The design of conservative finite element discretisations for the vectorial modified KdV equation

We design a consistent Galerkin scheme for the approximation of the vectorial modified Korteweg-de Vries equation. We demonstrate that the scheme conserves energy up to machine precision. In this sense the method is consistent with the energy balance of the continuous system. This energy balance ensures there is no numerical dissipation allowing for extremely accurate long time simulations free from numerical artifacts. Various numerical experiments are shown demonstrating the asymptotic convergence of the method with respect to the discretisation parameters. Some simulations are also presented that correctly capture the unusual interactions between solitons in the vectorial setting

On limit points of the sequence of normalized prime gaps

Let $p_n$ denote the $n$th smallest prime number, and let $\boldsymbol{L}$ denote the set of limit points of the sequence $\{(p_{n+1} - p_n)/\log p_n\}_{n = 1}^{\infty}$ of normalized differences between consecutive primes. We show that for $k = 9$ and for any sequence of $k$ nonnegative real numbers $\beta_1 \le \beta_2 \le ... \le \beta_k$, at least one of the numbers $\beta_j - \beta_i$ ($1 \le i < j \le k$) belongs to $\boldsymbol{L}$. It follows at least $12.5$ of all nonnegative real numbers belong to $\boldsymbol{L}$.Comment: Revised and improve

K-theory for Leavitt path algebras: computation and classification

We show that the long exact sequence for K-groups of Leavitt path algebras deduced by Ara, Brustenga, and Cortinas extends to Leavitt path algebras of countable graphs with infinite emitters in the obvious way. Using this long exact sequence, we compute explicit formulas for the higher algebraic K-groups of Leavitt path algebras over certain fields, including all finite fields and all algebraically closed fields. We also examine classification of Leavitt path algebras using K-theory. It is known that the K_0-group and K_1-group do not suffice to classify purely infinite simple unital Leavitt path algebras of infinite graphs up to Morita equivalence when the underlying field is the rational numbers. We prove for these Leavitt path algebras, if the underlying field is a number field (which includes the case when the field is the rational numbers), then the pair consisting of the K_0-group and the K_6-group does suffice to classify these Leavitt path algebras up to Morita equivalence.Comment: 34 pages; Version II Comments: A few typos corrected. Version III Comments: Bibliography updated. This is the version to be publishe

Insights into the early evolution of NF-kappaB signaling based on computational analyses of cnidarian genomes and transcriptomes

NF-kappaB is an ancient transcription factor that is known to play a central role in regulating cellular stress responses in vertebrates and insects, including the innate immune response, and the response to a range of physiochemical insults such as UV radiation and oxidative stress. The early evolution of this pathway is not well understood, because little is known about NF-kappaB signaling in so-called basal animal lineages (e.g., sponges, cnidarians) or closely related outgroups to the Metazoa. Key to understanding the function of a transcription factor is to identify the target genes whose transcription it regulates. To investigate the regulatory role of NF-kappaB in basal animals, specifically the sea anemone Nematostella vectensis, I developed ForSite, a computational tool that identifies putative transcription factor binding sites in the genome in proximity to expressed genes, and I helped to generate a new annotated reference transcriptome for N. vectensis. After demonstrating that ForSite could be used to identify a set of genes enriched for known NF-kappaB targets in human, I applied ForSite along with multiple winnowing criteria (co-localization of p300 binding; evolutionary conservation of target genes) to identify a high-priority list of potential NF-kappaB targets in the anemone. Among the most convincing set of likely target genes are members of a conserved anti-viral pathway, which suggests NF-kappaB plays an ancient role in innate immunity that dates to the cnidarian-bilaterian ancestor. Application of ForSite to two additional cnidarian species, Hydra magnipapillata and Acropora digitifera, failed to show significant conservation of regulation of biological processes by NF-kappaB among the cnidarian species

Referendum on the Revolution: The Pennsylvania Constitutional Debate, 1776-1784

The Pennsylvania constitution of 1776 ignited an extensive and intractable debate that remained at the center of the state’s politics throughout the Revolutionary period. This debate encompassed disagreement over a broad range of questions relating to the relationship between government and society, many of which brought into question the implications of the concept of popular sovereignty for governmental structure and popular political agency. Competing notions regarding these issues, while expressed within a general framework of consensus concerning the source of political authority [the people], revealed fundamentally different visions of governmental order. Partisans presented these visions as inextricably connected to their respective understandings of the American Revolution. This debate suggests that constitutionalism and political ideology were closely connected to, and mutually informative of, one another during the Revolution and that factions within the Patriot cause perceived their differing visions of government and brands of constitutionalism as inseparable from the cause of the Revolution itself

