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Einstein Field Equations are analytically evaluated for FRW metric and differential equations to describe evolution of the universe obtained. Relevant DEs are solved using numerical methods (NumPy and SciPy). Solutions are visualized using Matplotlib and Seaborn. Python scripts and animated solutions are publicly available here.

An alternative to standard model of cosmology ($\Lambda \mathrm{-CDM}$) is developed through scalar field models of dark energy. Stability analysis of radiation-matter-quintescence models are performed using symbolic(SymPy and Mathematica) and numerical(NumPy and SciPy) methods. Trajectories in the phase space are visualized using matplotlib.

Strong theory of the early universe is investigated starting from first principles. Model independent observational constraints are analysed using Bayesian interface with CosmoMC. Various inflaton models within and beyond the general relativity are tested against PLANCK datasets.

The viability of slow-roll approximation is examined by considering the structure of phase spaces in scalar--tensor theories of gravitation and the analysis is exemplified with a non-minimally coupled scalar field to the spacetime curvature. Observational constraints are analysed using Bayesian interface with CosmoMC using PLANCK 2018 datasets. You can access the article from here.

This personal project has started during COVID-19 outbreak. Case numbers are obtained by web scraping with Beautiful-Soap, local datasets are created, calculation of death/recovery rate, data fitting, visualization are performed with Python, native Excel functions and Adobe Illustrator. Daily numbers and charts are posted using automation scripts to social media through APIs. Currently, website is not active, however Instagram account is still available: @koronoloji_com

The project includes accessing the candlestick data through API, performing operations on data using Pandas and technical analysis libraries, plotting candlestick charts overlayed with indicators (RSI, MACD, Moving Averages) with Matplotlib, Seaborn and Plotly. The user also has access the relevant charts through Telegram Bot.

The project includes accessing the transaction history through broker(Binance/FTX) API, calculating profit/loss, average buy price, and the cost for each asset in the account. The user has access to portfolio through Telegram Bot by providing his/her API key.

SIR(Susceptible, Infectious, Recovered) model is derived analytically and coupled differential equations are simultaneously solved using existing methods of SciPy and manual implementation of RK4. Stability of the disease is determined using symbolic methods from SymPy. Evolution of the disease within the society is visualized using Matplotlib. In the same manner, spread of HIV infection in the body is modelled and compared with publicly available data from an academic journal.

Physical and chemical analyses of various forensic evidence from document forgery, ballistics and biological materials have been classified using Principal Component Analysis (PCA) from scikit-learn. A local database for each class of evidence has been created in order to match future evidence.