What does conventional morphometry miss?
Bone volume, thickness, and separation are useful, but they do not describe every aspect of connectivity, cavities, orientation, or organisation.
Mathematics · Scientific computing · Research
I study structure through mathematics.
I am John Rick Manzanares, a Filipino mathematician and computational researcher. I use topology, geometry, scientific computing, and machine learning to study complex structures and the information they preserve.
My doctoral research focuses on trabecular bone. I am interested in what its geometry and topology can tell us beyond conventional summary measurements, and how those descriptions can be connected to mechanics.
Current questions
The questions come before the tools.
I try to begin with a structural or scientific question, then choose the mathematics and computation that make the question precise enough to investigate.
Which descriptors remain meaningful when the frame changes?
Structural descriptors should reflect the object being studied rather than an arbitrary choice of coordinates whenever possible.
How can topology enter scientific machine learning?
I am interested in ways to preserve structural information when a model learns fields, operators, or mechanical responses.
Selected research
From mathematical structure to scientific evidence.
These projects share a common concern: how to extract information from complicated shape without losing the mathematical meaning of the descriptor or the scientific meaning of the result.
Doctoral research
Topology and bone fragility
Persistent homology, morphometry, and statistical modelling for trabecular structure and apparent bone strength.
Scientific computing
Computational bone morphometry
Transparent implementations of morphology, orientation, graph, and geometric descriptors for bone images in three dimensions.
Research software
Fast Ball Mapper
Efficient cover construction for Ball Mapper, with attention to exactness, range queries, performance, and reproducibility.
Research direction
Topology in scientific machine learning
Exploring how topological information can support neural operators and other models for scientific fields.
Research as an interface
A paper should not be the only doorway into a project.
The flagship bone research page is an experiment in communicating research through several layers. A reader can begin with the scientific question, explore a filtration, inspect a persistence diagram, read the mathematics, and then continue to the implementation.
Question→Intuition→Mathematics→Code
Explore the bone research interfacePublic work
Different ways to enter the work.
Research is more than a list of papers. This site also collects software, teaching material, explanatory notes, and selected writing.
Publications Papers, talks, and posters
Formal research outputs and selected scientific presentations.
Software Code that can be inspectedResearch packages, experimental repositories, and archived project code.
Teaching Learning by working through ideasCourses, exercise material, and mathematical presentations.
Notes Explanations with more roomMathematics, research notes, and occasional writing about academic life.
The idea behind this site
Banyuhay
Banyuhay is a Filipino word for metamorphosis or transformation. It describes the way I think about a life in mathematics: questions change, methods change, and the path itself becomes part of the work.
The site is meant to reflect that movement. It is a research space, a notebook, a software shelf, a teaching archive, and a record of ideas still becoming clearer.
Read about Banyuhay and my path →