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  1. Abstract

    Ecosystems like coral reefs mitigate rising coastal flood risks, but investments into their conservation remain low relative to the investments into engineered risk-mitigation structures. One reason is that quantifying the risk-reduction benefits of coral reefs requires an estimate of their fragility to severe stresses. Engineered structures typically have associated fragility functions which predict the probability of exceeding a damage state with the increasing loading intensity imposed by a stressor, like a hurricane. Here, we propose a preliminary framework for capturing the fragility of coral reefs towards hurricanes in an analogous way to that of an engineered structure. We base our framework on Disturbance Response Monitoring data collected in the Florida Keys and Puerto Rico following hurricanes Irma and Maria. We first establish a qualitatively consistent correlation between hurricane impacts and coral mortality rates using two surveys of coral health. We focus specifically on stony coral mortality as a metric for reef damage, simplifying the effect of coral morphology into a single quantitative index at the site scale. To quantify the loading intensity of a hurricane, we propose a Hurricane Wind Exposure Time that captures spatial variations in the exposure of different coral reef sites to hurricane force winds. Wemore »ultimately derive a simple empirical fragility function for the Florida Keys and Puerto Rico to support side-by-side comparisons of the cost-effectiveness of a coral reef and engineered solutions to flood risk reduction in these regions.

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  2. In this paper, we make a case for the importance of teaching secondary school level algebra to students with learning disabilities (LD). Furthermore, we illustrate how they struggle and present best-practices on how they are best supported. We demonstrate effective ways of how teachers can show students with LD how to solve challenging algebra problems. In particular, we depict how educators can help learners with LD show their work on paper in ways that support their thinking processes as they engage with challenging algebra problems.
  3. Monomeric boroles have been gaining attention as reagents for the synthesis of heterocycles due to their ability to insert atoms into the BC 4 ring in a single step. Although unique boron frameworks can be accessed via this methodology, the products feature aryl substitution on the carbon centers as steric bulk is required to preclude borole dimerization. This work demonstrates that insertion chemistry is possible with Diels–Alder dimeric boroles and that such reactivity is not exclusive to monomeric boroles with bulky groups. With 1-phenyl-2,3,4,5-tetramethylborole dimer, the formal 1,1-insertion of a nitrene and sulfur generate the six-membered aromatic 1,2-azaborine and 1,2-thiaborine, respectively. The isolation of the 1,2-thiaborine enabled the synthesis of an η 6 -chromium complex. Benzophenone and diphenylketene readily insert a CO unit to generate BOC 5 seven-membered rings confirming dimeric boroles can serve as monomeric synthons in 1,2-insertion reactions. An epoxide did not furnish the anticipated eight-membered BOC 6 ring, instead provided a bicyclic system with a BOC 3 ring. The insertion chemistry was demonstrated with two other borole dimers featuring different substitution with diphenylketene as a substrate. This work elevates borole insertion chemistry to a new level to access products that do not require bulky substitution.