On the Rational Type 0f Moment Angle Complexes

In this note it is shown that the moment angle complexes Z(K;(D^2,,S^1)) which are rationally elliptic are a product of odd spheres and a diskComment: This version avoids the use of an incorrect result from the literature in the proof of Theorem 1.3. There is some text overlap with arXiv:1410.645

Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

Career-computer simulation increases perceived importance of learning about rare diseases

Background: Rare diseases may be defined as occurring in less than 1 in 2000 patients. Such conditions are, however, so numerous that up to 5.9% of the population is afflicted by a rare disease. The gambling industry attests that few people have native skill evaluating probabilities. We believe that both students and academics, under-estimate the likelihood of encountering rare diseases. This combines with pressure on curriculum time, to reduce both student interest in studying rare diseases, and academic content preparing students for clinical practice. Underestimation of rare diseases, may also contribute to unhelpful blindness to considering such conditions in the clinic. Methods: We first developed a computer simulation, modelling the number of cases of increasingly rare conditions encountered by a cohort of clinicians. The simulation captured results for each year of practice, and for each clinician throughout the entirety of their careers. Four hundred sixty-two theoretical conditions were considered, with prevalence ranging from 1 per million people through to 64.1% of the population. We then delivered a class with two in-class on-line surveys evaluating student perception of the importance of learning about rare diseases, one before and the other after an in-class real-time computer simulation. Key simulation variables were drawn from the student group, to help students project themselves into the simulation. Results: The in-class computer simulation revealed that all graduating clinicians from that class would frequently encounter rare conditions. Comparison of results of the in-class survey conducted before and after the computer simulation, revealed a significant increase in the perceived importance of learning about rare diseases (p < 0.005). Conclusions: The computer career simulation appeared to affect student perception. Because the computer simulation demonstrated clinicians frequently encounter patients with rare diseases, we further suggest this should be considered by academics during curriculum review and design

Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes were written for the second author's lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition

Chamber basis of the Orlik-Solomon algebra and Aomoto complex

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.Comment: 16 page

Recycling bins, garbage cans or think tanks? Three myths regarding policy analysis institutes

The phrase 'think tank' has become ubiquitous – overworked and underspecified – in the political lexicon. It is entrenched in scholarly discussions of public policy as well as in the 'policy wonk' of journalists, lobbyists and spin-doctors. This does not mean that there is an agreed definition of think tank or consensual understanding of their roles and functions. Nevertheless, the majority of organizations with this label undertake policy research of some kind. The idea of think tanks as a research communication 'bridge' presupposes that there are discernible boundaries between (social) science and policy. This paper will investigate some of these boundaries. The frontiers are not only organizational and legal; they also exist in how the 'public interest' is conceived by these bodies and their financiers. Moreover, the social interactions and exchanges involved in 'bridging', themselves muddy the conception of 'boundary', allowing for analysis to go beyond the dualism imposed in seeing science on one side of the bridge, and the state on the other, to address the complex relations between experts and public policy

Poisson-de Rham homology of hypertoric varieties and nilpotent cones

We prove a conjecture of Etingof and the second author for hypertoric varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this conjecture holds for an arbitrary conical variety admitting a symplectic resolution if and only if it holds in degree zero for all normal slices to symplectic leaves. The Poisson-de Rham homology of a Poisson cone inherits a second grading. In the hypertoric case, we compute the resulting 2-variable Poisson-de Rham-Poincare polynomial, and prove that it is equal to a specialization of an enrichment of the Tutte polynomial of a matroid that was introduced by Denham. We also compute this polynomial for S3-varieties of type A in terms of Kostka polynomials, modulo a previous conjecture of the first author, and we give a conjectural answer for nilpotent cones in arbitrary type, which we prove in rank less than or equal to 2.Comment: 25 page