Theoretical study of polar and global ozone changes using a coupled radiative-dynamical 2-D model

An existing 2-D model has recently been updated to incorporate ozone-temperature feedbacks with more comprehensive radiative transfer calculations and more detailed temperature data input. Researchers address the following issues: (1) given the observed temperature changes for the past eight years, quantitatively how much ozone change can be produced by the dynamical effect of the temperature change over the Arctic and Antarctic; (2) how much of the reported change in globally averaged ozone can be accounted for by temperature changes; (3) the role of the diabatic circulation changes in the lower stratosphere in determining the timing of the polar spring maximum and minimum; and (4) the role of the seasonal change in the diabatic circulation in causing the fall minimum over the Arctic and Antarctic

A further extension of R\"odl's theorem

Fix $\varepsilon>0$ and a nonnull graph $H$. A well-known theorem of R\"odl from the 80s says that every graph $G$ with no induced copy of $H$ contains a linear-sized $\varepsilon$-restricted set $S\subseteq V(G)$, which means $S$ induces a subgraph with maximum degree at most $\varepsilon\vert S\vert$ in $G$ or its complement. There are two extensions of this result: $\bullet$ quantitatively, Nikiforov (and later Fox and Sudakov) relaxed the condition "no induced copy of $H$" into "at most $\kappa\vert G\vert^{\vert H\vert}$ induced copies of $H$ for some $\kappa>0$ depending on $H$ and $\varepsilon$"; and $\bullet$ qualitatively, Chudnovsky, Scott, Seymour, and Spirkl recently showed that there exists $N>0$ depending on $H$ and $\varepsilon$ such that $G$ is $(N,\varepsilon)$-restricted, which means $V(G)$ has a partition into at most $N$ subsets that are $\varepsilon$-restricted. A natural common generalization of these two asserts that every graph $G$ with at most $\kappa\vert G\vert^{\vert H\vert}$ induced copies of $H$ is $(N,\varepsilon)$-restricted for some $\kappa,N>0$ depending on $H$ and $\varepsilon$. This is unfortunately false, but we prove that for every $\varepsilon>0$, $\kappa$ and $N$ still exist so that for every $d\ge0$, every graph with at most $\kappa d^{\vert H\vert}$ induced copies of $H$ has an $(N,\varepsilon)$-restricted induced subgraph on at least $\vert G\vert-d$ vertices. This unifies the two aforementioned theorems, and is optimal up to $\kappa$ and $N$ for every value of $d$.Comment: 11 pages, revised according to the referees' comment