The Research Unit VolImpact: Revisiting the volcanic impact on atmosphere and climate – preparations for the next big volcanic eruption

This paper provides an overview of the scientific background and the research objectives of the Research Unit “VolImpact” (Revisiting the volcanic impact on atmosphere and climate – preparations for the next big volcanic eruption, FOR 2820). VolImpact was recently funded by the Deutsche Forschungsgemeinschaft (DFG) and started in spring 2019. The main goal of the research unit is to improve our understanding of how the climate system responds to volcanic eruptions. Such an ambitious program is well beyond the capabilities of a single research group, as it requires expertise from complementary disciplines including aerosol microphysical modelling, cloud physics, climate modelling, global observations of trace gas species, clouds and stratospheric aerosols. The research goals will be achieved by building on important recent advances in modelling and measurement capabilities. Examples of the advances in the observations include the now daily near-global observations of multi-spectral aerosol extinction from the limb-scatter instruments OSIRIS, SCIAMACHY and OMPS-LP. In addition, the recently launched SAGE III/ISS and upcoming satellite missions EarthCARE and ALTIUS will provide high resolution observations of aerosols and clouds. Recent improvements in modeling capabilities within the framework of the ICON model family now enable simulations at spatial resolutions fine enough to investigate details of the evolution and dynamics of the volcanic eruptive plume using the large-eddy resolving version, up to volcanic impacts on larger-scale circulation systems in the general circulation model version. When combined with state-of-the-art aerosol and cloud microphysical models, these approaches offer the opportunity to link eruptions directly to their climate forcing. These advances will be exploited in VolImpact to study the effects of volcanic eruptions consistently over the full range of spatial and temporal scales involved, addressing the initial development of explosive eruption plumes (project VolPlume), the variation of stratospheric aerosol particle size and radiative forcing caused by volcanic eruptions (VolARC), the response of clouds (VolCloud), the effects of volcanic eruptions on atmospheric dynamics (VolDyn), as well as their climate impact (VolClim)

Embedding Four-directional Paths on Convex Point Sets

A directed path whose edges are assigned labels "up", "down", "right", or "left" is called \emph{four-directional}, and \emph{three-directional} if at most three out of the four labels are used. A \emph{direction-consistent embedding} of an \mbox{$n$-vertex} four-directional path $P$ on a set $S$ of $n$ points in the plane is a straight-line drawing of $P$ where each vertex of $P$ is mapped to a distinct point of $S$ and every edge points to the direction specified by its label. We study planar direction-consistent embeddings of three- and four-directional paths and provide a complete picture of the problem for convex point sets.Comment: 11 pages, full conference version including all proof

Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat

Powers of Hamilton cycles in pseudorandom graphs

We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph $G$ is $(\varepsilon,p,k,\ell)$-pseudorandom if for all disjoint $X$ and $Y\subset V(G)$ with $|X|\ge\varepsilon p^kn$ and $|Y|\ge\varepsilon p^\ell n$ we have $e(X,Y)=(1\pm\varepsilon)p|X||Y|$. We prove that for all $\beta>0$ there is an $\varepsilon>0$ such that an $(\varepsilon,p,1,2)$-pseudorandom graph on $n$ vertices with minimum degree at least $\beta pn$ contains the square of a Hamilton cycle. In particular, this implies that $(n,d,\lambda)$-graphs with $\lambda\ll d^{5/2 }n^{-3/2}$ contain the square of a Hamilton cycle, and thus a triangle factor if $n$ is a multiple of $3$. This improves on a result of Krivelevich, Sudakov and Szab\'o [Triangle factors in sparse pseudo-random graphs, Combinatorica 24 (2004), no. 3, 403--426]. We also extend our result to higher powers of Hamilton cycles and establish corresponding counting versions.Comment: 30 pages, 1 figur

