CHAOS
The science
Current Position: Postdoc


Reservoir computing is a machine learning architecture that is a popular model in physics. While it doesn't fit the ML stereotype of being able to do insanely cool tasks, it is quite interesting to study since the reservoir itself is a dynamical system. The connections between the neurons are recurrent, and follow a differential equation that can be solved (numerically) to reveal interesting dynamical states/attractors. Thus the learning is encoded in the dynamical state of the reservoir computer in response to the input, which is a radically different way of thinking of about learning. This property of reservoir computers makes them an ideal candidate for understanding how learning occurs, i.e., not a black box, and learn chaotic models (hence, widely popular in modeling weather patterns). A bonus is that they can be implemented in hardware!
My research in reservoir computing spans a variety of topics that have resulted in three publications: Generalization of learning using very little data, Understanding how learning occurs through attractors in the reservoir dynamics, Separating chaotic signals e.g. a chaotic version of the cocktail party problem. 

This theme of research involves computational methods for medical application. This involves applying various techniques from multilayer networks, graph neural networks and statistics to predict disease subtypes in patients early on, and consequently preemptively treat them. In particular, I developed the 'Trajectory Clustering' algorithm that identifies disease subtypes in heterogenous multivariate diseases, where conventional methods face two main challenges challenges (1) unable to capture timeevolution of interactions, (2) can't handle multiple types of data (ordinal, categorical, continuous, phenotypic and genetic etc.). I collaborate with several clinicians on Parkinson's and Stroke. Three papers have resulted from this theme
Publications: Plos One paper. Biomedical Physics and Engineering Express paper. Stroke paper. and Talk at NetSci 2018, Paris here 
While graphs are a source of rich information about pairwise interactions, several real world networks involve interactions between more than two agents. For example three students meeting in a break room is a simultaneous 3way interaction (represented by a filled traingle), not 3 pairwise interactions. So many real networks are higherorder, and often misleadingly reduced to pairwise interactions. Simplicial complexes are powerful tools to model higher order interactions. The nice thing about them is that they have mathematical definitions and can be analyzed through the lens of topology and geometry. I am interested in developing a theoretical understanding of higherorder networks, particularly properties of the higher order (Hodge) Laplacian. I am also interested in various applications.
My most recent investigation involves spectral community detection in an arbitrary dimensional simplicial complex (any number of interacting nodes). I am also studying concepts such as 'holes' or cavities in higher order networks. Manuscript: Sanjukta Krishnagopal and Ginestra Bianconi 
We investigate the ways in which a machine learning architecture known as Reservoir Computing that loosely resembles neural dynamics learns concepts such as “similar” and “different” and other relationships between image pairs and generalizes these concepts to previously unseen classes of data. We find that the reservoir acts as a nonlinear filter that projects the input into the high dimensional reservoir space, where inputs from the same category cluster together (see figure), allowing for easy generalization to unseen data. Our architecture outperforms conventional pairbased methods such as Siamese Neural Networks.
Advised by Yiannis Aloimonos and Michelle Girvan Published in Complexity. Manuscript here 
We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart–Landau oscillators with fractal (hierarchical) connectivities. The study of fractal or selfsimilar topology is motivated by the network of neurons in the brain. Our results show that there is a direct correlation between topology and dynamics (see top figure)  hierarchical networks display hierarchical dynamics.
Advised by Prof. Eckehard Schoell, PhD Published in Philosophical Transactions of the Royal Society. Manuscript here 
We developed the image encryption algorithm based on the chaotic logistic map and cat map. A secret key is used to determine initial conditions and the input to the chaotic map function. The Lorenz map is then used for successive pixel encryption. To make the cipher more robust against any attack, the secret key is modified after encrypting each pixel of the image using Arnold’s cat map. Decryption follows the exact reverse. Figures on the right show original (top), encrypted (middle) and recovered after decryption (bottom) with minimal loss. The encrypted image is then hidden using a steganography technique that uses a cover image along with the Lorenz map to determine the location of the pixels to be hidden in the cover. Tests on efficiency and key sensitivity show that our doublekey method provides secure image encryption and realtime transmission.
Advised by Dr. Bijil Prakash Published in Proceedings of Fourth International Conference on Soft Computing, 2014 Manuscript here 
We processed data from the LGN and V1 regions of the brain in order to identify how visual stimulus from the two individual retina is nonlinearly combined in order to develop the corresponding neural response. With knowledge of the stimulus and data from the neural recording in the brain, we fit nonlinear filters that convolve with the input in order to produce the desired neural signals.
Advised by Prof. Dan Butts 
We introduce a Bidirectional Convolutional LSTM architecture for violence detection. The encoding of temporal features in both directions allows for a better video representation. Our method performs comparably with state of the art architectures on benchmarked datasets.
Conference proceedings, Workshop for Objectionable Content and Misinformation at ECCV 2018. Publication here 