Some well known inequalities for (h1, h2)-convex stochastic process via interval set inclusion relation

This note introduces the concept of (h1, h2)-convex stochastic processes using intervalvalued functions. First we develop Hermite-Hadmard (H.H) type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for (h1, h2)-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.http://www.aimspress.com/journal/MathMathematics and Applied Mathematic

4,4′-(Hexane-1,6-diyldi­oxy)dianiline

The complete molecule of the title compound, C18H24N2O2, is generated by a crystallographic inversion centre. The torsion angles in the hexa­methyl­ene chain are consistent with an anti­periplanar conformation, whereas the conformation of the O—CH2—CH2—CH2 unit is gauche. The three-dimensional crystal packing is stabilized by N—H⋯O and N—H⋯N hydrogen bonding

4-Methyl­benzyl 4-amino­benzoate

The dihedral angle between the two benzene rings in the title compound, C15H15NO2, is 65.28 (12)°. The crystal structure is stabilized by N—H⋯N and N—H⋯O hydrogen bonds, leading to the formation of supra­molecular chains along the a-axis direction

4-(4-Nitro­phen­oxy)butanol

The crystal structure of the title compound, C10H13NO4, features inter­molecular O—H⋯O(nitro) hydrogen bonding, which links mol­ecules into supra­molecular chains running parallel to the bc diagonal. There is also π–π stacking between 4-nitro­phenyl groups, the inter­planar distance between the nitro­benzene rings being 3.472 (2) Å

1,5-Bis(4-nitro­phen­oxy)penta­ne

The title compound, C17H18N2O6, crystallizes with two mol­ecules in the asymmetric unit. In both molecules, one of the C—C bonds of the penta­methyl­ene chain connecting the two aromatic rings is in a trans conformation and another displays a gauche conformation. The aromatic rings within each mol­ecule are nearly coplanar [dihedral angles = 3.36 (9) and 4.50 (9)°] and the nitro groups are twisted slightly out of the planes of their attached rings [dihedral angles = 8.16 (3)/6.6 (2) and 4.9 (4)/3.8 (3)°]

6-(4-Nitro­phen­oxy)hexa­nol

The title compound, C12H17NO4, features an almost planar mol­ecule (r.m.s. deviation for all non-H atoms = 0.070 Å). All methyl­ene C—C bonds adopt an anti­periplanar conformation. In the crystal structure the mol­ecules lie in planes parallel to (12) and the packing is stabilized by O—H⋯O hydrogen bonds

Negative regulation of floral transition in Arabidopsis by HOS15-PWR-HDA9 complex

Arabidopsis HOS15/PWR/HDA9 repressor complex, which is similar to the TBL1/NcoR1/HDAC complex in animals, plays a well-known role in epigenetic regulation. PWR and HDA9 have been reported to interact with each other and modulate the flowering time by repressing AGL19 expression, whereas HOS15 and HDA9, together with the photoperiodic evening complex, regulate flowering time through repression of GI transcription. However, the role of the HOS15/PWR/HDA9 core repressor complex as a functional unit in the regulation of flowering time is yet to be explored. In this study, we reported that the loss-of-function hos15-2/pwr/hda9 triple mutant accumulates higher transcript levels of AGL19 and exhibits an early flowering phenotype similar to those of hos15, pwr, and hda9 single mutants. Interestingly, the accumulation of HOS15 in the nucleus was drastically reduced in pwr and hda9 mutants. As a result, HOS15 could not perform its role in histone deacetylation or interaction with H3 in the nucleus. Furthermore, HOS15 is also associated with the same region of the AGL19 promoter known for PWR-HDA9 binding. The acetylation level of the AGL19 promoter was increased in the hos15-2 mutant, similar to the pwr and hda9 mutants. Therefore, our findings reveal that the HOS15/PWR/HDA9 repressor complex deacetylates the promoter region of AGL19, thereby negatively regulating AGL19 transcription, which leads to early flowering in Arabidopsis

