172 citations · 796 across the 66 of their papers we have counts for
6 papers · 1 filter
Dynamical Systems and Sheaves
Patrick Schultz, David I. Spivak, Christina Vasilakopoulou
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sor…
Pixel Arrays: A fast and elementary method for solving nonlinear systems
David I. Spivak, Magdalen R. C. Dobson, Sapna Kumari +1
We present a new method, called the pixel array method, for approximating all solutions in a bounding box for an arbitrary nonlinear system of relations. In contrast with other sol…
Understanding Social-Force Model in Psychological Principles of Collective Behavior
Peng N. Wang
To well understand crowd behavior, microscopic models have been developed in recent decades, in which an individual's behavioral/psychological status can be modeled and simulated.…
Homotopy composition of cospans
Joachim Kock, David I. Spivak
It is well known that the category of finite sets and cospans, composed by pushout, contains the universal {\em special} commutative Frobenius algebra. In this note we observe that…
Algebraic Databases
Patrick Schultz, David I. Spivak, Christina Vasilakopoulou +1
Databases have been studied category-theoretically for decades. The database schema -- whose purpose is to arrange high-level conceptual entities -- is generally modeled as a categ…
An algebra of open continuous time dynamical systems and networks
Eugene Lerman, David I. Spivak
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsyst…