6 papers
The Newlander-Nirenberg theorem for complex -manifolds
Tatyana Barron, Michael Francis
Melrose defined the b-tangent bundle of a smooth manifold M with boundary as the vector bundle whose sections are vector fields on M tangent to the boundary. Mendoza defined a comp…
Geometry and biological processes
Tatyana Barron, Sarah Lanthier
We suggest a geometric approach to modeling biochemical processes, aiming at those processes that occur in humans with food sensitivities or chemical sensitivities.
Dimensionality increase for error correction in the interaction between information space and the physical world
Tatyana Barron
The evolution of human intelligence led to the huge amount of data in the information space. Accessing and processing this data helps in finding solutions to applied problems based…
Mathematical models for therapeutic approaches involving electric conductors or shielding
Tatyana Barron
We set up a mathematical model for a DC current in a human tissue that shows an attenuation effect in an extended circuit. We give a positive lower bound on the time duration over…
Signals as submanifolds, and configurations of points
Tatyana Barron, Spencer Kelly, Colin Poulton
For the purposes of abstract theory of signal propagation, a signal is a submanifold of a Riemannian manifold. We obtain energy inequalities, or upper bounds, lower bounds on energ…
Geometric signals
Tatyana Barron
In signal processing, a signal is a function. Conceptually, replacing a function by its graph, and extending this approach to a more abstract setting, we define a signal as a subma…