Overview
I am a data scientist residing in Sydney, Australia. I am currently the Chief Data Officer at the NSW Cancer Institute. This is my personal website, which holds links to my notes and research, that mostly tend to be in the area of Mathematics, applications of Bayesian Machine Learning and Network Graphs, and Music Information Retrieval.

My research tends to be pretty interdisciplinary so I have included a notebook below that goes through the prerequisites for this kind of research, and I have a number of notebooks holding my study notes that you may find helpful.

When I find the time I work as a jazz guitarist around Sydney, Australia, and also use this website to hold jazz transcriptions (mostly solos of Keith Jarrett and Allan Holdsworth) and any compositions and recordings I am working on.

Jamie Gabriel
 

General Notebooks


Setup
I mostly use JupyterLab running through Docker to manage most things related to research. Full details and set up instructions here. Occasionally I like to work with the HTM Machine Intelligence algorithms which can be tricky to get going so I have included that in these notes. This set up is really nice across lots of different math research and works well across different operating systems.

If I am not using JupyterLab, it's usually RStudio & R these days and I tend to build anything web related in Shiny with Django as the backend.


Python for Math
I tend not to use Sage these days but here is a really nice way to install and config the Sage JupyterLab environment running on Docker. For full details of the Docker Image see https://hub.docker.com/r/cemulate/sagemath-jupyterlab/.


Latest
  • 16th January 22: Ascertaining the criteria needed for graph populations to be bounded or unbounded (ES2)

  • 15th January 22: Exploring the fundamental properties of graphs and graph populations(ES1_2)

  • 10th January 22: A new series of notes on Exceptional Structures in mathematics(ES1_1)

  • 15th December 21: Ascertaining the uniqueness of algebraic solutions to the geometric quintic equation (SPE26)

  • 19th December 21: Deriving an algebraic solution of the general quintic polynomial equation (SPE25)

  • 3rd December 21: An overview of the fundamental structures of Algebraic Calculus and area on a parabola (AC1_2)

  • 1st December 21: Outlining the foundations of Affine geometry to underpin the construction of dCB curves(DCB3)

  • 13th November 21: Using De Casteljau's algorithm and splitting dCB curves (DCB2)

  • 2nd November 21: Transforming the general quintic to geometric form (SPE24)

  • 27th October 21: Incorporating the patterns found in signs of coefficient to generate a general solution to polynomial equations (SPE23)

  • 23rd October 21: Introduction to DeCastelau Bezier Curves and the DCB Parametrization theorem (DCB1)

  • 10th October 21: Continuing to explore the bridge between BiTri numbers and polygonal subdivisions (SPE22)

  • 6th October 21: Exploring ternary operations on Fuss polygonal subdivisions and thier associated ternary trees (SPE21)

  • 2nd October 21: Exploring the link between polygon subdivisions and polynomial equations (SPE20)

  • 22nd September 21: Understanding the formal object that is a sum of all polygons with all of their subdivisions into triangles (SPE18)

  • 20th September 21: Understanding how Catalan and Fuss numbers relate to binary and ternary trees and how these trees can be created from n-gons (SPE16)

  • 2nd September 21: Exploring the structure of the quartic equation in relation to BiTriQuad numbers (SPE15)

  • 15th August 21: Exploring the relationship between solutions to polynomial equations, sides of polygons and BiTri numbers (SPE13_14)

  • 10th August 21: Continuing to explore patterns of matrices created by the solutions of polynomial equations, referencing Knuth, Stanley and Dickau (SPE11)

  • 4th August 21: Exploring different pattterns in the matrices created by the solutions of polynomial equations (SPE10)

  • 29th July 21: Extending the conjecture beyond Catalan numbers using matrices and examining resulting patterns using OEIS to find Catalan and Fuss numbers (SPE9)

  • 26th July 21: Comparing the conjecture for a solution to the general cubic using Catalan Numbers to traditional formulas (SPE8)

  • 15th July 21: Testing a conjecture for a solution to the general cubic using Catalan Numbers (SPE7)

  • 10th July 21: Extending the power series approach to the quartic case (SPE6)

  • 28th June 21: Unpacking the structure of coefficients in the solutions of general polynomials (SPE5)

  • 20th June 21: Finding patterns in solutions of general polynomials (SPE4)

  • 18th June 21: Extending the power series approach to the cubic case (SPE3)

  • 7th June 21: Discovering Catalan numbers in the solutions of general quadratics when using power series subsitution (SPE2)

  • 2nd June 21: The inherent difficulties that arise when solving higher degree polynomials using radicals (SPE1)