On uniform relationships between combinatorial problems

The enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic, with one of the most common frameworks for doing so being reverse mathematics. In this setting, one investigates which theorems provably imply which others in a weak formal theory roughly corresponding to computable mathematics. Since the proofs of such implications take place in classical logic, they may in principle involve appeals to multiple applications of a particular theorem, or to nonuniform decisions about how to proceed in a given construction. In practice, however, if a theorem Q implies a theorem P, it is usually because there is a direct uniform translation of the problems represented by P into the problems represented by Q, in a precise sense formalized by Weihrauch reducibility. We study this notion of uniform reducibility in the context of several natural combinatorial problems, and compare and contrast it with the traditional notion of implication in reverse mathematics. We show, for instance, that for all n; j; k 1, if j < k then Ramsey's theorem for n-tuples and k many colors is not uniformly, or Weihrauch, reducible to Ramsey's theorem for n-tuples and j many colors. The two theorems are classically equivalent, so our analysis gives a genuinely ner metric by which to gauge the relative strength of mathematical propositions. We also study Weak K�onig's Lemma, the Thin Set Theorem, and the Rainbow Ramsey's Theorem, along with a number of their variants investigated in the literature. Weihrauch reducibility turns out to be connected with sequential forms of mathematical principles, where one wishes to solve in nitely many instances of a particular problem simultaneously. We exploit this connection to uncover new points of di erence between combinatorial problems previously thought to be more closely related

Short-Term Hurricane Impacts on a Neotropical Community of Marked Birds and Implications for Early-Stage Community Resilience

Populations in fragmented ecosystems risk extirpation through natural disasters, which must be endured rather than avoided. Managing communities for resilience is thus critical, but details are sketchy about the capacity for resilience and its associated properties in vertebrate communities. We studied short-term resilience in a community of individually marked birds, following this community through the catastrophic destruction of its forest habitat by Hurricane Iris in Belize, Central America. We sampled for 58 d immediately before the storm, 28 d beginning 11 d after Hurricane Iris, and for 69 d approximately one year later. Our data showed that the initial capacity for resilience was strong. Many banded individuals remained after the storm, although lower post-hurricane recapture rates revealed increased turnover among individuals. Changes occurred in community dynamics and in abundances among species and guilds. Survivors and immigrants both were critical components of resilience, but in a heterogeneous, species-specific manner. Delayed effects, including higher fat storage and increased species losses, were evident one year later

SUSTAINABLE DEVELOPMENT AND HAZARDS MITIGATION IN THE UNITED STATES: DISASTERS BY DESIGN REVISITED

disaster, hazard, local sustainability, mitigation, reduction, second assessment, sustainable development,

Disaster warning response: the effects of different types of personal experience

In this paper, we seek to resolve the conflicting findings in literature about the effect of past hazard experience on response to warning. We find that different definitions of past experience in different studies are at the root of these conflicting findings. We disaggregate past experience into different types, identifying three types of past experiences that are most relevant in terms of affecting response. We test the relevance and importance of these three proposed types of past experience in an empirical context of warnings issued and response to these warning for two cyclonic events in India. We then provide the implications of the most relevant aspects of past hazard experience for emergency managers seeking to improve target audiences' response to warning

Weather Index Insurance and Climate Change: Opportunities and Challenges in Lower Income Countries

Weather index insurance underwrites a weather risk, typically highly correlated with agricultural production losses, as a proxy for economic loss and is gaining popularity in lower income countries. This instrument, although subject to basis risk and high start-up costs, should reduce costs over traditional agricultural insurance. Multilateral institutions have suggested that weather index insurance could enhance the ability of stakeholders in lower income countries to adapt to climate change. While weather index insurance could have several benefits in this context (e.g. providing a safety net to vulnerable households and price signals regarding the weather risk), climate change impacts increase the price of insurance due to increasing weather risk. Uncertainty about the extent of regional impacts compounds pricing difficulties. Policy recommendations for insurance market development include funding risk assessments, start-up costs and the extreme layer of risk. General premium subsidies are cautioned against as they may actually slow household adaptation. The Geneva Papers (2009) 34, 401–424. doi:10.1057/gpp.2009.11