Path integration method for stochastic responses of differential equations under Lévy white noise.

A path integration (PI) approach that is progressive for studying the stochastic response driven by Lévy white noise is presented. First, a probability mapping is constructed, which decouples the domain of interest for the system state and the probability space derived from the randomness of Lévy white noise within a short time interval. Then, solving the probability mapping yields the short-time response of the system. Finally, the stochastic evolution of the system can be grasped in a stepwise manner based on the fundamental concept of the PI method. The applicability and effectiveness of our approach in addressing the transient and stationary responses under Lévy white noises are verified by Monte Carlo simulation results. Moreover, the advances in utilization of this method are that it eliminates the restriction of the previous PI method on the controlling parameter of Lévy white noises, and it is highly efficient for solving responses of systems under Lévy white noises.

The identification of piecewise non-linear dynamical system without understanding the mechanism.

This paper designs an algorithm to distill the piecewise non-linear dynamical system from the data without prior knowledge. The system to be identified does not have to be written as a known model term or be thoroughly understood. We exploit the fact that an unknown piecewise non-linear system can be decomposed into the Fourier series as long as its equations of motion are Riemann integrable. Based on this property, we reduce the challenge of finding the correct model to discovering the Fourier series approximation. However, the Fourier series approximation of the piecewise function is inaccurate. The new method takes advantage of this weakness to determine whether the model has piecewise features and to find a way to discover the discontinuity set. Then, the dynamical system on each segment is identified as a pure Fourier series. Identification of intricate models can be achieved in simple steps. The results show that the method can accurately discover the equation of motion and precisely capture the non-smooth characteristic. Next, the prediction and further detailed analysis can be carried out.

Variation in Cell Wall Metabolism and Flesh Firmness of Four Apple Cultivars during Fruit Development.

Fruit ripening and softening are highly complex processes, and there is an interplay and coordination between the metabolic pathways that are involved in the biological processes. In this study, we aimed to elucidate the variation in the characters and possible causes of cell wall materials and morphological structure during apple fruits development. We studied the cell wall material (CWM), structure, cellular morphology, hydrolase activity, and the transcriptional levels of the related genes in four apple varieties 'Ruixue' and 'Ruixianghong' and their parents ('Pink Lady' and 'Fuji') during fruit development. The decrease in the contents of CWMs, sodium carbonate soluble pectin, hemicellulose, and cellulose were positively correlated with the decline in the hardness during the fruit development. In general, the activities of polygalacturonase, ß-galactosidase, and cellulase enzymes increased during the late developmental period. As the fruit grew, the fruit cells of all of the cultivars gradually became larger, and the cell arrangement became more relaxed, the fruit cell walls became thinner, and the intercellular space became larger. In conclusion, the correlation analysis indicated that the up-regulation of the relative expression levels of ethylene synthesis and cell wall hydrolase genes enhanced the activity of the cell wall hydrolase, resulting in the degradation of the CWMs and the depolymerization of the cell wall structure, which affected the final firmness of the apple cultivars in the mature period.

MdBBX21, a B-Box Protein, Positively Regulates Light-Induced Anthocyanin Accumulation in Apple Peel.

The red coloration of apple (Malus × domestica Borkh.) is due to the accumulation of anthocyanins in the fruit peel. Light is essential for anthocyanin biosynthesis in apple. In this study, we performed a transcriptome sequencing (RNA-seq) analysis of apple fruit exposed to light after unbagging. The identified differentially expressed genes included MdBBX21, which is homologous to Arabidopsis BBX21, suggesting it may be involved in light-induced anthocyanin biosynthesis. Additionally, MdBBX21 was localized in the nucleus and its gene was expressed earlier than MdMYB1 in apple peel treated with light. Overexpressing MdBBX21 in Arabidopsis and apple calli under light increased anthocyanin accumulation. Dual-luciferase and yeast one-hybrid assays confirmed that MdBBX21 binds to the MdHY5, MdBBX20, and MdBBX22-1/2 promoters and induces expression. At the same time, MdHY5 can also activate the expression of MdBBX21. Furthermore, bimolecular fluorescence complementation and yeast two-hybrid assays demonstrated that MdBBX21 can interact with MdHY5. This interaction can significantly enhance MdMYB1 promoter activity. These findings clarify the molecular mechanism by which MdBBX21 positively regulates light-induced anthocyanin accumulation in apple.

The stochastic bifurcation of the vibro-impact system on the impact surface via a new path integration method.

In this paper, a new path integration algorithm is proposed for the non-autonomous vibro-impact system. It can be used to obtain the stochastic response of the system at the impact instant. The innovation of this algorithm is that the fixed excitation phase at the impact instant is introduced. The fixed excitation phase and the impact surface are combined as the special impact surface, and the algorithm sets up the different evolution methods of the probability density function and the impact completion condition. It can directly capture the stochastic response of the system at the impact instant without any non-smooth approximations. The non-smooth characteristics of the impact can be well preserved. This new path integration algorithm has good applicability. It has no limitation on the restitution coefficient. The design idea of this algorithm may provide a framework for the non-smooth system subject to the periodic excitation. In the end, a linear vibro-impact system and a nonlinear vibro-impact system excited by the external periodic force are used as examples to show how our method could be implemented. The stochastic P-bifurcation phenomena induced by parameters also are considered. The Monte Carlo simulations verify the effectiveness and accuracy of the proposed path integration algorithm.

