4 papers
Reduction for flag-transitive symmetric 2-designs with gcd(k, λ) = p
Ziwei Lu, Yu Sun, Shenglin Zhou
We study symmetric 2-(v, k, λ) designs admitting a flag-transitive point-primitive subgroup G of automorphisms, where gcd(k, λ) = p and p is a prime. In this paper, we show that G…
A Counterexample to Fourier Alignment in Single-Neuron Modular Addition
Gautam Neelakantan Memana
We give a negative solution to MAIS-O60. We first construct an example in which an initially active ReLU neuron becomes completely inactive in finite time and thereafter remains fr…
Comparison theorems for weak solutions of nonlinear maximally sub-elliptic PDEs
Gautam Neelakantan Memana
We establish a comparison principle for viscosity subsolutions and supersolutions of a broad class of second-order quasilinear, maximally subelliptic PDEs on general manifolds. In…
A regularity theorem for fully nonlinear maximally subelliptic PDE
Gautam Neelakantan Memana
We prove a sharp interior regularity theorem for fully nonlinear maximally subelliptic PDE in non-isotropic Sobolev spaces adapted to maximally subelliptic operators. This result c…