$$ \newcommand{\boldphi}{\boldsymbol{\phi}} \newcommand\xmin {x_{\text{min}}} \newcommand{\gammaone} {\Gamma_{\alpha}^{\prime} (1-\alpha, \lambda \xmin)} \newcommand{\gammatwo}{\Gamma_{\alpha}^{\prime \prime} (1-\alpha, \lambda \xmin)} \newcommand{\gammazero}{\Gamma (1-\alpha, \lambda \xmin)} $$ The power-law distribution is of the form $f(x) \propto x^{-\alpha}$, where $\alpha$ is called the scaling parameter. It models many natural phenomena like acoustic attenuation, Curie–Von Schweidler law, neuronal avalanches, and others. As $x \to 0$,Continue reading “Bayesian Estimates for the Parameters of a Power-law Distribution with Exponential Cutoff using Monte Carlo Methods”
Category Archives: Projects
Bayesian Methods for the Estimation of Infection and Recovery Rates of an Epidemic from Stochastic SIR Data
This project was co-authored by Heather Johnston and Youngwoo Kwon $$ \newcommand{\boldphi}{\boldsymbol{\phi}} $$ Introduction COVID-19, or Coronavirus Disease 2019, was declared a pandemic by the World Health Organization on March 11, 2020. The disease originated in December 2019 in China and quickly spread around the world. Compared with the previous epidemics like Ebola and SARS,Continue reading “Bayesian Methods for the Estimation of Infection and Recovery Rates of an Epidemic from Stochastic SIR Data”
Analysis of Prevalence of Mental Illnesses and Suicide in Different Countries Using Gower Clustering Based Dimensionality Reduction of Growth Metrics and Simulation-Based Hypothesis Testing
Source code for this research: https://github.com/AnilBattalahalli/Analysis-Of-Mental-Illnesses Introduction In the last two decades, there have been significant developments in understanding the anatomy of the brain for mental illnesses like Major Depressive Disorder, Anxiety Disorder, Bipolar Disorder, Schizophrenia, Personality Disorder, etc. Most of these disorders, along with alcohol and drug abuse are studied together to analyze theContinue reading “Analysis of Prevalence of Mental Illnesses and Suicide in Different Countries Using Gower Clustering Based Dimensionality Reduction of Growth Metrics and Simulation-Based Hypothesis Testing”
People in the US have trouble pronouncing my name. So I over-engineered a Python program
My first name has literally two syllables. And it doesn’t have one of those á, é, í, ó, ú, ü, ñ or any other seizure-inducing accents as well. It is also insanely phonetic. I mean, look at the name “Isla”, it’s pronounced “EYE-la”. Huh?? In spite of my name being so simple to pronounce, hereContinue reading “People in the US have trouble pronouncing my name. So I over-engineered a Python program”
Robotic Navigation with Reinforcement Learning (Deep-Q)
This was an original research where reinforcement learning was used with a four-legged robot for its autonomous motion along with computer vision and Deep-Q Neural Network. We chose a 4 legged robot which has three servo motors per leg. We calibrated each servo motor and restricted its degree of freedom to a certain set thresholdContinue reading “Robotic Navigation with Reinforcement Learning (Deep-Q)”
Generation of Power Law Samples with Inverse Transform Sampling (Python, R and Julia)
Implementation of the Inverse Transform Sampling The probability density function of a power law distribution is given by, $$f(x\ | \ x_m,\alpha) = \frac{\alpha-1}{x_m} \left(\frac{x}{x_m}\right)^{-\alpha} \ , x>x_m$$ We can find the cumulative density function by, $$ \begin{aligned} F(x) &= \int_{-\infty}^x f(x\ | \ x_m,\alpha) \ dx\\ \\ &= \int_{-\infty}^x \frac{\alpha-1}{x_m} \left(\frac{x}{x_m}\right)^{-\alpha} I(x>x_m) \ dxContinue reading “Generation of Power Law Samples with Inverse Transform Sampling (Python, R and Julia)”
Interictal Spike detection from EEG with stationary waveform classification using Support Vector Machine (SVM)
This was an original Research aimed at devising a deep learning algorithm to learn and diagnose epileptogenic patterns from an EEG which indicate that a person has had an epileptic seizure. The research employed analyzing the nonlinear energy operator (NEO) of the stationary waves and then thresholding with a semi constant calculated from the energyContinue reading “Interictal Spike detection from EEG with stationary waveform classification using Support Vector Machine (SVM)”