Students' Production and Processing of Mathematical Explanations.

Discussion as a mechanism for learning has been emphasized in both curriculum standards and psychological theories. However, US students get few opportunities to explain their mathematical thinking during classroom instruction. This project is aimed at answering three related questions about the role of discussion in elementary student learning. 1) Are there fewer student explanations in the US than in higher achieving East Asian locales? What predicts the prevalence of student explanations and do those predictors vary across countries? A machine-learning system was developed and validated for identifying explanations using transcripts of 232 mathematics classes in Japan, Hong Kong, and United States. Results suggest that Japan and Hong Kong lessons feature more student explanations than US lessons do. In all countries, lessons with a higher proportion of student talk showed more explanation; in Hong Kong and Japan (but not in the US), teachers’ requests for procedures and reasoning, as well as their language modeling of contradicting opinions predicted increased student explanations. One reason for this difference may be that teachers in the East Asian settings were more stringent in what they accepted as an adequate explanation. 2) Do US students differ from their Chinese peers in the quality of their mathematical explanations? Chinese and US elementary students were interviewed about mathematical equivalence. Results indicated US students underperformed their Chinese peers in the accuracy and mathematical richness of students’ explanations. 3) Do students process peer explanations differently than those of adults? US elementary students watched matched mathematical explanations from children vs. adults. The ones who watched peer-produced explanations were more likely to recognize the insufficiency of explanations and provide elaborated reasoning. Moreover, difference in processing moderated the learning gain from pre- to post-tests of their understanding of mathematical equivalence. Overall, the current study showed that although US students are providing and hearing both fewer and lower quality explanations, they may still benefit from hearing peers’ less fluent or flawed explanations. Teachers play a crucial role in directing student explanations, but this role goes beyond the questions they ask to the way in which they socialize students about what is an acceptable explanation.PhDEducation & PsychologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108964/1/xypan_1.pd

Water uptake in parallel fractures

   Water uptake in rock fractures caused by rainfall plays a significant role in slope stability analysis. Since the fracture network system has complicated structures and multiple scales, the models based on the averaged system cannot account for these properties. On the other hand, a model describing a single fracture with fractal characteristics and surface roughness fails to deal with the case of multiple fractures at spatial scales. In this study, a fracture-network model is established to account for the complex structures and multiple scales of fractures. By considering the connectivity between fractures and the limited area of aquifer, capillary pressure formulations in different fractures are derived based on the Young-Laplace equation, and the final water level under specific rainfall conditions is also obtained. The cross-section shapes and exhaust conditions of rainwater infiltration have important influences on the final water level. The results indicate that the final water level is proportional to the ratio of perimeter to cross-section area when the fracture is a cylinder, and a circular pipe can reduce water level elevation in the fracture system.Cited as: Wang, J., Zhu, X., Pan, Y., Kou, J., Sun, S. Water uptake in parallel fractures. Capillarity, 2021, 4(1): 1-12, doi: 10.46690/capi.2021.01.0

GraphMoco:a Graph Momentum Contrast Model that Using Multimodel Structure Information for Large-scale Binary Function Representation Learning

In the field of cybersecurity, the ability to compute similarity scores at the function level is import. Considering that a single binary file may contain an extensive amount of functions, an effective learning framework must exhibit both high accuracy and efficiency when handling substantial volumes of data. Nonetheless, conventional methods encounter several limitations. Firstly, accurately annotating different pairs of functions with appropriate labels poses a significant challenge, thereby making it difficult to employ supervised learning methods without risk of overtraining on erroneous labels. Secondly, while SOTA models often rely on pre-trained encoders or fine-grained graph comparison techniques, these approaches suffer from drawbacks related to time and memory consumption. Thirdly, the momentum update algorithm utilized in graph-based contrastive learning models can result in information leakage. Surprisingly, none of the existing articles address this issue. This research focuses on addressing the challenges associated with large-scale BCSD. To overcome the aforementioned problems, we propose GraphMoco: a graph momentum contrast model that leverages multimodal structural information for efficient binary function representation learning on a large scale. Our approach employs a CNN-based model and departs from the usage of memory-intensive pre-trained models. We adopt an unsupervised learning strategy that effectively use the intrinsic structural information present in the binary code. Our approach eliminates the need for manual labeling of similar or dissimilar information.Importantly, GraphMoco demonstrates exceptional performance in terms of both efficiency and accuracy when operating on extensive datasets. Our experimental results indicate that our method surpasses the current SOTA approaches in terms of accuracy.Comment: 22 pages,7 figure

Broadband energy-efficient optical modulation by hybrid integration of silicon nanophotonics and organic electro-optic polymer

Silicon-organic hybrid integrated devices have emerging applications ranging from high-speed optical interconnects to photonic electromagnetic-field sensors. Silicon slot photonic crystal waveguides (PCWs) filled with electro-optic (EO) polymers combine the slow-light effect in PCWs with the high polarizability of EO polymers, which promises the realization of high-performance optical modulators. In this paper, a broadband, power-efficient, low-dispersion, and compact optical modulator based on an EO polymer filled silicon slot PCW is presented. A small voltage-length product of V{\pi}*L=0.282Vmm is achieved, corresponding to an unprecedented record-high effective in-device EO coefficient (r33) of 1230pm/V. Assisted by a backside gate voltage, the modulation response up to 50GHz is observed, with a 3-dB bandwidth of 15GHz, and the estimated energy consumption is 94.4fJ/bit at 10Gbit/s. Furthermore, lattice-shifted PCWs are utilized to enhance the optical bandwidth by a factor of ~10X over other modulators based on non-band-engineered PCWs and ring-resonators.Comment: 12 pages, 4 figures, SPIE Photonics West Conference 201

Design of Photovoltaic Tracking System Based on Fourier Fitting

[Introduction] In order to improve the power generation efficiency of photovoltaic brackets, the research and design focus is on a photovoltaic tracker based on Fourier fitting algorithm for apparent solar motion trajectory. [Method] The tracking accuracy of traditional solar motion trajectory algorithms was analyzed using MATLAB. Furthermore and an 8-order Fourier fitting solar motion trajectory tracking algorithm with better accuracy was proposed. The real-time solar motion trajectory was obtained combined with GNSS positioning technology. The system design employed the STM32 microcontroller as the microprocessor and adopted 6-axis acceleration sensor. The real-time tilt of the photovoltaic tracking bracket was determined by the projection of the gravity vector on its axis. Based on this, a three-dimensional operation model of the tracking bracket was established. By analyzing the cosine effect of sunlight on the bracket, the action angle required for the motor to operate can be obtained. At the same time, to solve the problem of shadow shielding between photovoltaic modules at dawn and dusk, the system added an inverse tracking algorithm. Considering the application of large-scale units, a master-slave motor synchronous control strategy was proposed. [Result] The Fourier fitting algorithm has higher tracking accuracy, reaching an accuracy of 10-2 orders of magnitude, one order of magnitude higher than traditional algorithms. At the same time, reverse tracking technology can save 24.3% of the photovoltaic array land area, significantly improving land use efficiency. [Conclusion] This study adopts a more accurate apparent solar motion trajectory tracking model, which effectively solves the cosine effect of solar radiation utilization, improves the power generation efficiency of power stations, realizes the construction of a safe and efficient green energy system, and promotes the promotion and achievement of China's goals of carbon peak and carbon neutrality