Tootfinder

A Saddle Point Algorithm for Robust Data-Driven Factor Model Problems
Shabnam Khodakaramzadeh, Soroosh Shafiee, Gabriel de Albuquerque Gleizer, Peyman Mohajerin Esfahani
https://arxiv.org/abs/2506.09776

A Saddle Point Algorithm for Robust Data-Driven Factor Model Problems
We study the factor model problem, which aims to uncover low-dimensional structures in high-dimensional datasets. Adopting a robust data-driven approach, we formulate the problem as a saddle-point optimization. Our primary contribution is a general first-order algorithm that solves this reformulation by leveraging a linear minimization oracle (LMO). We further develop semi-closed form solutions (up to a scalar) for three specific LMOs, corresponding to the Frobenius norm, Kullback-Leibler diver…

This https://arxiv.org/abs/2503.18789 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Sylvester program and Cayley algorithm for vector partition reduction
A vector partition problem asks for a number of nonnegative integer solutions to a system of several linear Diophantine equations with integer nonnegative coefficients. J.J. Sylvester put forward an idea of reduction of vector partition to a sum of scalar partitions. In the simplest case of two equations with positive coefficients A. Cayley performed a reduction of the corresponding double partition to a sum of scalar partitions using an algorithm subject to a set of conditions on the coefficie…

Linear programming bounds in homogeneous spaces, I: Optimal packing density
Maximilian Wackenhuth
https://arxiv.org/abs/2505.23572 https://

Linear programming bounds in homogeneous spaces, I: Optimal packing density
In this article we obtain linear programming bounds for the maximal sphere packing density of commutative spaces. A special case of our results solves a conjecture by Cohn and Zhao on linear programming bounds for sphere packings in hyperbolic space.

On the Inversion Modulo a Power of an Integer
Guangwu Xu, Yunxiao Tian, Bingxin Yang
https://arxiv.org/abs/2506.02491 https://arxiv.o…

On the Inversion Modulo a Power of an Integer
Recently, Koc proposed a neat and efficient algorithm for computing $x = a^{-1} \pmod {p^k}$ for a prime $p$ based on the exact solution of linear equations using $p$-adic expansions. The algorithm requires only addition and right shift per step. In this paper, we design an algorithm that computes $x = a^{-1} \pmod {n^k}$ for any integer $n>1$. The algorithm has a motivation from the schoolbook multiplication and achieves both efficiency and generality. The greater flexibility of our algorithm …

This https://arxiv.org/abs/2410.06307 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Model Predictive Control is Almost Optimal for Restless Bandit
We consider the discrete time infinite horizon average reward restless markovian bandit (RMAB) problem. We propose a \emph{model predictive control} based non-stationary policy with a rolling computational horizon $τ$. At each time-slot, this policy solves a $τ$ horizon linear program whose first control value is kept as a control for the RMAB. Our solution requires minimal assumptions and quantifies the loss in optimality in terms of $τ$ and the number of arms, $N$. We show that its sub-opt…

This https://arxiv.org/abs/2503.09605 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

QWENDY: Gene Regulatory Network Inference Enhanced by Large Language Model and Transformer
Knowing gene regulatory networks (GRNs) is important for understanding various biological mechanisms. In this paper, we present a method, QWENDY, that uses single-cell gene expression data measured at four time points to infer GRNs. Based on a linear gene expression model, it solves the transformation for the covariance matrices. Unlike its predecessor WENDY, QWENDY avoids solving a non-convex optimization problem and produces a unique solution. Then we enhance QWENDY by the transformer neural …