Non-Compositional Term Dependence for Information Retrieval

Modelling term dependence in IR aims to identify co-occurring terms that are too heavily dependent on each other to be treated as a bag of words, and to adapt the indexing and ranking accordingly. Dependent terms are predominantly identified using lexical frequency statistics, assuming that (a) if terms co-occur often enough in some corpus, they are semantically dependent; (b) the more often they co-occur, the more semantically dependent they are. This assumption is not always correct: the frequency of co-occurring terms can be separate from the strength of their semantic dependence. E.g. "red tape" might be overall less frequent than "tape measure" in some corpus, but this does not mean that "red"+"tape" are less dependent than "tape"+"measure". This is especially the case for non-compositional phrases, i.e. phrases whose meaning cannot be composed from the individual meanings of their terms (such as the phrase "red tape" meaning bureaucracy). Motivated by this lack of distinction between the frequency and strength of term dependence in IR, we present a principled approach for handling term dependence in queries, using both lexical frequency and semantic evidence. We focus on non-compositional phrases, extending a recent unsupervised model for their detection [21] to IR. Our approach, integrated into ranking using Markov Random Fields [31], yields effectiveness gains over competitive TREC baselines, showing that there is still room for improvement in the very well-studied area of term dependence in IR

Boxicity of graphs on surfaces

The boxicity of a graph $G=(V,E)$ is the least integer $k$ for which there exist $k$ interval graphs $G_i=(V,E_i)$, $1 \le i \le k$, such that $E=E_1 \cap ... \cap E_k$. Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface $\Sigma$ of genus $g$ is at most $5g+3$. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces.Comment: 9 pages, 2 figure

The cut metric, random graphs, and branching processes

In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the sequence of matrices of edge probabilities converges to an appropriate limit object (a kernel), but only in a very weak sense, namely in the cut metric. Our results thus generalize previous results on the phase transition in the already very general inhomogeneous random graph model we introduced recently, as well as related results of Bollob\'as, Borgs, Chayes and Riordan, all of which involve considerably stronger assumptions. We also prove corresponding results for random hypergraphs; these generalize our results on the phase transition in inhomogeneous random graphs with clustering.Comment: 53 pages; minor edits and references update

Evaluational adjectives

This paper demarcates a theoretically interesting class of "evaluational adjectives." This class includes predicates expressing various kinds of normative and epistemic evaluation, such as predicates of personal taste, aesthetic adjectives, moral adjectives, and epistemic adjectives, among others. Evaluational adjectives are distinguished, empirically, in exhibiting phenomena such as discourse-oriented use, felicitous embedding under the attitude verb `find', and sorites-susceptibility in the comparative form. A unified degree-based semantics is developed: What distinguishes evaluational adjectives, semantically, is that they denote context-dependent measure functions ("evaluational perspectives")—context-dependent mappings to degrees of taste, beauty, probability, etc., depending on the adjective. This perspective-sensitivity characterizing the class of evaluational adjectives cannot be assimilated to vagueness, sensitivity to an experiencer argument, or multidimensionality; and it cannot be demarcated in terms of pretheoretic notions of subjectivity, common in the literature. I propose that certain diagnostics for "subjective" expressions be analyzed instead in terms of a precisely specified kind of discourse-oriented use of context-sensitive language. I close by applying the account to `find x PRED' ascriptions

Relevance of mytilid shell microtopographies for fouling defence - a global comparison

Prevention of epibiosis is of vital importance for most aquatic organisms, which can have consequences for their ability to invade new areas. Surface microtopography of the shell periostracum has been shown to have antifouling properties for mytilid mussels, and the topography shows regional differences. This article examines whether an optimal shell design exists and evaluates the degree to which shell microstructure is matched with the properties of the local fouling community. Biomimics of four mytilid species from different regional provenances were exposed at eight different sites in both northern and southern hemispheres. Tendencies of the microtopography to both inhibit and facilitate fouling were detected after 3 and 6 weeks of immersion. However, on a global scale, all microtopographies failed to prevent fouling in a consistent manner when exposed to various fouling communities and when decoupled from other shell properties. It is therefore suggested that the recently discovered chemical anti-microfouling properties of the periostracum complement the anti-macrofouling defence offered by shell microtopography