Nonuniform and higher-order FDTD methods for the Schrödinger equation
An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions
A particular upper expectation as global belief model for discrete-time finite-state uncertain processes
To model discrete-time finite-state uncertain processes, we argue for the use of a global belief model in the form of an upper expectation that is the most conservative one under a set of basic axioms. Our motivation for these axioms, which describe how local and global belief models should be related, is based on two possible interpretations for a...
Mixed multiplicities and projective degrees of rational maps
Towards better concordance among contextualized evaluations in FAST-GDM problems
A flexible attribute-set group decision-making (FAST-GDM) problem consists in finding the most suitable option(s) out of the options under consideration, with a general agreement among a heterogeneous group of experts who can focus on different attributes to evaluate those options. An open challenge in FAST-GDM problems is to design consensus reach...
Local orientation-preserving symmetry preserving operations on polyhedra
Curves in characteristic 2 with non-trivial 2-torsion
Cais, Ellenberg and Zureick-Brown recently observed that over finite fields of characteristic two, all sufficiently general smooth plane projective curves of a given odd degree admit a non-trivial rational 2-torsion point on their Jacobian. We extend their observation to curves given by Laurent polynomials with a fixed Newton polygon, provided that...
Doubly robust tests of exposure effects under high-dimensional confounding.
Published in Biometrics
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is exacerbated in high-dimensional settings, where variable selection becomes unavoidable. This has prompted a fl...
New and Updated Semidefinite Programming Bounds for Subspace Codes
We show that $A_2(7,4) \leq 388$ and, more generally, $A_q(7,4) \leq (q^2-q+1)[7]_q + q^4 - 2q^3 + 3q^2 - 4q + 4$ by semidefinite programming for $q \leq 101$. Furthermore, we extend results by Bachoc et al. on SDP bounds for $A_2(n,d)$, where $d$ is odd and $n$ is small, to $A_q(n,d)$ for small $q$ and small $n$.
On a Criterion for Catalan's Conjecture
Published in The Ramanujan Journal
We give a new proof of a theorem of P. Mihailescu which states that the equation xp − yq = 1 is unsolvable with x, y integral and p, q odd primes, unless the congruences pq ≡ p (mod q2) and qp ≡ q (mod p2) hold.
