Arithmetic Properties of Abelian Varieties

Let $A$ be an abelian variety of dimension $g$, defined over a number field $K$. Denote by $N_A$ the norm of the conductor ideal of $A$. For each prime \fp in $K$ such that \fp\nmid N_A, denote by \overline{A}_{\fp} the reduction of $A$ modulo \fp, defined over the finite field \F_\fp. Questions around the distribution of certain properties \overline{A}_\fp have been extensively studied over the years, such as the Sato-Tate Conjecture from the 1960s, the Lang-Trotter Conjecture from the 1970s, and the Murty-Patankar Conjecture from the 2000s. This thesis revolves around this theme of research, as follows. When $K$ is the field of rationals, we focus on a higher-dimensional generalization of a conjecture formulated by S. Lang and H. Trotter about the Frobenius trace of an elliptic curve (i.e., an abelian variety of dimension 1). Under the assumption of the Generalized Riemann Hypothesis, we prove nontrivial upper bounds for the number of primes $p\leq x$ for which $\overline{A}_p$ has a prescribed Frobenius trace. These bounds improve prior results obtained by A.C. Cojocaru, R. Davis, A. Silverberg, and K.E. Stange in 2016 and H. Chen, N. Jones, and V. Serban in 2020. The bounds also recover the best-known results obtained for $g=1$ by M.R. Murty, V.K. Murty, and N. Saradha in 1988, combined with a refinement in the power of $\log x$ by D. Zywina in 2015. By restricting to an absolutely simple abelian surface with a commutative endomorphism ring, we prove nontrivial upper bounds for the number of primes \fp with norm bounded by $x$, for which \overline{A}_{\fp} splits into a product of abelian varieties of smaller dimensions. These bounds improve prior results obtained by J. Achter in 2012 and D. Zywina in 2014

Additional file 1 of Global burden of pelvic inflammatory disease and ectopic pregnancy from 1990 to 2019

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Table_1_Dimethylglycine Sodium Salt Alleviates Intrauterine Growth Restriction-Induced Low Growth Performance, Redox Status Imbalance, and Hepatic Mitochondrial Dysfunction in Suckling Piglets.docx

This study aimed to investigate the mechanism of redox status imbalance and hepatic mitochondrial dysfunction induced by intrauterine growth restriction (IUGR) and relieve this condition through dimethylglycine sodium salt (DMG-Na) supplementation during the suckling period. Thirty normal birth weight (NBW) and 30 IUGR newborns were selected from 20 sows. Briefly, 1 NBW and 1 IUGR newborn were obtained from each litter of 10 sows, and 10 NBW and 10 IUGR newborns were obtained. Additionally, 2 NBW and 2 IUGR newborns were obtained from each litter of another 10 sows, and 20 NBW newborns were allocated to the N [basic milk diets (BMDs)] and ND (BMDs+0.1% DMG-Na) groups. Furthermore, 20 IUGR newborns were assigned to the I (BMDs) and ID (BMDs+0.1% DMG-Na) groups. The results revealed that the growth performance, serum and hepatic redox status, and hepatic gene and protein expression levels were lower (P < 0.05) in the I group compared to the N group. Additionally, supplementation with DMG-Na (ND and ID groups) improved (P < 0.05) these parameters compared to the non-supplemented groups (N and I groups). In conclusion, the activity of Nrf2/SIRT1/PGC1α was inhibited in IUGR newborns, and this led to their hepatic dysfunctions. Supplementation with DMG-Na activated Nrf2/SIRT1/PGC1α in IUGR newborns, thereby improving their performance.</p

Additional file 1 of Induced abortions among Chinese adolescent girls

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Crown Ether Nanopores in Graphene Membranes for Highly Efficient CO₂/CH₄ and CO₂/CO Separation: A Theoretical Study

