Tracking movements of animals is essential for understanding behaviours in natural environments, as well as for investigating their neural correlates. Here we describe and evaluate the computer vision, statistical inference and statistical learning methods that we used to estimate positions, velocities and accelerations from videos of mice freely moving in a large arena. We provide code and sample data to reproduce all figures in the poster.

How distant cortical areas communicate with each other? This research combines state-ot-the-art electrophysiological recordings of large populations of single neurons, with optogenetic silencing, to investigate the causal influence of a higher-order visual area LM (V2 in mouse) on primary visual cortex (V1), and the influence of V1 on LM. I contributed a wonderful modeling tool: a linear dynamical system with external inputs model. With this model we can quantify precisely how visual inputs affect the dynamics of V1 and LM activity. Most importantly, we can estimate, for the first time, optogenetic stimulation receptive fields, quantifying how optogentic stimulation in a brain region (e.g., LM) modulates the activity of local (e.g., LM) or remote (e.g., V1) neural populations.

The derivative of a matrix functions is a four-dimensional tensor. Here I present key concepts from the differential calculus of matrix functions that allow to derive derivatives of matrix functions by only manipulating matrices, and not four-dimensional tensors. I illustrate the use of these concepts in didactic derivations of derivatives of two matrix functions, required to compute the derivative of the log-likelihood function of the probabilistic principal component analysis model.

We characterized microelectrode arrray recordings from cortical layers two and three of a person with epilepsy using a hidden Markov model with an autoregressive observation model. In agreement with previous studies, we found that seizure activity is highly stereotypical across different seizures separated by more than one hour from each other, and showed that seizures evolve as sequences of long-duration discrete states. Beyond previous studies, we showed that this stereotypicality and discreteness is evident outside seizures, in pre- and post-ictal periods.

We investigated low-dimensional structure of high-dimensional representations of micro-electrode array recordings from a person with epilepsy. We found that t-distributed stochastic neighbor embedding (t-SNE) finds two-dimensional descriptors of very high-dimensonal representation of epileptic recordings, which separates well inter-ictal, pre-ictal, ictal and post-ictal periods. We used XGBoost to build a parametric version of t-SNE, allowing to find low-dimensional descriptors in very long-duration recordings, typical of epilepsy. We used a novel clustering algorithm (Rodriguez and Laio 2014) to automatically discover structure in t-SNE low-dimensional descriptors and introduced a procedure to find this structure in very long-duration recordings.

This article contains scientific and methodological innovations. Scientifically, we discovered a new effect of the elapsed time between the presentation of a warning signal and the presentation of subsequent standard stimuli (stimuli to which subjects did not respond) on the coherence of the phase evoked by these standards. Methodolgically, we were able to detect this effect thanks to a single-trial analysis of the electroencephalogram using variational Bayes linear regression.

We are studying the hypothesis that epileptic activity (as recorded by high-density multi-electrode arrays in humans) can be efficiently represented in a low-dimensional space. We are using different low-dimensional representation methods (e.g., t-distributed stochastic neighbor embedding, hidden markov models, principal component analysis). To quantify the quality of these low-dimensional representations, we are comparing how well we can predict the occurence of seizures based on them.

Here we show that the traveling waves reported in Rapela 2016, 2017 do not occur continuously, but tend to appear before the initiation of a consonant-vowel syllable, tend to disappear before their termination, and during moments of silence, between productions of CVSs, TWs tend to reverse direction.

Nature is abundant in oscillatory activity, with oscillators that have the remarkable ability of synchronizing to external events. Using electrocorticographic (ECoG) recordings from a subject rhythmically producing consonant-vowel syllables (CVSs) we show that traveling waves over speech processing brain regions become precisely synchronized (in dynamical systems terms) to initiations of the production of CVSs. We use synchronization patterns to identify an extended traveling waves in voltages (filtered around the median frequency of speech production) moving from primary auditory to primary motor cortex, and a traveling waves in coupled high-gamma power moving along the same trajectory but in opposite direction.

Here I characterize high-density ECoG recordings from a patient producing consonant-vowel syllables (recordings from Bouchard et al., 2013). I show strong effects of the production of consonant-vowel syllables on the phase of low-frequency neural oscillation (phase alignment, phase-amplitude-coupling and traveling waves). To my knowledge, this is the first report of motor actions organizing (a) the phase coherence of low-frequency brain oscillations, (b) the coupling between the phase of these oscillations and the amplitude of high-frequency oscillations, and (c) traveling waves. It is also the first demonstration that traveling waves induce an organization of phase-amplitude coupling so that spiking across different spatial locations is synchronized to behaviorally relevant times.

