Stock loan valuation under a stochastic interest rate model

Stock loans are loans collateralized by stocks. They are modern fnancial products designed for investors with large equity positions. Mathematically, stock loans can be regarded as American call options with a time-dependent strike price once established. This study focuses on stock loans under a stochastic interest rate framework. The partial diferential equation (PDE) governing the value of the stock loan is derived by portfolio analysis. Boundary conditions are then prescribed to close the PDE system. In particular, boundary conditions along the interest rate direction are the focus of our derivation. After simplifying the pricing system by a series of transformations, the predictor-corrector method is adopted to solve the transformed PDE system numerically. Moreover, we introduce the alternating direction implicit (ADI) method in the two-factor model to improve the computational effciency. To ensure the stability of the predictor-corrector method, a hybrid finite difference scheme is adopted. Numerical results suggest that the current method is reliable and the stochastic interest rate leads to a higher optimal exercise price of the stock loan in comparison with that calculated from the Black-Scholes model

Shear banding in monodisperse polymer melt

We performed a series of molecular dynamics simulations on monodisperse polymer melts to investigate the formation of shear banding. Under high shear rates, shear banding occurs, which is accompanied with the entanglement heterogeneity intimately. Interestingly, the same linear relationship between the end-to-end distance $R_{ee}$ and entanglement density $Z$ is observed at homogeneous flow before the onset of shear banding and at shear banding state, where $R_{ee} \sim [ln(W_i^{0.87})- \xi_0]Z$ is proposed as the criterion to describe the dynamic force balance of molecular chain in flow with a high rate. We establish a scaling relation between the disentanglement rate $V_d$ and Weissenberg number $W_i$ as $V_d \sim W_i^{0.87}$ for stable flow in homogeneous shear and shear banding states. Deviating from this relation leads to force imbalance and results in the emergence of shear banding. The formation of shear banding prevents chain from further stretching and disentanglement. The transition from homogeneous shear to shear banding partially dissipates the increased free energy from shear and reduces the free energy of the system

Numerical calculation of free-energy barriers for entangled polymer nucleation.

The crystallization of entangled polymers from their melt is investigated using computer simulation with a coarse-grained model. Using hybrid Monte Carlo simulations enables us to probe the behavior of long polymer chains. We identify solid-like beads with a centrosymmetry local order parameter and compute the nucleation free-energy barrier at relatively high supercooling with adaptive-bias windowed umbrella sampling. Our results demonstrate that the critical nucleus sizes and the heights of free-energy barriers do not significantly depend on the molecular weight of the polymer; however, the nucleation rate decreases with the increase in molecular weight. Moreover, an analysis of the composition of the critical nucleus suggests that intra-molecular growth of the nucleated cluster does not contribute significantly to crystallization for this system.National Key R&D Program of China (2016YFB0302500); National Natural Science Foundation of China (51633009); Royal Society Newton Mobility Grant (MBAG/240 RG82754

Circulating Monocytes Act as a Common Trigger for the Calcification Paradox of Osteoporosis and Carotid Atherosclerosis via TGFB1-SP1 and TNFSF10-NFKB1 Axis

BackgroundOsteoporosis often occurs with carotid atherosclerosis and causes contradictory calcification across tissue in the same patient, which is called the “calcification paradox”. Circulating monocytes may be responsible for this unbalanced ectopic calcification. Here, we aimed to show how CD14+ monocytes contribute to the pathophysiology of coexisting postmenopausal osteoporosis and carotid atherosclerosis.MethodsWe comprehensively analyzed osteoporosis data from the mRNA array dataset GSE56814 and the scRNA-seq dataset GSM4423510. Carotid atherosclerosis data were obtained from the GSE23746 mRNA dataset and GSM4705591 scRNA-seq dataset. First, osteoblast and vascular SMC lineages were annotated based on their functional expression using gene set enrichment analysis and AUCell scoring. Next, pseudotime analysis was applied to draw their differentiated trajectory and identify the key gene expression changes in crossroads. Then, ligand–receptor interactions between CD14+ monocytes and osteoblast and vascular smooth muscle cell (SMC) lineages were annotated with iTALK. Finally, we selected calcification paradox-related expression in circulating monocytes with LASSO analysis.ResultsFirst, we found a large proportion of delayed premature osteoblasts in osteoporosis and osteogenic SMCs in atherosclerosis. Second, CD14+ monocytes interacted with the intermediate cells of the premature osteoblast and osteogenic SMC lineage by delivering TGFB1 and TNFSF10. This interaction served as a trigger activating the transcription factors (TF) SP1 and NFKB1 to upregulate the inflammatory response and cell senescence and led to a retarded premature state in the osteoblast lineage and osteogenic transition in the SMC lineage. Then, 76.49% of common monocyte markers were upregulated in the circulating monocytes between the two diseases, which were related to chemotaxis and inflammatory responses. Finally, we identified 7 calcification paradox-related genes on circulating monocytes, which were upregulated in aging cells and downregulated in DNA repair cells, indicating that the aging monocytes contributed to the development of the two diseases.ConclusionsOur work provides a perspective for understanding the triggering roles of CD14+ monocytes in the development of the calcification paradox in osteoporosis- and atherosclerosis-related cells based on combined scRNA and mRNA data. This study provided us with an elucidation of the mechanisms underlying the calcification paradox and could help in developing preventive and therapeutic strategies

Top Teachers’ Workshop: A Stage for the Development of Rural Teachers: Practical Exploration of the Training Strategy from the Rural Workshop of Teacher Liangbin Yi in Hangzhou

On the basis of improving teaching quality and enriching education mind, the rural workshop of Liangbin Yi in Hangzhou returns to the essence of teaching, truly promoting students’ development. This research topic is also the core of the teaching, scientific research, and management of the workshop. With the abundant teaching resources, the workshop conducted various teaching activities and exhibition activities, such as building the learning platform, holding the report sharing, summit forum, on-the-job training, and sending teachers to the countryside, through practical action research. It can also propel the curriculum reform, deepen the classroom teaching research, strengthen the unity of knowledge and action, improve teachers’ teaching theory and practical ability at the same time, and improve the evaluation system, which provided fully play to the guidance and demonstration of famous rural teacher workshop, and positively contributed to the rural teachers’ development