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For every compact, connected manifold $M$, we prove the existence of a sentence ${\mathrm{\varphi <\#comment/>}}_M$in the language of groups such that the homeomorphism group of another compact manifold $N$satisfies ${\mathrm{\varphi <\#comment/>}}_M$if and only if $N$is homeomorphic to $M$. We prove an analogous statement for groups of homeomorphisms preserving Oxtoby–Ulam probability measures. 

Significance Statement Although potentiating resilience is foundational to crop improvement, and despite the notion that cell wall (CW) protects against pathogens, the extent of pathogen‐induced CW changes and the CW composition requirements for a successful defense are largely unknown. By investigating the bacteria‐induced impact on the Arabidopsis CW, we found changes exclusively in infected leaves with the remodeling of distinct CW polysaccharides, including arabinogalactan proteins, whose loss is detrimental to defense, highlighting specific requirements for antagonizing pathogens and potentiating plant defenses. 

Abstract In recent decades, the interior regions of Eurasia and North America have experienced several unprecedentedly cold winters despite the global surface air temperature increases. One possible explanation of these increasing extreme cold winters comes from the so-called Warm Arctic Cold Continent (WACC) pattern, reflecting the effects of the amplified Arctic warming in driving the circulation change over surrounding continents. This study analyzed reanalysis data and model experiments forced by different levels of anthropogenic forcing. It is found that WACC exists on synoptic scales in observations, model’s historical and even future runs. In the future, the analysis suggests a continued presence of WACC but with a slightly weakened cold extreme due to the overall warming. Warm Arctic events under the warmer climate will be associated with not only a colder continent in East Asia but also a warmer continent, depending on the teleconnection process that is also complicated by the warmer Arctic. Such an increasingly association suggests a reduction in potential predictability of the midlatitude winter anomalies. 

In this expository note, we illustrate phenomena and conjectures about boundaries of hyperbolic groups by considering the special cases of certain amalgams of hyperbolic groups. While doing so, we describe fundamental results on hyperbolic groups and their boundaries by Bowditch [5] and Haissinsky [27], along with special treatments for the boundaries of free groups by Otal [48] and Cashen [15].