Equilibrium states of the pressure function for products of matrices

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to \R$ be the pressure function of $\{M_i\}_{i=1}^\ell$. We show that for each $q>0$, there are at most $d$ ergodic $q$-equilibrium states of $P$, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

The Return of the Repressed: three examples of how Chinese identity is being reconsolidated for the modern world

After setting the scene for an examination of the changes in culture and self-perception in China today, the authors explore three areas of activity which can be interpreted as illustrating these changes: (1) the current treatment of Confucius, as compared to the recent past; (2) the enthusiasm for the Chinese canon, which has developed from a grassroots movement into government policy; and (3) the way in which the presentation and content of public slogans have changed to, apparently, reflect the substitution of Communist nostrums for Confucian mores. In the first and second cases, the authors suggest that the authorities are acceding to the aspirations and prejudices of the people; rather than leading, they are following, and this has the effect of reinforcing the trend. The third—the gradual abandonment of the use of Marxist shibboleths in propaganda, and their replacement by Confucian adages—is not yet an established fact but, again, the trend is evident. China has revised and modernised its traditional culture and the first fruits of that can be seen in the words and behaviour of its political and intellectual leaders

Binscatter Regressions

We introduce the \texttt{Stata} (and \texttt{R}) package \textsf{Binsreg}, which implements the binscatter methods developed in \citet*{Cattaneo-Crump-Farrell-Feng_2019_Binscatter}. The package includes the commands \texttt{binsreg}, \texttt{binsregtest}, and \texttt{binsregselect}. The first command (\texttt{binsreg}) implements binscatter for the regression function and its derivatives, offering several point estimation, confidence intervals and confidence bands procedures, with particular focus on constructing binned scatter plots. The second command (\texttt{binsregtest}) implements hypothesis testing procedures for parametric specification and for nonparametric shape restrictions of the unknown regression function. Finally, the third command (\texttt{binsregselect}) implements data-driven number of bins selectors for binscatter implementation using either quantile-spaced or evenly-spaced binning/partitioning. All the commands allow for covariate adjustment, smoothness restrictions, weighting and clustering, among other features. A companion \texttt{R} package with the same capabilities is also available