Global burden and strength of evidence for 88 risk factors in 204 countries and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Background: Understanding the health consequences associated with exposure to risk factors is necessary to inform public health policy and practice. To systematically quantify the contributions of risk factor exposures to specific health outcomes, the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 aims to provide comprehensive estimates of exposure levels, relative health risks, and attributable burden of disease for 88 risk factors in 204 countries and territories and 811 subnational locations, from 1990 to 2021. Methods: The GBD 2021 risk factor analysis used data from 54 561 total distinct sources to produce epidemiological estimates for 88 risk factors and their associated health outcomes for a total of 631 risk–outcome pairs. Pairs were included on the basis of data-driven determination of a risk–outcome association. Age-sex-location-year-specific estimates were generated at global, regional, and national levels. Our approach followed the comparative risk assessment framework predicated on a causal web of hierarchically organised, potentially combinative, modifiable risks. Relative risks (RRs) of a given outcome occurring as a function of risk factor exposure were estimated separately for each risk–outcome pair, and summary exposure values (SEVs), representing risk-weighted exposure prevalence, and theoretical minimum risk exposure levels (TMRELs) were estimated for each risk factor. These estimates were used to calculate the population attributable fraction (PAF; ie, the proportional change in health risk that would occur if exposure to a risk factor were reduced to the TMREL). The product of PAFs and disease burden associated with a given outcome, measured in disability-adjusted life-years (DALYs), yielded measures of attributable burden (ie, the proportion of total disease burden attributable to a particular risk factor or combination of risk factors). Adjustments for mediation were applied to account for relationships involving risk factors that act indirectly on outcomes via intermediate risks. Attributable burden estimates were stratified by Socio-demographic Index (SDI) quintile and presented as counts, age-standardised rates, and rankings. To complement estimates of RR and attributable burden, newly developed burden of proof risk function (BPRF) methods were applied to yield supplementary, conservative interpretations of risk–outcome associations based on the consistency of underlying evidence, accounting for unexplained heterogeneity between input data from different studies. Estimates reported represent the mean value across 500 draws from the estimate's distribution, with 95% uncertainty intervals (UIs) calculated as the 2·5th and 97·5th percentile values across the draws. Findings: Among the specific risk factors analysed for this study, particulate matter air pollution was the leading contributor to the global disease burden in 2021, contributing 8·0% (95% UI 6·7–9·4) of total DALYs, followed by high systolic blood pressure (SBP; 7·8% [6·4–9·2]), smoking (5·7% [4·7–6·8]), low birthweight and short gestation (5·6% [4·8–6·3]), and high fasting plasma glucose (FPG; 5·4% [4·8–6·0]). For younger demographics (ie, those aged 0–4 years and 5–14 years), risks such as low birthweight and short gestation and unsafe water, sanitation, and handwashing (WaSH) were among the leading risk factors, while for older age groups, metabolic risks such as high SBP, high body-mass index (BMI), high FPG, and high LDL cholesterol had a greater impact. From 2000 to 2021, there was an observable shift in global health challenges, marked by a decline in the number of all-age DALYs broadly attributable to behavioural risks (decrease of 20·7% [13·9–27·7]) and environmental and occupational risks (decrease of 22·0% [15·5–28·8]), coupled with a 49·4% (42·3–56·9) increase in DALYs attributable to metabolic risks, all reflecting ageing populations and changing lifestyles on a global scale. Age-standardised global DALY rates attributable to high BMI and high FPG rose considerably (15·7% [9·9–21·7] for high BMI and 7·9% [3·3–12·9] for high FPG) over this period, with exposure to these risks increasing annually at rates of 1·8% (1·6–1·9) for high BMI and 1·3% (1·1–1·5) for high FPG. By contrast, the global risk-attributable burden and exposure to many other risk factors declined, notably for risks such as child growth failure and unsafe water source, with age-standardised attributable DALYs decreasing by 71·5% (64·4–78·8) for child growth failure and 66·3% (60·2–72·0) for unsafe water source. We separated risk factors into three groups according to trajectory over time: those with a decreasing attributable burden, due largely to declining risk exposure (eg, diet high in trans-fat and household air pollution) but also to proportionally smaller child and youth populations (eg, child and maternal malnutrition); those for which the burden increased moderately in spite of declining risk exposure, due largely to population ageing (eg, smoking); and those for which the burden increased considerably due to both increasing risk exposure and population ageing (eg, ambient particulate matter air pollution, high BMI, high FPG, and high SBP). Interpretation: Substantial progress has been made in reducing the global disease burden attributable to a range of risk factors, particularly those related to maternal and child health, WaSH, and household air pollution. Maintaining efforts to minimise the impact of these risk factors, especially in low SDI locations, is necessary to sustain progress. Successes in moderating the smoking-related burden by reducing risk exposure highlight the need to advance policies that reduce exposure to other leading risk factors such as ambient particulate matter air pollution and high SBP. Troubling increases in high FPG, high BMI, and other risk factors related to obesity and metabolic syndrome indicate an urgent need to identify and implement interventions