The two images below are from the article titled – Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structure, by Sanborn et al. (https://arxiv.org/abs/2407.09468v1)

The paper talk about how “the mathematics of topology, geometry and algebra provide a conceptual framework to categorize the nature of data found in machine learning.” The two figures, present a “graphical taxonomy, to categorize the structures of data.” The article the authors discuss two types of data that we generally encounter: “either data as coordinates in space—for example the coordinate of the position of an object in a 2D space; or data as signals over a space—for example, an image is a 3D (RGB) signal defined over a 2D space. In each case, the space can either be a Euclidean space or it can be equipped with topological, geometric and algebraic structures.”

The paper goes on to then “review a large and disparate body of literature of non-Euclidean generalizations of algorithms classically defined for data residing in Euclidean spaces.” The algorithms presented assume that certain topological, algebraic, or geometric structures of the data / problem are known. However, it does not go into discussion on methods where such structures are not known. For example, methods that fall into the category of topological data analysis, metric learning, or group learning are not covered.

The Centre for Computational and Data Sciences (CCDS), Independent University, Bangladesh (IUB), is proud to announce that James Peter Gomes, a dedicated undergraduate research student at CCDS and a Physics (Honors) major student in the Department of Physical Sciences, was selected earlier this year to participate in the prestigious CERN Summer Student Program 2024. He was the only Bangladeshi student amongst the 300 selected out of around 10,500 applicants worldwide. The fully funded 8 weeklong program was held at CERN’s Meyrin site in Geneva, Switzerland from 24th June to 16th August 2024.

For those who are not aware, CERN, the European Organization for Nuclear Research, stands as one of the world’s foremost centers for scientific inquiry and collaboration. Located near Geneva, Switzerland, CERN is renowned for its groundbreaking research in particle physics and its role in advancing our understanding of the fundamental forces and particles that govern the universe. Participation in the CERN Summer Student Program provides aspiring physicists like James with a unique opportunity to immerse themselves in this vibrant scientific community, engage in cutting-edge research projects, and collaborate with leading experts in the field.

Here’s what James has to say about his experience.

“During the internship, I worked as an associated personnel of the LHCb (Large Hadron Collider beauty) Detector Group (EP-LBD). This experimental collaboration mostly focuses on CP violation in nature, which distinguishes between particle and antiparticle in nature. This asymmetry is important for Cosmological observations. This very minute asymmetry requires very good statistics from the last dataset obtained from the collisions in the Large Hadron Collider (LHC) via the highly efficient detectors in the experimental setup. One also needs a good understanding of the detectors which is studied via simulations. My responsibilities included testing and exploring the integration of the GPU-based simulation prototype, AdePT (Accelerated demonstrator of electromagnetic Particle Transport), into the Gaussino simulation framework for the LHCb experiment. This initiative aimed at enhancement of the efficiency and accuracy of particle physics simulations, thereby advancing our understanding of fundamental particles and their interactions. My supervisors were incredibly supportive and patient throughout this project. They generously shared their expertise and guidance, always willing to answer my questions and clarify my doubts. Their mentorship was invaluable, as I was still learning to navigate the tools required for this work.

Furthermore, I participated in a series of lectures on physics, from the Standard Model to Beyond Standard Model to Quantum Gravity, delivered by CERN personnel, active researchers, and distinguished professors like David Tong, throughout the weekdays from July 2nd to August 2nd.

One of the program’s greatest benefits was the comprehensive support it provided to participants. We enjoyed CERN’s health insurance, a full travel allowance, and a daily stipend. Additionally, we had access to world-class facilities like laboratories, libraries, and computing resources. These resources were instrumental in fostering collaboration and advancing our research.

Quite interestingly, almost a third of the summer students were from Computer Science and Engineering background. In fact, I was one of the only 4 physics students out of the 11 summer students in the simulation team and the rest were from CSE relevant background. It seemed like my prior knowledge of specialized tools like ROOT, Pythia8, GEANT4, and FeynCalc proved invaluable in securing this internship. These skills are essential for the computing-intensive projects that CERN undertakes. CERN summer internship program, being computing-heavy, offers a valuable opportunity for students with strong programming and Linux skills.

I’m deeply grateful to my supervisor, Dr. Arshad Momen, for his invaluable guidance throughout my time at IUB. His patience and mentorship have been instrumental in helping me discover my passion for physics and choose the right path. I first met Arshad Sir in my first semester and have been fortunate to learn from his expertise ever since. It was thanks to his encouragement that I learned about the CERN Summer Student Program and developed the skills necessary to participate. I’m truly thankful for his support.”