Repository describing things I've done up to date
- add figures from analyses...?
- Possibly code links
- Reinstall Ubuntu on workstation, and get vpn and virtual log in working to run stuff :)
During this time period, I used MATLAB and Python to analyze epilepsy Stereoelectroencephalography (SEEG) data. Each patient had the varying channel data condensed into a network. All channels formed a weighted undirected graph between all other channels, with a coherence, or power similarity measure as the weighted edge between vertices. This graph was formed at an averaged time window over the entire time series with an overlap of a certain percentage.
Once the time series graph was formed, every graph produced an eigenvector centrality measure, which measures how important certain vertices are in the graph. From here, various data mining analyses were done to look for a notion of a pre-ictal state. The following analyses were carried out:
- Separate the preictal, ictal and postictal stages by +/-5, 10 minutes and then for each stage compute a gap statistic that leads to a statistical way of arriving at optimal k
- Compute k-means from each and plot state progression -> ictal state follows a state progression that is unsupervised and still follows that from publication -> postictal state follows some sort of state progression -> preictal was difficult to characterize
Used MATLAB to program a robust photometric stereo algorithm that uses low-rank matrix completion and recovery with Convex Programming. This solved a minimization of a nuclear norm with an l1-regularization term for sparsity. The nuclear norm replaces min(rank(A)), which is an intractable problem. This was solved efficiently using the Augmented Lagrange Multiplier (ALM) method.
Would be difficult to extend to the colonoscopy experiments in the Durr lab because of the limitation on the number of images gathered (n=4 vs. the n=10-20 for sufficient matrix recovery).
In this rotation, I investigated a paired word task to study the electrophysiology of basic memory mechanisms in retrieval. We were looking at spectral features of different paired words and the features during retrieval of the correct paired word.
For example, BRICK might be paired with CLOCK, and then later paired with GLASS. We are interested in determining if there are differences in spectral features in certain areas of the brain that encode these differences in word pair encodings. To analyze this data, we carried out the following procedure:
- Compute eeg voltage data from all channels
- Compute the Morlet Wavelet transform on all channels to obtain a power estimate at different frequency bands -> resulting eeg data from -1 seconds to 5 seconds after probeWord comes on the screen
- Notch filter at 59.5-60.5 Hz
- Z-transform with respect to a fixation period (or to the overall signal average signal)
- Separate all data by session and blocks and word pairs. Then compute a feature vector for all the different word pair groups: same words, reverse words, different words and compute the cosine similarity between these feature vectors.
- Principles of Biomedical Instrumentation
- Learned about sensors and biomedical circuitry for denoising and sampling human data (e.g. EEG, ECG, EMG) and creating a ECG/EMG circuit. Heavily exposed to circuit design of instrumentation amplifiers, op-amp circuits, filters and sampling data.
- Created an EMG/ECG concurrent sensor circuit with sautered components
- Created a Teensyduino controlled prototype with Flexiforce sensors for bio-gaming
- Principles of Complex Network Theory
- Applied Mathematics for Science and Engineering
- Learned about differential equations from ordinary 1st order, 2nd order, fourier series and partial differential equations.
- Looked at different methods of analytical solving such as, separation of variables,
- Honors Instrumentation
- Built a better prototype for bio-gaming with an improved design
- The Art of Data Science
- Worked on a research dataset with features of "predicted" synapses from electron microscopy data
- Learned about the data science methodology and how to apply various data visualizations, statistical methods and machine learning algorithms to data.
- Convex Optimization
- Covered convex analysis and theory, along with algorithms for solving non-smooth (un differentiable), smooth (differentiable) functions
- Covered Lagrangian duality theory for solving problems and acceleration methods for first-derivative methods. Looked at l1 regularization of objective functions.
- Learning Theory
- Covered Kalman filtering and its relations to solving state-space models, Bayesian inference and optimal feedback control theory
- Used Bellman equations and Kalman filter to simulate biological systems (e.g. head and eye movements)
- Game Enhanced Augmented Reality (GEAR): A platform for foot control of your computer to reduce tension and increase usability.
- HopHacks Clinical Search Index (CSI): A web platform for searching for relevant clinical trials related to your disease.
- Statistical Theory
- Bayesian Statistics (Yes)
- Nonlinear Optimization
- Digital Signal Processing (Yes)
- Models of the Neuron (Yes)
- Statistical Theory
- Nonlinear Optimization
- NSS Medical School Track
- Convex Optimization
- what is a minimizer, objective function, subdifferential, gradient, convex set, convex function
- What is Lagrangian duality
- algorithms for smooth, nonsmooth functions
- l1, l2 regularization
- acceleration methods (Nesterov)
- Learning Theory
- derivation of Kalman filter
- utilizing multiple sensor inputs
- derivation of Bellman equation
- general expectation-maximization (solving for expected log likelihood, and maximizing)
- Mathematics for Science and Engineering
- solving ordinary differential equations
- solving partial differential equations
- Green's theorem, laplacian, gradient
- power series
- Fourier series
- Separation of Variables
- Statistical Theory / Probability Theory
- Introduction to Differential Geometry
- Nonlinear Optimization
- Riemannian Geometry
- Advanced Bayesian Statistics
- Graph Theory