Multi-step-length gradient iterative method for separable nonlinear least squares problems

summary:Separable nonlinear least squares (SNLLS) problems are critical in various research and application fields, such as image restoration, machine learning, and system identification. Solving such problems presents a challenge due to their nonlinearity. The traditional gradient iterative algorithm often zigzags towards the optimal solution and is sensitive to the initial guesses of unknown parameters. In this paper, we improve the convergence rate of the traditional gradient method by implementing a multi-step-length gradient iterative algorithm. Moreover, we incorporate the variable projection (VP) strategy, taking advantage of the separable structure observed in SNLLS problems. We propose a multi-step-length gradient iterative-based VP (Mul-GI-VP) method to solve such nonlinear optimization problems. Our simulation results verify the feasibility and high efficiency of the proposed algorithm

Understanding Daily Travel Patterns of Subway Users – An Example from the Beijing Subway

The daily travel patterns (DTPs) present short-term and timely characteristics of the users’ travel behaviour, and they are helpful for subway planners to better understand the travel choices and regularity of subway users (SUs) in details. While several well-known subway travel patterns have been detected, such as commuting modes and shopping modes, specific features of many patterns are still confused or omitted. Now, based on the automatic fare collection (AFC) system, a data-mining procedure to recognize DTPs of all SUs has become possible and effective. In this study, DTPs are identified by the station sequences (SSs), which are modelled from smart card transaction data of the AFC system. The data-mining procedure is applied to a large weekly sample from the Beijing Subway to understand DTPs. The results show that more than 93% SUs of the Beijing Subway travel in 7 DTPs, which are remarkably stable in share and distribution. Different DTPs have their own unique characteristics in terms of time distribution, activity duration and repeatability, which provide a wealth of information to calibrate different types of users and characterize their travel patterns.</p

Quadratically convergent multiple roots finding method without derivatives

AbstractIn this paper, an iteration method without derivatives for multiple roots is proposed. This method proved to be quadratically convergent. Its efficiency and accuracy are illustrated by numerical experiments

Virus efficacy of recombined Autographa californica M nucleopolyhedrovirus (AcMNPV) on tea pest Ectropis obliqua

Ectropis obliqua is a major tea pest and chitin synthase (CHS) plays a key role in the pest growth and development. A 192 bp conserved domain from E. obliqua CHS gene was cloned and it was used to construct recombined Autographa californica M nucleopolyhedrovirus (AcMNPV) with double-stranded RNA interference (dsRNAi) method. The recombined AcMNPV virus could propagate in host cells sf9. Injection test showed that the virus efficacy of the recombined AcMNPV on E. obliqua larvae was significantly enhanced. It is considered that the CHS dsRNAi mediated by the nuclear polyhedrosis virus will be interesting for development of alternative bio-pesticide to control the tea pest E. obliqua.Keywords: Chitin synthase, baculovirus, double-stranded RNA interference, Ectropis obliquaAfrican Journal of Biotechnology Vol. 9(33), pp. 5412-5418, 16 August, 201

2,2-Dimethyl-5-[(pyridin-2-yl­amino)­methyl­idene]-1,3-dioxane-4,6-dione

In the title compound, C12H12N2O4, the dihedral angle between the pyridine and enamine planes is 3.5 (3)°, while the angle between the dioxanedione (seven atoms) and enamine planes is 4.6 (3)°. The dioxane ring approximates an envelope conformation

Critical Behavior of Ferromagnetic Ising Model on Triangular Lattice

We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate data for large lattices with $L=8,10,12,15,20,25,30,40,50$. The spin updating algorithm we employ has the advantages of both metropolis and single-update methods. Our study indicates that the transition to be continuous at $T_c=3.6403(2)$. A convincing finite-size scaling analysis of the model yield $\nu=0.9995(21)$, $\beta/\nu=0.12400(18)$, $\gamma/\nu=1.75223(22)$, $\gamma'/\nu=1.7555(22)$, $\alpha/\nu=0.00077(420)$ (scaling) and $\alpha/\nu=0.0010(42)$(hyperscaling) respectively. Estimates of present scheme yield accurate estimates for all critical exponents than those obtained with Monte Carlo methods and show an excellent agreement with their well-established predicted values

Poly[μ2-benzene-1,3-dicarboxyl­ato-κ2 O:O′-μ2-1,3-di-4-pyridylpropane-κ2 N:N′-zinc(II)]

The title compound, [Zn(C8H4O4)(C13H14N2)]n, was obtained by the hydro­thermal reaction of Zn(OAc)2·H2O with 1,3-di-4-pyridylpropane (bpp) and isophthalic acid (H2ip). The ZnII ion is coordinated by two bpp and two ip ligands in a distorted tetra­hedral environment. Each ligand coordinates in a bridging mode to connect ZnII ions into a three-dimensional diamondoid-type structure