Gorenstein projective and injective dimensions over Frobenius extensions

Let $R\subset A$ be a Frobenius extension of rings. We prove that: (1) for any left $A$-module $M$, $_{A}M$ is Gorenstein projective (injective) if and only if the underlying left $R$-module $_{R}M$ is Gorenstein projective (injective). (2) if $\mathrm{G}\text{-}\mathrm{proj.dim}_{A}M<\infty$, then $\mathrm{G}\text{-}\mathrm{proj.dim}_{A}M = \mathrm{G}\text{-}\mathrm{proj.dim}_{R}M$, the dual for Gorenstein injective dimension also holds. (3) if the extension is split, then $\mathrm{G}\text{-}\mathrm{gldim}(A)= \mathrm{G}\text{-}\mathrm{gldim}(R)$.Comment: A corrigendum version of Comm. Algebra,46(12):5348-5354, 2018. A typo in Proposition 3.2 is fixed, and the assumption that the extension is split is added for Theorem 3.3, 3.4, and Corollary 3.5. arXiv admin note: text overlap with arXiv:1707.0588

Dynamic evolution of cross-correlations in the Chinese stock market

We study the dynamic evolution of cross-correlations in the Chinese stock market mainly based on the random matrix theory (RMT). The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different moving windows, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes

Genetically encoded fluorescent redox probes.

Redox processes are involved in almost every cell of the body as a consequence of aerobic life. In the past decades, redox biology has been increasingly recognized as one of the key themes in cell signaling. The progress has been accelerated by development of fluorescent probes that can monitor redox conditions and dynamics in cells and cell compartments. This short paper focuses on fluorescent redox probes that are genetically encoded, and discusses their properties, molecular mechanism, advantages and pitfalls. Our recent work on reaction-based encoded probes that are responsive to particular redox signaling molecules is also reviewed. Future challenges and directions are also commented