129 citations · 156 across the 10 of their papers we have counts for
10 papers
A New Approach to Euler Calculus for Continuous Integrands
Carl McTague
Euler calculus is based on integrating simple functions with respect to the Euler characteristic. This paper makes the case for extending Euler calculus to continuous integrands by…
On the Greatest Common Divisor of Binomial Coefficients
Carl McTague
Every binomial coefficient aficionado knows that the greatest common divisor of the binomial coefficients equals if for some $…
Shrinking the Fibers of a Submersion Splits the Riemann Tensor
Carl McTague
This paper uses Karcher's formulation [Kar99] of the O'Neill tensors [O'N66,Gra67] to derive a concise formula for the family of curvature forms obtained by shrinking the fib…
tmf Is Not a Ring Spectrum Quotient of String Bordism
Carl McTague
This paper shows that is not a ring spectrum quotient of . In fact, for any prime and any sequence of homogeneous ele…
The Cayley plane and String bordism
Carl McTague
This paper shows that, away from 6, the kernel of the Witten genus is precisely the ideal consisting of (bordism classes of) Cayley plane bundles with connected structure group, bu…
Enumerating Finitary Processes
B. D. Johnson, J. P. Crutchfield, C. J. Ellison +1
We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of epsilon-machines. We characterize epsilon-machines in the lang…
The Cayley Plane and the Witten Genus
Carl McTague
This paper defines a new genus, the Cayley plane genus. By definition it is the universal multiplicative genus for oriented Cayley plane bundles. The main result (Theorem 2) is tha…
Stiefel-Whitney Numbers for Singular Varieties
Carl McTague
This paper determines which Stiefel-Whitney numbers can be defined for singular varieties compatibly with small resolutions. First an upper bound is found by identifying the F_2-ve…
The Organization of Intrinsic Computation: Complexity-Entropy Diagrams and the Diversity of Natural Information Processing
David P. Feldman, Carl S. McTague, James P. Crutchfield
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a m…
Automated Pattern Detection--An Algorithm for Constructing Optimally Synchronizing Multi-Regular Language Filters
Carl S. McTague, James P. Crutchfield
In the computational-mechanics structural analysis of one-dimensional cellular automata the following automata-theoretic analogue of the \emph{change-point problem} from time serie…