Understanding and Implementation of Case Teaching Method

As a kind of teaching method, case teaching method has its own practical value and scope of application. In practice, it mainly consists of some links such as “knowledge preparation”, “case arrangement” and “provoking guidance”. Knowledge preparation could be implemented through a variety of forms and the teaching process that is prepared for analysis has its unique feature. Cases can be selected from the aspects of “event level”, “fact capacity” and “understanding degree”. And they would endow natural events with the educational significance. Setting questions teachers could stimulate students’ interest of analysis. And during the process of analysis, it is supposed to lead students use topic concept to analyze these questions around the cases

On global ACC for foliated threefolds

In this paper, we prove the rational coefficient case of the global ACC for foliated threefolds. Specifically, we consider any lc foliated log Calabi-Yau triple $(X,\mathcal{F},B)$ of dimension $3$ whose coefficients belong to a set $\Gamma$ of rational numbers satisfying the descending chain condition, and prove that the coefficients of $B$ belong to a finite set depending only on $\Gamma$. To prove our main result, we introduce the concept of generalized foliated quadruples, which is a mixture of foliated triples and Birkar-Zhang's generalized pairs. With this concept, we establish a canonical bundle formula for foliations in any dimension. As for applications, we extend Shokurov's global index conjecture in the classical MMP to foliated triples and prove this conjecture for threefolds with nonzero boundaries and for surfaces. Additionally, we introduce the theory of rational polytopes for functional divisors on foliations and prove some miscellaneous results.Comment: 22 pages. Add a paragraph on pages 3-4. Proposition 6.4 and Lemma 7.2 strengthened. Small modification of the proof of 8.1. Reference update

Number of Repetitions in Re-randomization Tests

In covariate-adaptive or response-adaptive randomization, the treatment assignment and outcome can be correlated. Under this situation, re-randomization tests are a straightforward and attractive method to provide valid statistical inference. In this paper, we investigate the number of repetitions in the re-randomization tests. This is motivated by the group sequential design in clinical trials, where the nominal significance bound can be very small at an interim analysis. Accordingly, re-randomization tests lead to a very large number of required repetitions, which may be computationally intractable. To reduce the number of repetitions, we propose an adaptive procedure and compare it with multiple approaches under pre-defined criteria. Monte Carlo simulations are conducted to show the performance of different approaches in a limited sample size. We also suggest strategies to reduce total computation time and provide practical guidance in preparing, executing and reporting before and after data are unblinded at an interim analysis, so one can complete the computation within a reasonable time frame

THE MINIMAL LOG DISCREPANCY AND ITS APPLICATIONS IN BIRATIONAL GEOMETRY

In this article, I will discuss some recent results related to the minimal log discrepancies in dimension two and dimension three based on [HLL22] and [HL20]. I will also discuss some of their applications in birational geometry

Shaping contactless forces through anomalous acoustic scattering

Waves impart momentum and exert force on obstacles in their path. The transfer of wave momentum is a fundamental mechanism for contactless manipulation, yet the rules of conventional scattering intrinsically limit the radiation force based on the shape and the size of the manipulated object. Here, we show that this intrinsic limit can be overcome for acoustic waves with subwavelength-structured metasurfaces, where the force becomes controllable by the arrangement of surface features, independent of the object's overall shape and size. Harnessing such anomalous metasurface scattering, we demonstrate complex actuation phenomena: self-guidance, where a metasurface object is autonomously guided by an acoustic wave, and contactless pulling, where a metasurface object is pulled by the wave. Our results show that bringing metasurface physics, and its full arsenal of tools, to the domain of mechanical manipulation opens the door to diverse actuation mechanisms that are beyond the limits of traditional wave-matter interactions

Identification of Benzo[a]pyrene-metabolizing bacteria in forest soils by using DNA-based stable-isotope probing

DNA-based stable-isotope probing (DNA-SIP) was used in this study to investigate the uncultivated bacteria with benzo[a]pyrene (BaP) metabolism capacities in two Chinese forest soils (Mt. Maoer in Heilongjiang Province and Mt. Baicaowa in Hubei Province). We characterized three different phylotypes with responsibility for BaP degradation, none of which were previously reported as BaP-degrading microorganisms by SIP. In Mt. Maoer soil microcosms, the putative BaP degraders were classified as belonging to the genus Terrimonas (family Chitinophagaceae, order Sphingobacteriales), whereas Burkholderia spp. were the key BaP degraders in Mt. Baicaowa soils. The addition of metabolic salicylate significantly increased BaP degradation efficiency in Mt. Maoer soils, and the BaP-metabolizing bacteria shifted to the microorganisms in the family Oxalobacteraceae (genus unclassified). Meanwhile, salicylate addition did not change either BaP degradation or putative BaP degraders in Mt. Baicaowa. Polycyclic aromatic hydrocarbon ring-hydroxylating dioxygenase (PAH-RHD) genes were amplified, sequenced, and quantified in the DNA-SIP (13)C heavy fraction to further confirm the BaP metabolism. By illuminating the microbial diversity and salicylate additive effects on BaP degradation across different soils, the results increased our understanding of BaP natural attenuation and provided a possible approach to enhance the bioremediation of BaP-contaminated soils