Here we demonstrate that the activity of neural ensembles can be quantitatively modeled using an ensemble dynamical model of the probability density function that a neuron in the ensemble will fire at a given time (Omurtag et al., 2000). For populations of Integrate and Fire neurons, we validate that the probability density function resulting from the integration of the previous model precisely agrees with large-scale simulation of interacting single neurons. The previous ensemble dynamical models is a high-dimensional system of nonlinear differential equations. To facilitate the estimation of its parameters from neural recordings we implemented a dimensionality reduction method (Knight, 2000). We developed a maximum-likelihood method to infer the value of model parameters from data. Finally, we showed that the ensemble dynamical model and the method to estimate its parameters accurately approximate the high-gamma power evoked by pure tones in the auditory cortex of rodents.

We performed audio-visual attention-shift EEG experiments, where subjects had to quickly and repeatedly switch their attention between the visual and the auditory modalities (SWITCH blocks), or steadily fix their attention on a single modality (FOCUS blocks). Using a novel experimental design we studied oscillatory attention-related activity generated by attention-shifting cues, by stimuli following these cues, and interactions between them. We observed that the amount of oscillatory attention-related activity generated by the first visual stimuli after a cue was larger in SWITCH that in FOCUS blocks, and that the enhanced activity in SWITCH blocks decayed progressively for stimuli following the first one. The results from this study suggest that cross-modal switches of attention may generate a transient attentional arousal in all the modalities involved in multimodal attention experiments.

We proposed a novel intervention to train the speed and accuracy of attention orienting and eye movements in Autism Spectrum Disorder (ASD). Training eye movements and attention could not only affect those important functions directly, but could also result in broader improvement of social communication skills. To this end we described a system that would allow ASD children to improve their fixation skills while playing a computer game controlled by an eye tracker. Because this intervention will probably be time consuming, this system should be designed to be used at homes. To make this possible, we proposed an implementation based on wireless and dry electrooculography (EOG) technology. If successful, this system would develop an approach to therapy that would improve clinical and behavioral function in children and adults with ASD. As our initial steps in this direction, we described the design of a computer game to be used in this system, and the predictions of gaze position from EOG data recorded while a subject played this game.

This thesis contains technical and scientific contributions. Technically, we develop methods to estimate generic non-parametric models of visual cells from their responses to arbitrary, including natural, stimuli. In the first part of this thesis, we introduce the Volterra Relevant Space Technique (VRST), that allows the estimation of spatial Volterra models of visual cells from their responses to natural stimuli. Disregarding temporal properties of the response generation mechanism for the estimation of spatial Volterra models is a good first approximation. However, in most conditions responses of visual cells are not spatial, but spatio temporal. So, in the second part of this dissertation we build the extended Projection Pursuit Regression (ePPR) algorithm, that estimates a very general model for the characterization of visual cells in space and time. The generality of the ePPR model reveals differences in response properties of cortical cells to natural and random stimuli that had not been observed with existing models. Thus, scientifically this thesis shows that using natural stimuli for the characterization of visual cells is relevant to understand natural vision.

We developed the extended Projection Pursuit Regression (ePPR) algorithm that, by using an efficient projection pursuit estimation algorithm, allows to estimate a very general linear-nonlinear model of visual cells using arbitrary, including natural, stimuli. We showed that ePPR compares favorably to spike-triggered and information-theoretic techniques.

We introduced the Volterra Relevant Space Technique to estimate spatial Volterra models of visual cells from their responses to natural stimuli.

We built a system for 3D PET image reconstructions using a statistically optimal maximum a posteriori (MAP) reconstruction algorithm. To speed up the reconstruction process we implemented a pararellized version of the reconstruction algorithm, and run the reconstructions on a cluster of personal computers. To allow scanning facilities remotely access our reconstruction system, we developed a Java interace to the cluster that only requires a standard Web browser to run 3D PET image reconstructions.

I constructed a technique that learned from a training collection of HTML documents the optimal way to combine several HTML ranking heuristics into a single similarity measure for HTML documents.

Using Web Browser Intelligence (WBI), an agent architecture that works on behalf ofthe user to personalize the work with the World Wide Web, I develop "The Big Memory", an application that helps to reuse information in a big organization environment. The Big Memory builds groups (or clusters) of HTML documents; these documents are different from standard digital documents in that they are structured documents. After making a survey on available document clustering methods, whose results are described in the present work, I realized that there were not specific strategies for clustering HTML documents. Clustering algorithms are based on a document similarity measure. I designed a mechanism for incorporating information about the structure of HTML documents to a given similarity measure. This mechanism transforms a similarity measure into an enriched similarity measure. I compare the performance of a standard similarity measure to the performance of its enriched counterpart, showing that using the structure of HTML documents can help to find their similarity. A clustering algorithm using the enriched similarity measure will be optimized for HTML documents.