**ChaosNet: ****A Chaos based Artificial Neural Network Architecture For Classification**** **(with Harikrishnan NB, Aditi Kathpalia and Snehanshu Saha)

Inspired by chaotic firing of neurons in the brain, we propose ** ChaosNet**—a novel chaos based artificial neural network architecture for classification tasks.

**is built using layers of neurons, each of which is a 1D chaotic map known as the Generalized Luröth Series (GLS) that has been shown in earlier works to possess very useful properties for compression, cryptography, and for computing XOR and other logical operations. In this work, we design a novel learning algorithm on**

*ChaosNet***that exploits the topological transitivity property of the chaotic GLS neurons. The proposed learning algorithm gives consistently good performance accuracy in a number of classification tasks on well known publicly available datasets with very limited training samples. Even with as low as seven (or fewer) training samples/class (which accounts for less than 0.05% of the total available data),**

*ChaosNet***yields performance accuracies in the range of 73.89%−98.33%. We demonstrate the robustness of**

*ChaosNet***to additive parameter noise and also provide an example implementation of a two layer**

*ChaosNet***for enhancing classification accuracy. We envisage the development of several other novel learning algorithms on**

*ChaosNet***in the near future.**

*ChaosNet*For further details, see: arXiv:1910.02423v1 [cs.LG], arXiv:1905.12601 [q-bio.NC]

Published in Chaos (AIP): https://aip.scitation.org/doi/10.1063/1.5120831

**Causality Testing **(with Aditi Kathpalia)

Causality testing, the act of determining cause and effect from measurements, is widely used in physics, climatology, neuroscience, econometrics and other disciplines. As a result, a large number of causality testing methods based on various principles have been developed. Causal relationships in complex systems are typically accompanied by entropic exchanges which are encoded in patterns of dynamical measurements. A data compression algorithm which can extract these encoded patterns could be used for inferring these relations. This motivates us to propose, for the first time, a generic causality testing framework based on data compression. The framework unifies existing causality testing methods and enables us to innovate a novel Compression-Complexity Causality measure. This measure is rigorously tested on simulated and real-world time series and is found to overcome the limitations of Granger Causality and Transfer Entropy, especially for noisy and non-synchronous measurements. Additionally, it gives insight on the `kind' of causal influence between input time series by the notions of positive and negative causality.

For further details, see: https://arxiv.org/abs/1710.04538

Published in PeerJ-CS: https://peerj.com/articles/cs-196/

**Information, Complexity and Consciousness **(with Mohit Virmani)

**Neural Signal Multiplexing**(with K R Sahasranand)

**Perspectives on Complexity**(with Karthi Balasubramanian)

**Complexity**". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. We explore the following perspectives on complexity: "effort-to-describe" (Shannon entropy H, Lempel-Ziv complexity LZ), "effort-to-compress" (ETC complexity) and "degree-of-order" (Subsymmetry or SubSym). While Shannon entropy and LZ are very popular and widely used, ETC is a recently proposed measure for time series. We also propose a novel normalized measure SubSym based on the existing idea of counting the number of subsymmetries or palindromes within a sequence. We compare the performance of these complexity measures on the following tasks: a) characterizing complexity of short binary sequences of lengths 4 to 16, b) distinguishing periodic and chaotic time series from 1D logistic map and 2D H\'{e}non map, and c) distinguishing between tonic and irregular spiking patterns generated from the "Adaptive exponential integrate-and-fire" neuron model. Our study reveals that each perspective has its own advantages and uniqueness while also having an overlap with each other.

**Aging and Cardiovascular Complexity**(with Karthi Balasubramanian)