Singularity in signal theory

Singularity in signal theory

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Introduction to Singularity Theory

These three lectures were given in Trieste, SISSA, on September 30, October 5, and October 6, 2010. Many thanks to Professor Andrei Agrachev for inviting me and for very useful for me math discussions. Many thanks to all listeners for questions, comments, and patience (the lectures were twice longer than scheduled). I am very thankful to Alesha Remizov who took all the job on publishing these n...

Naked Singularity in a Modified Gravity Theory

Abstract. The cosmological constant induced by quantum fluctuation of the graviton on a given background is considered as a tool for building a spectrum of different geometries. In particular, we apply the method to the Schwarzschild background with positive and negative mass parameter. In this way, we put on the same level of comparison the related naked singularity (−M) and the positive mass ...

On some problems in singularity theory

Modeling neuronal bursting: singularity theory meets neurophysiology∗

Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting. The proposed approach combines singularity theory and geometric singular perturbations to unfold the geometry of multiple time-scales attractors in the neighborhood of high-codimension singularities. We detect a three-time scale bursting attractor in the u...