My little horse may think it queer
To stop without a town house near
Between the woods and frozen lake,
The darkest evening of the year.

He gives the harness bells a shake
To ask if there is some mistake;
The only other sound's the sweep
Of easy wind and downy flake.

Forests are wonderful and deep,
But I have promisses to keep
And miles to go before I sleep,
And miles to go before I sleep.

Pãdurea cui e, am aflat.
El însã locuieşte-n sat
Şi nu va şti cã i-am privit
Omãtul cum îi ninge-n hat.

Cãlutul meu a stat uimit,
Nu la vreo casã m-am oprit
Ci lîngã lacul înghetat
De-ntunecatul asfintit.

El hamul şi l-a scuturat
Sã-ntrebe de m-am înşelat,
Şi-afarã nici un zgomot încã,
Doar fulgul blînd de vînt suflat.

Pãdurea-i tainicã şi-adîncã,
Dar ce-ai promis e scris in stîncã,
Şi-odihna e departe încã,
Şi-odihna e departe încã.

Real Dynamics

Complexity of real dynamical systems, topological entropy

Thesis advisor: Prof. Jack Milnor , IMS Stony Brook

Ph.D. thesis title: The Connected Isentrope Conjecture in a Space of Quartic Polynomials
(or in preprint version , also to be found at http://www.math.sunysb.edu/preprints.html )

Detailed abstract in postscript format

Some related pictures

Some important references I used:
    J.Milnor, Dynamics in One Complex Variable
    M.Lyubich, Six Lectures On Real and Complex Dynamics
    J.Milnor, Hyperbolic Components in Spaces of Polynomial Maps
    J.Milnor, C.Tresser, On Entropy and Monotonicity for Real Cubic Maps
    O.Kozlowski, W.Shen, S. van Strien, Rigidity for Real Plynomials

Neural models of synaptic learning

(joint work with Prof. Paul Adams and Kingsley Cox, Neuroscience Department, Stony Brook)

Synaptic plasticity and network dynamics in learning and memory processes
Preprints on:
    An extended Hebbian model of unsupervised learning
    On estimating the quality of synaptic transmission in an Oja learning network (model based on geometry and filling factor)
    On estimating the quality of synaptic transmission in an Oja learning network (model based on chemical transmission and binding)

Related articles:
    F. Botelho, J. Jamison, A learning rule with generalized Hebbian synapses
    F. Botelho, J. Jamieson, paper1

Synaptic Darwinism

Formal neural networks

Cortical development and plasticity related to learning, memory and attention modulation

(with the Carlos Brody lab, Cold Spring Harbor Laboratories)

The role of GABA-ergic inhibition in promoting synaptic competition-regulation of synaptic depression through gating post-synaptic action potentials (project description)

Some references:
    S.Song, K.Miller, L.Abbott, Competitive Hebbian Learning Through Spike-Timing-Dependent Synaptic Plasticity
    J.J.Hopfield, C.Brody, Learning Rules and Network Repair in Spike-Timing-Based Computation Networks
    S.Song, L.Abbott, Cortical Dvelopment and Remapping through Spike Timing-Dependent Plasticity

Attentional modulation and vision

Kinetic theory

Clinical neuroscience

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

2.9 - PRECALCULUS:

3.3 - CALCULUS:

Syllabus
Schedule and homework assignments at www.math.sunysb.edu/~ancuta/syllabus3.3.html