Amalgamation of real zero polynomials

With this article, we hope to launch the investigation of what we call the real zero amalgamation problem. Whenever a polynomial arises from another polynomial by substituting zero for some of its variables, we call the second polynomial an extension of the first one. The real zero amalgamation problem asks when two (multivariate real) polynomials have a common extension (called amalgam) that is a real zero polynomial. We show that the obvious necessary conditions are not sufficient. Our counterexample is derived in several steps from a counterexample to amalgamation of matroids by Poljak and Turz\'ik. On the positive side, we show that even a degree-preserving amalgamation is possible in three very special cases with three completely different techniques. Finally, we conjecture that amalgamation is always possible in the case of two shared variables. The analogue in matroid theory is true by another work of Poljak and Turz\'ik. This would imply a very weak form of the Generalized Lax Conjecture.Comment: 24 page

Unified Methods in Collecting, Preserving, and Archiving Coral Bleaching and Restoration Specimens to Increase Sample Utility and Interdisciplinary Collaboration

Coral reefs are declining worldwide primarily because of bleaching and subsequent mortality resulting from thermal stress. Currently, extensive efforts to engage in more holistic research and restoration endeavors have considerably expanded the techniques applied to examine coral samples. Despite such advances, coral bleaching and restoration studies are often conducted within a specific disciplinary focus, where specimens are collected, preserved, and archived in ways that are not always conducive to further downstream analyses by specialists in other disciplines. This approach may prevent the full utilization of unexpended specimens, leading to siloed research, duplicative efforts, unnecessary loss of additional corals to research endeavors, and overall increased costs. A recent US National Science Foundation-sponsored workshop set out to consolidate our collective knowledge across the disciplines of Omics, Physiology, and Microscopy and Imaging regarding the methods used for coral sample collection, preservation, and archiving. Here, we highlight knowledge gaps and propose some simple steps for collecting, preserving, and archiving coral-bleaching specimens that can increase the impact of individual coral bleaching and restoration studies, as well as foster additional analyses and future discoveries through collaboration. Rapid freezing of samples in liquid nitrogen or placing at −80 °C to −20 °C is optimal for most Omics and Physiology studies with a few exceptions; however, freezing samples removes the potential for many Microscopy and Imaging-based analyses due to the alteration of tissue integrity during freezing. For Microscopy and Imaging, samples are best stored in aldehydes. The use of sterile gloves and receptacles during collection supports the downstream analysis of host-associated bacterial and viral communities which are particularly germane to disease and restoration efforts. Across all disciplines, the use of aseptic techniques during collection, preservation, and archiving maximizes the research potential of coral specimens and allows for the greatest number of possible downstream analyses

Urban coral reefs: Degradation and resilience of hard coral assemblages in coastal cities of East and Southeast Asia

© 2018 The Author(s) Given predicted increases in urbanization in tropical and subtropical regions, understanding the processes shaping urban coral reefs may be essential for anticipating future conservation challenges. We used a case study approach to identify unifying patterns of urban coral reefs and clarify the effects of urbanization on hard coral assemblages. Data were compiled from 11 cities throughout East and Southeast Asia, with particular focus on Singapore, Jakarta, Hong Kong, and Naha (Okinawa). Our review highlights several key characteristics of urban coral reefs, including “reef compression” (a decline in bathymetric range with increasing turbidity and decreasing water clarity over time and relative to shore), dominance by domed coral growth forms and low reef complexity, variable city-specific inshore-offshore gradients, early declines in coral cover with recent fluctuating periods of acute impacts and rapid recovery, and colonization of urban infrastructure by hard corals. We present hypotheses for urban reef community dynamics and discuss potential of ecological engineering for corals in urban areas