A. R. Aithal

Scalable Training of Mixture-of-Experts Models with Megatron Core

Zijie Yan, Hongxiao Bai, Xin Yao, Dennis Liu et autres

Scaling Mixture-of-Experts (MoE) training introduces systems challenges absent in dense models. Because each token activates only a subset of experts, this sparsity allows total parameters to grow much faster than per-token computation, creating coupled constraints across memory, communication, and computation. Optimizing one …

Convex polygons and the isoperimetric problem in simply connected space forms $M_κ^2$

A. R. Aithal, Anisa M. H. Chorwadwala

In this article, we prove that there exists a unique perimeter minimizer among all piecewise smooth simple closed curves in $M_κ^2$ enclosing area $A > 0$ $(A \leq 2π$ if $κ = 1)$, and it is a circle in $M_κ^2$ of radius …

The first Dirichlet Eigenvalue of the Laplacian in a Class of Doubly Connected Domains in Complex Projective Space

Akanksha V. Rane, A. R. Aithal

in (code pays fourni par la source)

On a functional connected to the laplacian in a family of punctured regular polygons in ℝ2

A. R. Aithal, Acushla Sarswat

in (code pays fourni par la source)

On the extrema of Dirichlet’s first eigenvalue of a family of punctured regular polygons in two dimensional space forms

A. R. Aithal, Rajesh Raut

in (code pays fourni par la source)

On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms

M. H. C. Anisa, A. R. Aithal

Let $B_1$ be a ball of radius $r_1$ in $S^n(\Hy^n)$, and let $B_0$ be a smaller ball of radius $r_0$ such that $\bar{B_0}\subset B_1$. For $S^n$ we consider $r_1< π$. Let $u$ be a solution of the problem $-\La u =1$ in …

in (code pays fourni par la source)

On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms

M. H. C. Anisa, A. R. Aithal

in (code pays fourni par la source)

Splitting types of holomorphic bundles associated to some harmonic maps

A. R. Aithal, D. S. Nagaraj

in (code pays fourni par la source)

Harmonic maps from S² to HP²

A. R. Aithal

In this paper, we describe all harmonic maps from the Riemann 2-sphere to HP 2 y the quaternion 2-projective space.In example 1.3, all isotropic harmonic maps from S 2 to HP n are given.A particular class of nonisotropic harmonic maps from S …

Harmonic Maps from S 2 to G 2 (C5 )

A. R. Aithal

in (code pays fourni par la source)