An exploration of two infinite families of snarks

Thesis (M.S.) University of Alaska Fairbanks, 2019In this paper, we generalize a single example of a snark that admits a drawing with even rotational symmetry into two infinite families using a voltage graph construction techniques derived from cyclic Pseudo-Loupekine snarks. We expose an enforced chirality in coloring the underlying 5-pole that generated the known example, and use this fact to show that the infinite families are in fact snarks. We explore the construction of these families in terms of the blowup construction. We show that a graph in either family with rotational symmetry of order m has automorphism group of order m2m⁺¹. The oddness of graphs in both families is determined exactly, and shown to increase linearly with the order of rotational symmetry.Chapter 1: Introduction -- 1.1 General Graph Theory -- Chapter 2: Introduction to Snarks -- 2.1 History -- 2.2 Motivation -- 2.3 Loupekine Snarks and k-poles -- 2.4 Conditions on Triviality -- Chapter 3: The Construction of Two Families of Snarks -- 3.1 Voltage Graphs and Lifts -- 3.2 The Family of Snarks, Fm -- 3.3 A Second Family of Snarks, Rm -- Chapter 4: Results -- 4.1 Proof that the graphs Fm and Rm are Snarks -- 4.2 Interpreting Fm and Rm as Blowup Graphs -- 4.3 Automorphism Group -- 4.4 Oddness -- Chapter 5: Conclusions and Open Questions -- References

Fixing Rule 702: The PCAST Report and Steps to Ensure the Reliability of Forensic Feature-Comparison Methods in the Criminal Courts

In response to PCAST’s recommendation, the Standing Advisory Committee on Evidence Rules convened a meeting on forensic expert testimony, Daubert, and Rule 702 on October 27, 2017, at Boston College Law School to inform itself about the issues.22 The meeting included presentations by twenty-six speakers (including myself) and discussion among the attendees. The purpose of this Article is to summarize aspects of the PCAST report relevant to its recommendation to the Standing Advisory Committee on Evidence Rules and to propose a path forward with respect to Rule 702

Random planar maps and graphs with minimum degree two and three

We find precise asymptotic estimates for the number of planar maps and graphs with a condition on the minimum degree, and properties of random graphs from these classes. In particular we show that the size of the largest tree attached to the core of a random planar graph is of order c log(n) for an explicit constant c. These results provide new information on the structure of random planar graphs.Comment: 32 page

Vietnamese and the NP/DP parameter

This paper investigates the place of Vietnamese in the NP/DP typology as formulated by Bošković (2005, 2008, 2009, 2010). We show that Bošković’s NP/DP parameter breaks down into at least three separate parameters. In many languages, these three parameters line up in a consistent manner and conspire to give the impression that there is a single macro-parameter at work. However, due to its mixed status, Vietnamese reveals that there are in fact three smaller parameters (nominal, clausal, and quantificational) at work, and that these are independently fixed (as [–DP], [+TP], and [–movement], respectively). Moreover, Vietnamese can in general be classified as a topic-prominent language, a classification which requires more research but which plays an important role in determining the behavior of Vietnamese with regard to many of the syntactic properties discussed

Are there any stable magnetic fields in barotropic stars?

We construct barotropic stellar equilibria, containing magnetic fields with both poloidal and toroidal field components. We extend earlier results by exploring the effect of different magnetic field and current distributions. Our results suggest that the boundary treatment plays a major role in whether the poloidal or toroidal field component is globally dominant. Using time evolutions we provide the first stability test for mixed poloidal-toroidal fields in barotropic stars, finding that all these fields suffer instabilities due to one of the field components: these are localised around the pole for toroidal-dominated equilibria and in the closed-field line region for poloidal-dominated equilibria. Rotation provides only partial stabilisation. There appears to be very limited scope for the existence of stable magnetic fields in barotropic stars. We discuss what additional physics from real stars may allow for stable fields.Comment: 16 pages, 11 figures. Some minor revision from v1, including a new figure; results unchanged. Now published in MNRA

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The distribution of lectins across the phylum Nematoda : a genome-wide search

Nematodes are a very diverse phylum that has adapted to nearly every ecosystem. They have developed specialized lifestyles, dividing the phylum into free-living, animal, and plant parasitic species. Their sheer abundance in numbers and presence in nearly every ecosystem make them the most prevalent animals on earth. In this research nematode-specific profiles were designed to retrieve predicted lectin-like domains from the sequence data of nematode genomes and transcriptomes. Lectins are carbohydrate-binding proteins that play numerous roles inside and outside the cell depending on their sugar specificity and associated protein domains. The sugar-binding properties of the retrieved lectin-like proteins were predicted in silico. Although most research has focused on C-type lectin-like, galectin-like, and calreticulin-like proteins in nematodes, we show that the lectin-like repertoire in nematodes is far more diverse. We focused on C-type lectins, which are abundantly present in all investigated nematode species, but seem to be far more abundant in free-living species. Although C-type lectin-like proteins are omnipresent in nematodes, we have shown that only a small part possesses the residues that are thought to be essential for carbohydrate binding. Curiously, hevein, a typical plant lectin domain not reported in animals before, was found in some nematode species

Understanding plant responses to drought: how important is woody tissue photosynthesis?

Within trees, it is known that a part of the respired CO2 is assimilated in chlorophyll-containing stem and branch tissues. However, the role of this woody tissue photosynthesis in tree functioning remains unclear, in particular under drought stress conditions. In this study, stem diameter and leaf photosynthesis were measured for one-year-old cutting-derived plants of Populus nigra 'Monviso' under both well-watered and drought stress conditions. Half of the plants were subjected to a stem and branch light-exclusion treatment to prevent woody tissue photosynthesis to occur, while the other trees served as controls. Drought stress was induced in both treatments by limiting the water supply. We found that under well-watered conditions, light-exclusion resulted in reduced stem radial daily growth rate (DG) relative to DG observed for control trees. In response to drought, stem shrinkage of the light-excluded trees was more pronounced as compared to the control trees. Maximum leaf net photosynthesis (A(max)) decreased more rapidly in light-excluded trees compared to the controls during drought stress. Our results are the first to report on the potentially significant role of woody tissue photosynthesis in tree drought stress tolerance. Moreover, our study implies that the impact of assimilation of respired CO2 on tree functioning extends beyond local stem processes and indicates that woody tissue photosynthesis is potentially a key factor in understanding plant responses to drought stress