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 on 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”

# Category Archives: Math

## Is the Dirichlet Function Riemann-Darboux Integrable?

The Dirichlet Function The Dirichlet function is one of the easiest function to define. It’s literally, $$ \begin{aligned} f(x)=\left\{ \begin{array}{ll} 1, & \text{if $x$ is rational}\\ 0, & \text{if $x$ is irrational} \end{array} \right. \end{aligned} $$ or using the symbols from number theory/set theory that almost no one remembers, $$ \begin{aligned} f(x)=\left\{ \begin{array}{ll} 1, &Continue reading “Is the Dirichlet Function Riemann-Darboux Integrable?”

## Curvilinear Vector Algebra Toolbox for MATLAB

I have used MATLAB throughout my engineering. I had vector algebra course where we studied multiple vector algebra operations like gradient, curl and divergence in not just cartesian, but also cylindrical and spherical coordinates. One of my friends needed an implementation of vector algebra in curvilinear coordinates for MATLAB. But the same was not availableContinue reading “Curvilinear Vector Algebra Toolbox for MATLAB”

## 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)”