On the topological entropy of saturated sets for amenable group actions

Let $(X,\rho,G)$ be a $G-$action topological system, where $G$ is a countable infinite discrete amenable group and $X$ a compact metric space. We prove a variational principle for topological entropy of saturated sets for systems which have specification and uniform separation properties. As an application, we compute the topological entropy of level sets and irregular sets

Associations of plasma very-long-chain SFA and the metabolic syndrome in adults

Plasma levels of very-long-chain SFA (VLCSFA) are associated with the metabolic syndrome (MetS). However, the associations may vary by different biological activities of individual VLCSFA or population characteristics. We aimed to examine the associations of VLCSFA and MetS risk in Chinese adults. Totally, 2008 Chinese population aged 35–59 years were recruited and followed up from 2010 to 2012. Baseline MetS status and plasma fatty acids data were available for 1729 individuals without serious diseases. Among 899 initially metabolically healthy individuals, we identified 212 incident MetS during the follow-up. Logistic regression analysis was used to estimate OR and 95 % CI. Cross-sectionally, each VLCSFA was inversely associated with MetS risk; comparing with the lowest quartile, the multivariate-adjusted OR for the highest quartile were 0·18 (95 % CI 0·13, 0·25) for C20 : 0, 0·26 (95 % CI 0·18, 0·35) for C22 : 0, 0·19 (95 % CI 0·13, 0·26) for C24 : 0 and 0·16 (0·11, 0·22) for total VLCSFA (all Pfor trend<0·001). The associations remained significant after further adjusting for C16 : 0, C18 : 0, C18 : 3n-3, C22 : 6n-3, n-6 PUFA and MUFA, respectively. Based on follow-up data, C20 : 0 or C22 : 0 was also inversely associated with incident MetS risk. Among the five individual MetS components, higher levels of VLCSFA were most strongly inversely associated with elevated TAG (≥1·7 mmol/l). Plasma levels of VLCSFA were significantly and inversely associated with MetS risk and individual MetS components, especially TAG. Further studies are warranted to confirm the findings and explore underlying mechanisms

DenoSent: A Denoising Objective for Self-Supervised Sentence Representation Learning

Contrastive-learning-based methods have dominated sentence representation learning. These methods regularize the representation space by pulling similar sentence representations closer and pushing away the dissimilar ones and have been proven effective in various NLP tasks, e.g., semantic textual similarity (STS) tasks. However, it is challenging for these methods to learn fine-grained semantics as they only learn from the inter-sentence perspective, i.e., their supervision signal comes from the relationship between data samples. In this work, we propose a novel denoising objective that inherits from another perspective, i.e., the intra-sentence perspective. By introducing both discrete and continuous noise, we generate noisy sentences and then train our model to restore them to their original form. Our empirical evaluations demonstrate that this approach delivers competitive results on both semantic textual similarity (STS) and a wide range of transfer tasks, standing up well in comparison to contrastive-learning-based methods. Notably, the proposed intra-sentence denoising objective complements existing inter-sentence contrastive methodologies and can be integrated with them to further enhance performance. Our code is available at https://github.com/xinghaow99/DenoSent.Comment: AAAI 202

Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals

Recent progress in controllable functionalization of graphene surfaces enables the experimental realization of complex functionalized graphene nanostructures, such as Sierpinski carpet (SC) fractals. Herein, we model the SC fractals formed by hydrogen and fluorine functionalized patterns on graphene surfaces, namely, H-SC and F-SC, respectively. We then reveal their electronic properties and quantum transport features. From calculated results of the total and local density of state, we find that states in H-SC and F-SC have two characteristics: (i) low-energy states inside about |E/t|<1 (with t as the near-neighbor hopping) are localized inside free graphene regions due to the insulating properties of functionalized graphene regions, and (ii) high-energy states in F-SC have two special energy ranges including -2.3<E/t<-1.9 with localized holes only inside free graphene areas and 3<E/t<3.7 with localized electrons only inside fluorinated graphene areas. The two characteristics are further verified by the real-space distributions of normalized probability density. We analyze the fractal dimension of their quantum conductance spectra and find that conductance fluctuations in these structures follow the Hausdorff dimension. We calculate their optical conductivity and find that several additional conductivity peaks appear in high energy ranges due to the adsorbed H or F atoms