We develop a theory for estimation of a high-dimensional sparse parameter θ defined as a minimizer of a population loss function LD(θ,g0) which, in addition to θ, depends on a, potentially infinite ...

Abstract: In a previous paper we have presented a kernel method for antenna array processing using gaussian kernels as basis functions (Approximated Kernel Orthogonalization, AKO) and shown that it ...

Let µ be a probability measure on the real line with finite moments of all orders. Apply the Gram-Schmidt orthogonalization process to the system {1, x, x², . . . , xn, . . .} to get orthogonal ...

This manuscript reports a useful computational study of information encoding across the monkey prefrontal and pre-motor cortices during decision making. While many of the conclusions are supported ...

Summary: New research reveals how the brain separates internally generated noise from sensory signals, ensuring stable perception. The study shows that in lower visual areas, spontaneous brain ...

Scientists from the University of Tokyo performed two-photon imaging in the visual cortex of marmoset monkeys to examine spontaneous and visual stimulus-evoked neuronal activities (top left). Visual ...

Abstract: The paper addresses the modeling and control of the orthogonalization plants for textile industry. An innovative mathematical theory of the textile yarns correction phenomenon, particularly ...

ABSTRACT: A method for determining the extrema of a real-valued and differentiable function for which its dependent variables are subject to constraints and that avoided the use of Lagrange ...

1 Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN, USA. 2 Department of Computer Science, State University of Montes Claros, Montes Claros, MG, Brazil. A method for ...

Ensuring the safety and ethical behavior of large language models (LLMs) in responding to user queries is of paramount importance. Problems arise from the fact that LLMs are designed to generate text ...

The CholeskyQR2 for Ill-conditioned Matrices (CholeskyQR2-IM) library is a modern C++ implementation designed to compute the QR factorization of extremely ill-conditioned tall-and-skinny matrices. It ...