Research in Optimisation
To expand my previous work on the relativize and algebraic separations of PLS and FP at TUM, I am working with Andreas S. Schulz to find an algebraic separation of a subclass of PLS, CLS from FP. I also will investigate the local search variants of #P and ⊕P.
I will also be pursuing a promising technique I developed over the summer to solve the non-shortest path problem with an efficient randomised algorithm (more details coming soon).
Rapid Image Colorisation
As a term project for a parallel architecture course at CMU I am implementing a performant, conditional generative adversarial neural network (model inspired by ) which given a large number of diverse satellite images, rapidly generates a reasonable colorisation.
Due to the project focus on performance (as opposed to inventiveness of the ML model) the project will be written in C, and including performance enhancing optimisations such as parallelism, will be a major priority (more details coming soon).
Computational Additive Combinatorics
I am working with Steven J. Miller from Williams College on an additive combinatorics project which concerning More Sums than Differences (MSTD) sets. There has been a great deal of analysis on the behaviour of random sum sets under various probabilistic assumptions which large-scale computation was a central part of. I am writing performant code taking advantage of streaming algorithms and parallel architecture to greatly increase the scope of prior research to understanding n-iterated sumsets (more details coming soon).
Past Research & School Projects
Hardness of Polynomial Local Search
Worked at the Technical University of Munich researching local search heuristics in a complexity theoretic context. Explored local search algorithms on H-minor free graph families, along with the applicability of relativization and algebraization to quantifying the hardness of PLS.
The main result involves a generalisation of a result of Scott Aaronson he coins ‘the transfer principle’ as it allows one to ‘lift’ results from communication complexity to algebraic query complexity. I use this result in combination with a very recent communication lower bound of computing the minimum of a boolean function given that its truth table is split across two parties to show that any proof of FP and PLS must not be algebraize.
Overall my results show that any proof that separates or collapses FP and PLS will require sufficiently advanced techniques (on par with those of P and NP). Which, in my opinion this lends some credibility to the opinion that FP is not equal to PLS (however this is not directly supported by these results).
Machine Learning Algorithm for Sensitive Data Identification
Worked with CHIMPS lab at Carnegie Mellon School of Computer Science to develop a machine learning based algorithm to identify sensitive data in natural language.
Given that NER has been studied in considerable detail, in both the context of formal and informal text, a core technique involved in the algorithm was to create a measurement of grammatical correctness to selectively well-tested NLP techniques (more details coming soon).
Designed and studied image processing and machine learning algorithms to perform automatic quantitative analysis of biological data from labs.
Employed symbolic programming to explore and compare various probabilistic and automata based models for early-stage microscopic, vascular tumor growth.
Discrete Differential Geometry
Explored numerical and algorithmic challenges of translating ideas in smooth differential geometry into the discrete setting for computation on 3D geometry. Implemented algorithms solving problems related to discrete exterior calculus, curvature, conformal parameterization, and geodesic distance.
Participated in a CMU challenge to combat financial illiteracy, and designed an app that seamlessly integrates public educational resources with a motivational incentives structure inspired by Apple’s activity app.
The app presents users with a list of short educational which introduce them to a general idea in finance. After watching the video, users gain access to more specific guides, along with a quiz to test the knowledge they learned.
Users can also set budgeting, spending, or educational goals, and view how close they are to achieving them in the Apple Activity app inspired rings. Finally users have the option to invite friends to compete with them.
Deeply explored the design of a radical, new operating system through many iterations, prototypes, and parts of working code. blckOS is a culmination of my experience in theoretical computer science, HCI, and design.
Notable features include: home screen that uses circle packing heuristics to efficiently display apps, an interface which naturally blends with the world around it using sensor data, along with an intelligent use of 3D graphics and AR throughout the interface (more details coming soon).
Designed and programmed an intuitive and functional calculator with support for a range of operations far beyond the default calculator on the iPhone, specifically oriented towards discrete mathematics.
The app also supported multiple color schemes, and even night mode (at the time of writing the app, this was a unique feature).
3D Game Design
Created Black Horizon Games Urban Map Pack — a series of gritty and dark game environments based on famous ghost towns like Pripyat, the outskirts of Chernobyl, and abandoned winter villages. During development over five gaming websites wrote about my work.
Worked as a level designer on the popular Crysis mod, Casus Belli.
Designed concept images for State of Emergency, a Crysis 2 mod.
Placed 2nd in the Just Make Games Halloween Contest.