05/06/2023 – D. Baraskiewicz

Applications of Fractal Geometry in DNA and Genome Studies

In this paper I will cover some methods involving fractal geometry that are used in the analysis of DNA sequences. This paper will have a particular focus on the identification and study of VNTRs (Variable Number of Tandem Repeats), which are repeated sequences of nucleotides within a DNA sequence. The ability to identify VNTRs and their location within a DNA sequence leads to many applications, which are covered in the conclusion. This paper will also be concerned with the identification of other properties such as long-range power law correlations, patches and coding/non-coding regions. The Indicator Matrix method, the DNA walk and Detrended Fluctuation Analysis are explored, with the Indicator Matrix Method chosen as the most effective.

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02/12/2022 – H. Pearson

Combinatorial Games

We begin by developing the standard theory of normal play impartial games. Then misère quotients are introduced, which we will use to prove a powerful periodicity theorem for both normal and misère octal games. Finally, we develop the nim product to form the field of nimbers and solve a related computationally interesting game using using the tartan theorem.

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07/02/2022 – M. A. Vogiatzi

Acoustic Metamaterials and Future Research Challenges

In this work, we explore acoustic metamaterials (AMM), a fairly new and active field of research. Initially, we present an overview of the advances in the field and explain the metamaterial properties. Then, we delve further and focus on the sound absorption and insulation applications of these materials. Finally, we report on the current state of knowledge, present the problem of the narrow band efficiency of AMM and give possible solutions based on the literature.

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20/12/2021 – X. Yin

A Review of AMR Effects in FM Semiconductors

Anisotropic magnetoresistance (AMR) is a property of magnetic materials that has many applications in the field of spintronics. This review firstly describes the basic physics of the phenomenon, then provides an insight on the useful applications of this effect in the field of spintronics. Finally, a few summaries of recent research being carried out to understand the effect of AMR in semiconductors, in particular, the ferromagnetic(FM) semiconductor GaMgAs (gallium manganese arsenide), are given. The summaries focus on two widely studied advancements of AMR research: enhancing the Curie temperature and observing TAMR effects in GaMgAs. A conclusion and speculations about future research direction are included at the end.

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20/12/2021 – M. Draskovits

The Role of Nanoradios and Nanosensors in Scientific Observation

We have decided to diverge from the structure of scientific articles in the presentation of this work, voting for an in medias res approach on practical research which might better serve the needs of the reader. Focusing on the benefits of nanotechnology in delivering scientific measurements, we attempt to give an overview on nanosensors and nanoradios, their role in observation and future potential applications. We shall introduce the fundamentals of nanoscience to allow readers a deeper understanding of the topic. In this article, we define nanosensors as devices, capable of measuring at least one parameter, with a size not exceeding 100 nm, although some authors also include any equipment beyond this size limit that can be used to measure properties on this scale.

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05/2021 – O. Daisey

Quadratic Forms, K-Theory and Galois Cohomology

We present an account of the basic theory of quadratic forms, central simple algebras over a field, and Milnor’s K-theory, which culminates in a complete exposition of Alexander Merkurjev’s 2006 proof of the norm residue homomorphism of degree two.

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04/2019 – D. L. Fairbairn

Computational Methods in Graph Connectivity

Connectivity invariants aim to give a quantifiable measure of robustness to analyze the effect of failure on a network. This report introduces the notions of vertex and edge connectivity of a graph, giving explicit steps for their calculation. Whitney’s Inequality relates these connectivity invariants and the minimal vertex degree. Fundamental theorems in connectivity, such as, Menger’s Theorem, Whitney’s Theorem and the duality between maximal flow and minimal capacity cuts will be discussed in-depth. A solution to the edge connectivity augmentation problem will be presented using the cactus representation. Construction of the cactus representation will be detailed in meticulous steps with a critical analysis of current literature. An introduction to the basic concepts of graph theory, graph representations, complexity theory and algorithmic problem solving are also included.

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17/04/2018 – D. T. Dobrowolski

From Spinors to Twistors: Eliminating Redundancies in Scattering Amplitudes

The scattering amplitude of an interaction may be used to determine its cross-section and thereby the probability of its occurrence in a particle collider. Thus, a reliable computation of the scattering amplitude may easily be compared to experiment, thereby providing a useful tool for evaluating the successes and failures of the Standard Model. Ultimately this implies that highly accurate computation of scattering amplitudes could be particularly crucial in developing a more fundamental theory of particle physics. Scattering amplitudes, however, can be computationally expensive to calculate, especially for greater multiplicities
and at higher orders. This is a result of multiple redundancies present in the theory, which may be removed by a number of techniques that have been developed for this purpose. In this paper, an outline of some of these techniques is given and examples are provided so as to demonstrate their efficacy.

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