Computing maximum cliques in B2B_2-EPG graphs

EPG graphs, introduced by Golumbic et al. in 2009, are edge-intersection graphs of paths on an orthogonal grid. The class $B_k$-EPG is the subclass of EPG graphs where the path on the grid associated to each vertex has at most $k$ bends. Epstein et al. showed in 2013 that computing a maximum clique in $B_1$-EPG graphs is polynomial. As remarked in [Heldt et al., 2014], when the number of bends is at least $4$, the class contains $2$-interval graphs for which computing a maximum clique is an NP-hard problem. The complexity status of the Maximum Clique problem remains open for $B_2$ and $B_3$-EPG graphs. In this paper, we show that we can compute a maximum clique in polynomial time in $B_2$-EPG graphs given a representation of the graph. Moreover, we show that a simple counting argument provides a ${2(k+1)}$-approximation for the coloring problem on $B_k$-EPG graphs without knowing the representation of the graph. It generalizes a result of [Epstein et al, 2013] on $B_1$-EPG graphs (where the representation was needed)

On the Brightness and Waiting-time Distributions of a Type III Radio Storm observed by STEREO/WAVES

Type III solar radio storms, observed at frequencies below approximately 16 MHz by space borne radio experiments, correspond to the quasi-continuous, bursty emission of electron beams onto open field lines above active regions. The mechanisms by which a storm can persist in some cases for more than a solar rotation whilst exhibiting considerable radio activity are poorly understood. To address this issue, the statistical properties of a type III storm observed by the STEREO/WAVES radio experiment are presented, examining both the brightness distribution and (for the first time) the waiting-time distribution. Single power law behavior is observed in the number distribution as a function of brightness; the power law index is approximately 2.1 and is largely independent of frequency. The waiting-time distribution is found to be consistent with a piecewise-constant Poisson process. This indicates that during the storm individual type III bursts occur independently and suggests that the storm dynamics are consistent with avalanche type behavior in the underlying active region.Comment: 14 pages, 4 figures, 1 table. Accepted for publication in Astrophysical Journal Letter

Bridge-Depth Characterizes Which Structural Parameterizations of Vertex Cover Admit a Polynomial Kernel

We study the kernelization complexity of structural parameterizations of the Vertex Cover problem. Here, the goal is to find a polynomial-time preprocessing algorithm that can reduce any instance (G,k) of the Vertex Cover problem to an equivalent one, whose size is polynomial in the size of a pre-determined complexity parameter of G. A long line of previous research deals with parameterizations based on the number of vertex deletions needed to reduce G to a member of a simple graph class ?, such as forests, graphs of bounded tree-depth, and graphs of maximum degree two. We set out to find the most general graph classes ? for which Vertex Cover parameterized by the vertex-deletion distance of the input graph to ?, admits a polynomial kernelization. We give a complete characterization of the minor-closed graph families ? for which such a kernelization exists. We introduce a new graph parameter called bridge-depth, and prove that a polynomial kernelization exists if and only if ? has bounded bridge-depth. The proof is based on an interesting connection between bridge-depth and the size of minimal blocking sets in graphs, which are vertex sets whose removal decreases the independence number

Kernelization for Graph Packing Problems via Rainbow Matching

We introduce a new kernelization tool, called rainbow matching technique, that is appropriate for the design of polynomial kernels for packing problems. Our technique capitalizes on the powerful combinatorial results of [Graf, Harris, Haxell, SODA 2021]. We apply the rainbow matching technique on two (di)graph packing problems, namely the Triangle-Packing in Tournament problem (\TPT), where we ask for a directed triangle packing in a tournament, and the Induced 2-Path-Packing (\IPP) where we ask for a packing of $k$ induced paths of length two in a graph. The existence of a sub-quadratic kernels for these problems was proven for the first time in [Fomin, Le, Lokshtanov, Saurabh, Thomass\'e, Zehavi. ACM Trans. Algorithms, 2019], where they gave a kernel of $\mathcal{O}(k^{3/2})$ vertices and $\mathcal{O}(k^{5/3})$ vertices respectively. In the same paper it was questioned whether these bounds can be (optimally) improved to linear ones. Motivated by this question, we apply the rainbow matching technique and prove that \TPT admits an (almost linear) kernel of $k^{1+\frac{\mathcal{O}(1)}{\sqrt{\log{k}}}}$ vertices and that \IPP admits kernel of $\mathcal{O}(k)$ vertices

Width of Radio-Loud and Radio-Quiet CMEs

In the present paper we report on the difference in angular sizes between radio-loud and radio-quiet CMEs. For this purpose we compiled these two samples of events using Wind/WAVES and SOHO/LASCO observations obtained during 1996-2005. It is shown that the radio-loud CMEs are almost two times wider than the radio-quiet CMEs (considering expanding parts of CMEs). Furthermore we show that the radio-quiet CMEs have a narrow expanding bright part with a large extended diffusive structure. These results were obtained by measuring the CME widths in three different ways.Comment: Solar Physic, in pres

