45 citations · 57 across the 11 of their papers we have counts for
11 papers
On the distribution of the minimal length of addition chains
Jean-Marie De Koninck, Nicolas Doyon, William Verreault
A sequence of integers is called an addition chain of length if with for all integers . We denote by…
On the convergence of doubly stochastic Markov chains
Ludovick Bouthat, Nicolas Doyon, Javad Mashreghi +1
We characterize the asymptotic behavior of time-homogeneous doubly stochastic Markov chains. Our investigation revolves around understanding the dynamics of products of doubly stoc…
On the minimal length of addition chains
Jean-Marie De Koninck, Nicolas Doyon, William Verreault
We denote by the minimal length of an addition chain leading to and we define the counting function …
The determining role of covariances in large networks of stochastic neurons
Vincent Painchaud, Patrick Desrosiers, Nicolas Doyon
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both…
Classes of Holomorphic Multicomplex-Valued Functions Generated by Elliptic-Admissible Involutions
Nicolas Doyon, Pierre-Olivier Parisé, William Verreault
We classify and count the real-algebra involutions of the multicomplex algebra that map each element of its canonical monomial basis to a signed monomial…
Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition
Vincent Painchaud, Nicolas Doyon, Patrick Desrosiers
Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: activ…
Bounds for the counting function of the Jordan-Pólya numbers
Jean-Marie De Koninck, Nicolas Doyon, A. Arthur Bonkli Razafindrasoanaivolala +1
A positive integer is said to be a Jordan-Pólya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-Pó…
Repetitions of multinomial coefficients and a generalization of Singmaster's conjecture
Jean-Marie de Koninck, Nicolas Doyon, William Verreault
Given two integers and , let stand for the number of multinomial coefficients, with terms, equal to . We study the behavior of and show that…
Spectral dimension reduction of complex dynamical networks
Edward Laurence, Nicolas Doyon, Louis J Dubé +1
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes)…
TE-TM Electromagnetic modes and states in quantum physics
Réal Tremblay, Nicolas Doyon, Julien Beaudoin-Bertrand
We propose, as another pedagogical approach, a quantification of the e.m. field better adapted in isolated systems, a quantification of e.m. fields in finite-spacetime which does n…
as a Physical Constant of Classical Optics and Electrodynamics
Real Tremblay, Nicolas Doyon, Claudine Ni Allen
The Planck constant () plays a pivotal role in quantum physics. Historically, it has been proposed as postulate, part of a genius empirical relationship in order…