Heating the Solar Atmosphere by the Self-Enhanced Thermal Waves Caused by the Dynamo Processes

We discuss a possible mechanism for heating the solar atmosphere by the ensemble of thermal waves, generated by the photospheric dynamo and propagating upwards with increasing magnitudes. These waves are self-sustained and amplified due to the specific dependence of the efficiency of heat release by Ohmic dissipation on the ratio of the collisional to gyro- frequencies, which in its turn is determined by the temperature profile formed in the wave. In the case of sufficiently strong driving, such a mechanism can increase the plasma temperature by a few times, i.e. it may be responsible for heating the chromosphere and the base of the transition region.Comment: v2: A number of minor corrections and additional explanations. AASTeX, 5 pages, 2 EPS figures, submitted to The Astrophysical Journa

Algorithms and Bounds for Very Strong Rainbow Coloring

A well-studied coloring problem is to assign colors to the edges of a graph $G$ so that, for every pair of vertices, all edges of at least one shortest path between them receive different colors. The minimum number of colors necessary in such a coloring is the strong rainbow connection number (\src(G)) of the graph. When proving upper bounds on \src(G), it is natural to prove that a coloring exists where, for \emph{every} shortest path between every pair of vertices in the graph, all edges of the path receive different colors. Therefore, we introduce and formally define this more restricted edge coloring number, which we call \emph{very strong rainbow connection number} (\vsrc(G)). In this paper, we give upper bounds on \vsrc(G) for several graph classes, some of which are tight. These immediately imply new upper bounds on \src(G) for these classes, showing that the study of \vsrc(G) enables meaningful progress on bounding \src(G). Then we study the complexity of the problem to compute \vsrc(G), particularly for graphs of bounded treewidth, and show this is an interesting problem in its own right. We prove that \vsrc(G) can be computed in polynomial time on cactus graphs; in contrast, this question is still open for \src(G). We also observe that deciding whether \vsrc(G) = k is fixed-parameter tractable in $k$ and the treewidth of $G$. Finally, on general graphs, we prove that there is no polynomial-time algorithm to decide whether \vsrc(G) \leq 3 nor to approximate \vsrc(G) within a factor $n^{1-\varepsilon}$, unless P$=$NP

Improved Distributed Algorithms for Exact Shortest Paths

Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm of Becker et al. [DISC'17] which deterministically computes $(1+o(1))$-approximate shortest paths in $\tilde O(D+\sqrt n)$ time, where $D$ is the hop-diameter of the graph. Up to logarithmic factors, this time complexity is optimal, matching the lower bound of Elkin [STOC'04]. The question of exact shortest paths however saw no algorithmic progress for decades, until the recent breakthrough of Elkin [STOC'17], which established a sublinear-time algorithm for exact single source shortest paths on undirected graphs. Shortly after, Huang et al. [FOCS'17] provided improved algorithms for exact all pairs shortest paths problem on directed graphs. In this paper, we present a new single-source shortest path algorithm with complexity $\tilde O(n^{3/4}D^{1/4})$. For polylogarithmic $D$, this improves on Elkin's $\tilde{O}(n^{5/6})$ bound and gets closer to the $\tilde{\Omega}(n^{1/2})$ lower bound of Elkin [STOC'04]. For larger values of $D$, we present an improved variant of our algorithm which achieves complexity $\tilde{O}\left( n^{3/4+o(1)}+ \min\{ n^{3/4}D^{1/6},n^{6/7}\}+D\right)$, and thus compares favorably with Elkin's bound of $\tilde{O}(n^{5/6} + n^{2/3}D^{1/3} + D )$ in essentially the entire range of parameters. This algorithm provides also a qualitative improvement, because it works for the more challenging case of directed graphs (i.e., graphs where the two directions of an edge can have different weights), constituting the first sublinear-time algorithm for directed graphs. Our algorithm also extends to the case of exact $\kappa$-source shortest paths...Comment: 26 page

Solving Partition Problems Almost Always Requires Pushing Many Vertices Around

A fundamental graph problem is to recognize whether the vertex set of a graph G can be bipartitioned into sets A and B such that G[A] and G[B] satisfy properties Pi_A and Pi_B, respectively. This so-called (Pi_A,Pi_B)-Recognition problem generalizes amongst others the recognition of 3-colorable, bipartite, split, and monopolar graphs. A powerful algorithmic technique that can be used to obtain fixed-parameter algorithms for many cases of (Pi_A,Pi_B)-Recognition, as well as several other problems, is the pushing process. For bipartition problems, the process starts with an "almost correct" bipartition (A\u27,B\u27), and pushes appropriate vertices from A\u27 to B\u27 and vice versa to eventually arrive at a correct bipartition. In this paper, we study whether (Pi_A,Pi_B)-Recognition problems for which the pushing process yields fixed-parameter algorithms also admit polynomial problem kernels. In our study, we focus on the first level above triviality, where Pi_A is the set of P_3-free graphs (disjoint unions of cliques, or cluster graphs), the parameter is the number of clusters in the cluster graph G[A], and Pi_B is characterized by a set H of connected forbidden induced subgraphs. We prove that, under the assumption that NP not subseteq coNP/poly, (Pi_A,Pi_B)-Recognition admits a polynomial kernel if and only if H contains a graph of order at most 2. In both the kernelization and the lower bound results, we make crucial use of the pushing process

