Pictorial Guide to the Groupers (Teleostei: Serranidae) of the Western North Atlantic

This guide was developed to assist with the identification of western North Atlantic grouper species of the genera Alphestes, Cephalopholis, Dermatolepis, Epinephelus, Gonioplectrus, Mycteroperca, and Paranthias. The primary purpose for assembling the guide is for use with projects that deploy underwater video camera systems. The most vital source of information used to develop the guide was an archive of underwater video footage recorded during fishery projects. These video tapes contain 348 hours of survey activity and are maintained at the National Marine Fisheries Service (NMFS), Pascagoula, Mississippi. This footage spans several years (1980-92) and was recorded under a wide variety of conditions depicting diverse habitats from areas of the western North Atlantic Ocean, Caribbean Sea, and Gulf of Mexico. Published references were used as sources of information for those species not recorded on video footage during NMFS projects. These references were also used to augment information collected from video footage to provide broader and more complete descriptions. The pictorial guide presents information for all 25 grouper species reported to occur in the western North Atlantic. Species accounts provide descriptive text and illustrations depicting documented phases for the various groupers. In addition, species separation sheets based on important identification features were constructed to further assist with species identification. A meristic table provides information for specimens captured in conjunction with videoassisted fishery surveys. A computerized version enables guide users to amend, revise, update, or customize the guide as new observations and information become available. (PDF file contains 52 pages.

The highly connected even-cycle and even-cut matroids

The classes of even-cycle matroids, even-cycle matroids with a blocking pair, and even-cut matroids each have hundreds of excluded minors. We show that the number of excluded minors for these classes can be drastically reduced if we consider in each class only the highly connected matroids of sufficient size.Comment: Version 2 is a major revision, including a correction of an error in the statement of one of the main results and improved exposition. It is 89 pages, including a 33-page Jupyter notebook that contains SageMath code and that is also available in the ancillary file

On perturbations of highly connected dyadic matroids

Geelen, Gerards, and Whittle [3] announced the following result: let $q = p^k$ be a prime power, and let $\mathcal{M}$ be a proper minor-closed class of $\mathrm{GF}(q)$-representable matroids, which does not contain $\mathrm{PG}(r-1,p)$ for sufficiently high $r$. There exist integers $k, t$ such that every vertically $k$-connected matroid in $\mathcal{M}$ is a rank-$(\leq t)$ perturbation of a frame matroid or the dual of a frame matroid over $\mathrm{GF}(q)$. They further announced a characterization of the perturbations through the introduction of subfield templates and frame templates. We show a family of dyadic matroids that form a counterexample to this result. We offer several weaker conjectures to replace the ones in [3], discuss consequences for some published papers, and discuss the impact of these new conjectures on the structure of frame templates.Comment: Version 3 has a new title and a few other minor corrections; 38 pages, including a 6-page Jupyter notebook that contains SageMath code and that is also available in the ancillary file

The Templates for Some Classes of Quaternary Matroids

Subject to hypotheses based on the matroid structure theory of Geelen, Gerards, and Whittle, we completely characterize the highly connected members of the class of golden-mean matroids and several other closely related classes of quaternary matroids. This leads to a determination of the eventual extremal functions for these classes. One of the main tools for obtaining these results is the notion of a frame template. Consequently, we also study frame templates in significant depth.Comment: 83 pages; minor corrections in Version 4; accepted for publication by Journal of Combinatorial Theory, Series

BSE: Risk, Uncertainty, and Policy Change

The authors discuss how, in our risk society, a range of potential risks and uncertainties are associated with new technologies and new diseases, such as BSE. These risks bring with them worries about human health, while the ability to assess and manage new health scares is an essential skill for government and related industries

On Density-Critical Matroids

For a matroid $M$ having $m$ rank-one flats, the density $d(M)$ is $\tfrac{m}{r(M)}$ unless $m = 0$, in which case $d(M)= 0$. A matroid is density-critical if all of its proper minors of non-zero rank have lower density. By a 1965 theorem of Edmonds, a matroid that is minor-minimal among simple matroids that cannot be covered by $k$ independent sets is density-critical. It is straightforward to show that $U_{1,k+1}$ is the only minor-minimal loopless matroid with no covering by $k$ independent sets. We prove that there are exactly ten minor-minimal simple obstructions to a matroid being able to be covered by two independent sets. These ten matroids are precisely the density-critical matroids $M$ such that $d(M) > 2$ but $d(N) \le 2$ for all proper minors $N$ of $M$. All density-critical matroids of density less than $2$ are series-parallel networks. For $k \ge 2$, although finding all density-critical matroids of density at most $k$ does not seem straightforward, we do solve this problem for $k=\tfrac{9}{4}$.Comment: 16 page

Templates for Representable Matroids

The matroid structure theory of Geelen, Gerards, and Whittle has led to a hypothesis that a highly connected member of a minor-closed class of matroids representable over a finite field is a mild modification (known as a perturbation) of a frame matroid, the dual of a frame matroid, or a matroid representable over a proper subfield. They introduced the notion of a template to describe these perturbations in more detail. In this dissertation, we determine these templates for various classes and use them to prove results about representability, extremal functions, and excluded minors. Chapter 1 gives a brief introduction to matroids and matroid structure theory. Chapters 2 and 3 analyze this hypothesis of Geelen, Gerards, and Whittle and propose some refined hypotheses. In Chapter 3, we define frame templates and discuss various notions of template equivalence. Chapter 4 gives some details on how templates relate to each other. We define a preorder on the set of frame templates over a finite field, and we determine the minimal nontrivial templates with respect to this preorder. We also study in significant depth a specific type of template that is pertinent to many applications. Chapters 5 and 6 apply the results of Chapters 3 and 4 to several subclasses of the binary matroids and the quaternary matroids---those matroids representable over the fields of two and four elements, respectively. Two of the classes we study in Chapter 5 are the even-cycle matroids and the even-cut matroids. Each of these classes has hundreds of excluded minors. We show that, for highly connected matroids, two or three excluded minors suffice. We also show that Seymour\u27s 1-Flowing Conjecture holds for sufficiently highly connected matroids. In Chapter 6, we completely characterize the highly connected members of the class of golden-mean matroids and several other closely related classes of quaternary matroids. This leads to a determination of the extremal functions for these classes, verifying a conjecture of Archer for matroids of sufficiently large rank

Field-Induced Breakup of Emulsion Droplets Stabilized by Colloidal Particles

We simulate the response of a particle-stabilized emulsion droplet in an external force field, such as gravity, acting equally on all $N$ particles. We show that the field strength required for breakup (at fixed initial area fraction) decreases markedly with droplet size, because the forces act cumulatively, not individually, to detach the interfacial particles. The breakup mode involves the collective destabilization of a solidified particle raft occupying the lower part of the droplet, leading to a critical force per particle that scales approximately as $N^{-1/2}$.Comment: 4 pages, plus 3 pages of supplementary materia