Mary

Mary Aprahamian

The University of Manchester
School of Mathematics
Alan Turing Building, 2.111
M13 9PL, Manchester, UK

+44 (0)161 306 3670 (office)

Mary.Aprahamian[at]manchester.ac.uk

Résumé

Here is a brief overview of my experience so far. My full CV offers more detail.


Download my CV

Current position

I am a postdoc in the Numerical Linear Algebra group at the School of Mathematics, The University of Manchester. I am working with Prof. Nick Higham on the project Functions of Matrices: Theory and Computation. I have worked on some special matrix functions and have a strong interest in network analysis.


My research

Education

I recently defended my thesis Theory and Algorithms for Periodic Functions of Matrices, with Applications , which was completed under the supervision of Prof. Nick Higham at The University of Manchester. I completed my undergraduate degree in Mathematics at The University of Edinburgh in 2011. Prior to this I attended the Red Cross Nordic UWC in Norway, where I studied for an International Baccalaureate Diploma.

RCNUWC

Personal

I was born and raised in Varna, at the Black Sea coast of Bulgaria and I am ethnically Armenian. In my spare time I enjoy reading Maths papers at different locations in the world.


Kaliakra

Research

Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms (with Nick Higham), MIMS EPrint 2016.4.

MATLAB codes.

Theoretical and computational aspects of matrix inverse trigonometric and inverse hyperbolic functions are studied. Conditions for existence are given, all possible values are characterized, and principal values are defined and shown to be unique primary matrix functions. Various functional identities are derived, some of which are new even in the scalar case, with care taken to specify precisely the choices of signs and branches. Key tools used in the derivations are the matrix unwinding function and the matrix sign function. A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree rational approximation is derived.

Matching Exponential-Based and Resolvent-Based Centrality Measures (with Des Higham and Nick Higham), Journal of Complex Networks. Advance Access Published June 29, 2015.

The relative importance of nodes in a network can be quantified via functions of the adjacency matrix. Two popular choices of function are the exponential, which is parameter-free, and the resolvent function, which yields the Katz centrality measure. Katz centrality can be the more computationally efficient, especially for large directed networks, and has the benefit of generalizing naturally to time-dependent network sequences, but it depends on a parameter. We give a prescription for selecting the Katz parameter based on the objective of matching the centralities of the exponential counterpart. For our new choice of parameter the resolvent can be very ill conditioned, but we argue that the centralities computed in floating point arithmetic can nevertheless reliably be used for ranking. Experiments on six real networks show that the new choice of Katz parameter leads to rankings of nodes that generally match those from the exponential centralities well in practice.

The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential (with Nick Higham), SIAM J. Matrix Anal. Appl. 35 (1): 88-109, 2014.

MATLAB codes.

Audio recording and slides of my talk on the unwinding function at the SIAM Annual Meeting 2013.

A new matrix function corresponding to the scalar unwinding number of Corless, Hare, and Jeffrey is introduced. This matrix unwinding function, is shown to be a valuable tool for deriving identities involving the matrix logarithm and fractional matrix powers. The unwinding function is also shown to be closely connected with the matrix sign function. An algorithm for computing the unwinding function based on the Schur–Parlett method with a special reordering is proposed. It is shown that matrix argument reduction using the matrix unwinding function can give significant computational savings in the evaluation of the exponential by scaling and squaring algorithms.

Conferences and visits

Here you can find some of the meetings I have attended recently and some I am planning to attend in the near future.