Massimiliano Tamborrino

. PhD student in Statistics and Probability Theory, Department of Mathematical Sciences, University of Copenhagen, since December 1 2009.
Master degree in Mathematics in 2009 at Mathematical Department, University of Torino, Italy.

Research interests

I'm working within the field of Statistic and Probability Theory. In particular, I'm interested in dependence structures in neuronal data. My principal supervisor is Susanne Ditlevsen, while my co-supervisor is Rune Berg (Department of Neuroscience and pharmacology).

I studied the connections in a neuronal network, modelling the dynamics of each neuron via jump and diffusion processes. We proved the weak convergence of a specific multivariate Markov jump process to a multivariate Ornstein Uhlenbeck process. Assuming a more general Markov jump process convergent weakly to a diffusion, we showed the weak convergence of the vector of its first passage times (FPTs) to that of the diffusion. In a different work, a method to detect dependencies between spike trains of pairs of neurons through copulas has been proposed. Finally, FPTs for 2 dimensional Wiener and LIF models have been theoretically and numerically analysed to describe the spike activity.
Keywords: Multivariate jump and diffusion processes, diffusion approximations, first passage times, copulas, neural connectivity .

Now, I'm focusing on a new work developed with my advisor and Professor Petr Lansky, from the Institute of Physiology in Prague. We are investigating the detection of the response latency (i.e. the intertime between the delivery of a stimulus and the response) in presence of spontaneous activity. This represents a difficult task, since the first spike after the stimulus might be due to spontaneous or evoked activity. Moreover, the response to the stimulus may happen after a delay time θ. Under opportune assumptions, we propose non-parametric and parametric estimators of θ and of the response latency.
Keywords: first-spike latency, non-parametric and parametric estimation, renewal process.

Publications

Sacerdote, L. and Tamborrino, M. (2010) Leaky Integrate and Fire models coupled through copulas: association properties of the Interspike Intervals. Chinese Journal of Physiology, vol.53 (6): 396-406.
Sacerdote, L., Tamborrino, M. and Zucca, C. (2012) Detecting dependencies between spike trains of pairs of neurons through copulas. Brain Research, Vol. 1434: 243-256.
Tamborrino, M., Sacerdote, L. and Jacobsen, M. (2011) Diffusion approximation and first passage time for multivariate jump processes. Submitted.
Tamborrino, M., Ditlevsen, S. and Lansky, P. (2012) Identification of noisy responce latency. Submitted.

Talks
2010 9th International Neural Coding Workshop, Lymassol, Cyprus. Dependencies Between Spike Times of a Couple of Neurons Mod- eled via a Two-Dimensional LIF Model .
2011 Annual Meeting in the KU Statistic Networks , Holte, Danmark. Weak convergence of k-dimensional Stein's processes to k-dimensional Ornstein Uhlenbeck processes .
2011 Institute of Physiology, Academy of Sciences of the Czech Republic, Prague, Czech Republic. Investigation of the Response Latency (Seminar).
2011 Statistical Methods For Dynamical Stochastic Models, Heidelberg, Germany. Diffusion Approximation and First Passage Time for Multivariate Jump Processes (Poster) .
2011 8th European Conference on Mathematical and Theoretical Biology, Krakow, Poland. Investigation of the Response Latency .
2011 ISI Satellite meeting , Copenhagen, Denmark. Identification of Noisy Response Latency.
2012 Welcome home workshop, Turin, Italy. Identification of Noisy Response Latency.

Teaching

Stochastic Processes (Instructor). Spring 2010, Block 4.
Stochastic Processes (Instructor). Autumn 2010, Block 2.
Stochastic Processes (Instructor). Autumn 2011, Block 2.

Contact information

Massimiliano Tamborrino
PhD student
Department of Mathematical Sciences
Universitetsparken 5
DK-2100 Copenhagen Ø, Denmark

Tel. +45 35320736
email: mt@math.ku.dk