Id1/NR2B Receptor Pathway Regulates Rat Cochlear Sensory Epithelial Cell Survival after Radiation.

Survival of cochlear sensory epithelial cells may be regulated by inhibitor of differentiation-1 (Id1) and the N-methyl-D-aspartic acid (NMDA) receptor. However, it is unclear whether Id1 and the NMDA receptor are involved in the radiation-mediated survival of rat cochlear sensory epithelial cells. Here, we show that the percentage of apoptotic cells increased, the percentage of cells in the S phase decreased, Id1 mRNA and protein expression decreased and the NMDA receptor subtype 2B (NR2B) mRNA and protein level increased in OC1 cells after radiation. Cells infected with the Id1 gene exhibited higher Id1 mRNA and protein levels and lower NR2B mRNA and protein levels than the control cells. In contrast, after transfection of the Id1 siRNA into OC1 cells, Id1 mRNA and protein expression decreased and NR2B mRNA and protein expression increased relative to that of the control group. Additionally, treatment with ifenprodil for 24 h before radiation reduced apoptosis and increased the percentage of cells in the S phase. Our results suggest that Id1 and NR2B might regulate the survival of OC1 cells following radiation.

Comparison of chirp versus click and tone pip stimulation for cervical vestibular evoked myogenic potentials.

The current study explored differences among cervical vestibular evoked myogenic potentials (cVEMP) that were evoked by CE-chirp and click and tone pip in healthy controls, and tried to explain the differences of cVEMP between the three of them. Thirty normal volunteers were used as subjects for CE-chirp and click and tone-pip (Blackman pip) stimuli. The latency of P1, N1, peak-to-peak P1-N1 amplitude, and cVEMP interaural difference were obtained and analyzed. The response rates of cVEMP were 93 % for click and 100 % for both Blackman pip and CE-chirp, respectively. The P1 and N1 latencies of cVEMP evoked by CE-chirp were the shortest, followed by click, with Blackman pip the longest (F = 6,686.852, P < 0.001). All indices of cVEMP evoked by the three stimuli showed no significant difference between the left and right ears or between genders. cVEMP responses were significantly different between the three stimuli. Compared with the currently used stimulus, CE-chirp can evoke cVEMP with shorter latencies and demonstrates increased speed and reliability.

[Influence of the quantified surface electromyography of sternocleidomastoid on cervical vestibular evoked myogenic potential].

OBJECTIVE: This study investigated the correlations between electromyography (EMG) of sternocleidomastoid (SCM) and cervical vestibular evoked myogenic potentials (cVEMP), and intended to quantify the influence of EMG of SCM on cVEMP by recording the EMG of SCM and cVEMP in different head positions. METHODS: Thirty healthy subjects (60 ears), without the history of ear illnesses, were enrolled in this study. In addition, the recruited subjects also showed favorable differentiation of cVEMP waves induced by Blackman pip cVEMP, and EMG were recorded in different head positions(with sagittal at 90°, 60°,45° and 30°angle), as well as to analyze and quantify the influence of EMG on cVEMP. RESULTS: In the case of the different EMG levels: P1 latency, (12.50 ± 2.39)ms; N1 latency, (19.79 ± 3.16)ms, and the latencies shown no statistical difference (P > 0.05). The amplitude was affected by EMG level, there was significant difference between the amplitudes(F = 55.47, P < 0.01). The different head positions on subjects their EMG level or area of EMG effects were statistically significant (P < 0.01). The study found a linear dependence of the amplitude from the EMG levels(r(2) = 0.591, Adjusted-r(2) = 9.590). CONCLUSIONS: The cVEMP amplitude increases as a function of EMG target level, and the latency remains constant. The quantized data will increase the amplitude in clinical diagnosis application of sensitivity, and it will improve the diagnosis of the vestibular system diseases and some related diseases.

99mTc-labeled HAb18 McAb Fab fragment for radioimmunoimaging in nude mice bearing human hepatocellular carcinoma.

AIM:To establish a method of labeling anti-hepatoma McAb (HAb18) Fab fragment modifier with (99m)Tc.METHODS:HAb18 Fab was modified with 2-iminotholane and labeled with (99m)Tc by transchelation from (99m)Tc GH.Labeling yield, radiochemical purity and immunoreactivity were determined by thin layer chromatography (TLC-SG), paper chromatography (PC), gel chromatography (GC) and cell binding assay, respectively. The nude mice bearing human hepatoma were used for radioimmunoimaging (RII).RESULTS:A radiolabeling yield of 50%-80% was obtained, and immunoreactivity (IR) was 30%-40%. Radioimaging results showed that (99m)Tc-HAb18 McAb Fab fragment was concentrated in the tumor 4-8 hours after injection,and the maximum concentration was seen in 12-24 hours,and the T/NT value was 5.18 and 7.48 at 6h and 8h after the injection.CONCLUSION: (99m)Tc-HAb18 McAb Fab fragment could be specifically localized in the tumor of nude mice bearing human hepatocellular carcinoma within 24 hours and this method might be effectively used for labeling McAb Fab fragment with (99m)Tc.