Regular left-orders on groups

A regular left-order on finitely generated group $G$ is a total, left-multiplication invariant order on $G$ whose corresponding positive cone is the image of a regular language over the generating set of the group under the evaluation map. We show that admitting regular left-orders is stable under extensions and wreath products and give a classification of the groups all whose left-orders are regular left-orders. In addition, we prove that solvable Baumslag-Solitar groups $B(1,n)$ admits a regular left-order if and only if $n\geq -1$. Finally, Hermiller and Sunic showed that no free product admits a regular left-order, however we show that if $A$ and $B$ are groups with regular left-orders, then $(A*B)\times \mathbb{Z}$ admits a regular left-order.Comment: 41 pages,9 figure

Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.Comment: Accepted at ICML 202

Radiographic Disclosure of Fournier’s Gangrene

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Deep knowledge tracing with learning curves

Knowledge tracing (KT) models students' mastery level of knowledge concepts based on their responses to the questions in the past and predicts the probability that they correctly answer subsequent questions in the future. Recent KT models are mostly developed with deep neural networks and have demonstrated superior performance over traditional approaches. However, they ignore the explicit modeling of the learning curve theory, which generally says that more practices on the same knowledge concept enhance one's mastery level of the concept. Based on this theory, we propose a Convolution-Augmented Knowledge Tracing (CAKT) model and a Capsule-Enhanced CAKT (CECAKT) model to enable learning curve modeling. In particular, when predicting a student's response to the next question associated with a specific knowledge concept, CAKT uses a module built with three-dimensional convolutional neural networks to learn the student's recent experience on that concept, and CECAKT improves CAKT by replacing the global average pooling layer with capsule networks to prevent information loss. Moreover, the two models employ LSTM networks to learn the overall knowledge state, which is fused with the feature learned by the convolutional/capsule module. As such, the two models can learn the student's overall knowledge state as well as the knowledge state of the concept in the next question. Experimental results on four real-life datasets show that CAKT and CECAKT both achieve better performance compared to existing deep KT models

Comparative Agreement Analysis of Differences in 1,5-Anhydroglucitol, Glycated Albumin, and Glycated Hemoglobin A1c Levels between Fasting and Postprandial States in Steamed Bread Meal Test

Background. Our previous study indicated that serum 1,5-anhydroglucitol (1,5-AG) levels slightly increased after a glucose load; therefore, this study was conducted to explore short-term changes in 1,5-AG levels after a steamed bread meal test (SBMT) and compare the agreement of 1,5-AG, glycated albumin (GA), and glycated hemoglobin A1c (HbA1c) levels between fasting and postprandial states after an SBMT. Methods. 104 participants were recruited and underwent a 100 g SBMT. Fasting, 30 min, and 120 min of 1,5-AG, GA, and HbA1c were measured. Results. Levels of 1,5-AG slightly increased from 30 to 120 min after an SBMT (P0.05), and Bland-Altman difference plot showed that 100% of data points for HbA1c30 and HbA1c120 fell within the limits of agreement; 94.2%, 96.2%, 95.2%, and 95.2% of data points for 1,5-AG30, 1,5-AG120, GA30, and GA120 fell within the limits of agreement, respectively. Conclusion. Agreement analyses indicated good stability of 1,5-AG, GA, and HbA1c levels after the SBMT. HbA1c had an optimal stability, which was superior to that of GA or 1,5-AG

Biomedical Teleacupuncture between China and Austria Using Heart Rate Variability—Part 2: Patients with Depression

It has been shown in previous studies that the autonomic nervous system can be affected by acupuncture. Within this study, teleacupuncture between China and Austria is used for quantifying the effects of heart rate (HR) and heart rate variability (HRV) in 33 Chinese patients (27 females, 6 males; mean age ± SD 49.5 ± 13.1 years; range 22–72 years) suffering from depression. Electrocardiographic signals before, during, and after acupuncture at the acupoint Baihui (GV20) were recorded in Harbin and analyzed in Graz using teleacupuncture. HRV data were analyzed in the time and frequency domain. Mean HR decreased significantly (P < 0.05) during and after acupuncture, whereas total HRV increased significantly after the third acupuncture stimulation period (P < 0.05) and also 5–10 minutes after (P < 0.05) acupuncture. The study shows that HRV could be a useful parameter for quantifying clinical effects of acupuncture on the autonomic nervous system