A Novel Proof based on the method of infinite descent for Fermat’s Last Theorem

Fermat’s Last Theorem is that for each  k >=3  (k is an integer), the equation  involving x, y and z has no positive integer solution. This paper proposed a novel proof for the Fermat’s last theorem by the methods of infinite descent and complex variable analysis

A hybrid representation based simile component extraction

Simile, a special type of metaphor, can help people to express their ideas more clearly. Simile component extraction is to extract tenors and vehicles from sentences. This task has a realistic significance since it is useful for building cognitive knowledge base. With the development of deep neural networks, researchers begin to apply neural models to component extraction. Simile components should be in cross-domain. According to our observations, words in cross-domain always have different concepts. Thus, concept is important when identifying whether two words are simile components or not. However, existing models do not integrate concept into their models. It is difficult for these models to identify the concept of a word. What’s more, corpus about simile component extraction is limited. There are a number of rare words or unseen words, and the representations of these words are always not proper enough. Exiting models can hardly extract simile components accurately when there are low-frequency words in sentences. To solve these problems, we propose a hybrid representation-based component extraction (HRCE) model. Each word in HRCE is represented in three different levels: word level, concept level and character level. Concept representations (representations in concept level) can help HRCE to identify the words in cross-domain more accurately. Moreover, with the help of character representations (representations in character levels), HRCE can represent the meaning of a word more properly since words are consisted of characters and these characters can partly represent the meaning of words. We conduct experiments to compare the performance between HRCE and existing models. The experiment results show that HRCE significantly outperforms current models

Enhance Primordial Black Hole Abundance through the Non-linear Processes around Bounce Point

The non-singular bouncing cosmology is an alternative paradigm to inflation, wherein the background energy density vanishes at the bounce point, in the context of Einstein gravity. Therefore, the non-linear effects in the evolution of density fluctuations ($\delta \rho$) may be strong in the bounce phase, which potentially provides a mechanism to enhance the abundance of primordial black holes (PBHs). This article presents a comprehensive illustration for PBH enhancement due to the bounce phase. To calculate the non-linear evolution of $\delta \rho$, the Raychaudhuri equation is numerically solved here. Since the non-linear processes may lead to a non-Gaussian probability distribution function for $\delta \rho$ after the bounce point, the PBH abundance is calculated in a modified Press-Schechter formalism. In this case, the criterion of PBH formation is complicated, due to complicated non-linear evolutionary behavior of $\delta \rho$ during the bounce phase. Our results indicate that the bounce phase indeed has potential to enhance the PBH abundance sufficiently. Furthermore, the PBH abundance is applied to constrain the parameters of bounce phase, providing a complementary to the surveys of cosmic microwave background and large scale structure.Comment: 17 pages, 6 figure

Multi-aspect Repetition Suppression and Content Moderation of Large Language Models

Natural language generation is one of the most impactful fields in NLP, and recent years have witnessed its evolution brought about by large language models (LLMs). As the key instrument for writing assistance applications, they are generally prone to replicating or extending offensive content provided in the input. In low-resource data regime, they can also lead to repetitive outputs (Holtzman et al., 2019) [1]. Usually, offensive content and repetitions are mitigated with post-hoc methods, including n-gram level blocklists, top-k and nucleus sampling. In this paper, we introduce a combination of exact and non-exact repetition suppression using token and sequence level unlikelihood loss, repetition penalty during training, inference, and post-processing respectively. We further explore multi-level unlikelihood loss to the extent that it endows the model with abilities to avoid generating offensive words and phrases from the beginning. Finally, with comprehensive experiments, we demonstrate that our proposed methods work exceptionally in controlling the repetition and content quality of LLM outputs

Experimental investigation and mechanism analysis on rock damage by high voltage spark discharge in water : effect of electrical conductivity

