A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with general mobility

In this paper, we propose and analyze a linear second-order numerical method for solving the Allen-Cahn equation with general mobility. The proposed fully-discrete scheme is carefully constructed based on the combination of first and second-order backward differentiation formulas with nonuniform time steps for temporal approximation and the central finite difference for spatial discretization. The discrete maximum bound principle is proved of the proposed scheme by using the kernel recombination technique under certain mild constraints on the time steps and the ratios of adjacent time step sizes. Furthermore, we rigorously derive the discrete $H^{1}$ error estimate and energy stability for the classic constant mobility case and the $L^{\infty}$ error estimate for the general mobility case. Various numerical experiments are also presented to validate the theoretical results and demonstrate the performance of the proposed method with a time adaptive strategy.Comment: 25pages, 5 figure

A linear doubly stabilized Crank-Nicolson scheme for the Allen-Cahn equation with a general mobility

In this paper, a linear second order numerical scheme is developed and investigated for the Allen-Cahn equation with a general positive mobility. In particular, our fully discrete scheme is mainly constructed based on the Crank-Nicolson formula for temporal discretization and the central finite difference method for spatial approximation, and two extra stabilizing terms are also introduced for the purpose of improving numerical stability. The proposed scheme is shown to unconditionally preserve the maximum bound principle (MBP) under mild restrictions on the stabilization parameters, which is of practical importance for achieving good accuracy and stability simultaneously. With the help of uniform boundedness of the numerical solutions due to MBP, we then successfully derive $H^{1}$-norm and $L^{\infty}$-norm error estimates for the Allen-Cahn equation with a constant and a variable mobility, respectively. Moreover, the energy stability of the proposed scheme is also obtained in the sense that the discrete free energy is uniformly bounded by the one at the initial time plus a {\color{black}constant}. Finally, some numerical experiments are carried out to verify the theoretical results and illustrate the performance of the proposed scheme with a time adaptive strategy

Impaired Functional Criticality of Human Brain during Alzheimer's Disease Progression

The progression of Alzheimer's Disease (AD) has been proposed to comprise three stages, subjective cognitive decline (SCD), mild cognitive impairment (MCI), and AD. Was brain dynamics across the three stages smooth? Was there a critical transition? How could we characterize and study functional criticality of human brain? Based on dynamical characteristics of critical transition from nonlinear dynamics, we proposed a vertex-wise Index of Functional Criticality (vIFC) of fMRI time series in this study. Using 42 SCD, 67 amnestic MCI (aMCI), 34 AD patients as well as their age-, sex-, years of education-matched 54 NC, our new method vIFC successfully detected significant patient-normal differences for SCD and aMCI, as well as significant negative correlates of vIFC in the right middle temporal gyrus with total scores of Montreal Cognitive Assessment (MoCA) in SCD. In comparison, standard deviation of fMRI time series only detected significant differences between AD patients and normal controls. As an index of functional criticality of human brain derived from nonlinear dynamics, vIFC could serve as a sensitive neuroimaging marker for future studies; considering much more vIFC impairments in aMCI compared to SCD and AD, our study indicated aMCI as a critical stage across AD progression

Research and Practice on the Construction of Laser Intelligent Equipment Teaching Base Built by School and Enterprise

Laser technology is a highly advanced field. It requires a certain level of theoretical knowledge and practical skills to be applied to practice. Therefore, the research on the construction of a laser intelligent equipment teaching base (LIETB) jointly built by schools and enterprises will be studied. First, the necessity of constructing a LIETB from three aspects is given such as the characteristics of the LIETB, the importance of constructing the LIETB, and the significance of the school-enterprise joint construction model for the teaching base. Secondly, a practical plan for the construction of a LIETB is proposed. Finally, the evaluation methods and indicators for the practical effects of the school-enterprise joint construction of the LIETB are improved from two aspects, such as teaching effectiveness and employment situation evaluation methods. This study is of great significance for improving students’ practical environment and skill training, further enhancing the quality and quantity of laser intelligent equipment(LIE) application talents, promoting industry-university-research cooperation, and promoting the development of related industries

The effect of osteopontin and osteopontin-derived peptides on preterm brain injury

Background: Osteopontin (OPN) is a highly phosphorylated sialoprotein and a soluble cytokine that is widely expressed in a variety of tissues, including the brain. OPN and OPN-derived peptides have been suggested to have potential neuroprotective effects against ischemic brain injury, but their role in preterm brain injury is unknown. Methods: We used a hypoxia-ischemia (HI)-induced preterm brain injury model in postnatal day 5 mice. OPN and OPN-derived peptides were given intracerebroventricularly and intranasally before HI. Brain injury was evaluated at 7 days after the insults. Results: There was a significant increase in endogenous OPN mRNA and OPN protein in the mouse brain after the induction of HI at postnatal day 5. Administration of full-length OPN protein and thrombin-cleaved OPN did not affect preterm brain injury. This was demonstrated with both intracerebroventricular and intranasal administration of OPN as well as in OPN-deficient mice. Interestingly, both N134–153 and C154–198 OPN-derived peptides increased the severity of brain injury in this HI-induced preterm brain injury model. Conclusions: The neuroprotective effects of OPN are age-dependent, and, in contrast to the more mature brain, OPN-derived peptides potentiate injury in postnatal day 5 mice. Intranasal administration is an efficient way of delivering drugs to the central nervous system (CNS) in neonatal mice and is likely to be an easy and noninvasive method of drug delivery to the CNS in preterm infants

