Edge Shear Flows and Particle Transport near the Density Limit in the HL-2A Tokamak

Edge shear flow and its effect on regulating turbulent transport have long been suspected to play an important role in plasmas operating near the Greenwald density limit $n_G$. In this study, equilibrium profiles as well as the turbulent particle flux and Reynolds stress across the separatrix in the HL-2A tokamak are examined as $n_G$ is approached in ohmic L-mode discharges. As the normalized line-averaged density $\bar{n}_e/n_G$ is raised, the shearing rate of the mean poloidal flow $\omega_{\rm sh}$ drops, and the turbulent drive for the low-frequency zonal flow (the Reynolds power $\mathcal{P}_{Re}$) collapses. Correspondingly, the turbulent particle transport increases drastically with increasing collision rates. The geodesic acoustic modes (GAMs) gain more energy from the ambient turbulence at higher densities, but have smaller shearing rate than low-frequency zonal flows. The increased density also introduces decreased adiabaticity which not only enhances the particle transport but is also related to a reduction in the eddy-tilting and the Reynolds power. Both effects may lead to the cooling of edge plasmas and therefore the onset of MHD instabilities that limit the plasma density

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

Multidimensional Binary Vector Assignment problem: standard, structural and above guarantee parameterizations

In this article we focus on the parameterized complexity of the Multidimensional Binary Vector Assignment problem (called \BVA). An input of this problem is defined by $m$ disjoint sets $V^1, V^2, \dots, V^m$, each composed of $n$ binary vectors of size $p$. An output is a set of $n$ disjoint $m$-tuples of vectors, where each $m$-tuple is obtained by picking one vector from each set $V^i$. To each $m$-tuple we associate a $p$ dimensional vector by applying the bit-wise AND operation on the $m$ vectors of the tuple. The objective is to minimize the total number of zeros in these $n$ vectors. mBVA can be seen as a variant of multidimensional matching where hyperedges are implicitly locally encoded via labels attached to vertices, but was originally introduced in the context of integrated circuit manufacturing. We provide for this problem FPT algorithms and negative results ($ETH$-based results, $W$[2]-hardness and a kernel lower bound) according to several parameters: the standard parameter $k$ i.e. the total number of zeros), as well as two parameters above some guaranteed values.Comment: 16 pages, 6 figure

Some Curvature Problems in Semi-Riemannian Geometry

In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the construction of Lorentzian metrics which satisfy the dominant energy condition.Comment: 25 pages, LaTeX, 4 figure

Infrared Emission from Supernova Remnants: Formation and Destruction of Dust

We review the observations of dust emission in supernova rem- nants (SNRs) and supernovae (SNe). Theoretical calculations suggest that SNe, particularly core-collapse, should make significant quantities of dust, perhaps as much as a solar mass. Observations of extragalactic SNe have yet to find anywhere near this amount, but this may be the result of observa- tional limitations. SN 1987A, in the process of transitioning from a SN to an SNR, does show signs of a significant amount of dust forming in its ejecta, but whether this dust will survive the passage of the reverse shock to be injected into the ISM is unknown. IR observations of SNRs have not turned up significant quantities of dust, and the dust that is observed is generally swept-up by the forward shock, rather than created in the ejecta. Because the shock waves also destroy dust in the ISM, we explore the question of whether SNe might be net destroyers, rather than net creators of dust in the universe.Comment: Published in the Springer Handbook of Supernova

Fast Algorithms for Join Operations on Tree Decompositions

Treewidth is a measure of how tree-like a graph is. It has many important algorithmic applications because many NP-hard problems on general graphs become tractable when restricted to graphs of bounded treewidth. Algorithms for problems on graphs of bounded treewidth mostly are dynamic programming algorithms using the structure of a tree decomposition of the graph. The bottleneck in the worst-case run time of these algorithms often is the computations for the so called join nodes in the associated nice tree decomposition. In this paper, we review two different approaches that have appeared in the literature about computations for the join nodes: one using fast zeta and M\"obius transforms and one using fast Fourier transforms. We combine these approaches to obtain new, faster algorithms for a broad class of vertex subset problems known as the [\sigma,\rho]-domination problems. Our main result is that we show how to solve [\sigma,\rho]-domination problems in $O(s^{t+2} t n^2 (t\log(s)+\log(n)))$ arithmetic operations. Here, t is the treewidth, s is the (fixed) number of states required to represent partial solutions of the specific [\sigma,\rho]-domination problem, and n is the number of vertices in the graph. This reduces the polynomial factors involved compared to the previously best time bound (van Rooij, Bodlaender, Rossmanith, ESA 2009) of $O( s^{t+2} (st)^{2(s-2)} n^3 )$ arithmetic operations. In particular, this removes the dependence of the degree of the polynomial on the fixed number of states~$s$.Comment: An earlier version appeared in "Treewidth, Kernels, and Algorithms. Essays Dedicated to Hans L. Bodlaender on the Occasion of His 60th Birthday" LNCS 1216

The Minimum Shared Edges Problem on Grid-like Graphs

We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can be decided on bounded (i.e. finite) grids in linear time when both dimensions are either small or large compared to the number $p$ of paths. On the contrary, we show that MSE remains NP-hard on subgraphs of bounded grids. Finally, we study MSE from a parametrised complexity point of view. It is known that MSE is fixed-parameter tractable with respect to the number $p$ of paths. We show that, under standard complexity-theoretical assumptions, the problem parametrised by the combined parameter $k$, $p$, maximum degree, diameter, and treewidth does not admit a polynomial-size problem kernel, even when restricted to planar graphs

A realistic assessment of methods for extracting gene/protein interactions from free text

Background: The automated extraction of gene and/or protein interactions from the literature is one of the most important targets of biomedical text mining research. In this paper we present a realistic evaluation of gene/protein interaction mining relevant to potential non-specialist users. Hence we have specifically avoided methods that are complex to install or require reimplementation, and we coupled our chosen extraction methods with a state-of-the-art biomedical named entity tagger. Results: Our results show: that performance across different evaluation corpora is extremely variable; that the use of tagged (as opposed to gold standard) gene and protein names has a significant impact on performance, with a drop in F-score of over 20 percentage points being commonplace; and that a simple keyword-based benchmark algorithm when coupled with a named entity tagger outperforms two of the tools most widely used to extract gene/protein interactions. Conclusion: In terms of availability, ease of use and performance, the potential non-specialist user community interested in automatically extracting gene and/or protein interactions from free text is poorly served by current tools and systems. The public release of extraction tools that are easy to install and use, and that achieve state-of-art levels of performance should be treated as a high priority by the biomedical text mining community

Theoretical and experimental approaches to understand morphogen gradients

Morphogen gradients, which specify different fates for cells in a direct concentration-dependent manner, are a highly influential framework in which pattern formation processes in developmental biology can be characterized. A common analysis approach is combining experimental and theoretical strategies, thereby fostering relevant data on the dynamics and transduction of gradients. The mechanisms of morphogen transport and conversion from graded information to binary responses are some of the topics on which these combined strategies have shed light. Herein, we review these data, emphasizing, on the one hand, how theoretical approaches have been helpful and, on the other hand, how these have been combined with experimental strategies. In addition, we discuss those cases in which gradient formation and gradient interpretation at the molecular and/or cellular level may influence each other within a mutual feedback loop. To understand this interplay and the features it yields, it becomes essential to take system-level approaches that combine experimental and theoretical strategies