Linear maps on nonnegative symmetric matrices preserving a given independence number

The independence number of a square matrix $A$, denoted by $\alpha(A)$, is the maximum order of its principal zero submatrices. Let $S_n^{+}$ be the set of $n\times n$ nonnegative symmetric matrices with zero trace, and let $J_n$ be the $n\times n$ matrix with all entries equal to one. Given any integers $n,t$ with $2\le t\le n-1$, we prove that a linear map $\phi: S_n^+\rightarrow S_n^+$ satisfies $\phi(J_n-I_n)=J_n-I_n$ and $$\alpha(\phi(X))=t~\iff \alpha(X)=t {~~~~\rm for~ all~}X\in S_n^+$$ if and only if there is a permutation matrix $P$ such that $$\phi(X)=P^TXP{~~~~\rm for~ all~}X\in S_n^+.$

Auroral event detection using spatiotemporal statistics of local motion vectors

The analysis and exploration of auroral dynamics are very significant for studying auroral mechanisms. This paper proposes a method based on auroral dynamic processes for detecting auroral events automatically. We first obtained the motion fields using the multiscale fluid flow estimator. Then, the auroral video frame sequence was represented by the spatiotemporal statistics of local motion vectors. Finally, automatic auroral event detection was achieved. The experimental results show that our methods could detect the required auroral events effectively and accurately, and that the detections were independent on any specific auroral event. The proposed method makes it feasible to statistically analyze a large number of continuous observations based on the auroral dynamic process

The impact of different sentiment in investment decisions: evidence from China’s stock markets IPOs

In this study, we used data on China’s initial public offerings (IPOs), market volatility and macro environment before and after two stock crashes during 2006–2016 to investigate how different investor sentiment affects IPO first-day flipping. The empirical results show that the expected returns of allocated investors are affected by sentiment, with allocated investors having higher psychological expectations of future returns during an optimistic bull market and their optimism discouraging first-day flipping, while higher risk-free interest rate levels and rising broad market indices also discourage first-day flipping and tend to sell in the future. The pessimistic bear market during which allocated investors have lower psychological expectations of future returns, their pessimism will promote first-day flipping, and the increase in the risk-free rate level will also promote first-day flipping, which is the opposite of the optimistic bull market, indicating that their risk aversion has increased and they tend to sell on the same day. We also found an anomaly that the greater the decline in the broad market index during a pessimistic bear market, the more inclined the allocated investors are to sell in the future when the broad market index rises in an attempt to gain higher returns. These findings help explain and understand the impact of market and macro index fluctuations on investor behavior under different investor sentiments

A case study based on ground observations of the conjugate ionospheric response to interplanetary shock in polar regions

Data acquired by imaging relative ionospheric opacity meters (riometers), ionospheric total electron content (TEC) monitors, and three-wavelength auroral imagers at the conjugate Zhongshan station (ZHS) in Antarctica and Yellow River station (YRS) in the Arctic were analyzed to investigate the response of the polar ionosphere to an interplanetary shock event induced by solar flare activity on July 12, 2012. After the arrival of the interplanetary shock wave at the magnetosphere at approximately 18:10 UT, significantly enhanced auroral activity was observed by the auroral imagers at the ZHS. Additionally, the polar conjugate observation stations in both hemispheres recorded notable evolution in the two-dimensional movement of cosmic noise absorption. Comparison of the ionospheric TEC data acquired by the conjugate pair showed that the TEC at both sites increased considerably after the interplanetary shock wave arrived, although the two stations featured different sunlight conditions (polar night in July in the Antarctic region and polar day in the Arctic region). However, the high-frequency (HF) coherent radar data demonstrated that different sources might be responsible for the electron density enhancement in the ionosphere. During the Arctic polar day period in July, the increased electron density over YRS might have been caused by anti-sunward convection of the plasma irregularity, whereas in Antarctica during the polar night, the increased electron density over ZHS might have been caused by energetic particle precipitation from the magnetotail. These different physical processes might be responsible for the different responses of the ionosphere at the two conjugate stations in response to the same interplanetary shock event