We then show how to use our MaxIS approximation algorithms to compute a $2$-approximation for maximum weight matching without incurring any additional round penalty in the $\mathsf{CONGEST}$ model. We use a known reduction for simulating algorithms on the line graph while incurring congestion, but we show our algorithm is part of a broad family of \emph{local aggregation algorithms} for which we describe a mechanism that allows the simulation to run in the $\mathsf{CONGEST}$ model without an additional overhead. Next, we show that for maximum weight matching, relaxing the approximation factor to ($2+\varepsilon$) allows us to devise a distributed algorithm requiring $O(\frac{\log \Delta}{\log\log\Delta})$ rounds for any constant $\varepsilon>0$. For the unweighted case, we can even obtain a $(1+\varepsilon)$-approximation in this number of rounds. These algorithms are the first to achieve the provably optimal round complexity with respect to dependency on $\Delta$

A Market Shaping Approach for the Biopharmaceutical Industry: Governing Innovation Towards the Public Interest

Enhancing research and development and ensuring equitable pricing and access to cutting-edge treatments are both vital to a biopharmaceutical innovation system that works in the public interest. However, despite delivering numerous therapeutic advances, the existing system suffers from major problems: a lack of directionality to meet key needs, inefficient collaboration, high prices that fail to reflect the public contribution, and an overly-financialized business model