Research
I am advised by Jean-Marc Fellous and Michael Chertkov. The primary research questions we are tackling is given just the observational data (such as, spike train neural data), is it possible to find the causal relationship between the variables (neurons). The causal relationhip in our case refers to the functional connectivity between neurons, which refers to the dynamic neural communication that describes the statistical dependence between neurons (Olaf S, 2013). Our approach involves extracting a Directed Acyclic Graph (DAG) from the data that best represents the statistical relationship between neurons that occur in response to input stimuli and during sleep. We focus on DAG because together with the functional connectivity of neurons, we are also interested in the order in which neurons are connected and DAGs naturally provide this order through the directionality of the edges. Extracting the neurons involved in replay and the order in which the replay episodes propagate, highlights the role of place cells in spatial navigation, providing insights into learning and decision-making in complex environments.
The activity of place cells, which are the neurons in hippocampus, is widely understood to provide insights into how humans and other agents, such as rats, navigate the space around them. Hippocampal replay is characterized by the reactivation of neural sequences during non-exploratory states. That is, when the rat goes to sleep or rest, it shows a similar firing activity as observed during the task exploration, indicating that the rat is revisiting the task in sleep and storing the memory of what was explored. The generation of replay is crucial for memory consolidation and retention and is key to retrieving previous memories. Replay episodes contain information about the causality structure within a network of neurons, which helps to experimentally track how the memories are formed during learning. When the rat is reintroduced to a task sometime later during wakefulness, the exploration performance indicates how well the memory of the task was stored and if the learning has occurred. We investigate the relationship between replay and causality relationship among neurons by simulating the activity of a network of neurons in the hippocampal area called the place cells. These cells spike (or fire) in response to visiting specific locations in any environment.
We use the NEURON simulation environment to implement synapses with uncorrelated background noise for realistic neural behavior. The conductance of the synaptic currents is scaled by a connectivity matrix that we can control to introduce causality structures in subgroups of neurons. The poster below was prepared for the Neuroscience 2023 conference and it describes how we generate the data so that the synchrony of spikes occurs due to the synaptic strength between neurons and not due to the changes in firing rates. For this poster, we considered symmetric connections between neurons (that is, no direction of connection between two neurons) and discovered that the prevalent spike counting algorithm performs better for smaller networks and higher weights and that sparser connectivity shows minimal differences between the actual and shuffled spike coincidence counts.
Next, we focused on data with specified directions for synaptic connectivity between neurons and considered improvements to the spike counting algorithm. For the poster below, which was prepared for the Neuroscience 2024 conference, we compare the results from three approaches designed to identify those subgroups of neurons and their firing order, if any. The first approach uses spike counts over some fixed synchrony window to allocate spikes that occur within the specified timeframe, the second approach leverages spectral analysis with the Fourier transform to analyze the spiking activity in a frequency space, and the third approach extracts a directed acyclic graph that best describes the causality relationship between neurons by capturing the underlying causal structure using Direct LiNGAM method (Shimizu, 2006). The Direct LiNGAM (Linear Non-Gaussian Acylic Model) focuses on the non-Gaussianity in the data generating process and uses ordinary linear regression with difference of mutual information between two neurons to find the causal ordering between all neurons using the spike train data. All three methods are tested against the ground-truth connectivity matrix to evaluate the robustness and weaknesses of the algorithms for both symmetric and non-symmetric connections and discovered that non-Gaussianity is a necessary assumption to find true causal ordering.
Currently, we are focused on developing an algorithm using similar assumptions to those of the Direct LiNGAM method without relying on linear regression to assess hippocampal replay in datasets collected as the rats solve complex navigation problems in megaspace.