Alumni

## Bio

Carlos Martin is a student at the Columbia University School of Engineering and Applied Science. He intends to pursue a major in applied physics and applied mathematics with a minor in computer science. Carlos is a member of the Egleston Scholars Program, which recognizes exceptional undergraduate students from Columbia Engineering. The program provides students with research opportunities, enhanced advising, and faculty mentorship.

Last summer, Carlos worked at Canada's National Laboratory for Particle and Nuclear Physics (TRIUMF), home to the world's largest cyclotron. His work focused on laser ion sources and laser resonance ionization spectroscopy, a method for selectively generating radioactive ion beams used in particle and nuclear physics experiments. This summer he will be working at the Columbia Lightwave Research Laboratory and the Columbia Plasma Physics Laboratory. The Lightwave Research Lab investigates data capacity and routing in optical networks, which use light signals to transmit information. Carlos will be investigating optical computing architectures and developing the lab's simulator. In the Plasma Physics Lab, which studies plasma instabilities and conducts controlled fusion energy experiments, he will be working on developing a mathematical model and computer simulation of an electron-positron plasma in a dipole field.

Carlos is deeply interested in fundamental physics research, particularly in the fields of cosmology and quantum gravity. He is also interested in exploring artificial general intelligence through reinforcement learning techniques and evolutionary algorithms. He has worked with artificial neural networks, discretization schemes for electromagnetism, Eulerian and Lagrangian methods for fluid dynamics, and rigid body dynamics using numerical integration.

He looks forward to participating in the Wolfram Science Summer School and applying Wolfram technology to his fields of interest.

## Project: Functionals of Cellular Automaton Rules

We model the collection of possible neighborhood configurations in an elementary cellular automaton as a discrete manifold over which the transition function or rule takes on Boolean values. We find the Dirichlet energy of different rules through the Boolean differential calculus by summing over all possible neighborhood configurations. We also perform spectral analysis of different elementary cellular automaton rules using the Walsh\[Dash]Hadamard transform. The same analysis can be applied to transition functions that act on an entire causal network of cells, with cells in the first layer as the input and cells in the last layer as the output.

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