Masters Thesis
May,2016-August,2017
Indian Statistical Institute, Kolkata
Dr.Kuntal Ghosh, Assistant Professor, ISI Kolkata
We are trying to understand the mechanism of vision by modeling psychophysical properties of vision. The reconstruction of the 3-d world around us from a 2-d retinal image is an ill-posed problem(Hadamard). So intelligent vision systems use biases to regularize this problem to a well-posed one. Illusions provide a way of studying the visual biases of the human vision system. We are trying to model geometric illusion to understand why these illusions are perceived and what are the processes involved.
Till now we have used a Lateral Inhibition based DOG filter and a concept of perceptual distance to explain a few geometric illusions. We trying to explain a few others by using the concept of geodesic on a perceptual field.
Summer 2015
Indian Institute of Technology, Delhi
Dr.Sumeet Agarwal, Assistant Professor, IIT Delhi
National Networks Mathematical and Computational Biology.
All cells of a multicellular organism contains the same set of genes. But their protein make-up can be drastically different both spatially and temporally due to regulation. Gene regulation is the process by which the conversion of the information stored in genes to protein end product is controlled. Knowledge of the interactions among genes and gene products that occur within a cell is vital for understanding cellular behavior. This is done by reconstructing the GRN form gene expression data. DNA micro-arrays have facilitated the collection of expression data.
One of the most successful methods of GRN reconstruction is using Bayesian Inference. Bayesian Networks are attractive for their ability to describe complex stochastic processes, and since they provide clear methodologies for learning from (noisy)observations. Bayesian Networks have a scope for incorporating prior knowledge about the model parameters into the learning process. This feature is exploited to incorporate expert knowledge in the inference to make the inference more accurate.
In this internship we tried to incorporate such a expert knowledge about the topology of the GRNs, the small world property. The already reconstructed GRNs of model organisms tend to have the small world property, so we tried to use it as prior knowledge for higher organisms.
Summer 2014
National Institute of Technology, Allahabad
Dr. Manoj Kumar
The understanding of blood flow dynamics is of immense importance in medical science as it helps to understand the relation between blood flow and vascular diseases and the change in flow characteristics under these circumstances. Some prosthetic or extra-corporeal flow devices like Haemo-dialyser which mimic and provide replacement for some body processes can be improved by study of blood flow. Exact mathematical description of blood flows can be quite complicated and almost impossible to solve but some simplified models can approximate the real situation to a great extent.