Improving the continuum limit of gradient flow step scaling

We introduce a non-perturbative improvement for the renormalization group step scaling function based on the gradient flow running coupling, which may be applied to any lattice gauge theory of interest. Considering first SU(3) gauge theory with $N_f = 4$ massless staggered fermions, we demonstrate that this improvement can remove $O(a^2)$ lattice artifacts, and thereby increases our control over the continuum extrapolation. Turning to the 12-flavor system, we observe an infrared fixed point in the infinite-volume continuum limit. Applying our proposed improvement reinforces this conclusion by removing all observable $O(a^2)$ effects. For the finite-volume gradient flow renormalization scheme defined by $c = \sqrt{8t} / L = 0.2$, we find the continuum conformal fixed point to be located at $g_\star^2 = 6.2(2)$Comment: 12 pages, 4 figures; Minor changes, published versio

A Communication Application Design Framework Based on Mesh Network Architecture for Folk Song Dissemination

This document suggests a pair of optimization and enhancement algorithms for Mesh network architecture to foster the spread of folk songs and evaluates these algorithms within a communication design framework. Proposed are communication applications utilizing Mesh network architecture. The average end-to-end delay of the improved expected transmission time metric algorithm is is lower than that of other algorithms; The channel allocation algorithm of wireless mesh network structure improves the throughput by about 16% with the same number of data streams; The real-time reliable data transmission delay of the folk music dissemination framework is significantly lower than that of the non-realtime reliable data network; The mean delay from start to finish in the real-time dependable data transfer within the folk music distribution system is markedly less compared to that in a non-realtime dependable data network.; The folk music communication framework's real-time reliable data transmission experiences an average end-to-end delay, with an average data reception rate surpassing that of non-real-time reliable data, and the real-time reliable data. The rate of receiving usable data from start to finish remains largely unaltered regardless of the amount of communication data; Upon functional testing of the Application (APP), the Central Processing Unit (CPU) usage rate in most tasks remains under 10%; however, during the system's operation, both the occupied memory and CPU usage on the Personal Computer (PC) side is significantly lower. During the operation of the framework, the PC side's occupied memory and CPU usage rate maintain a comparatively steady state

Finite size scaling of conformal theories in the presence of a near-marginal operator

The slowly evolving gauge coupling of gauge-fermion systems near the conformal window makes numerical investigations of these models challenging. We consider finite size scaling and show that this often used technique leads to inconsistent results if the leading order scaling corrections are neglected. When the corrections are included the results become consistent not only between different operators but even when data obtained at different gauge couplings or with different lattice actions are combined. Our results indicate that the SU(3) 12-fermion system is conformal with mass anomalous dimension $\gamma_m=0.235(15)$