On the anti-concentration functions of some familiar families of distributions

Let $\{X_{\alpha}\}$ be a family of random variables following a certain type of distributions with finite expectation $\mathbf{E}[X_{\alpha}]$ and finite variance ${\rm Var}(X_{\alpha})$, where $\alpha$ is a parameter. Motivated by the recent paper of Hollom and Portier (arXiv: 2306.07811v1), we study the anti-concentration function $(0, \infty)\ni y\to \inf_{\alpha}\mathbf{P}\left(|X_{\alpha}-\mathbf{E}[X_{\alpha}]|\geq y \sqrt{{\rm Var}(X_{\alpha})}\right)$ and find its explicit expression. We show that, for certain familiar families of distributions, including uniform distributions, exponential distributions, non-degenerate Gaussian distributions and student's $t$-distribution, the anti-concentration function is not identically zero, while for some other familiar families of distributions, including binomial, Poisson, negative binomial, hypergeometric, Gamma, Pareto, Weibull, log-normal and Beta distributions, the anti-concentration function is identically zero.Comment: 15 page

The asymptotic behavior of rarely visited edges of the simple random walk

In this paper, we study the asymptotic behavior of the number of rarely visited edges (i.e., edges that visited only once) of a simple symmetric random walk on $\mathbb{Z}$. Let $\alpha(n)$ be the number of rarely visited edges up to time $n$. First, we evaluate $\mathbb{E}(\alpha(n))$, show that $n\to \mathbb{E}(\alpha(n))$ is non-decreasing in $n$ and that $\lim\limits_{n\to+\infty}\mathbb{E}(\alpha(n))=2$. Then we study the asymptotic behavior of $\mathbb{P} (\alpha(n)>a(\log n)^2)$ for any $a>0$ and use it to show that there exists a constant $C\in(0,+\infty)$ such that $\limsup\limits_{n\to+\infty}\frac{\alpha(n)}{(\log n)^2}=C$ almost surely

A statistical examination of the link between environmental performance and legal practices: an evaluation of China’s strategies for residual legislative power allocation

This study investigates the correlation between the environmental legal practices of different countries and their environmental performance. It entails an empirical analysis of cross-sectional environmental data collected from 34 countries, including members of the Organization for Economic Cooperation and Development (OECD) and the BRICs nations (Brazil, Russia, India, China, and South Africa). Then the study explores the correlation between a country’s environmental performance and both the environmental policy stringency and regulatory enforcement. The findings from this global assessment are subsequently corroborated through an examination of China’s environmental time series data spanning a decade, revealing a significant relationship between a country’s environmental performance and regulatory enforcement. These results validate the Incomplete Law Theory within the field of environmental law. Moreover, as the second most populous and the third-largest country in terms of land area globally, China’s environmental protection strategies and performance play a pivotal role in influencing international environmental outcomes. Consequently, the study conducts a case study on China’s environmental legal practices and provides suggestions for enhancing China’s allocation strategies of residual legislative power. The study advocates for the optimization of residual legislative power allocation within local environmental law enforcement agencies and a balanced distribution of public and private residual legislative power. This approach reinforces the government’s role in strategic formulation

Inhibitory effects of Gynura procumbens ethanolic extract on nitric oxide production and inducible nitric oxide synthase (iNOS) protein expression in macrophages

Nitric oxide (NO) overproduction by inducible nitric oxide synthase (iNOS) may be associated with acute and chronic inflammations. Macrophages as important cells in the innate immune system are able to be stimulated and can lead to iNOS activation and excessive NO production. Gynura procumbens is a medicinal plant traditionally used in treating various ailments including inflammation but the mechanism of anti-inflammatory activity of this plant is still elusive. This study was carried out to investigate the anti-inflammatory therapeutic effects of Gynura procumbens ethanolic extract on NO production and iNOS protein expression in RAW 264.7 macrophages stimulated with lipopolysaccharide (LPS). Cell viability of RAW 264.7 macrophages treated with Gynura procumbens ethanolic extract was determined by MTT assay. NO production was determined by Griess assay following Gynura procumbens ethanolic extract treatment alone or in combination with LPS stimulation. Protein expression of iNOS was determined by western blot. RAW 264.7 macrophages viability of more than 90% was observed after 24 h treatment with Gynura procumbens ethanolic extract concentration range of 3.9 μg/mL to 500 μg/mL. Significant inhibition of NO production level has been identified in LPS-stimulated RAW 264.7 cells pre-treated with 250 μg/mL Gynura procumbens ethanolic extract (p<0.05) while all selected concentrations of Gynura procumbens ethanolic extract showed no significant alteration of NO production in the absence of LPS stimulation. Pre-treatment of 250 μg/mL Gynura procumbens ethanolic extract also demonstrated significant suppression of iNOS protein expression in LPS-stimulated RAW 264.7 cells (p<0.05). In conclusion, this study demonstrates that Gynura procumbens ethanolic extract exhibits anti-inflammatory potential through inhibition of NO production and iNOS protein expression in LPS-stimulated macrophages, suggesting that this plant could be further researched for its beneficial use in inflammatory disorders

PHF8-GLUL axis in lipid deposition and tumor growth of clear cell renal cell carcinoma.

For clear cell renal cell carcinoma (ccRCC), lipid deposition plays important roles in the development, metastasis, and drug resistance. However, the molecular mechanisms underlying lipid deposition in ccRCC remain largely unknown. By conducting an unbiased CRISPR-Cas9 screening, we identified the epigenetic regulator plant homeodomain finger protein 8 (PHF8) as an important regulator in ccRCC lipid deposition. Moreover, PHF8 is regulated by von Hippel-Lindau (VHL)/hypoxia-inducible factor (HIF) axis and essential for VHL deficiency-induced lipid deposition. PHF8 transcriptionally up-regulates glutamate-ammonia ligase (GLUL), which promotes the lipid deposition and ccRCC progression. Mechanistically, by forming a complex with c-MYC, PHF8 up-regulates TEA domain transcription factor 1 (TEAD1) in a histone demethylation-dependent manner. Subsequently, TEAD1 up-regulates GLUL transcriptionally. Pharmacological inhibition of GLUL by l-methionine sulfoximine not only repressed ccRCC lipid deposition and tumor growth but also enhanced the anticancer effects of everolimus. Thus, the PHF8-GLUL axis represents a potential therapeutic target for ccRCC treatment

Novel loci and pathways significantly associated with longevity

Only two genome-wide significant loci associated with longevity have been identified so far, probably because of insufficient sample sizes of centenarians, whose genomes may harbor genetic variants associated with health and longevity. Here we report a genome-wide association study (GWAS) of Han Chinese with a sample size 2.7 times the largest previously published GWAS on centenarians. We identified 11 independent loci associated with longevity replicated in Southern-Northern regions of China, including two novel loci (rs2069837-IL6; rs2440012-ANKRD20A9P) with genome-wide significance and the rest with suggestive significance (P < 3.65 × 10(−5)). Eight independent SNPs overlapped across Han Chinese, European and U.S. populations, and APOE and 5q33.3 were replicated as longevity loci. Integrated analysis indicates four pathways (starch, sucrose and xenobiotic metabolism; immune response and inflammation; MAPK; calcium signaling) highly associated with longevity (P ≤ 0.006) in Han Chinese. The association with longevity of three of these four pathways (MAPK; immunity; calcium signaling) is supported by findings in other human cohorts. Our novel finding on the association of starch, sucrose and xenobiotic metabolism pathway with longevity is consistent with the previous results from Drosophilia. This study suggests protective mechanisms including immunity and nutrient metabolism and their interactions with environmental stress play key roles in human longevity

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference