Remarks on an operator Wielandt inequality

Let $A$ be a positive operator on a Hilbert space $\mathcal{H}$ with $0<m\leq A\leq M$ and $X$ and $Y$ are two isometries on $\mathcal{H}$ such that $X^{*}Y=0$. For every 2-positive linear map $\Phi$, define $$\Gamma=\left(\Phi(X^{*}AY)\Phi(Y^{*}AY)^{-1}\Phi(Y^{*}AX)\right)^{p}\Phi(X^{*}AX)^{-p}, \, \, \, p>0.$$ We consider several upper bounds for $\frac{1}{2}|\Gamma+\Gamma^{*}|$. These bounds complement a recent result on operator Wielandt inequality.Comment: 6page

The Causes of Chronic and Transient Poverty and Their Implications for Poverty Reduction Policy in Rural China

The study focuses on two components of total poverty: chronic and transient poverty, and investigates their relative importance in total observed poverty, as well as the determinants of each components. We found that transient poverty accounts for a large proportion of total poverty observed in the poor rural areas of China. By analyzing the determinants of the two types of poverty, we found that household demographic characteristics, such as age of the head of households, family sizes, labour participation ratio, and educational level of the head of the households, are very important to the poverty status of households. These factors matter more to chronic poverty than transient poverty, and have greater impacts on the poverty measured by consumption than that measured by income. Besides the demographic factors of households, other household factors like physical stocks, the composition of income, and the amount of cultivated lands also have significant effects on both chronic and transient poverty. It is also confirmed that change in cash holding and saving and borrowing grain are used by rural households to cope with income variation and smooth their consumption. Attributes of community where the households reside are also important to poverty. With very few exceptions, we did not find that poverty programs have significant impact on poverty reduction at the households' level. We interpreted this as the poverty programs benefiting the wealthy more than the poor in a given poor area. The main reason for this could be that the implementation design of these programs fails to target the poor.Income risk, chronic poverty, transient poverty, poverty program evaluation, China

Random Finite Set Theory and Optimal Control of Large Collaborative Swarms

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using Model Predictive Control (MPC) to overcome the aforementioned challenges. Computationally efficient solutions are obtained via the Iterative Linear Quadratic Regulator (ILQR). Information divergence is used to define the distance between the swarm RFS and the desired swarm configuration. Then, a stochastic optimal control problem is formulated using a modified L2^2 distance. Simulation results using MPC and ILQR show that swarm intensities converge to a target destination, and the RFS control formulation can vary in the number of target destinations. ILQR also provides a more computationally efficient solution to the RFS swarm problem when compared to the MPC solution. Lastly, the RFS control solution is applied to a spacecraft relative motion problem showing the viability for this real-world scenario.Comment: arXiv admin note: text overlap with arXiv:1801.0731

PROTEOMIC IDENTIFICATION OF HISTONE POST-TRANSLATIONAL MODIFICATIONS INDUCED BY DNA DOUBLE-STRAND BREAKS AND NOVEL PROTEINS INVOLVED IN THE DNA DAMAGE RESPONSE

Inaccurate repair of DNA double-strand breaks (DSBs) can lead to DNA mutation and chromosome rearrangements, causing human diseases such as cancer. Although we know the basic mechanisms of DSB repair, the added complexities in the chromatin context are unclear. This is partially due to the lack of unbiased systems for identifying proteins and post-translational modifications (PTMs) involved in DSB repair. In this work, we established a novel method, termed DSB-ChAP-MS (Double Strand Break-Chromatin Affinity Purification with Mass Spectrometry), for the affinity purification of a sequence-specific single copy endogenous chromosomal locus containing a DSB, followed by the proteomic identification of enriched proteins and histone PTMs. Providing validation of the DSB-ChAP-MS approach, we found many histone PTMs that had been previously implicated in the DNA damage response, as well as multiple new histone PTMs enriched on chromatin bearing a DSB from budding yeast. One of these, methylation of histone H3 on lysine 125, has not previously been reported. Among the novel proteins enriched at a DSB were the phosphatase Sit4, the RNA pol II degradation factor Def1, the mRNA export protein Yra1 and the HECT E3 ligase Tom1. Each of these proteins was required for resistance to radiomimetics. Yra1 and Def1 were required for DSB repair per se, while Sit4 was required for rapid inactivation of the DNA damage checkpoint after DSB repair. Thus, our unbiased proteomics approach has led to the unexpected discovery of novel roles for these and other proteins in the DNA damage response