Computer Generated Images for Quadratic Rational Maps with a Periodic Critical Point

We describe an algorithm for distinguishing hyperbolic components in the parameter space of quadratic rational maps with a periodic critical point. We then illustrate computer images of the hyperbolic components of the parameter spaces V1 - V4, which were produced using our algorithm. We also resolve the singularities of the projective closure of V5 by blowups, giving an alternative proof that as an algebraic curve, the geometric genus of V5 is 1. This explains why we are unable to produce an image for V5.Comment: 12 pages, 8 figure

Against Minimalist Responses to Moral Debunking Arguments

Moral debunking arguments are meant to show that, by realist lights, moral beliefs are not explained by moral facts, which in turn is meant to show that they lack some significant counterfactual connection to the moral facts (e.g., safety, sensitivity, reliability). The dominant, “minimalist” response to the arguments—sometimes defended under the heading of “third-factors” or “pre-established harmonies”—involves affirming that moral beliefs enjoy the relevant counterfactual connection while granting that these beliefs are not explained by the moral facts. We show that the minimalist gambit rests on a controversial thesis about epistemic priority: that explanatory concessions derive their epistemic import from what they reveal about counterfactual connections. We then challenge this epistemic priority thesis, which undermines the minimalist response to debunking arguments (in ethics and elsewhere)

Evolutionary Debunking and Moral Relativism

Our aim here is to explore the prospects of a relativist response to moral debunking arguments. We begin by clarifying the relativist thesis under consideration, and we explain why relativists seem well-positioned to resist the arguments in a way that avoids the drawbacks of existing responses. We then show that appearances are deceiving. At bottom, the relativist response is no less question-begging than standard realist responses, and – when we turn our attention to the strongest formulation of the debunking argument – the virtues of relativism turn out to be vices

Secant varieties of P^2 x P^n embedded by O(1,2)

We describe the defining ideal of the rth secant variety of P^2 x P^n embedded by O(1,2), for arbitrary n and r at most 5. We also present the Schur module decomposition of the space of generators of each such ideal. Our main results are based on a more general construction for producing explicit matrix equations that vanish on secant varieties of products of projective spaces. This extends previous work of Strassen and Ottaviani.Comment: 21 page

Flow alteration-ecology relationships in Ozark Highland streams: Consequences for fish, crayfish and macroinvertebrate assemblages

We examined flowalteration-ecology relationships in benthic macroinvertebrate, fish, and crayfish assemblages in Ozark Highland streams, USA, over two years with contrasting environmental conditions, a drought year (2012) and a flood year (2013). We hypothesized that: 1) there would be temporal variation in flow alteration-ecology relationships between the two years, 2) flow alteration-ecology relationshipswould be stronger during the drought year vs the flood year, and 3) fish assemblages would show the strongest relationships with flow alteration. We used a quantitative richest-targeted habitat (RTH) method and a qualitative multihabitat (QMH) method to collect macroinvertebrates at 16 USGS gaged sites during both years. We used backpack electrofishing to sample fish and crayfish at 17 sites in 2012 and 11 sites in 2013.Weused redundancy analysis to relate biological response metrics, including richness, diversity, density, and community-based metrics, to flow alteration.We found temporal variation in flow alteration-ecology relationships for all taxa, and that relationships differed greatly between assemblages. We found relationships were stronger for macroinvertebrates during the drought year but not for other assemblages, and that fish assemblage relationships were not stronger than the invertebrate taxa. Magnitude of average flow, frequency of high flow, magnitude of high flow, and duration of high flow were the most important categories of flow alteration metrics across taxa. Alteration of high and average flows was more important than alteration of low flows. Of 32 important flow alteration metrics across years and assemblages, 19 were significantly altered relative to expected values. Ecological responses differed substantially between drought and flood years, and this is likely to be exacerbated with predicted climate change scenarios. Differences in flow alteration-ecology relationships among taxonomic groups and temporal variation in relationships illustrate that a complex suite of variables should be considered for effective conservation of stream communities related to flow alteration

Max filtering with reflection groups

Given a finite-dimensional real inner product space V and a finite subgroup G of linear isometries, max filtering affords a bilipschitz Euclidean embedding of the orbit space V/G. We identify the max filtering maps of minimum distortion in the setting where G is a reflection group. Our analysis involves an interplay between Coxeter's classification and semidefinite programming

Consider the Kirtland \u27s Warbler

This paper challenges the conventional wisdom of departments of parks and recreation raking sport management under their wing. Based on a review of the sport management literature and a polling of s port management and park and recreation educators, we argue that departments of parks and recreation are bur temporary refuges for migrarory sport management programs that eventually will want to build their ow n nests. Efforts to accommodate sport management only serve co undermine the mission of academic programs in parks and recreation by sapping resources, compromising the education of park and recreation majors, and eroding park and recreation faculty members\u27 sense of professional purpose