Combinatorial Alexander Duality -- a Short and Elementary Proof

Let X be a simplicial complex with the ground set V. Define its Alexander dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The combinatorial Alexander duality states that the i-th reduced homology group of X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a given commutative ring R). We give a self-contained proof.Comment: 7 pages, 2 figure; v3: the sign function was simplifie

Genus expansion for real Wishart matrices

We present an exact formula for moments and cumulants of several real compound Wishart matrices in terms of an Euler characteristic expansion, similar to the genus expansion for complex random matrices. We consider their asymptotic values in the large matrix limit: as in a genus expansion, the terms which survive in the large matrix limit are those with the greatest Euler characteristic, that is, either spheres or collections of spheres. This topological construction motivates an algebraic expression for the moments and cumulants in terms of the symmetric group. We examine the combinatorial properties distinguishing the leading order terms. By considering higher cumulants, we give a central limit-type theorem for the asymptotic distribution around the expected value

Strategies for Developing and Documenting Products of Public Scholarship in Research and Creative Activity

This guidance is Part 1 of an intended 3 part series with the remaining guides to focus on strategies to document public and community-engaged scholarship as excellence in Teaching followed by Service.This document builds on the IUPUI Concept Paper on Public Scholarship and provides a planning and documentation tool to aid faculty in preparing their dossier for promotion and tenure. Candidates can use this document to aid in their planning and gathering of evidence. Primary and unit committees can use this guidance in mentoring junior colleagues. The specific guidance in this document focuses on planning for and documenting their public and community-engaged scholarship as research and creative activity as is adapted from prior work by Jordan (2007)

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Forest dynamics following spruce budworm outbreaks in the northern and southern mixedwoods of central Quebec

The effects of 20th century spruce budworm (Choristoneura fumiferana (Clem.)) outbreaks on forest dynamics was examined in the southern and northern parts of the mixedwood forest zone in central Quebec, Canada. In each region, three study areas were placed in unmanaged stands that had not burned for more than 200 years. Disturbance impacts and forest succession were evaluated using aerial photographs and dendrochronology. Spruce budworm outbreaks occurred around 1910, 1950, and 1980 in both regions. The 1910 outbreak seemed to have limited impact in both regions, and the 1950 outbreak caused heavy mortality in conifer stands (mostly of balsam fir, Abies balsamea (L.) Mill.) in the southern region. The 1980 outbreak caused major mortality in the northern region, but had little impact in the southern region. Successive spruce budworm outbreaks led to a massive invasion by hardwood species in the last century in the southern region but not in the northern region. The reason for such contrasting dynamics between regions is unknown, but we hypothesize that differences in disturbance intensities, influenced by climate, played a major role. Results from this study emphasize that generalizations about the effect of spruce budworm outbreaks on forest dynamics cannot be derived from observations made during a single outbreak or at a single location

Early above- and below-ground responses of subboreal conifer seedlings to various levels of deciduous canopy removal

We examined the growth of understory conifers, following partial or complete deciduous canopy removal, in a field study established in two regions in Canada. In central British Columbia, we studied the responses of three species (Pseudotsuga menziesii var. glauca (Beissn.) Franco, Picea glauca (Moench) Voss x Picea engelmannii Parry ex Engelm., and Abies lasiocarpa (Hook.) Nutt.), and in northwestern Quebec, we studied one species (Abies balsamea (L.) Mill.). Stem and root diameter and height growth were measured 5 years before and 3 years after harvesting. Both root and stem diameter growth increased sharply following release but seedlings showed greater root growth, suggesting that in the short term, improvement in soil resource capture and transport, and presumably stability, may be more important than an increase in stem diameter and height growth. Response was strongly size dependent, which appears to reflect greater demand for soil resources as well as higher light levels and greater tree vigour before release for taller individuals. Growth ratios could not explain the faster response generally attributed to true fir species or the unusual swift response of spruces. Good prerelease vigour of spruces, presumably favoured by deciduous canopies, could explain their rapid response to release

Paleobiology of titanosaurs: reproduction, development, histology, pneumaticity, locomotion and neuroanatomy from the South American fossil record

Fil: García, Rodolfo A.. Instituto de Investigación en Paleobiología y Geología. Museo Provincial Carlos Ameghino. Cipolletti; ArgentinaFil: Salgado, Leonardo. Instituto de Investigación en Paleobiología y Geología. General Roca. Río Negro; ArgentinaFil: Fernández, Mariela. Inibioma-Centro Regional Universitario Bariloche. Bariloche. Río Negro; ArgentinaFil: Cerda, Ignacio A.. Instituto de Investigación en Paleobiología y Geología. Museo Provincial Carlos Ameghino. Cipolletti; ArgentinaFil: Carabajal, Ariana Paulina. Museo Carmen Funes. Plaza Huincul. Neuquén; ArgentinaFil: Otero, Alejandro. Museo de La Plata. Universidad Nacional de La Plata; ArgentinaFil: Coria, Rodolfo A.. Instituto de Paleobiología y Geología. Universidad Nacional de Río Negro. Neuquén; ArgentinaFil: Fiorelli, Lucas E.. Centro Regional de Investigaciones Científicas y Transferencia Tecnológica. Anillaco. La Rioja; Argentin

Perspectives in visual imaging for marine biology and ecology: from acquisition to understanding

Durden J, Schoening T, Althaus F, et al. Perspectives in Visual Imaging for Marine Biology and Ecology: From Acquisition to Understanding. In: Hughes RN, Hughes DJ, Smith IP, Dale AC, eds. Oceanography and Marine Biology: An Annual Review. 54. Boca Raton: CRC Press; 2016: 1-72