Estimation in discretely observed diffusions killed at a threshold

Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modeled as discretely observed diffusions which are killed when the threshold is reached. Statistical inference is often based on the misspecified likelihood ignoring the presence of the threshold causing severe bias, e.g. the bias incurred in the drift parameters of the Ornstein-Uhlenbeck model for biological relevant parameters can be up to 25-100%. We calculate or approximate the likelihood function of the killed process. When estimating from a single trajectory, considerable bias may still be present, and the distribution of the estimates can be heavily skewed and with a huge variance. Parametric bootstrap is effective in correcting the bias. Standard asymptotic results do not apply, but consistency and asymptotic normality may be recovered when multiple trajectories are observed, if the mean first-passage time through the threshold is finite. Numerical examples illustrate the results and an experimental data set of intracellular recordings of the membrane potential of a motoneuron is analyzed.Comment: 29 pages, 5 figure

A study of dependency features of spike trains through copulas

Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence of direct links between neuron from data is still a not completely solved problem. To enlarge the number of tools for detecting the underlying network structure, we propose here the use of copulas, pursuing on a research direction we started in [1]. Here, we adapt their use to distinguish different types of connections on a very simple network. Our proposal consists in choosing suitable random intervals in pairs of spike trains determining the shapes of their copulas. We show that this approach allows to detect different types of dependencies. We illustrate the features of the proposed method on synthetic data from suitably connected networks of two or three formal neurons directly connected or influenced by the surrounding network. We show how a smart choice of pairs of random times together with the use of empirical copulas allows to discern between direct and un-direct interactions

Neuromorphic cross correlation of digital spreading codes

Includes abstract.Includes bibliographical references (leaves 85-88).The study of neural networks is inspired by the mystery of how the brain works. In a quest to solve this mystery, scientists and engineers hope that they will learn how to build more powerful computational systems that are capable of processing information much more efficiently than today’s digital computer systems. This dissertation involves a biologically inspired circuit which can be used as an alternative for a cross correlation engine. Cross correlation engines are widely used in spread spectrum, wireless communication systems that use digital spreading codes to divide a single communication medium into separate channels. This technology is used in many systems such as GPS, ZigBee and GSM mobile communications. The technology is renowned for its robustness and security since it is highly tolerant to signal jamming and spoofing. Digital spreading in wireless communication is also widely used in military systems and has recently been proposed for use in the medical sector for neural prostheses. A limitation of using digital spreading is that the computational demands on the cross correlation engine are normally quite high and is generally considered to be the limiting factor in designing low-power portable devices. In recent developments proposed by Tapson, it was shown that a two-neuron mutual inhibition network can be used to generate a cross correlation like function (Tapson et al., 2008). In this work, the two-neuron cross correlation engine is analysed specifically for application on a particular set of digital spreading codes called Gold codes. Based on the analysis, the neuron’s response to an input signal is optimised in favour of yielding a neural cross correlation that resembles the mathematical cross correlation more closely. The aim is to find a biologically inspired computer that is practically viable in an electrical engineering application involving a digital spread spectrum communication system

Spatiotemporal Pattern Detection with Neuromorphic Circuits

In this dissertation, neuromorphic circuits are used to implement spiking neural networks in order to detect spatiotemporal patterns. Unsupervised training and detection-by-design techniques were used to attain the appropriate connectomes and perform pattern detection. Unsupervised training was performed by feeding random digital spikes with a repeating embedded spatiotemporal pattern to a spiking neural network composed of leaky integrate-and-fire neurons and memristor-R(t) element circuits which implement spike-timing-dependent plasticity learning rules. Detection-by-design was achieved using neuromporphic circuits and digital logic gates. When detection-by-design was achieved using both neuromorphic circuits and digital logic gates, a network was created of spatiotemporal pattern detector circuits, each of which was capable of detecting the three fundamental spatiotemporal patterns (NA-NA-Δt, NA-NB-Δt, and NA-NB-Coincidence), in order to detect combinations of two-spike features in the desired spatiotemporal pattern. The spatiotemporal pattern was detected when all of the two-spike features were detected. Similarly, when detection-by-design was achieved using only neuromorphic circuits, a Complex Pattern Detecting Network was was formed by combining Simple Pattern Detecting Networks, each of which was capable of detecting the three fundamental spatiotemporal patterns. The Complex Pattern Detector was used in a proof-of-concept to demonstrate a detect-and-generate spatiotemporal symbol computing paradigm