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It is well-known that both the pathwidth and the outer-planarity of a graph can be used to obtain lower bounds on the height of a planar straight-line drawing of a graph. But both bounds fall short for some graphs. In this paper, we consider two other parameters, the (simple) homotopy height and the (simple) grid-major height. We discuss the relationship between them and to the other parameters, and argue that they give lower bounds on the straight-line drawing height that are never worse than the ones obtained from pathwidth and outer-planarity.
We present the first in-depth statistical survey of flare source heights observed by RHESSI. Flares were found using a flare-finding algorithm designed to search the 6-10 keV count-rate when RHESSIs full sensitivity was available in order to find the
In algebraic geometry there is the notion of a height pairing of algebraic cycles, which lies at the confluence of arithmetic, Hodge theory and topology. After explaining a motivating example situation, we introduce new directions in this subject.
We study Doppler velocity measurements at multiple heights in the solar atmosphere using a set of six filtergrams obtained by the Helioseismic magnetic Imager on board the Solar Dynamics Observatory. There are clear and significant phase differences
Glivenkos theorem states that a formula is derivable in classical propositional logic $mathrm{CL}$ iff under the double negation it is derivable in intuitionistic propositional logic $mathrm{IL}$: $mathrm{CL}vdashvarphi$ iff $mathrm{IL}vdash eg egvar
We prove non-asymptotic stretched exponential tail bounds on the height of a randomly sampled node in a random combinatorial tree, which we use to prove bounds on the heights and widths of random trees from a variety of models. Our results allow us t