Optimal parameter for the SOR-like iteration method for solving the system of absolute value equations

The SOR-like iteration method for solving the absolute value equations~(AVE) of finding a vector $x$ such that $Ax - |x| - b = 0$ with $\nu = \|A^{-1}\|_2 < 1$ is investigated. The convergence conditions of the SOR-like iteration method proposed by Ke and Ma ([{\em Appl. Math. Comput.}, 311:195--202, 2017]) are revisited and a new proof is given, which exhibits some insights in determining the convergent region and the optimal iteration parameter. Along this line, the optimal parameter which minimizes $\|T_\nu(\omega)\|_2$ with $$T_\nu(\omega) = \left(\begin{array}{cc} |1-\omega| & \omega^2\nu \\ |1-\omega| & |1-\omega| +\omega^2\nu \end{array}\right)$$ and the approximate optimal parameter which minimizes $\eta_{\nu}(\omega) =\max\{|1-\omega|,\nu\omega^2\}$ are explored. The optimal and approximate optimal parameters are iteration-independent and the bigger value of $\nu$ is, the smaller convergent region of the iteration parameter $\omega$ is. Numerical results are presented to demonstrate that the SOR-like iteration method with the optimal parameter is superior to that with the approximate optimal parameter proposed by Guo, Wu and Li ([{\em Appl. Math. Lett.}, 97:107--113, 2019]). In some situation, the SOR-like itration method with the optimal parameter performs better, in terms of CPU time, than the generalized Newton method (Mangasarian, [{\em Optim. Lett.}, 3:101--108, 2009]) for solving the AVE.Comment: 23 pages, 7 figures, 7 table

Self-partitioning SlipChip for slip-induced droplet formation and human papillomavirus viral load quantification with digital LAMP

Human papillomavirus (HPV) is one of the most common sexually transmitted infections worldwide, and persistent HPV infection can cause warts and even cancer. Nucleic acid analysis of HPV viral DNA can be very informative for the diagnosis and monitoring of HPV. Digital nucleic acid analysis, such as digital PCR and digital isothermal amplification, can provide sensitive detection and precise quantification of target nucleic acids, and its utility has been demonstrated in many biological research and medical diagnostic applications. A variety of methods have been developed for the generation of a large number of individual reaction partitions, a key requirement for digital nucleic acid analysis. However, an easily assembled and operated device for robust droplet formation without preprocessing devices, auxiliary instrumentation or control systems is still highly desired. In this paper, we present a self-partitioning SlipChip (sp-SlipChip) microfluidic device for the slip-induced generation of droplets to perform digital loop-mediated isothermal amplification (LAMP) for the detection and quantification of HPV DNA. In contrast to traditional SlipChip methods, which require the precise alignment of microfeatures, this sp-SlipChip utilized a design of “chain-of-pearls” continuous microfluidic channel that is independent of the overlapping of microfeatures on different plates to establish the fluidic path for reagent loading. Initiated by a simple slipping step, the aqueous solution can robustly self-partition into individual droplets by capillary pressure-driven flow. This advantage makes the sp-SlipChip very appealing for the point-of-care quantitative analysis of viral load. As a proof of concept, we performed digital LAMP on an sp-SlipChip to quantify human papillomaviruses (HPVs) 16 and 18 and tested this method with fifteen anonymous clinical samples

Effects of nutritional nursing intervention based on glycemic load for patient with gestational diabetes mellitus

Objectives: To determine the effects of nutritional nursing intervention based on glycemic load (GL) for patients with gestational diabetes mellitus. Material and methods: One hundred thirty-four patients diagnosed with gestational diabetes mellitus at our hospital were selected from March 2015 to March 2017 and randomly divided into the observation (n = 67) and control groups (n = 67). All of the patients in the observation and control groups received conventional nutritional nursing. In addition, the patients in the observation group received nutritional nursing intervention based on GL. The changes in blood glucose levels and pregnancy outcomes were compared between the two groups after intervention. Results: There were significant differences in fasting blood glucose (FBG) and the 2h postprandial glucose (2hPG) levels between the two groups (P &lt; 0.05). There was a lower incidence of premature delivery, fetal macrosomia, eclampsia, preg- nancy hypertension syndrome, and fetal distress in the observation group. Conclusions: Nutritional nursing intervention based on GL is more effective than traditional nutritional nursing for patients with gestational diabetes, and can effectively control the blood glucose level, reduce the incidence of pregnant complica- tions, and improve the pregnancy outcome. Thus, nutritional nursing intervention based on GL deserves to be popularized.

