Related papers: Extreme value statistics of nerve transmission del…
We study the statistical properties of a simple genetic regulatory network that provides heterogeneity within a population of cells. This network consists of a binary genetic switch in which stochastic flipping between the two switch states…
Spiking Neural Networks (SNNs) compute and communicate with asynchronous binary temporal events that can lead to significant energy savings with neuromorphic hardware. Recent algorithmic efforts on training SNNs have shown competitive…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
In the context of spiking neural networks, temporal coding of signals is increasingly preferred over the rate coding hypothesis due to its advantages in processing speed and energy efficiency. In temporal coding, synaptic delays are crucial…
We study the computational capacity of a model neuron, the Tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random…
We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase-lock…
Recent experiments have indicated that many biological systems self-organise near their critical point, which hints at a common design principle. While it has been suggested that information transmission is optimized near the critical…
Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of…
In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time…
By using the wavelet transformation (WT), we have analyzed the response of an ensemble of $N$ (=1, 10, 100 and 500) Hodgkin-Huxley (HH) neurons to {\it transient} $M$-pulse spike trains ($M=1-3$) with independent Gaussian noises. The…
It will be discussed the statistics of the extreme values in time series characterized by finite-term correlations with non-exponential decay. Precisely, it will be considered the results of numerical analyses concerning the return…
Precursor peaks in the wavenumber $k_{\mathrm{peak}}(t)$ maximizing the curl-of-vorticity spectrum have been observed to precede the dissipation peak in decaying turbulence. Because small perturbations in the initial condition can shift…
Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are…
The functional significance of correlations between action potentials of neurons is still a matter of vivid debates. In particular it is presently unclear how much synchrony is caused by afferent synchronized events and how much is…
We study a learning rule based upon the temporal correlation (weighted by a learning kernel) between incoming spikes and the internal state of the postsynaptic neuron, building upon previous studies of spike timing dependent synaptic…
Spike train signals recorded from a large population of neurons often exhibit low-dimensional spatio-temporal structure and modeled as conditional Poisson observations. The low-dimensional signals that capture internal brain states are…
We consider the extreme value statistics of $N$ independent and identically distributed random variables, which is a classic problem in probability theory. When $N\to\infty$, fluctuations around the maximum of the variables are described by…
Spiking neural networks have gained significant attention due to their brain-like information processing capabilities. The use of surrogate gradients has made it possible to train spiking neural networks with backpropagation, leading to…
For energy-efficient computation in specialized neuromorphic hardware, we present spiking neural coding, an instantiation of a family of artificial neural models grounded in the theory of predictive coding. This model, the first of its…
Many properties of perceptual decision making are well-modeled by deep neural networks. However, such architectures typically treat decisions as instantaneous readouts, overlooking the temporal dynamics of the decision process. We present…