Chimeric antigen receptor T-cell (CAR-T) offers a revolutionary solution to the treatment of cancer. It has demonstrated particularly high efficacy in some cancer treatments, such as haematological malignancies. However, this method still faces significant challenges. In the treatment of solid tumor, it may lead to off-target toxicity, accelerated T-cell exhaustion, and cytokine storms resulting from excessive T-cell activity. Facing the dense stroma of the tumour microenvironment(TME), the introduction of lysosomal CAR-T cells expressing PH20 or CAR-T cells targeting fibroblast activation protein breaks down the external structure of the tumour, facilitating the entry of other CAR-T cells into the tumour to carry out killing. Knocking out the MCT-1 and A2AR genes can enhance the resistance of CAR-T cells to the TME. This approach inhibits the inflow of lactate and adenosine, thereby maintaining CAR-T cell viability. Employing multi-gene knockout or base editing techniques to modify the PD-1 gene weakens the immunosuppressive effects of the TME on CAR-T cells. Overexpressing some genes in the T cells, such as c-JUN, can enhance cellular activity, enabling the cells to survive long-term within the TME and sustain their cytotoxic effects. To prevent off-target effects and uncontrolled activation of CAR-T cells, synthetic Notch circuits have been engineered. This system is a dual-antigen recognition system and can help CAR-T cell better recognise tumor cells. This article reviews the research progress in CAR-T cell therapy, methods to enhance therapeutic efficacy, and offers a perspective on future research directions.

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Importance Sampling (IS) is a fundamental variance reduction technique in Monte Carlo simulation, particularly for estimating rare event probabilities. Its core idea is to find a better sampling measureℚunder which the target events occur more frequently, to reduce the cost of simulation of rare events. However, determining such an optimalℚis notoriously difficult, often leading to complicated partial differential equations (PDE) that many classical methods fail. This paper aims to introduce a novel geometric perspective of this optimization problem that we consider all proper likelihood ratios as a manifold, and use the natural gradient property to design the algorithm, which avoids PDE and outperforms the ordinary stochastic gradient descent (SGD) algorithm. Under standard regularity and Novikov conditions, we establish the almost sure convergence of the proposed algorithm utilizing the Robbins-Siegmund theorem and end up with numerical validation on option pricing and portfolio risk assessment, confirming that the geometric approach significantly enhances variance reduction efficiency.

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The calculation of definite integrals is typically complex and might have an error, which demands a more generalized and convenient method. The traditional techniques like universal substitution and integration by parts tend to give complicated integrands and time-consuming calculations. These definite integral problems are then converted by the residue theorem into straightforward summation problems of definite residues via contour integration on the complex plane to significantly decrease number of steps in calculations. By using the Laurent series to expand a complex function with a simple pole in denominator and take the limit as approaches the pole, a general formula to calculate residue of simple poles is given. In terms of a singularity with order at the pole, taking derivative of the series leads to the residue. The overall formula can be directly used on definite integral with trig in denominator with the appropriate choice of root of the function inside the unit circle. Using the transformation between the functions of sine and cosine, the limit can be simplified to obtain the residue. These conversions allow the general formulae of calculating a residue and through the residue theorem the resultant integral is simply obtained.

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With the continuous upgrading of China's consumption structure, college students, as an important young consumer group, have attracted increasing attention to their consumption behavior characteristics and influence mechanisms. This study selected college students as the research object and obtained 105 valid sample data through questionnaire surveys. Reliability and validity tests, K-means cluster analysis and multiple linear regression analysis methods were adopted to explore the characteristics of college students' consumption structure and its influence mechanism on consumption satisfaction. The research results show that college students' consumption behavior has obvious grouping characteristics and can be divided into two categories: "low consumption/thrifty type" and "higher consumption/active type". The consumption patterns between various categories have great differences at different consumption levels, especially the consumption differences in entertainment and social aspects are more obvious. Consumption categories also greatly affect consumers' satisfaction, and the satisfaction of high-consumption students is much higher than that of low-consumption students. In addition, budget planning is beneficial to improve satisfaction, but factors such as the awareness of rational consumption, the influence of the surrounding environment and the pursuit of quality of life do not show a particularly significant effect. This research is conducive to deepening the understanding of the differences in college students' consumption behavior and providing some references for colleges and universities to carry out rational consumption education.

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