Informal payments in developing countries' public health sector

In China and some other developing countries' public health sectors, many patients give their doctors a payment outside the official channel before a major treatment. This secret payment has been documented as informal payment in the literature. We argue that the fundamental cause for informal payments is that patients have more information about doctors' skill than the government does. The price, set by the government, for services offered by doctors cannot fully differentiate patients' various needs. As a consequence, informal payment rises as a tool for patients to compete for the skillful doctor. We study the welfare implications of different policies that can potentially be used to regulate such payments. Patient heterogeneity plays a central role in welfare implications of different policies: when patients' willingness-to-pay differs a lot, informal payments should be allowed and when it differs little, informal payments should be banned. Also we show that selling the right to choose physicians publicly always improves social welfare.informal payments; public health sector; welfare; efficiency

Dimension Estimates on Circular (s,t)(s,t)-Furstenberg Sets

In this paper, we show that circular $(s,t)$-Furstenberg sets in $\mathbb R^2$ have Hausdorff dimension at least $$\max\{\frac{t}3+s,(2t+1)s-t\} \text{ for all $0<s,t\le 1$}.$$ This result extends the previous dimension estimates on circular Kakeya sets by Wolff.Comment: 24 pages, 8 figure

On the Dimension of Kakeya Sets in the First Heisenberg Group

We define Kakeya sets in the Heisenberg group and show that the Heisenberg Hausdorff dimension of Kakeya sets in the first Heisenberg group is at least 3. This lower bound is sharp since, under our definition, the $\{xoy\}$-plane is a Kakeya set with Heisenberg Hausdorff dimension 3.Comment: 11 pages, 3 figure

Beyond Higgs Couplings: Probing the Higgs with Angular Observables at Future e+e−e^+ e^- Colliders

We study angular observables in the $e^+e^-\to Z H\to \ell^+ \ell^-\,b\bar{b}$ channel at future circular $e^+ e^-$ colliders such as CEPC and FCC-ee. Taking into account the impact of realistic cut acceptance and detector effects, we forecast the precision of six angular asymmetries at CEPC (FCC-ee) with center-of-mass energy $\sqrt{s} =$ 240 GeV and 5 (30) ${\rm ab}^{-1}$ integrated luminosity. We then determine the projected sensitivity to a range of operators relevant for the Higgs-strahlung process in the dimension-6 Higgs EFT. Our results show that angular observables provide complementary sensitivity to rate measurements when constraining various tensor structures arising from new physics. We further find that angular asymmetries provide a novel means of both probing BSM corrections to the $H Z \gamma$ coupling and constraining the "blind spot" in indirect limits on supersymmetric scalar top partners.Comment: 28 pages, 9 figures. v2: references added, matches published version in JHE

Existence of hyperbolic motions to a class of Hamiltonians and generalized NN-body system via a geometric approach

For the classical $N$-body problem in $\mathbb{R}^d$ with $d\ge2$, Maderna-Venturelli in their remarkable paper [Ann. Math. 2020] proved the existence of hyperbolic motions with any positive energy constant, starting from any configuration and along any non-collision configuration. Their original proof relies on the long time behavior of solutions by Chazy 1922 and Marchal-Saari 1976, on the H\"{o}lder estimate for Ma\~{n}\'{e}'s potential by Maderna 2012, and on the weak KAM theory. We give a new and completely different proof for the above existence of hyperbolic motions. The central idea is that, via some geometric observation, we build up uniform estimates for Euclidean length and angle of geodesics of Ma\~{n}\'{e}'s potential starting from a given configuration and ending at the ray along a given non-collision configuration. Note that we do not need any of the above previous studies used in Maderna-Venturelli's proof. Moreover, our geometric approach works for Hamiltonians $\frac12\|p\|^2-F(x)$, where $F(x)\ge 0$ is lower semicontinuous and decreases very slowly to $0$ faraway from collisions. We therefore obtain the existence of hyperbolic motions to such Hamiltonians with any positive energy constant, starting from any admissible configuration and along any non-collision configuration. Consequently, for several important potentials $F\in C^{2}(\Omega)$, we get similar existence of hyperbolic motions to the generalized $N$-body system $\ddot{x} = \nabla_x F(x)$, which is an extension of Maderna-Venturelli [Ann. Math. 2020].Comment: 37 pages, 6 figure

Does A Customers Own Review Behavior Have An Impact On Its Purchase Behavior? Analyzing The Impact Of Review Platform On Group-Buying Platform-----A Study Based On Dianping.Com

With the development of Web 2.0, traditional customers have increasingly transferred to online purchase and created a large volume of User Generated Content (UGC) on the Internet. The changes brought traditional customer relationship management a great impact and forced companies to adapt, change and evolve. The previous researches have studied the influence of crowds’ feedback on customer’s purchase behavior, but little researches explore the impact of customer’s own review behavior on its purchase behavior. In this paper, our study seeks insights into analyzing the impact of customer’s own review behavior on its purchase behavior and discovering how this effect could be fully utilized to predict customer’s next stage churn. Based on data from Dianping.com, a famous comprehensive website which contains review and purchase platforms, we build the Logit regression model, considering customer’s own review and purchase behavior and finding the impact of user’s own review behavior on purchase behavior. Finally, we also use ten-fold cross-validation to prove the stability of our model