On the mixing properties of piecewise expanding maps under composition with permutations, II: Maps of non-constant orientation

For an integer $m \geq 2$, let $\mathcal{P}_m$ be the partition of the unit interval $I$ into $m$ equal subintervals, and let $\mathcal{F}_m$ be the class of piecewise linear maps on $I$ with constant slope $\pm m$ on each element of $\mathcal{P}_m$. We investigate the effect on mixing properties when $f \in \mathcal{F}_m$ is composed with the interval exchange map given by a permutation $\sigma \in S_N$ interchanging the $N$ subintervals of $\mathcal{P}_N$. This extends the work in a previous paper [N.P. Byott, M. Holland and Y. Zhang, DCDS, {\bf 33}, (2013) 3365--3390], where we considered only the "stretch-and-fold" map $f_{sf}(x)=mx \bmod 1$.Comment: 27 pages 6 figure

THE LINKAGE BETWEEN TRANSCRIPTION CONTROL AND EPIGENETIC REGULATION: THE SNAIL STORY AND BEYOND

Epigenetic deregulation contributes significantly to the development of multiple human diseases, including cancer. While great effort has been made to elucidate the underlying mechanism, our knowledge on epigenetic regulation is still fragmentary, an important gap being how the diverse epigenetic events coordinate to control gene transcription. In the first part of our study, we demonstrated an important link between Snail-mediated transcriptional control and epigenetic regulation during cancer development. Specifically, we found that the highly conserved SNAG domain of Snail sequentially and structurally mimics the N-terminal tail of histone H3, thereby functions as a molecular “hook”, or pseudo substrate, for recruiting histone lysine specific demethylase 1 (LSD1) repressor complex to the E-cadherin promoter. Furthermore, we showed that Snail and LSD1 are both required for E-cadherin repression and EMT induction, and their expression is highly correlated with each other in multiple human tumor tissues. Our findings have important clinical ramifications in that compounds mimicking the SNAG domain may disrupt Snail-LSD1 interaction and inhibit EMT and metastasis. In the second part of our study, we designed a batch of compounds based on the structure of the SNAG domain and are currently screening for candidates capable of competing with SNAG peptide for LSD1 binding. In addition, we applied a peptide pulldown/mass spectrometry-coupled analysis to identify SNAG-interacting proteins, among which are many chromatin enzymes and modulators. Functional characterization of these proteins will help to elucidate the Snail-mediated epigenetic regulation process. In the third part of our study, we found that Snail interacts with poly(ADP-ribose) polymerase 1 (PARP1) through a potential pADPr-binding motif and is subject to poly(ADP-ribosyl)ation, which can stabilize the Snail-LSD1 complex for enhanced PTEN suppression under DNA damage condition. Our findings added another layer to the delicate Snail transcriptional machinery, and indicated that PARP inhibitors may be applied in combination with conventional chemotherapies to target cancers with high expression of Snail and LSD1. In summary, we demonstrated that Snail cooperates with multiple epigenetic machineries to induce EMT as well as survival of tumor cells. Our findings contribute to a better appreciation of Snail-mediated epigenetic network as well as diversification of therapeutic strategies against cancer

Renormalization-group exponents for superconducting phases in two-leg ladders

In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the divergent logarithmic length $l_d$ and a set of renormalization-group exponents, also works rather well. The superconducting phases in a doped two-leg ladder are studied and classified by these renormalization-group exponents as demonstration. Finally, non-trivial constraints among the exponents are derived and explained.Comment: 4 pages, 3 figures; minor revisions with references adde

Experimental Demonstration of an Indoor VLC Positioning System Based on OFDMA

We propose an indoor visible light communication (VLC) and positioning system using the orthogonal frequency division multiplexing access (OFDMA) scheme, which can provide both indoor positioning and communications. Three subcarriers with the maximum received signal intensity with respect to three light-emitting diodes (LEDs) are selected for indoor positioning based on the trilateration algorithm. The experiment results show that the proposed system with quadrature phase shift keying (QPSK) mapping offers a mean positioning error and an error vector magnitude of 1.68 cm and more than 15 dB, respectively

Research on AR cultural and creative design of Yangming Culture under the background of the integration of culture and technology

The integration of science and technology and culture is a general trend in today’s society, which provides more ways for cultural exchange and interaction and promotes social development. This study analyzes the application value of AR technology in the design of cultural and creative products, and reconstructs the process of AR cultural and creative products through the double drill model, and designs Yangming cultural products based on AR technology. It can be seen from the research that AR technology is gradually integrated with culture, which can bring new breakthroughs in the transmission, preservation, creation and consumption of culture. This has played a better role in the dissemination and protection of other traditional Chinese culture and even intangible cultural heritage, further broadening the design space of cultural and creative products, and making new breakthroughs in the integration of science and technology and culture