11,898 research outputs found
A Gauss-Kuzmin theorem for continued fractions associated with non-positive interger powers of an integer
We consider a family of interval maps introduced by
Hei-Chi Chan [5] as generalizations of the Gauss transformation. For the
continued fraction expansion arising from , we solve its
Gauss-Kuzmin-type problem by applying the method of Rockett and Sz\"usz [18].Comment: 18 page
The mathematical research of William Parry FRS
In this article we survey the mathematical research of the late William (Bill) Parry, FRS
Spatio-temporal spike trains analysis for large scale networks using maximum entropy principle and Monte-Carlo method
Understanding the dynamics of neural networks is a major challenge in
experimental neuroscience. For that purpose, a modelling of the recorded
activity that reproduces the main statistics of the data is required. In a
first part, we present a review on recent results dealing with spike train
statistics analysis using maximum entropy models (MaxEnt). Most of these
studies have been focusing on modelling synchronous spike patterns, leaving
aside the temporal dynamics of the neural activity. However, the maximum
entropy principle can be generalized to the temporal case, leading to Markovian
models where memory effects and time correlations in the dynamics are properly
taken into account. In a second part, we present a new method based on
Monte-Carlo sampling which is suited for the fitting of large-scale
spatio-temporal MaxEnt models. The formalism and the tools presented here will
be essential to fit MaxEnt spatio-temporal models to large neural ensembles.Comment: 41 pages, 10 figure
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