Mathematical Mechanism on Dynamical System Algorithms of the Ising Model

Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for solving the Ising model. Over the past decades, some continuous approaches or algorithms have been proposed from physical, mathematical or computational views for optimizing the Ising model such as quantum annealing, the coherent Ising machine, simulated annealing, adiabatic Hamiltonian systems, etc.. However, the mathematical principle of these algorithms is far from being understood. In this paper, we reveal the mathematical mechanism of dynamical system algorithms for the Ising model by Morse theory and variational methods. We prove that the dynamical system algorithms can be designed to minimize a continuous function whose local minimum points give all the candidates of the Ising model and the global minimum gives the minimizer of Ising problem. Using this mathematical mechanism, we can easily understand several dynamical system algorithms of the Ising model such as the coherent Ising machine, the Kerr-nonlinear parametric oscillators and the simulated bifurcation algorithm. Furthermore, motivated by the works of C. Conley, we study transit and capture properties of the simulated bifurcation algorithm to explain its convergence by the low energy transit and capture in celestial mechanics. A detailed discussion on $2$-spin and $3$-spin Ising models is presented as application.Comment: 39 pages, 2 figures(including 8 sub-figures

Microstructures and Properties of Extruded Al-0.6Mg-0.6Si Aluminium Alloy for High-speed Vehicle

AbstractThe Al-0.6Mg-0.6Si aluminium alloy was extruded for high-speed vehicle. The microstructure and mechanical property of extruded Al-0.6Mg-0.6Si aluminium alloy were investigated. The results of experimentation show that the tensile strength of extruded Al-0.6Mg-0.6Si aluminum alloy is above of 245MPa, and the percentage elongation after fracture is better than 8%. The microstructure is rolling structure, and the coarse second phases distribute in α-Al solid solution matrix structure. The second phases are inclusions, coarse stable phases of β′ (Mg2Si) or their collection. The tiny β′ (Mg2Si) strengthening precipitation phases mostly distribute in the grain boundary. The size of β′ strengthening phase is about 5nm. The width of no precipitation band is above of 50nm. The fatigue life is 1.061×105 cycle when σmax=0.75σb. The fatigue cracks initiate in surface of extruded Al-0.6Mg-0.6Si aluminium alloy sample. The fatigue fracture is composed of the initiation zone, the propagation zone, and the sudden fracture zone, which is characteristic of a mixed-type fatigue fracture

Linkage Between SecA Dimerization and Ligand Binding

Abstract. Introduction and Objectives:. There have, yet, been only few attempts to phonetically characterize the vocalizations of pain, although there is wide agreement that moaning, groaning, or other nonverbal utterance can be indicative of pain. We studied the production of vowels “u,” “a,” “i”, and “schwa” (central vowel, sounding like a darker “e” as in hesitations like “ehm”)—as experimental approximations to natural vocalizations. Methods:. In 50 students vowel production and self-report ratings were assessed during painful and nonpainful heat stimulation (hot water immersion) as well as during baseline (no-stimulation). The phonetic parameters extracted were pitch (mean F0), phonatory fluctuations (range F0) and loudness (acoustic energy level). Results:. Only for the vowels “u” and “schwa,” which might be considered best approximations to moaning and groaning, did pitch and loudness increase during pain. Furthermore, changes from nonpainful to painful stimulations in these parameters also significantly predicted concurrent changes in pain ratings. Conclusion:. Vocalization characteristics of pain seem to be best described by an increase in pitch and in loudness. Future studies using more specific and comprehensive phonetic analyses will surely help to provide an even more precise characterization of vocalizations because of pain