Black Phosphorus Q-Switched Large-Mode-Area Tm-Doped Fiber Laser

We report on a passively Q-switched fiber laser with black phosphorus as saturable absorber. By employing the sol-gel fabricated large-mode-area Tm-doped fiber as gain medium, a high-energy Q-switched fiber laser has been demonstrated which delivers the maximum pulse energy of 11.72 μJ with the pulse width of 660 ns at the wavelength of 1954 nm. Our experimental results indicate that BP Q-switched large-mode-area Tm-doped fiber laser is an effective and reliable approach to generate high-energy pulses at 2 μm

The immune response after hypoxia-ischemia in a mouse model of preterm brain injury

Background: Preterm brain injury consists primarily of periventricular leukomalacia accompanied by elements of gray-matter injury, and these injuries are associated with cerebral palsy and cognitive impairments. Inflammation is believed to be an important contributing factor to these injuries. The aim of this study was to examine the immune response in a postnatal day (PND) 5 mouse model of preterm brain injury induced by hypoxia-ischemia (HI) that is characterized by focal white and gray-matter injury. Methods: C57Bl/6 mice at PND 5 were subjected to unilateral HI induced by left carotid artery ligation and subsequent exposure to 10% O2 for 50 minutes, 70 minutes, or 80 minutes. At seven days post-HI, the white/gray-matter injury was examined. The immune responses in the brain after HI were examined at different time points after HI using RT-PCR and immunohistochemical staining. Results: HI for 70 minutes in PND 5 mice induced local white-matter injury with focal cortical injury and hippocampal atrophy, features that are similar to those seen in preterm brain injury in human infants. HI for 50 minutes resulted in a small percentage of animals being injured, and HI for 80 minutes produced extensive infarction in multiple brain areas. Various immune responses, including changes in transcription factors and cytokines that are associated with a T-helper (Th)1/Th17-type response, an increased number of CD4+ T-cells, and elevated levels of triggering receptor expressed on myeloid cells 2 (TREM-2) and its adaptor protein DNAX activation protein of 12 kDa (DAP12) were observed using the HI 70 minute preterm brain injury model. Conclusions: We have established a reproducible model of HI in PND 5 mice that produces consistent local white/gray-matter brain damage that is relevant to preterm brain injury in human infants. This model provides a useful tool for studying preterm brain injury. Both innate and adaptive immune responses are observed after HI, and these show a strong pro-inflammatory Th1/Th17-type bias. Such findings provide a critical foundation for future studies on the mechanism of preterm brain injury and suggest that blocking the Th1/Th17-type immune response might provide neuroprotection after preterm brain injury

The Effect of Social Exclusion on Trust Among Youth Orphaned by HIV/AIDS: Evidence From an Event-Related Potentials Study

Grounded in a follow-up study among children who lost one or both parents to HIV in central China in the early 2000s, we conducted an event-related potentials (ERPs) experiment to explore the effect of social exclusion on trust and the corresponding neurophysiological mechanism among youth orphaned by HIV/AIDS (“AIDS orphans”). A sample of 31 AIDS orphans (26.16 ± 3.34 years old; 15 female) and 32 age and development status matched controls (25.02 ± 3.45 years old; 14 female) participated in the study. They were all assigned to play Cyberball, a virtual ball-tossing game that reliably induced social exclusion (15 orphans, 16 controls) and inclusion (16 orphans, 16 controls). Then, they played the Trust Game by taking the role of trustor with their electroencephalograms (EEGs) being recorded during the game. In the Trust Game, each participant was required to decide whether to trust their partners in over 150 trials (decision-making stage). The partner’s reciprocation strategies were pre-programmed by the experimenter (with an overall reciprocating rate of 50%). All participants were provided with post-decision feedback about the outcome of their decisions (gain or loss of game points) in each trial (outcome evaluation stage). We analyzed their behavioral responses at the decision-making stage and ERP components at the outcome evaluation stage. Behavioral results showed that the proportion of orphans choosing trust was significantly higher than the controls, and the trust ratio of the orphan exclusion (OE) group was significantly higher than that of the orphan inclusion (OI) group, control exclusion (CE) group, and control inclusion (CI) group. Furthermore, the response time of the OE group was significantly shorter than that of other groups. ERP results indicated that the amplitude of the feedback-related negativity (FRN) in the OI group was significantly more negative than that in the CI group with loss feedback, while there was no significant difference between the OE and OI groups. Similarly, the P300 amplitudes following outcome feedback were larger in the CI group than that in the OI group with gain feedback and had no significant difference between OE and OI

Polycomb group proteins EZH2 and EED directly regulate androgen receptor in advanced prostate cancer

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149265/1/ijc32118.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149265/2/ijc32118_am.pd