Complete bounded λ\lambda-hypersurfaces in the weighted volume-preserving mean curvature flow

In this paper, we study the complete bounded $\lambda$-hypersurfaces in weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded $\lambda$-hypersurfaces with $|A|\leq\alpha$ and get some applications of the volume comparison theorem. Secondly, we consider the relation among $\lambda$, extrinsic radius $k$, intrinsic diameter $d$, and dimension $n$ of the complete $\lambda$-hypersurface, and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded $\lambda$-hypersurface with some natural and general restrictions

Performance of a Multiple-Access DCSK-CC System over Nakagami-mm Fading Channels

In this paper, we propose a novel cooperative scheme to enhance the performance of multiple-access (MA) differential-chaos-shift-keying (DCSK) systems. We provide the bit-error-rate (BER) performance and throughput analyses for the new system with a decode-and-forward (DF) protocol over Nakagami-$m$ fading channels. Our simulated results not only show that this system significantly improves the BER performance as compared to the existing DCSK non-cooperative (DCSK-NC) system and the multiple-input multiple-output DCSK (MIMO-DCSK) system, but also verify the theoretical analyses. Furthermore, we show that the throughput of this system approximately equals that of the DCSK-NC system, both of which have prominent improvements over the MIMO-DCSK system. We thus believe that the proposed system can be a good framework for chaos-modulation-based wireless communications.Comment: 4 pages, 5 figures, accepted, IEEE ISCAS, 201

The Long-Term Consequences of Family Planning in Old Age: Evidence from China\u27s Later, Longer, Fewer Campaign

Family planning plays a central role in contemporary population policies. However, little is known about its long-term consequences in old age. In this study, we examine how family planning policies implemented in China in the early 1970s affect the quality of life of the Chinese elderly forty years later. The direction of the effect is theoretically unclear. On the one hand, having fewer children allows parents to reallocate more resources to themselves, improving their well-being. On the other hand, having fewer children also leads to less care and companionship from children in old age. To empirically investigate the effect of family planning, we identify the causal impact by exploiting the provincial heterogeneity in implementing the Later, Longer, Fewer (LLF) policies in the early 1970s. We find that the LLF policies greatly reduced the number of children born to couples by 0.85. Parents also receive less support from children in terms of living arrangements, inter vivos transfers, and emotional support. Finally, we find that the impacts of the family planning policies on elderly parent\u27s physical and mental well-being are drastically different: whereas parents who are more exposed to the family planning policies consume more and enjoy slightly better physical health status, they report more severe depression symptoms

The State of Mental Health Among the Elderly Chinese

China introduced its stringent family planning policies from the early 1970s, known as the Later, Longer, Fewer policies, and followed it with the One-Child Policy from 1979. The number of children born to Chinese parents significantly decreased from 5.7 in late 1960s to 2.5 in 1988. In Chen and Fang (2019), we show that family planning policies have drastically different effects on elderly parents\u27 physical and mental well-beings. Whereas parents more exposed to the family planning policies consume more and enjoy slightly better physical health status, they report more severe depression symptoms. In this paper, we present a more complete picture of the difference in mental health among residents in rural and urban areas, between males and females, between different education groups, between those with one child and those with more than one children, and between widowed and non-widowed. We highlight the role of family support (from children and spouse) for the mental health status among the elderly Chinese

Optimal Scoring Rule Design

This paper introduces an optimization problem for proper scoring rule design. Consider a principal who wants to collect an agent's prediction about an unknown state. The agent can either report his prior prediction or access a costly signal and report the posterior prediction. Given a collection of possible distributions containing the agent's posterior prediction distribution, the principal's objective is to design a bounded scoring rule to maximize the agent's worst-case payoff increment between reporting his posterior prediction and reporting his prior prediction. We study two settings of such optimization for proper scoring rules: static and asymptotic settings. In the static setting, where the agent can access one signal, we propose an efficient algorithm to compute an optimal scoring rule when the collection of distributions is finite. The agent can adaptively and indefinitely refine his prediction in the asymptotic setting. We first consider a sequence of collections of posterior distributions with vanishing covariance, which emulates general estimators with large samples, and show the optimality of the quadratic scoring rule. Then, when the agent's posterior distribution is a Beta-Bernoulli process, we find that the log scoring rule is optimal. We also prove the optimality of the log scoring rule over a smaller set of functions for categorical distributions with Dirichlet priors