Bounded Representations of Interval and Proper Interval Graphs

Klavik et al. [arXiv:1207.6960] recently introduced a generalization of recognition called the bounded representation problem which we study for the classes of interval and proper interval graphs. The input gives a graph G and in addition for each vertex v two intervals L_v and R_v called bounds. We ask whether there exists a bounded representation in which each interval I_v has its left endpoint in L_v and its right endpoint in R_v. We show that the problem can be solved in linear time for interval graphs and in quadratic time for proper interval graphs. Robert's Theorem states that the classes of proper interval graphs and unit interval graphs are equal. Surprisingly the bounded representation problem is polynomially solvable for proper interval graphs and NP-complete for unit interval graphs [Klav\'{\i}k et al., arxiv:1207.6960]. So unless P = NP, the proper and unit interval representations behave very differently. The bounded representation problem belongs to a wider class of restricted representation problems. These problems are generalizations of the well-understood recognition problem, and they ask whether there exists a representation of G satisfying some additional constraints. The bounded representation problems generalize many of these problems

A quasilocal calculation of tidal heating

We present a method for computing the flux of energy through a closed surface containing a gravitating system. This method, which is based on the quasilocal formalism of Brown and York, is illustrated by two applications: a calculation of (i) the energy flux, via gravitational waves, through a surface near infinity and (ii) the tidal heating in the local asymptotic frame of a body interacting with an external tidal field. The second application represents the first use of the quasilocal formalism to study a non-stationary spacetime and shows how such methods can be used to study tidal effects in isolated gravitating systems.Comment: REVTex, 4 pages, 1 typo fixed, standard sign convention adopted for the Newtonian potential, a couple of lines added to the discussion of gauge dependent term

A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem

The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new characterization of c-planarity. It leads to efficient algorithms for c-planarity testing in the following cases. (i) Every cluster and every co-cluster (complement of a cluster) has at most two connected components. (ii) Every cluster has at most five outgoing edges. Moreover, the cd-tree reveals interesting connections between c-planarity and planarity with constraints on the order of edges around vertices. On one hand, this gives rise to a bunch of new open problems related to c-planarity, on the other hand it provides a new perspective on previous results.Comment: 17 pages, 2 figure

A Planarity Test via Construction Sequences

Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple reduction from planarity testing to the problem of computing a certain construction of a 3-connected graph. The approach is different from previous planarity tests; as key concept, we maintain a planar embedding that is 3-connected at each point in time. The algorithm runs in linear time and computes a planar embedding if the input graph is planar and a Kuratowski-subdivision otherwise

Effect of aerosol radiative forcing uncertainty on projected exceedance year of a 1.5 °c global temperature rise

© 2020 The Author(s). Published by IOP Publishing Ltd. Anthropogenic aerosol emissions are predicted to decline sharply throughout the 21st century, in line with climate change and air quality mitigation policies, causing a near-term warming of climate that will impact our trajectory towards 1.5 °C above pre-industrial temperatures. However, the persistent uncertainty in aerosol radiative forcing limits our understanding of how much the global mean temperature will respond to near-term reductions in anthropogenic aerosol emissions. We quantify the model and scenario uncertainty in global mean aerosol radiative forcing up to 2050 using statistical emulation of a perturbed parameter ensemble for emission reduction scenarios consistent with three Shared Socioeconomic Pathways. We then use a simple climate model to translate the uncertainty in aerosol radiative forcing into uncertainty in global mean temperature projections, accounting additionally for the potential correlation of aerosol radiative forcing and climate sensitivity. Near-term aerosol radiative forcing uncertainty alone causes an uncertainty window of around 5 years (2034-2039) on the projected year of exceeding a global temperature rise of 1.5 °C above pre-industrial temperatures for a middle of the road emissions scenario (SSP2-RCP4.5). A correlation between aerosol radiative forcing and climate sensitivity would increase the 1.5 °C exceedance window by many years. The results highlight the importance of quantifying aerosol radiative forcing and any relationship with climate sensitivity in climate models in order to reduce uncertainty in temperature projections

The importance of comprehensive parameter sampling and multiple observations for robust constraint of aerosol radiative forcing

© 2018 Author(s). Observational constraint of simulated aerosol and cloud properties is an essential part of building trustworthy climate models for calculating aerosol radiative forcing. Models are usually tuned to achieve good agreement with observations, but tuning produces just one of many potential variants of a model, so the model uncertainty cannot be determined. Here we estimate the uncertainty in aerosol effective radiative forcing (ERF) in a tuned climate model by constraining 4 million variants of the HadGEM3-UKCA aerosol-climate model to match nine common observations (top-of-atmosphere shortwave flux, aerosol optical depth, PM2.5, cloud condensation nuclei at 0.2% supersaturation (CCN0.2), and concentrations of sulfate, black carbon and organic carbon, as well as decadal trends in aerosol optical depth and surface shortwave radiation.) The model uncertainty is calculated by using a perturbed parameter ensemble that samples 27 uncertainties in both the aerosol model and the physical climate model, and we use synthetic observations generated from the model itself to determine the potential of each observational type to constrain this uncertainty. Focusing over Europe in July, we show that the aerosol ERF uncertainty can be reduced by about 30% by constraining it to the nine observations, demonstrating that producing climate models with an observationally plausible base state can contribute to narrowing the uncertainty in aerosol ERF. However, the uncertainty in the aerosol ERF after observational constraint is large compared to the typical spread of a multi-model ensemble. Our results therefore raise questions about whether the underlying multi-model uncertainty would be larger if similar approaches as adopted here were applied more widely. The approach presented in this study could be used to identify the most effective observations for model constraint. It is hoped that aerosol ERF uncertainty can be further reduced by introducing process-related constraints; however, any such results will be robust only if the enormous number of potential model variants is explored

Four Lessons in Versatility or How Query Languages Adapt to the Web

Exposing not only human-centered information, but machine-processable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule- and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and re-published. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logic-based) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for tree-shaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”

Photoproduction of pions and properties of baryon resonances from a Bonn-Gatchina partial wave analysis

Masses, widths and photocouplings of baryon resonances are determined in a coupled-channel partial wave analysis of a large variety of data. The Bonn-Gatchina partial wave formalism is extended to include a decomposition of t- and u-exchange amplitudes into individual partial waves. The multipole transition amplitudes for $\gamma p\to p\pi^0$ and $\gamma p\to n\pi^+$ are given and compared to results from other analyses.Comment: 18 pages, 14 figure

P-wave excited baryons from pion- and photo-induced hyperon production

We report evidence for $N(1710)P_{11}$, $N(1875)P_{11}$, $N(1900)P_{13}$, $\Delta(1600)P_{33}$, $\Delta(1910)P_{31}$, and $\Delta(1920)P_{33}$, and find indications that $N(1900)P_{13}$ might have a companion state at 1970\,MeV. The controversial $\Delta(1750)P_{31}$ is not seen. The evidence is derived from a study of data on pion- and photo-induced hyperon production, but other data are included as well. Most of the resonances reported here were found in the Karlsruhe-Helsinki (KH84) and the Carnegie-Mellon (CM) analyses but were challenged recently by the Data Analysis Center at GWU. Our analysis is constrained by the energy independent $\pi N$ scattering amplitudes from either KH84 or GWU. The two $\pi N$ amplitudes from KH84 or GWU, respectively, lead to slightly different $\pi N$ branching ratios of contributing resonances but the debated resonances are required in both series of fits.Comment: 22 pages, 28 figures. Some additional sets of data are adde