Anca Radulescu's home page

So then I made a drawing.

He looked at it carefully, then he said:No. This sheep is already very sickly. Make me another.

My friend smiled gently and indulgently. You see yourself, he said, that this is not a sheep. This is a ram. It has horns. So then I did my drawing over once more.

But it was rejected too, just like the others. This one is too old. I want a sheep that will live a long time. By this time my patience was exhausted, because I was in a hurry to start taking my engine apart. So I tossed off this drawing.

And I threw out an explanation with it. This is only his box. The sheep you asked for is inside.

    Anca Rădulescu
    Department of Applied Mathematics
    University of Colorado at Boulder
     office: ECOT 338
     office phone number: 735-6209
     email: radulesc at colorado dot edu

Research interests and publications

Curriculum Vitae

Real Dynamics

I am interested in how the dynamic complexity of a system evolves under deformations. This evolution is in general only partly understood. Following classical methods, I approach simple examples of dynamical systems from a quantitative perspective and I make use of the topological entropy as a particularly useful complexity measure.

Complexity of real dynamical systems, topological entropy

The connected isentropes conjecture in a space of quartic polynomials, 2007. Discrete and Continuous Dynamical Systems - Series B, 19 (1) 139-175.

Computing topological entropy in a space of quartic polynomials , 2007. Journal of Statistical Physics, 130 (2) 373-385.

Neural models of synaptic learning

(with Paul Adams , Neuroscience Department, Stony Brook University)

Recent work on Long Term Potentiation in brain slices shows that Hebb's rule is not completely synapse-specific, possibly due to intersynapse calcium diffusion. We extend the classical Oja unsupervised learning model of a single linear neuron to include Hebbian infidelity, by introducing an error matrix which expresses the crosstalk between Hebbian updating at different connections.

Synaptic plasticity and network dynamics in learning and memory processes

Hebbian inspecificity in Oja unsupervised learning (with Paul Adams and Kingsley Cox), 2009. To appear in the Journal of Theoretical Biology (ArXiv)

Clinical neuroscience

(with the Laboratory for the Study of Emotion and Cognition, Stony Brook University Hospital)

My research targets in particular schizophrenia and attention deficit hyperactivity disorder (ADHD). Both are surprisingly widespread illnesses, with complex symptoms and mysterious causes, with dramatic impact on both individual and society. I am workig on developing a rigorous mathematical tool-box for the study of the dynamics and complexity of the two conditions.

A complex systems approach to dysregulation in psychiatric conditions

Schizophrenia - a parameters, game?, 2008. Journal of Theoretical Biology, 254 (1) 89-98 (ArXiv)

A systems approach to prefrontal-limbic dysregulation in schizophrenia , 2008 (with L. R. Mujica-Parodi). Neuropsychobiology, 57 (4) 206-216.

A multi-etiology model of systemic degeneration in schizophrenia, 2009. To appear in the Journal of Theoretical Biology (ArXiv)

A principal component network analysis of prefrontal-limbic fMRI time series in schizophrenia patients and healthy controls, 2009 (with L.R. Mujica-Parodi). To appear in Psychiatry Research: Neuroimaging.

Miscellaneous papers and work in progress

Psychic embedding - vision and delusion, under review (Cogprints)

Combinatorics of sawtooth families and neural networks , in preparation

A dynamical systems model of schizophrenia, with Randy O'Reilly, in preparation

Delusion and chaos: a review of the brain dynamics studies of schizophrenia, in preparation