Exponential Decay for Damped Klein-Gordon Equations on Asymptotically Cylindrical and Conic Manifolds

We study the decay of the global energy for the damped Klein-Gordon equation on non-compact manifolds with finitely many cylindrical and subconic ends up to bounded perturbation. We prove that under the Geometric Control Condition, the decay is exponential, and that under the weaker Network Control Condition, the decay is logarithmic, by developing the global Carleman estimate with multiple weights

On the difference of mean subtree orders under edge contraction

Given a tree $T$ of order $n,$ one can contract any edge and obtain a new tree $T^{*}$ of order $n-1.$ In 1983, Jamison made a conjecture that the mean subtree order, i.e., the average order of all subtrees, decreases at least $\frac{1}{3}$ in contracting an edge of a tree. In 2023, Luo, Xu, Wagner and Wang proved the case when the edge to be contracted is a pendant edge. In this article, we prove that the conjecture is true in general

DISSECTING THE ROLES OF HUMAN SMC COMPLEXES IN TRANSCRIPTION REGULATION AND CHROMATIN ORGANIZATION

Metazoans utilize a constellation of distal regulatory elements to control gene transcription, and therefore they have to forge highly complex chromatin loops to spatially bridge these regulatory elements and genes in the three-dimensional (3D) genome. However, the hierarchy of chromatin contacts and their underlying mechanisms are not well-understood. SMC complexes including Cohesin complex and Condensin complex has been widely proposed to organize 3D genome structure, and further regulate metazoans’ gene transcription. Here, we aim to dissect the direct functions of SMC complexes (both Cohesin and Condensin) in transcriptional regulation and 3D genome organization, by utilizing an inducible protein degradation system. Nascent transcriptome analysis revealed that Cohesin acute depletion impacts the nascent transcription at promoter regions rather than at the entire gene bodies, indicating a potential role of Cohesin in RNA polymerase II pause-release. Combined analysis with MYC degradation nascent transcriptome showed Cohesin complex and MYC are co-regulating a large portion of MYC targeted genes. Moreover, our nascent transcriptome with different signals’ stimulus demonstrated Cohesin complex is generally not required for TNF-alpha and heat-shock stimulated transcriptional events. To further understand the hierarchy of 3D genome, high-resolution H3K27ac HiChIP analysis after Cohesin depletion revealed that there is a large portion of regulatory chromatin loops persist after Cohesin depletion. This is a significant finding suggesting that Cohesin is not a universal organizer of short-range enhancer-gene loops. We further showed that Cohesin-antagonized extra-long-distance super-enhancer loops are mediated by BRD4 phase separation, validating an emerging hypothesis that LLPS (Liquid-liquid phase separation) can drive chromatin contacts. For Condensin complex, our nascent transcriptome data after Condensin I depletion indicated that Condensin I modulates TNF-alpha stimulated transcription, but not the basal transcription program. Also, Hi-C analysis after Condensin I depletion revealed that Condensin I has a role in counteracting A/B compartmental interaction. Our work has provided a functional dissection of roles played by human SMC complexes in transcription regulation and 3D genome organization

Investigation of climate variability and climate change impacts on corn yield in the Eastern Corn Belt, USA

The increasing demand for both food and biofuels requires more corn production at global scale. However, current corn yield is not able to meet bio-ethanol demand without jeopardizing food security or intensifying and expanding corn cultivation. An alternative solution is to utilize cellulose and hemi-cellulose from perennial grasses to fulfill the increasing demand for biofuel energy. A watershed level scenario analysis is often applied to figure out a sustainable way to strike the balance between food and fuel demands, and maintain environment integrity. However, a solid modeling application requires a clear understanding of crop responses under various climate stresses. This is especially important for evaluating future climate impacts. Therefore, correct representation of corn growth and yield projection under various climate conditions (limited or oversupplied water) is essential for quantifying the relative benefits of alternative biofuel crops. The main objective of this study is to improve the evaluation of climate variability and climate change effects on corn growth based on plant-water interaction in the Midwestern US via a modeling approach. Traditional crop modeling methods with the Soil and Water Assessment Tool (SWAT) are improved from many points, including introducing stress parameters under limited or oversupplied water conditions, improving seasonal crop growth simulation from imagery-based LAI information, and integrating CO2 effects on crop growth and crop-water relations. The SWAT model’s ability to represent crop responses under various climate conditions are evaluated at both plot scale, where observed soil moisture data is available and watershed scale, where direct soil moisture evaluation is not feasible. My results indicate that soil moisture evaluation is important in constraining crop water availability and thus better simulates crop responses to climate variability. Over a long term period, drought stress (limited moisture) explains the majority of yield reduction across all return periods at regional scale. Aeration stress (oversupplied water) results in higher yield decline over smaller spatial areas. Future climate change introduces more variability in drought and aeration stress, resulting in yield reduction, which cannot be compensated by positive effects brought by CO2 enhancement on crop growth. Information conveyed from this study can also provide valuable suggestions to local stakeholders for developing better watershed management plans. It helps to accurately identify climate sensitive cropland inside a watershed, which could be potential places for more climate resilient plants, like biofuel crops. This is a sustainable strategy to maintain both food/fuel provision, and mitigate the negative impact of future climate change on cash crops