The effect of vandalism on fibre composite structures

With the emergence of fibre composite structures in real world civil engineering structures the effect of damage to these structures needs to be known. This study will limit to real world tools being used to tamper and damage the fibre composite to desired levels not just to destruction. The damage to the fibre composites will be from a cutting implement, a blunt impact implement, a sharp impact implement and small amounts of fire. This project seeks to investigate the effect of common types of vandalism on fibre composite structures, define the typical kinds of vandalism and with what tools they occur with and whether any of these defects will have a negative effect on the structural integrity of the beam or structure. Define the amount of damage needed before noticeable negative effects start to occur in the structure and investigating whether these effects translate into large scale environments. The objectives of this research were to research the background information regarding fibre composites design and the typical usage of the fibre composite materials. Investigate and document levels of vandalism for testing, analyse and test unaffected samples to provide a standard. Analyse and test vandalised samples with ranging levels of vandalism, and investigate the effect of vandalism in integrated fibre composite structures/elements.For the sandwich composites the ease of cutting the material has been found and that has been found to be significant. The panels used also were found to be susceptible to burning of the skin but the inner core was immune to burning. With the blunt and sharp impact damage was found to be fairly significant in ultimate load but not very effective in reducing flexural stiffness. The blunt damage if excessive was very effective. The pultrusions were found to be extremely resistant to burning where no damage was found or damage was irrelevant. The pultrusion was also found to be very resistant to blunt impact where little to no damage was able to be recorded. Like the pultrusions counterpart the ability to be cut was significant. Further research is needed in to the fatigue behaviour of damaged fibre composites. The effect the damage has to the fibre composites needs further refinement and the ability of the damage to affect large specimen and full scale panels needs to be undertake

Re-examining associated bone groups from southern England and Yorkshire, c4000BC to AD1550.

In recent years, zooarchaeology has started to move beyond purely economic interpretations towards a social zooarchaeology. In particular, these `social' interpretations have often concentrated upon Associated Bone Groups (ABGs), also referred to as `special animal deposits' or `animal burials', rather than upon the disarticulated and fragmented faunal remains more commonly recovered from archaeological sites. Previous studies of these ABG deposits have largely been limited to a single period and a small sample of sites. The majority of studies have also been concentrated on the Wessex region and have not examined in detail the osteological composition of these deposits. The purpose of this thesis is to move beyond these limitations. Therefore, it investigates the nature of ABGs from the Neolithic to the Medieval period for the contrasting regions of southern England and Yorkshire. This has been achieved by collecting detailed information for ABGB from publicly available sourcesa nd analysing it utilising modern database technology. Overall, data from 2,062 ABGs have been collected, 1,863 from the southern England region and 199 from Yorkshire. Although the majority of previous literature concerns Iron Age deposits, in fact the largest proportion of ABGB from both regions comes from Romano-British sites. Furthermore, their nature is highly variable within and between periods and regions. The previous interpretation of these deposits is also an important factor. Currently, ABG deposits from prehistoric and Romano-British contexts are commonly viewed as the results of ritual activities. I iowever, deposits of more recent date are more often considered to be the result of mundane actions. The review of previous literature shows that the interpretation of these deposits is changeable and linked to development in archaeological paradigms. This study collected data on ABGs published from the 1940's onwards, allowing these changes in interpretation to be tracked and, importantly, to review the links between the nature of the deposit and its interpretation. Results show that the interpretation of these deposits is influenced by key publications and current periodbased assumptions, with ritual interpretations often only given at a meta-level.F or example, Iron Age deposits are seen as `ritual', yet this does not provide information on the actions and the associated meaning and agenda which created them. This thesis shows that each ABG is unique, and to apply a meta-level interpretation to all ABGs, even from the same period, would be inaccurate and inappropriate. A biographical approach to the investigation of these deposits is developed, which leads to a more considered and informed view and can help us move away from a generalized interpretation. A biographical approach shows there is no standard type of ABG, which means there can be no standard interpretation. There are trends in the creation of ABGs, but each bone group is created by specific actions and it is the investigation of these individual events that moves us closer to the societies we wish to understand. This study has shown the value of not only utilising specialist data, but integrating such knowledge with other archaeological evidence. Use of this methodology will enable us to move beyond the perceived economic straightjacket towards a social zooarchacology