High voltage spark discharge (HVSD) could generate strong pressure waves that can be combined with a rotary drill bit to improve the penetration rate in unconventional oil and gas drilling. However, there has been little investigation of the effect of electrical conductivity on rock damage and the fragmentation mechanism caused by HVSD. Therefore, we conducted experiments to destroy cement mortar, a rock-like material, in water with five conductivity levels, from 0.5 mS/cm to 20 mS/cm. We measured the discharge parameters, such as breakdown voltage, breakdown delay time, and electrical energy loss, and investigated the damage mechanism from stress waves propagation using X-ray computed tomography. Our study then analyzed the influence of conductivity on the surface damage of the sample by the pore size distribution and the cumulative pore area, as well as studied the dependence of internal damage on conductivity by through-transmission ultrasonic inspection technique. The results indicated that the increase in electrical conductivity decreased the breakdown voltage and breakdown delay time and increased the energy loss, which led to a reduction in the magnitude of the pressure wave and, ultimately, reduced the sample damage. It is worth mentioning that the relationship between the sample damage and electrical conductivity is non-linear, showing a two-stage pattern. The findings suggest that stress waves induced by the pressure waves play a significant role in sample damage where pores and two types of tensile cracks are the main failure features. Compressive stresses close horizontal cracks inside the sample and propagate vertical cracks, forming the tensile cracks-I. Tensile stresses generated at the sample-water interface due to the reflection of stress waves produce the tensile cracks-II. Our study is the first to investigate the relationship between rock damage and electrical conductivity, providing insights to guide the design of drilling tools based on HVSD

Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and RCD(K,∞)RCD(K,\infty) spaces

We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon estimates for heat semigroups and applies to Gaussian and $RCD(K, \infty)$ spaces. As a consequence, we obtain quantitative stability for regular Lagrangian flows in Gaussian settings

Theaflavin Ameliorates Cerebral Ischemia-Reperfusion Injury in Rats Through Its Anti-Inflammatory Effect and Modulation of STAT-1

Theaflavin, a major constituent of black tea, possesses biological functions such as the antioxidative, antiviral, and anti-inflammatory ones. The purpose of this study was to verify whether theaflavin reduces focal cerebral ischemia injury in a rat model of middle cerebral artery occlusion (MCAO). Male Sprague-Dawley rats were anesthetized and subjected to 2 hours of MCAO followed 24 hours reperfusion. Theaflavin administration (5, 10, and 20 mg/kg, IV) ameliorated infarct and edema volume. Theaflavin inhibited leukocyte infiltration and expression of ICAM-1, COX-2, and iNOS in injured brain. Phosphorylation of STAT-1, a protein which mediates intracellular signaling to the nucleus, was enhanced 2-fold over that of sham group and was inhibited by theaflavin. Our study demonstrated that theaflavin significantly protected neurons from cerebral ischemia-reperfusion injury by limiting leukocyte infiltration and expression of ICAM-1, and suppressing upregulation of inflammatory-related prooxidative enzymes (iNOS and COX-2) in ischemic brain via, at least in part, reducing the phosphorylation of STAT-1

Triglyceride-glucose index trajectory and stroke incidence in patients with hypertension:a prospective cohort study

Background It has been suggested that the baseline triglyceride-glucose (TyG) index, a simple surrogate measure for insulin resistance, is significantly associated with the occurrence of stroke. Nevertheless, the impact of longitudinal patterns of TyG on the stroke risk in hypertensive patients is still unknown. Hence, this study aimed to investigate the association between TyG index trajectory and stroke risk among hypertensive patients. Methods This prospective study included 19,924 hypertensive patients from the Kailuan Study who underwent three waves survey and were free of myocardial infarction, cancer and stroke before or during 2010. The TyG index was calculated as ln [fasting triglyceride (mg/dL) x fasting plasma glucose (mg/dL)/2], and latent mixed modelling was used to identify the trajectory of TyG during the exposure period (2006-2010). Furthermore, the Cox proportional hazard models were applied to estimate the hazard ratio (HR) and 95% confidence interval (CI) for incident stroke of different trajectory groups. Results Five distinct TyG trajectory were identified during 2006-2010: low-stable (n = 2483; range, 8.03-8.06), moderate low-stable (n = 9666; range, 8.58-8.57), moderate high-stable (n = 5759; range, 9.16-9.09), elevated-stable (n = 1741; range, 9.79-9.75), and elevated-increasing (n = 275; range, 10.38-10.81). During the median follow-up of 9.97 years, 1,519 cases of incident stroke were identified, including 1,351 with ischemic stroke and 215 with hemorrhage stroke. After adjusting for confounding variables, the HR and 95% CI of stroke were 2.21 (1.49,3.28) for the elevated-increasing group, 1.43 (1.13,1.83) for the elevated-stable group, 1.35 (1.10,1.64) for the moderate high-stable group, 1.26 (1.06,1.52) for the moderate low-stable group, respectively, when compare with the low-stable group. Similar results were observed in ischemic stroke, but a significant association was not found between TyG trajectory and risk of hemorrhage stroke. Conclusion A long-term elevated TyG index in hypertensive patients is associated with an increased risk of stroke, especially ischemic stroke. This finding implies that regular monitoring of TyG index may assist in identifying individuals at a higher risk of stroke among patients with hypertension