Determination and estimation of optimal quarantine duration for infectious diseases with application to data analysis of COVID-19

Quarantine measure is a commonly used non-pharmaceutical intervention during the outbreak of infectious diseases. A key problem for implementing quarantine measure is to determine the duration of quarantine. In this paper, a policy with optimal quarantine duration is developed. The policy suggests different quarantine durations for every individual with different characteristic. The policy is optimal in the sense that it minimizes the average quarantine duration of uninfected people with the constraint that the probability of symptom presentation for infected people attains the given value closing to 1. The optimal solution for the quarantine duration is obtained and estimated by some statistic methods with application to analyzing COVID-19 data

Exponential decay for damped Klein-Gordon equations on asymptotically cylindrical and conic manifolds

We study the decay of the global energy for the damped Klein-Gordon equation on non-compact manifolds with finitely many cylindrical and subconic ends up to bounded perturbation. We prove that under the Geometric Control Condition, the decay is exponential, and that under the weaker Network Control Condition, the decay is logarithmic, by developing the global Carleman estimate with multiple weights

Neighbourhood greenspace quantity, quality and socioeconomic inequalities in mental health

There is tentative evidence suggesting that socioeconomically disadvantaged groups may benefit more from access to neighbourhood greenspace and therefore could be a lever for narrowing socioeconomic inequalities (‘equigenesis’) in mental health, although studies are equivocal. One potential explanation for this inconsistency is differences in study designs, particularly how greenspace is measured. Most previous studies are from high income countries, and there has been no investigations into equigenic environments in China. Using survey data collected from 26 neighbourhoods in Guangzhou, China, this study examines whether local greenspaces may narrow socioeconomic inequalities in health (i.e. equigenesis) in the Chinese context. The study is the first to explore the contribution of greenspace in reducing socioeconomic inequalities in mental health in the Chinese context. It uses Normalized Difference Vegetation Index (NDVI), Street View Greenness (SVG) and self-reported neighbourhood greenness quality as estimates of residential greenness exposure Results show that SVG-quantity, SVG-quality and self-reported greenspace quality narrow the neighbourhood socioeconomic inequalities in mental health. Our findings demonstrate the importance of improving equity in local green infrastructure for promoting health equity through urban planning and design, including improving access to green spaces, and providing more street trees in socioeconomically disadvantaged neighbourhoods

Sharp bounds for variance of treatment effect estimators in the finite population in the presence of covariates

In a completely randomized experiment, the variances of treatment effect estimators in the finite population are usually not identifiable and hence not estimable. Although some estimable bounds of the variances have been established in the literature, few of them are derived in the presence of covariates. In this paper, the difference-in-means estimator and the Wald estimator are considered in the completely randomized experiment with perfect compliance and noncompliance, respectively. Sharp bounds for the variances of these two estimators are established when covariates are available. Furthermore, consistent estimators for such bounds are obtained, which can be used to shorten the confidence intervals and improve the power of tests. Confidence intervals are constructed based on the consistent estimators of the upper bounds, whose coverage rates are uniformly asymptotically guaranteed. Simulations were conducted to evaluate the proposed methods. The proposed methods are also illustrated with two real data analyses.Comment: Accepted by Statistica Sinic

PlaneDepth: Plane-Based Self-Supervised Monocular Depth Estimation

Self-supervised monocular depth estimation refers to training a monocular depth estimation (MDE) network using only RGB images to overcome the difficulty of collecting dense ground truth depth. Many previous works addressed this problem using depth classification or depth regression. However, depth classification tends to fall into local minima due to the bilinear interpolation search on the target view. Depth classification overcomes this problem using pre-divided depth bins, but those depth candidates lead to discontinuities in the final depth result, and using the same probability for weighted summation of color and depth is ambiguous. To overcome these limitations, we use some predefined planes that are parallel to the ground, allowing us to automatically segment the ground and predict continuous depth for it. We further model depth as a mixture Laplace distribution, which provides a more certain objective for optimization. Previous works have shown that MDE networks only use the vertical image position of objects to estimate the depth and ignore relative sizes. We address this problem for the first time in both stereo and monocular training using resize cropping data augmentation. Based on our analysis of resize cropping, we combine it with our plane definition and improve our training strategy so that the network could learn the relationship between depth and both the vertical image position and relative size of objects. We further combine the self-distillation stage with post-processing to provide more accurate supervision and save extra time in post-processing. We conduct extensive experiments to demonstrate the effectiveness of our analysis and improvements.Comment: 12 pages, 7 figure

Optimal backward uniqueness and polynomial stability of second order equations with unbounded damping

For general second order evolution equations, we prove an optimal condition on the degree of unboundedness of the damping, that rules out finite-time extinction. We show that control estimates give energy decay rates that explicitly depend on the degree of unboundedness, and establish a dilation method to turn existing control estimates for one propagator into those for another in the functional calculus. As corollaries, we prove Schr\"odinger observability gives decay for unbounded damping, weak monotonicity in damping, and quantitative unique continuation and optimal propagation for fractional Laplacians. As applications, we establish a variety of novel and explicit energy decay results to systems with unbounded damping, including singular damping, linearised gravity water waves and Euler--Bernoulli plates.Comment: 50 pages, 2 figure