Learning neural connectivity from firing activity: efficient algorithms with provable guarantees on topology.

The connectivity of a neuronal network has a major effect on its functionality and role. It is generally believed that the complex network structure of the brain provides a physiological basis for information processing. Therefore, identifying the network's topology has received a lot of attentions in neuroscience and has been the center of many research initiatives such as Human Connectome Project. Nevertheless, direct and invasive approaches that slice and observe the neural tissue have proven to be time consuming, complex and costly. As a result, the inverse methods that utilize firing activity of neurons in order to identify the (functional) connections have gained momentum recently, especially in light of rapid advances in recording technologies; It will soon be possible to simultaneously monitor the activities of tens of thousands of neurons in real time. While there are a number of excellent approaches that aim to identify the functional connections from firing activities, the scalability of the proposed techniques plays a major challenge in applying them on large-scale datasets of recorded firing activities. In exceptional cases where scalability has not been an issue, the theoretical performance guarantees are usually limited to a specific family of neurons or the type of firing activities. In this paper, we formulate the neural network reconstruction as an instance of a graph learning problem, where we observe the behavior of nodes/neurons (i.e., firing activities) and aim to find the links/connections. We develop a scalable learning mechanism and derive the conditions under which the estimated graph for a network of Leaky Integrate and Fire (LIf) neurons matches the true underlying synaptic connections. We then validate the performance of the algorithm using artificially generated data (for benchmarking) and real data recorded from multiple hippocampal areas in rats.

Noise facilitation in associative memories of exponential capacity.

Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns that satisfy certain subspace constraints. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate associatively, such as hippocampus and olfactory cortex. Here we consider associative memories with boundedly noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprising, we show that internal noise improves the performance of the recall phase while the pattern retrieval capacity remains intact: the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a functional benefit to noisy neurons in biological neuronal networks.

Electrochromic Sensor Augmented with Machine Learning for Enzyme-Free Analysis of Antioxidants.

Our study presents an electrochromic sensor that operates without the need for enzymes or multiple oxidant reagents. This sensor is augmented with machine learning algorithms, enabling the identification, classification, and prediction of six different antioxidants with high accuracy. We utilized polyaniline (PANI), Prussian blue (PB), and copper-Prussian blue analogues (Cu-PBA) at their respective oxidation states as electrochromic materials (ECMs). By designing three readout channels with these materials, we were able to achieve visual detection of antioxidants without relying on traditional "lock and key" specific interactions. Our sensing approach is based on the direct electrochemical reactions between oxidized electrochromic materials (ECMsox) as electron acceptors and various antioxidants, which act as electron donors. This interaction generates unique fingerprint patterns by switching the ECMsox to reduced electrochromic materials (ECMsred), causing their colors to change. Through the application of density functional theory (DFT), we demonstrated the molecular-level basis for the distinct multicolor patterns. Additionally, machine learning algorithms were employed to correlate the optical patterns with RGB data, enabling complex data analysis and the prediction of unknown samples. To demonstrate the practical applications of our design, we successfully used the EC sensor to diagnose antioxidants in serum samples, indicating its potential for the on-site monitoring of antioxidant-related diseases. This advancement holds promise for various applications, including the real-time monitoring of antioxidant levels in biological samples, the early diagnosis of antioxidant-related diseases, and personalized medicine. Furthermore, the success of our electrochromic sensor design highlights the potential for exploring similar strategies in the development of sensors for diverse analytes, showcasing the versatility and adaptability of this approach.

Nonbinary associative memory with exponential pattern retrieval capacity and iterative learning.

We consider the problem of neural association for a network of nonbinary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later, the same network should be able to recall the previously memorized patterns from their noisy versions. Prior work in this area consider storing a finite number of purely random patterns, and have shown that the pattern retrieval capacities (maximum number of patterns that can be memorized) scale only linearly with the number of neurons in the network. In our formulation of the problem, we concentrate on exploiting redundancy and internal structure of the patterns to improve the pattern retrieval capacity. Our first result shows that if the given patterns have a suitable linear-algebraic structure, i.e., comprise a subspace of the set of all possible patterns, then the pattern retrieval capacity is exponential in terms of the number of neurons. The second result extends the previous finding to cases where the patterns have weak minor components, i.e., the smallest eigenvalues of the correlation matrix tend toward zero. We will use these minor components (or the basis vectors of the pattern null space) to increase both the pattern retrieval capacity and error correction capabilities. An iterative algorithm is proposed for the learning phase, and two simple algorithms are presented for the recall phase. Using analytical methods and simulations, we show that the proposed methods can tolerate a fair amount of errors in the input while being able to memorize an exponentially large number of patterns.