Measuring hidden phenotype:Quantifying the shape of barley seeds using the Euler characteristic transform

Shape plays a fundamental role in biology. Traditional phenotypic analysis methods measure some features but fail to measure the information embedded in shape comprehensively. To extract, compare and analyse this information embedded in a robust and concise way, we turn to topological data analysis (TDA), specifically the Euler characteristic transform. TDA measures shape comprehensively using mathematical representations based on algebraic topology features. To study its use, we compute both traditional and topological shape descriptors to quantify the morphology of 3121 barley seeds scanned with X-ray computed tomography (CT) technology at 127 μm resolution. The Euler characteristic transform measures shape by analysing topological features of an object at thresholds across a number of directional axes. A Kruskal-Wallis analysis of the information encoded by the topological signature reveals that the Euler characteristic transform picks up successfully the shape of the crease and bottom of the seeds. Moreover, while traditional shape descriptors can cluster the seeds based on their accession, topological shape descriptors can cluster them further based on their panicle. We then successfully train a support vector machine to classify 28 different accessions of barley based exclusively on the shape of their grains. We observe that combining both traditional and topological descriptors classifies barley seeds better than using just traditional descriptors alone. This improvement suggests that TDA is thus a powerful complement to traditional morphometrics to comprehensively describe a multitude of 'hidden' shape nuances which are otherwise not detected.</p

An LTL proof system for runtime verification

We propose a local proof system for LTL formalising deductions within the constraints of Runtime Verification (RV), and show how such a system can be used as a basis for the construction of online runtime monitors. Novel soundness and completeness results are proven for this system. We also prove decidability and incrementality properties for a monitoring algorithm constructed from it. Finally, we relate its expressivity to existing symbolic analysis techniques used in RV.peer-reviewe

NASA's surface biology and geology designated observable: A perspective on surface imaging algorithms

The 2017–2027 National Academies' Decadal Survey, Thriving on Our Changing Planet, recommended Surface Biology and Geology (SBG) as a “Designated Targeted Observable” (DO). The SBG DO is based on the need for capabilities to acquire global, high spatial resolution, visible to shortwave infrared (VSWIR; 380–2500 nm; ~30 m pixel resolution) hyperspectral (imaging spectroscopy) and multispectral midwave and thermal infrared (MWIR: 3–5 μm; TIR: 8–12 μm; ~60 m pixel resolution) measurements with sub-monthly temporal revisits over terrestrial, freshwater, and coastal marine habitats. To address the various mission design needs, an SBG Algorithms Working Group of multidisciplinary researchers has been formed to review and evaluate the algorithms applicable to the SBG DO across a wide range of Earth science disciplines, including terrestrial and aquatic ecology, atmospheric science, geology, and hydrology. Here, we summarize current state-of-the-practice VSWIR and TIR algorithms that use airborne or orbital spectral imaging observations to address the SBG DO priorities identified by the Decadal Survey: (i) terrestrial vegetation physiology, functional traits, and health; (ii) inland and coastal aquatic ecosystems physiology, functional traits, and health; (iii) snow and ice accumulation, melting, and albedo; (iv) active surface composition (eruptions, landslides, evolving landscapes, hazard risks); (v) effects of changing land use on surface energy, water, momentum, and carbon fluxes; and (vi) managing agriculture, natural habitats, water use/quality, and urban development. We review existing algorithms in the following categories: snow/ice, aquatic environments, geology, and terrestrial vegetation, and summarize the community-state-of-practice in each category. This effort synthesizes the findings of more than 130 scientists

A model of solid-solution interactions in acid organic soils, based on the complexation properties of humic substances

CHAOS (Complexation by Humic Acids in Organic Soils) is a quantitative chemical model of organic soils that incorporates complexation by the functional groups of humic substances and non-specific ion-exchange reactions. The two types of interaction are linked by the net humic charge, Z, which depends on the extents of proton and metal complexation, and which in turn determines ionic concentrations in the diffuse part of the electrical double layer, by a Donnan equilibrium. CHAOS was found to account satisfactorily for the results of acid-base titration experiments (pH range 3–5) with soil samples, giving reasonable simultaneous predictions of solution pH and concentration of A13+. Predictive calculations with CHAOS suggest that organic soils acidified by acid rain would respond on a time-scale of years-to-decades to reductions in rain acidity. An associated effect might be an increase in the concentration of dissolved organic matter in the soil solution