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The development and measurable improvements in performance of large language models on natural language tasks opens the opportunity to utilize large language models in an educational setting to replicate human tutoring, which is often costly and inaccessible. We are particularly interested in large language models from the GPT series, created by OpenAI. In the original study we found that the quality of explanations generated with GPT-3.5 was poor, where two different approaches to generating explanations resulted in a 43% and 10% successrate. In a replication study, we were interested in whether the measurable improvements in GPT-4 performance led to a higher rate of success for generating valid explanations compared to GPT-3.5. A replication of the original study was conducted by using GPT-4 to generate explanations for the same problems given to GPT-3.5. Using GPT-4, explanation correctness dramatically improved to a success rate of 94%. We were further interested in evaluating if GPT-4 explanations were positively perceived compared to human-written explanations. A preregistered, follow-up study was implemented where 10 evaluators were asked to rate the quality of randomized GPT-4 and teacher-created explanations. Even with 4% of problems containing some amount of incorrect content, GPT-4 explanations were preferred over human explanations. 

Large language models have recently been able to perform well in a wide variety of circumstances. In this work, we explore the possi- bility of large language models, specifically GPT-3, to write explanations for middle-school mathematics problems, with the goal of eventually us- ing this process to rapidly generate explanations for the mathematics problems of new curricula as they emerge, shortening the time to inte- grate new curricula into online learning platforms. To generate expla- nations, two approaches were taken. The first approach attempted to summarize the salient advice in tutoring chat logs between students and live tutors. The second approach attempted to generate explanations us- ing few-shot learning from explanations written by teachers for similar mathematics problems. After explanations were generated, a survey was used to compare their quality to that of explanations written by teachers. We test our methodology using the GPT-3 language model. Ultimately, the synthetic explanations were unable to outperform teacher written explanations. In the future more powerful large language models may be employed, and GPT-3 may still be effective as a tool to augment teach- ers’ process for writing explanations, rather than as a tool to replace them. The explanations, survey results, analysis code, and a dataset of tutoring chat logs are all available at https://osf.io/wh5n9/. 

The monitoring of data streams with a network structure have drawn increasing attention due to its wide applications in modern process control. In these applications, high-dimensional sensor nodes are interconnected with an underlying network topology. In such a case, abnormalities occurring to any node may propagate dynamically across the network and cause changes of other nodes over time. Furthermore, high dimensionality of such data significantly increased the cost of resources for data transmission and computation, such that only partial observations can be transmitted or processed in practice. Overall, how to quickly detect abnormalities in such large networks with resource constraints remains a challenge, especially due to the sampling uncertainty under the dynamic anomaly occurrences and network-based patterns. In this paper, we incorporate network structure information into the monitoring and adaptive sampling methodologies for quick anomaly detection in large networks where only partial observations are available. We develop a general monitoring and adaptive sampling method and further extend it to the case with memory constraints, both of which exploit network distance and centrality information for better process monitoring and identification of abnormalities. Theoretical investigations of the proposed methods demonstrate their sampling efficiency on balancing between exploration and exploitation, as well as the detection performance guarantee. Numerical simulations and a case study on power network have demonstrated the superiority of the proposed methods in detecting various types of shifts. Note to Practitioners —Continuous monitoring of networks for anomalous events is critical for a large number of applications involving power networks, computer networks, epidemiological surveillance, social networks, etc. This paper aims at addressing the challenges in monitoring large networks in cases where monitoring resources are limited such that only a subset of nodes in the network is observable. Specifically, we integrate network structure information of nodes for constructing sequential detection methods via effective data augmentation, and for designing adaptive sampling algorithms to observe suspicious nodes that are likely to be abnormal. Then, the method is further generalized to the case that the memory of the computation is also constrained due to the network size. The developed method is greatly beneficial and effective for various anomaly patterns, especially when the initial anomaly randomly occurs to nodes in the network. The proposed methods are demonstrated to be capable of quickly detecting changes in the network and dynamically changes the sampling priority based on online observations in various cases, as shown in the theoretical investigation, simulations and case studies. 

With the greater application of machine learning models in educational contexts, it is important to understand where such meth- ods perform well as well as how they may be improved. As such, it is important to identify the factors that contribute to prediction error in order to develop targeted methods to enhance model accuracy and mitigate risks of algorithmic bias and unfairness. Prior works have led to the development and application of automated assessment methods that leverage machine learning and natural language processing. The performance of these methods have often been reported as being posi- tive, but other prior works have identified aspects on which they may be improved. Particularly in the context of mathematics, the presence of non-linguistic characters and expressions have been identified to con- tribute to observed model error. In this paper, we build upon this prior work by observing a developed automated assessment model for open- response questions in mathematics. We develop a new approach which we call the “Math Term Frequency” (MTF) model to address this issue caused by the presence of non-linguistic terms and ensemble it with the previously-developed assessment model. We observe that the inclusion of this approach notably improves model performance. Finally, we observe how well this ensembled method extrapolates to student responses in the context of Algorithms, a domain similarly characterized by a large number of non-linguistic terms and expressions. This work represents an example of practice of how error analyses can be leveraged to address model limitations. 

5G has received significant interest from commercial as well as defense industries. However, resiliency in 5G remains a major concern for its use in military and defense applications. In this paper, we explore physical layer resiliency enhancements for 5G and use narrow-band Internet of Things (NB-IoT) as a study case. Two physical layer modifications, frequency hopping, and direct sequence spreading, are analyzed from the standpoint of implementation and performance. Simulation results show that these techniques are effective to harden the resiliency of the physical layer to interference and jamming. A discussion of protocol considerations for 5G and beyond is provided based on the results