In-flight calibration of STEREO-B/WAVES antenna system

The STEREO/WAVES (SWAVES) experiment on board the two STEREO spacecraft (Solar Terrestrial Relations Observatory) launched on 25 October 2006 is dedicated to the measurement of the radio spectrum at frequencies between a few kilohertz and 16 MHz. The SWAVES antenna system consists of 6 m long orthogonal monopoles designed to measure the electric component of the radio waves. With this configuration direction finding of radio sources and polarimetry (analysis of the polarization state) of incident radio waves is possible. For the evaluation of the SWAVES data the receiving properties of the antennas, distorted by the radiation coupling with the spacecraft body and other onboard devices, have to be known accurately. In the present context, these properties are described by the antenna effective length vectors. We present the results of an in-flight calibration of the SWAVES antennas using the observations of the nonthermal terrestrial auroral kilometric radiation (AKR) during STEREO roll maneuvers in an early stage of the mission. A least squares method combined with a genetic algorithm was applied to find the effective length vectors of the STEREO Behind (STEREO-B)/WAVES antennas in a quasi-static frequency range ($L_{antenna} \ll \lambda_{wave}$) which fit best to the model and observed AKR intensity profiles. The obtained results confirm the former SWAVES antenna analysis by rheometry and numerical simulations. A final set of antenna parameters is recommended as a basis for evaluations of the SWAVES data

Interplanetary shocks lacking type II radio bursts

We report on the radio-emission characteristics of 222 interplanetary (IP) shocks. A surprisingly large fraction of the IP shocks (~34%) is radio quiet (i.e., the shocks lacked type II radio bursts). The CMEs associated with the RQ shocks are generally slow (average speed ~535 km/s) and only ~40% of the CMEs were halos. The corresponding numbers for CMEs associated with radio loud (RL) shocks are 1237 km/s and 72%, respectively. The RQ shocks are also accompanied by lower peak soft X-ray flux. CMEs associated with RQ (RL) shocks are generally accelerating (decelerating). The kinematics of CMEs associated with the km type II bursts is similar to those of RQ shocks, except that the former are slightly more energetic. Comparison of the shock The RQ shocks seem to be mostly subcritical and quasi-perpendicular. The radio-quietness is predominant in the rise phase and decreases through the maximum and declining phases of solar cycle 23. The solar sources of the shock-driving CMEs follow the sunspot butterfly diagram, consistent with the higher-energy requirement for driving shocks

Radio-loud CMEs from the disk center lacking shocks at 1 AU

A coronal mass ejection (CME) associated with a type II burst and originating close to the center of the solar disk typically results in a shock at Earth in 2-3 days and hence can be used to predict shock arrival at Earth. However, a significant fraction (about 28%) of such CMEs producing type II bursts were not associated with shocks at Earth. We examined a set of 21 type II bursts observed by the Wind/WAVES experiment at decameter-hectometric (DH) wavelengths that had CME sources very close to the disk center (within a central meridian distance of 30 degrees), but did not have a shock at Earth. We find that the near-Sun speeds of these CMEs average to ~644 km/s, only slightly higher than the average speed of CMEs associated with radio-quiet shocks. However, the fraction of halo CMEs is only ~30%, compared to 54% for the radio-quiet shocks and 91% for all radio-loud shocks. We conclude that the disk-center radio-loud CMEs with no shocks at 1 AU are generally of lower energy and they drive shocks only close to the Sun and dissipate before arriving at Earth. There is also evidence for other possible processes that lead to the lack of shock at 1 AU: (i) overtaking CME shocks merge and one observes a single shock at Earth, and (ii) deflection by nearby coronal holes can push the shocks away from the Sun-Earth line, such that Earth misses these shocks. The probability of observing a shock at 1 AU increases rapidly above 60% when the CME speed exceeds 1000 km/s and when the type II bursts propagate to frequencies below 1 MHz.Comment: 33 pages, 11 figures, 2 table

Space VLBI at Low Frequencies

At sufficiently low frequencies, no ground-based radio array will be able to produce high resolution images while looking through the ionosphere. A space-based array will be needed to explore the objects and processes which dominate the sky at the lowest radio frequencies. An imaging radio interferometer based on a large number of small, inexpensive satellites would be able to track solar radio bursts associated with coronal mass ejections out to the distance of Earth, determine the frequency and duration of early epochs of nonthermal activity in galaxies, and provide unique information about the interstellar medium. This would be a "space-space" VLBI mission, as only baselines between satellites would be used. Angular resolution would be limited only by interstellar and interplanetary scattering.Comment: To appear in "Astrophysical Phenomena Revealed by Space VLBI", ed. H. Hirabayashi, P. Edwards, and D. Murphy (ISAS, Japan

Hard X-ray emission from a flare-related jet

<p><b>Aims:</b> We aim to understand the physical conditions in a jet event which occurred on the 22nd of August 2002, paying particular attention to evidence for non-thermal electrons in the jet material.</p> <p><b>Methods:</b> We investigate the flare impulsive phase using multiwavelength observations from the Transition Region and Coronal Explorer (TRACE) and the Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) satellite missions, and the ground-based Nobeyama Radioheliograph (NoRH) and Radio Polarimeters (NoRP).</p> <p><b>Results:</b> We report what we believe to be the first observation of hard X-ray emission formed in a coronal jet. We present radio observations which confirm the presence of non-thermal electrons present in the jet at this time. The evolution of the event is best compared with the magnetic reconnection jet model in which emerging magnetic field interacts with the pre-existing coronal field. We calculate an apparent jet velocity of ~500 km s-1 which is consistent with model predictions for jet material accelerated by the <b>J</b> X <b>B</b> force resulting in a jet velocity of the order of the Alfvén speed (~100–1000 km s-1).</p&gt