Gas separation is a critical step in various applications, e.g., industrial separation and purification and carbon capture and separation, although it remains challenging due to the presence of impurities in the end product, even with state-of-the-art separation membranes. In this study, we demonstrate, using a molecular dynamics simulation approach, that graphene membranes embedded with crown ether nanopores exhibit unprecedented separation efficiency for CO2/CH4 and CO2/CO. Our investigation of the performance of three crown ether pores reveals that Pore-2 enables rapid transport of CO2 while effectively blocking CH4/CO in most cases, resulting in remarkably high selectivity. In CO2/CH4 mixtures, the perfect selectivity and exceptional CO2 transport are achieved through a combination of two gases size difference and robust trapping of CO2 by Pore-2. For CO2/CO mixtures, the subtle difference in electrostatic interaction between Pore-2 and the two gases, with the carbon in CO2 possessing a higher positive charge than that in CO, is responsible for the selective separation of CO2/CO. The separation capacity of Pore-2 under different gas feed ratios and temperatures undergoes a slight performance reduction in some cases. Our findings highlight the superior performance of graphene crown ether nanopores for CO2/CH4 and CO2/CO separation, suggesting their potential as advanced gas sieving membranes

Scene-15

Dataset Source: http://www.cvr.ai.uiuc.edu/ponce_grp/data

Data_Sheet_1_Predicting Spike Features of Hodgkin-Huxley-Type Neurons With Simple Artificial Neural Network.PDF

Hodgkin-Huxley (HH)-type model is the most famous computational model for simulating neural activity. It shows the highest accuracy in capturing neuronal spikes, and its model parameters have definite physiological meanings. However, HH-type models are computationally expensive. To address this problem, a previous study proposed a spike prediction module (SPM) to predict whether a spike will take place 1 ms later based on three voltage values with intervals of 1 ms. Although SPM does well, it fails to evaluate the informative features of the spike. In this study, the feature prediction module (FPM) based on simple artificial neural network (ANN) was proposed to predict spike features including maximum voltage, minimum voltage, and dropping interval. Nine different HH-type models were adopted whose firing patterns cover most of the firing behaviors observed in the brain. Voltage and spike feature samples under constant external input current were collected for training and testing. Experiment results illustrated that the combination of SPM and FPM can accurately predict the spiking part of different HH-type models and can generalize to unseen types of input current. The combination of SPM and FPM may offer a possible way to simulate the action potentials of biological neurons with high accuracy and efficiency.</p

Effect of heat shock on <i>HSPs</i> and m⁶A mRNA methylation related genes.

Expression of HSPA1B (HSP70) (A), HSPB1 (HSP27) (B), METTL3 (C), METTL14 (D), FTO (E), and YTHDF2 (F) mRNA at 6 h, 12 h, 24 h after heat shock in HepG2 cells. Data are shown as mean ± SEM (n = 3). *p value ≤ 0.05, **p value ≤ 0.01.</p

Table1_Subdividing end-use energy consumption based on household characteristics and climate conditions: insights from urban China.DOCX

Rapidly increasing household energy consumption poses significant challenges to global warming mitigation and the transition to low-carbon economies, particularly in China. This paper addresses this issue by introducing a comprehensive segmentation model which effectively subdivides household energy usage into five end-uses: cooking/hot water, heating, cooling, lighting, and power. The segmentation model uncovers compelling insights into urban end-use energy consumption patterns across China and variations among provinces. We observe a consistent increase in urban household end-use energy consumption and per capita energy consumption levels over the past decade. Heating and cooking/hot water emerge as the dominant contributors to household energy consumption, accounting for 26% and 40% of the total, respectively. Furthermore, it is found that higher levels of urbanization and improved living conditions are positively correlated with increased power energy consumption. The declining number of household members, primarily due to the prevalence of nuclear families, has resulted in higher energy end-use, particularly in both developed and underdeveloped economic areas. This paper serves as a valuable foundation for understanding and quantifying household end-use energy consumption. The findings contribute to a more comprehensive understanding of energy consumption patterns, facilitating a cleaner and more sustainable transformation of energy consumption structures.</p