Notes on Contraction Theory

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system combinations, a property of interest in modelling biological systems

The Social Wasps (Hymenoptera: Vespidae) of Indiana

An updated taxonomic treatment of the social wasps (Hymenoptera: Vespidae) of Indiana is made. Illustrated identification keys are provided for species of Polistes, Vespa, Vespula, and Dolichovespula. New distributional records and biological notes are provided for each species

Distribution and biological notes for some Cerambycidae (Coleoptera) occurring in the southeastern United States

New distribution records and new host records are provided for 33 species of Cerambycidae in Florida and Georgia

Notes on a PDE System for Biological Network Formation

We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transport networks. The model describes the pressure field using a Darcy's type equation and the dynamics of the conductance network under pressure force effects. Randomness in the material structure is represented by a linear diffusion term and conductance relaxation by an algebraic decay term. The analytical part extends the results of Haskovec, Markowich and Perthame regarding the existence of weak and mild solutions to the whole range of meaningful relaxation exponents. Moreover, we prove finite time extinction or break-down of solutions in the spatially onedimensional setting for certain ranges of the relaxation exponent. We also construct stationary solutions for the case of vanishing diffusion and critical value of the relaxation exponent, using a variational formulation and a penalty method. The analytical part is complemented by extensive numerical simulations. We propose a discretization based on mixed finite elements and study the qualitative properties of network structures for various parameters values. Furthermore, we indicate numerically that some analytical results proved for the spatially one-dimensional setting are likely to be valid also in several space dimensions.Comment: 33 pages, 12 figure

Random many-particle systems: applications from biology, and propagation of chaos in abstract models

The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric speciation, i.e. the process in which a genetically homogeneous population is split in two or more different species sharing the same habitat, and models for swarming animals. The second part of the paper deals with abstract many particle systems, and methods for rigorously deriving mean field models.Comment: These are notes from a series of lectures given at the 5$^{th}$ Summer School on Methods and Models of Kinetic Theory, Porto Ercole, 2010. They are submitted for publication in "Rivista di Matematica della Universit\`a di Parma

Inventory of the Clark Hubbs' Papers, 1946-1999

Dr. Clark Hubbs was a professor in the School of Biological Sciences, Section of Integrative Biology at The University of Texas at Austin, for his entire career, from 1949 until his death in 2008. He founded the University’s Fish Collection, which is now part of the Texas Natural History Collections and deposited more fish specimens than anyone else has, or likely ever will. Hubbs published over 300 articles during his career and his idea for a book on the fishes of Texas began the Fishes of Texas Project. The Clark Hubbs Papers measures 24.5 linear feet and includes research notes, reprints, field notes, manuscripts, and some student records dating from 1946-1999.Integrative Biolog