194 research outputs found
Analysis of CDO tranche valuation and the 2008 credit crisis
No full textIncludes bibliographical references.The causes of the 2008 financial crisis were wide ranging. Some financial commentators have suggested there were significant inadequacies in the models used to price complex derivatives such as synthetic Collaterilised Debt Obligations (CDOs). We discuss the technical properties of CDOs and the modeling approaches used by CDO traders and the watchdog credit rating agencies. We look at how the pricing models fared before and during the financial crisis. Comparing our model prices to market synthetic CDO prices, we investigate how well these pricing models captured the underlying financial risks of trading in CDOs
On the Lebesgue integral and the Lebesgue measure: mathematical applications in some sectors of Chern-Simons theory and Yang-Mills gauge theory and mathematical connections with some sectors of String Theory and Number Theory
No full textIn this paper, in the Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In the Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in the Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings
An O(n log n) algorithm for finding dissimilar strings
No full textLet be a finite alphabet and . A string is said to be -dissimilar to , if no length substring of is equal to any length substring of . We present an algorithm which on input and an integer outputs an integer and such that:
- is -dissimilar to .
- There does not exist a string of length which is dissimilar to .Technical report LCSR-TR-26
Representing Finite Groups: A Semisimple Introduction
No full textThis graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material.
Representing Finite Groups: A Semisimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A final chapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematics and mathematical physics will also find this book useful.
A separate solutions manual is available for instructors.https://repository.lsu.edu/facultybooks/1505/thumbnail.jp
A new explicit formula for the solution of the Black-Merton-Scholes equation
No full textThe Black-Merton-Scholes equation plays a fundamental role in the option
pricing theory. Our main purpose is to derive an explicit formula for its solu-
tion, using simple tools from operator semigroups. The paper includes also an
expository treatment of how the equation arises
The Moduli Space of Flat Connections on Oriented Surfaces with Boundary
No full textAbstractA 2-form is constructed on the space of connections on a principal bundle over an oriented surface with boundary. This induces a symplectic structure for the moduli space of flat connections with boundary holonomies lying in prescribed conjugacy classes. The Yang–Mills quantum field measure is described for this situation. This measure converges to the normalized symplectic volume measure in the “classical” limit
Assessment of dopaminergic neuron degeneration in a C. elegans model of Parkinson's disease
No full textTransgenic Caenorhabditis elegans that expresses the full-length wild-type human α-synuclein in dopaminergic neurons provides a well-established Parkinson's disease (PD) nematode model. Here, we present a detailed protocol to monitor and dissect the molecular underpinnings of age-associated neurodegeneration using this PD nematode model. This protocol includes preparation of nematode growth media and bacterial food sources, as well as procedures for nematode growth, synchronization, and treatment. We then describe procedures to assess dopaminergic neuronal death in vivo using fluorescence imaging. For complete details on the use and execution of this protocol, please refer to SenGupta et al. (2021). © 2022 The Author(s
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