Jimmy Mathews -- personal webpage

I am a researcher in the Nadeem Lab at Memorial Sloan Kettering Cancer Center. I was previously a scientific data engineer at the Allen Institute, a postdoctoral researcher in the Deasy Lab, and before that a PhD student in the mathematics department at Stony Brook University.

Actor:	Willem Dafoe, Steve Buscemi
Comedian:	Alan Resnick
Game designer:	Nifflas
Computer game:	ZZT From Anna Anthropy's book ZZT: "Not everyone has played ZZT, but everyone who played it became a game designer."
Capitalism apologist:	Scott Alexander
Jimmy:	Baldwin
Movie:	Schizopolis, Coherence
18th century mathematician:	Nicolas de Condorcet
19th century mathematician:	Jean Gaston Darboux
Contemporary mathematician:	Robert Bryant, Sergei Tabachnikov
Algebraic variety:	G(2,4)
Lie algebra:	so(3)
Design pattern:	Flyweight
Non-human primate:	Pan
Prehistoric human:	Homo habilis

My research interests include:

Systems biology and complex systems. Graphs, categories, and operads.
Software design patterns and database design patterns. OWL ontology.
Philosophy of biology and science.
Low-dimensional geometry. Synthetic projective and differential geometry.
Differential forms and geometric PDEs.
Lie groups and their representations. Tensor and symmetry methods in data analysis.

2020	Functional network analysis reveals an immune tolerance mechanism in cancer Joint with Saad Nadeem, Maryam Pouryahya, Zehor Belkhatir, Joseph O. Deasy, Arnold J. Levine, Allen Tannenbaum
2019	Robust and interpretable PAM50 reclassification exhibits survival advantage for myoepithelial and immune phenotypes Joint with Saad Nadeem, Arnold J. Levine, Maryam Pouryahya, Joseph O. Deasy, and Allen Tannenbaum
2019	Isotropic and Coisotropic Subvarieties of Grassmannians Primary author Kathlen Kohn
2018	A Schur transform for spatial stochastic processes
2018	Molecular phenotyping using networks, diffusion, and topology: soft tissue sarcoma Joint with Maryam Pouryahya, Caroline Moosmüller, Ioannis Kevrekidis, Joseph O. Deasy, and Allen Tannenbaum
2017	Curve jets, submanifolds families, and envelopes My PhD thesis.
2016	Multi-focal tensors as invariant differential forms

SPT	Spatial Profiling Toolbox for spatial characterization of the tumor microenvironment in multiplex images.
coincidencetest	A library and supplemental tools implementing an exact test for co-occurrence of multiple binary features.

gman	A general-purpose text-mode graph navigation and annotation tool.
4D tensor invariants	A Macaulay2 program to calculate 4d tensor invariants using the umbral calculus as described in Grosshans, Rota, and Stein.
perspective cube tool	Geogebra tool for constructing cubes in perspective, and a note explaining how to draw cubes on paper. Drawn from George Francis' A Topological Picturebook.

Summary notes of Ehresmann and Vanbremeersch Memory Evolutive Systems Part A and Part B.

November 2019	Wasserstein and Fisher-Rao from de Rham and Poincare. BMCC Mathematics Department Colloquium.
September 2017	Handout about curve jets, from a talk at TU Berlin
July 2017	Multi-focal tensors as invariant differential forms, and envelopes of line congruences SIAM mini-symposium on algebraic vision, in Atlanta, Georgia

	A dividing ball is shown (left) together with its space of bitangent lines (right).
	The envelope of a 1-parameter line family in the 2D plane, illustrated by means of the surface in 3D slope-space corresponding to the first derivative (contact elements) of the line family.
	The envelope of a certain 1-parameter family of quadric surfaces is 2 spheres.
	The (first order) envelope of a certain 1-parameter family of quadric surfaces is a standard quartic torus.
	The (first order) envelope of a certain 1-parameter family of plane conics is 2 circles.
	The envelope of the wavefronts emitted at speed c by a point source, also moving at constant speed c, along a given circle (blue). This is a second-order envelope, with family members making order 2 contact with the envelope curve.
	The apparent contour (blue) of a standard quartic torus, shown from the point of viewing (left), and from another angle (right). High resolution images here and here.
	An interesting linkage.
	A torus embedding in SO(3), in a 3-dimensional disc chart for SO(3).

	A triple front tuck.
	A bony growth on the upper part of my right mandibular condyle, caused by an injury during a martial arts class. CT scan at about 3 months post-injury. You also get a good view of my unerupted upper-right wisdom tooth.

Solar car	Chess
Box house	Box house 2.0
Forest near Tömörbulag	Manifold storage area, apparently. Seen in Germany.