Fröhlich suggested considering invariants of ON together with the trace pairing (x, y) → TrN/Q(xy). This leads to local and global Hermitian discriminants of (ON, Tr) in “Hermitian classgroups.” Cassou-Noguès and Taylor showed these discriminants were enough to determine both local and global symplectic root numbers. This approach will be generalized to projective schemes over Z in lecture 3. O...

although old texts are distorted or changed due to various reasons such as unfamiliarity of writers who take them away from their origin and make it difficult to achieve a correct edition by using of the manuscripts, especially when there is a unique manuscript of the text or the existing manuscript is different with the other available versions, the correction of each text should be usually do...

Literature Review (LR) and Manuscript Preparatory (MP) tasks are two key activities for researchers. While process-based and technologicaloriented interventions have been introduced to bridge the apparent gap between novices and experts for LR tasks, there are very few approaches for MP tasks. In this paper, we introduce a novel task of shortlisting important papers from the reading list of res...

Algorithmic decipherment is a prime example of a truly unsupervised problem. The first step in the decipherment process is the identification of the encrypted language. We propose three methods for determining the source language of a document enciphered with a monoalphabetic substitution cipher. The best method achieves 97% accuracy on 380 languages. We then present an approach to decoding ana...

The aim of this project is to research the possibilities of applying unsupervised learning techniques for natural language and other sequential data to undeciphered texts and manuscripts. The undeciphered text used is the Voynich Manuscript, a mysterious book from the 15th or 16th century that is written in an unknown script. Some methods that could be applied to manuscripts such as these will ...

Introduction 2 1. The Group Law on Pell Conics and Elliptic Curves 2 1.1. Group Law on Conics 2 1.2. Group Law on Elliptic curves 3 2. The Group Structure 3 2.1. Finite Fields 3 2.2. p-adic Numbers 3 2.3. Integral and Rational Points 4 3. Applications 4 3.1. Primality Tests 4 3.2. Factorization Methods 5 4. 2-Descent 5 4.1. Selmer and Tate-Shafarevich Group 5 4.2. Heights 6 5. Analytic Methods ...

have many interesting applications. Though the authors describe why this approach should capture unique dynamics, I was disappointed to find that no new insight into the earth system or demonstrations of the application of this model to new problems are described in this manuscript. They do mention some possible applications, but do not show any applications here. This manuscript would be impro...

Based upon new global class field concepts leading to two-dimensional global Langlands correspondences, a modular representation of cusp forms is proposed in terms of global elliptic bisemimodules which are (truncated) Fourier series over R . As application, the conjectures of Shimura-Taniyama-Weil, Birch-Swinnerton-Dyer and Riemann are analyzed.