6 citations · 6 across the 9 of their papers we have counts for
10 papers
Galois-Orbit Structure, Ramanujan Sums, and Stable-Range Collapse for Cyclotomic Cosine Formulas
Juan D. Vélez, Carlos A. Cadavid
We study cyclotomic cosine evaluations beyond the fully symmetric setting by combining Galois-orbit structure with finite-frequency expansions. First, for truncation-compatible pol…
Diffusion Computation versus Quantum Computation: A Comparative Model for Order Finding and Factoring
Carlos A. Cadavid, Paulina Hoyos, Jay Jorgenson +2
We study a hybrid computational model for integer factorization in which the only non-classical resource is access to an \emph{iterated diffusion process} on a finite graph. Concre…
Using TeV Cosmic Rays to probe the Heliosphere's Boundary with the Local Interstellar Medium
Paolo Desiati, Juan Carlos Díaz Vélez, Gwenael Giacinti +4
The heliosphere is the magnetic structure formed by the Sun's atmosphere extending into the local interstellar medium (ISM). The boundary separating the heliosphere from the ISM is…
Discrete diffusion-type equation on regular graphs and its applications
Carlos A. Cadavid, Paulina Hoyos, Jay Jorgenson +2
We derive an explicit formula for the fundamental solution to the discrete-time diffusion equation on the -regular tree in terms of the di…
On an approach for evaluating certain trigonometric character sums using the discrete time heat kernel
Carlos A. Cadavid, Paulina Hoyos, Jay Jorgenson +2
In this article we develop a general method by which one can explicitly evaluate certain sums of -th powers of products of elementary trigonometric functions evaluated…
Observation of Cosmic Ray Anisotropy with Nine Years of IceCube Data
Frank McNally, Rasha Abbasi, Paolo Desiati +7
The IceCube Observatory has collected over 577 billion cosmic-ray induced muon events in its final configuration from May 2011 to May 2020. We used this data set to provide an unpr…
On the Topological Structure of the (Non-) Finitely-generated Locus of Frobenius Algebras emerging from Stanley-Reisner Rings
Edisson Gallego, Juan D. Vélez, Sergio D. Molina-Aristizabal +2
In this paper we study initial topological properties of the (non-)finitely-generated locus of Frobenius Algebra coming from Stanley-Reisner rings defined through face ideals. More…
An integer factorization algorithm which uses diffusion as a computational engine
Carlos A. Cadavid, Paulina Hoyos, Jay Jorgenson +2
In this article we develop an algorithm which computes a divisor of an integer , which is assumed to be neither prime nor the power of a prime. The algorithm uses discrete time…
Limits of quotients of real polynomial functions of three variables
Juan D. Vélez, Juan P. Hernández, Carlos A. Cadavid
An algorithm for computing the limit of a quotient of bivariate real analytic functions has been developed by one of the authors in (Limits of quotients of bivariate real analytic…
Hurwitz complete sets of factorizations in the modular group and the classification of Lefschetz elliptc fibrations over the disk
J. D. Vélez, C. Cadavid, L. Moreno
Given any matrix B in SL(2,Z), we will describe an algorithm that provides at least one elliptic fibration over the disk, relatively minimal and Lefschetz, within each topological…