Automatic differentiation

Posted on 2018-06-03

This post serves as a documentation of my study of autodiff as well as a explainer of the subject. For my learning I benefited a lot from Toronto CSC321 slides and the autodidact project which is a pedagogical implementation of Autograd. That said, any mistakes in this note are mine (especially since some of the knowledge is obtained from interpreting slides!), and if you do spot any I would be grateful if you can let me know.

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Updates on open research

Posted on 2018-04-29

It has been 9 months since I last wrote about open (maths) research. Since then two things happened which prompted me to write an update.

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The Mathematical Bazaar

Posted on 2017-08-07

In this essay I describe some problems in academia of mathematics and propose an open source model, which I call open research in mathematics.

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Open mathematical research and launching toywiki

Posted on 2017-04-25

As an experimental project, I am launching toywiki.

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A \(q\)-Robinson-Schensted-Knuth algorithm and a \(q\)-polymer

Posted on 2016-10-13

(Latest update: 2017-01-12) In Matveev-Petrov 2016 a \(q\)-deformed Robinson-Schensted-Knuth algorithm (\(q\)RSK) was introduced. In this article we give reformulations of this algorithm in terms of Noumi-Yamada description, growth diagrams and local moves. We show that the algorithm is symmetric, namely the output tableaux pair are swapped in a sense of distribution when the input matrix is transposed. We also formulate a \(q\)-polymer model based on the \(q\)RSK and prove the corresponding Burke property, which we use to show a strong law of large numbers for the partition function given stationary boundary conditions and \(q\)-geometric weights. We use the \(q\)-local moves to define a generalisation of the \(q\)RSK taking a Young diagram-shape of array as the input. We write down the joint distribution of partition functions in the space-like direction of the \(q\)-polymer in \(q\)-geometric environment, formulate a \(q\)-version of the multilayer polynuclear growth model (\(q\)PNG) and write down the joint distribution of the \(q\)-polymer partition functions at a fixed time.

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