China's Sovereign Wealth Fund : Weakness and Challenges

The establishment of sovereign wealth funds in large developing countries has generated hot debate among participants in the international financial market. When accumulated foreign exchange reserves surpass a sufficient and an appropriate level, the costs, risks and impacts on the macro-economy of countries holding reserves need to be considered. The Chinese Government established China Investment Corporation (CIC) in 2007 to diversify its investment of foreign reserves and to raise investment income. However, because of certain conflicts of interest and institution-design caveats, CIC possesses some internal weakness, including a vague orientation, mixed investment strategies and inefficient bureaucratic style. Although the subprime crisis has softened certain regulations and lessened rejection by the USA of CIC potential investments, the increased volatility and uncertainty of the market means that CIC is facing some new challenges in terms of its investment decisions. Moreover, CIC is competing with other Chinese investment institutions for injections of funds from the Chinese Government.CIC, external challenge, internal weakness, foreign exchange reserve management

Recovery of contextuality based on mirror-like state discrimination in PT- and anti-PT-symmetric systems

In the past decades, researches on parity-time (PT) and anti-parity-time(APT) systems have garnered unprecedented attention, showcasing their various intriguing characteristics and promising potentiality in extending canonical Hermitian quantum mechanics. However, despite significant endeavors devoted to this new field of physics, non-Hermitian dynamics of contextuality still remains an uncharted region, either in PT-symmetry or APT-symmetry systems. Since contextuality has also been proven to be the core resource for quantum state discrimination (QSD) tasks, here we systematically investigate the novel performance of contextuality through QSD in both systems, taking mirror-symmetric three-state minimum error discrimination (MED) and maximum confidence discrimination (MCD) scenarios as two examples. The time evolution of contextuality in two scenarios and eight regimes (four regimes for each scenario) are comprehensively compared and analyzed, with the difference of initial states also considered. In the symmetry-unbroken regimes, our simulation shows periodic oscillations of contextuality for both MED and MCD scenarios, the period of which is state-independent but related to non-Hermiticity of the system. Both MED and MCD shows non-trivial recovery of contextuality exceeding its initial value in PT system, which is only existent for MCD in APT system. In the symmetry-broken regimes, the success probabilities of both scenarios start from a prompt decay at first, ending up with a stable value which is constantly 1/3. Non-triviality is found only for MCD scenario in PT system, where the recovered contextuality exceeds its initial value.Comment: 6 pages, 4 figure

he Cauchy problem for the Novikov equation under a nonzero background: Painlev\'e asymptotics in a transition zone

In this paper, we investigate the Painlev\'e asymptotics in a transition zone for the solutions to the Cauchy problem of the Novikov equation under a nonzero background \begin{align} &u_{t}-u_{txx}+4 u_{x}=3uu_xu_{xx}+u^2u_{xxx}, \nonumber &u(x, 0)=u_{0}(x),\nonumber \end{align} where $u_0(x)\rightarrow \kappa>0, \ x\rightarrow \pm \infty$and$u_0(x)-\kappa$is assumed in the Schwarz space. This result is established by performing the$\overline\partial-steepest descent analysis to a Riemann-Hilbert problem associated with the the Cauchy problem in a new spatial scale \begin{equation*} y = x - \int_{x}^{\infty} \left((u-u_{xx}+1)^{2/3}-1\right)ds, \end{equation*} for large times in the transition zone y/t \approx -1/8 $. It is shown that the leading order term of the asymptotic approximation comes from the contribution of solitons, while the sub-leading term is related to the solution of the Painlev\'e \uppercase\expandafter{\romannumeral2} equation.n.Comment: 52 page

The Degasperis-Procesi equation on the line: Soliton resolution, asymptotic stability of NN-soliton solutions and Painlev\'e asymptotics

In this paper, we study the long time asymptotic behavior to the Cauchy problem of the Degasperis-Procesi (DP) equation with $3\times3$ matrix Lax pair \begin{align} &u_t-u_{txx}+3\kappa u_x+4uu_x=3u_x u_{xx}+uu_{xxx}, \nonumber &u(x,0)=u_{0}(x),\nonumber \end{align} where $\kappa$ is a positive parameter. It is shown that the solution of the Cauchy problem can be characterized via a $3\times3$ matrix Riemann-Hilbert (RH) problem in a new scale $(y,t)$. We divide the upper half-plane $(y,t)\in \mathbb{R}\times \mathbb{R}^+$ into three kinds of space-time regions: I. solitonic regions $\xi 3$, II. solitonless region $-3/8<\xi< 3$ and III. transition regions $\xi \approx -3/8$ and $\xi\approx 3$.With $\overline\partial$ steepest descent analysis and double limit technique, we obtain a complete long-time asymptotics for the solution $u(x,t)$ in three different space-time regions. The corresponding residual error functions come from singularities and a $\overline\partial$-equation respectively. Our first asymptotic result from soliton region I is characterized with a sum of single solitons with different velocity. This is a verification of soliton resolution conjecture for DP equation. Our second asymptotic result from the solitonless region II is characterized with parabolic cylinder function. Our third asymptotic result from the transition region III can be expressed in terms of the Painlev\'{e} II equation.Comment: 81 page

Experimental demonstration of Contextual Advantage in minimum error and maximum confidence mirror-state discrimination

Contextuality is well known as a vital resource for locating the boundary between classical and quantum theories, as well as identifying tasks showing quantum advantage. In a surge of recent works [Schmid and Spekkens, Phys.Rev.X 8, 011015 (2018); Mukherjee, Naonit and Pan, Phys.Rev.A 106, 012216 (2022); Flatt, Lee, Carceller, Brask and Bae, PRX QUANTUM 3, 030337 (2022)], it has also been shown that contextuality is the crucial resource in quantum state discrimination (QSD) tasks, including minimum error discrimination (MED) and maximum confidence discrimination (MCD), together with many other figure-of-merits. Despite the fundamental progress made by those aforementioned works, none of them mention about how to realize their fancy proposals, which is doubtlessly necessary for the final goal of applying this resource in real QSD tasks. In this paper, we report the first experimental demonstration of contextual advantage in both MED and MCD for three mirror-symmetric states using interferometric quantum walk, which can be easily generalized to any figure-of-merit in QSD. Our experiment agrees well with the result of theoretical simulation, and also shows the great potentiality of leveraging this method to explore a simpler version for the witness of contextuality, as well as demonstrating quanutm advantage of various tasks that require QSD.Comment: 6 pages, 5 figure