Dhruva Venkita Raman

Background - Research - Publications

Position: Research Associate

Office Location: BN4-86

E-mail: dvr23 [at] cam.ac.uk

Background

Research Interests

Let me begin by saying that I am easily interested in a variety of research topics, and am happy to talk to any potential collaborators or curious non-specialists.

My high-level interests lie in the construction and analysis of mathematical models of physical processes. Increasing computing power has allowed for the emergence of highly parameterised, nonlinear models of extremely complex systems. Extracting useful information from such models, however, remains a hard task for several reasons. One is model identifiability: in such models, the map from model behaviour to model parameter values is rarely unique. To take a simple example, the dynamics of a damped harmonic oscillator do not change if we multiply the mass, damping coefficient, and spring stiffness by a (nonzero) constant. In this case, model identifiability is restored, and mechanistic insight gained, by reparameterising the model in terms of its angular frequency and damping ratio. Even technically identifiable models are often practically unidentifiable, in that changing some combinations of parameters exerts a near-zero influence on model behaviour. For example, think of decreasing the time-constant of a subsystem of chemical reactions that already equilibrates near-instantaneously with respect to a larger system. I have worked on algorithms for finding less obvious unidentifiabilities (whether exact or practical) in large-scale models that, as with the oscillator example, allow for restoration of identifiability, reduction in the number of model parameters, and provision of mechanistic insight. I have also worked on the dual, statistical problem of quantifying the uncertainty associated with parameter estimates made from noisy data.

I am currently interested in models of neural circuits in the brain. There is increasing experimental evidence that such circuits continually rewire and change their physical parameters even while expressing the same behaviour. Insight into why this occurs, however, is currently lacking. Traditionally, computational models of such neural circuits have assumed a one-to-one correspondence between a particular behaviour and the underlying neural circuit. I am building models that dispense with the previous assumption, in order to investigate what advantages are conferred by this counter-intuitive behaviour.

Publications

Valmorbida, Giorgio; DVR; James Anderson. "Bounds for Input-and State-to-Output Properties of Uncertain Linear Systems." arXiv preprint arXiv:1505.05335 (2015).

DVR ; James Anderson; Antonis Papachristodoulou. "On the performance of nonlinear dynamical systems under parameter perturbation." Automatica 63 (2016): 265-273.

DVR ; James Anderson; Antonis Papachristodoulou. "A New Approach to Estimating the Robustness of Parameter Estimates to Measurement Noise". Proceedings of the American Control Conference 2016: 1820-1825.

Emilie Dufresne; Heather Harrington; DVR."The Geometry of Sloppiness." arXiv preprint arXiv:1608.05679 (2016).

Dissertations

DPhil Thesis: `On the Identifiability of Highly Parameterised Models of Physical Processes' (Link forthcoming)

MMath Dissertation ( MMathessay.pdf): 'A Probabilistic Analysis of the Dynamics of Stochastic Equations determined by the Gillespie Algorithm'