Univoque bases of real numbers: simply normal bases, irregular bases and multiple rationals

Given a positive integer $M$ and a real number $x\in(0,1]$, we call $q\in(1,M+1]$ a univoque simply normal base of $x$ if there exists a unique simply normal sequence $(d_i)\in\{0,1,\ldots,M\}^\mathbb N$ such that $x=\sum_{i=1}^\infty d_i q^{-i}$. Similarly, a base $q\in(1,M+1]$ is called a univoque irregular base of $x$ if there exists a unique sequence $(d_i)\in\{0,1,\ldots, M\}^\mathbb N$ such that $x=\sum_{i=1}^\infty d_i q^{-i}$ and the sequence $(d_i)$ has no digit frequency. Let $\mathcal U_{SN}(x)$ and $\mathcal U_{I_r}(x)$ be the sets of univoque simply normal bases and univoque irregular bases of $x$, respectively. In this paper we show that for any $x\in(0,1]$ both $\mathcal U_{SN}(x)$ and $\mathcal U_{I_r}(x)$ have full Hausdorff dimension. Furthermore, given finitely many rationals $x_1, x_2, \ldots, x_n\in(0,1]$ so that each $x_i$ has a finite expansion in base $M+1$, we show that there exists a full Hausdorff dimensional set of $q\in(1,M+1]$ such that each $x_i$ has a unique expansion in base $q$.Comment: 25 pages, 2 figure

Forging National Identity: Journey from Economic Struggles to Cultural Harmony

After gaining independence from colonial rule, faced a complex domestic situation. To avoid religious and cultural conflicts among its diverse ethnic groups, the government adopted a multicultural governance approach for multi-ethnic management, supplemented by a supranational identity governance strategy, which maintained social harmony and stability. In this process, the political system ensured a basic balance of power among ethnic groups, a pragmatic economic development model met the survival needs of various ethnicities, and a liberal cultural environment preserved the historical heritage of each group. However, harmonious Singapore still falls short of becoming a true nation-state. To achieve the goal of nation-building, the Singaporean government has begun to emphasize cultural identity and seeks to foster a sense of being "Singaporean." With English as the lingua franca, Singaporeans can communicate in a common language, the preservation of historical buildings retains a shared cultural memory, and efforts to promote "shared values" are gradually fostering national identity among citizens

Improving Person Re-identification by Attribute and Identity Learning

Person re-identification (re-ID) and attribute recognition share a common target at learning pedestrian descriptions. Their difference consists in the granularity. Most existing re-ID methods only take identity labels of pedestrians into consideration. However, we find the attributes, containing detailed local descriptions, are beneficial in allowing the re-ID model to learn more discriminative feature representations. In this paper, based on the complementarity of attribute labels and ID labels, we propose an attribute-person recognition (APR) network, a multi-task network which learns a re-ID embedding and at the same time predicts pedestrian attributes. We manually annotate attribute labels for two large-scale re-ID datasets, and systematically investigate how person re-ID and attribute recognition benefit from each other. In addition, we re-weight the attribute predictions considering the dependencies and correlations among the attributes. The experimental results on two large-scale re-ID benchmarks demonstrate that by learning a more discriminative representation, APR achieves competitive re-ID performance compared with the state-of-the-art methods. We use APR to speed up the retrieval process by ten times with a minor accuracy drop of 2.92% on Market-1501. Besides, we also apply APR on the attribute recognition task and demonstrate improvement over the baselines.Comment: Accepted to Pattern Recognition (PR

Paris polyphylla extract inhibits proliferation and promotes apoptosis in A549 lung cancer cells

Purpose: To investigate the effect of Paris polyphylla extract (PPE) on proliferation and apoptosis in A549 human lung cancer cells.Methods: Morphological changes were examined by microscopy in A549 cells after exposure to PPE. Trypan blue staining of living cells was used to aid the construction of the cell growth curve after treatment with different concentrations of PPE. The influence of PPE on cell proliferation, apoptosis and cell cycle were determined by MTT assay. Protein expressions of key apoptosis-related enzymes were determined by immuno-cytochemical method.Results: PPE inhibited the growth of A549 lung cancer cells at a concentration range of 12.5 – 200.0 μg/mL. Flow cytometry revealed that PPE promoted apoptosis in A549 cells. The proportion of cells in G0/G1-phase increased significantly (p < 0.01), while the proportion of cells in S- and G2/M-phases decreased correspondingly, indicating that the cells were in G0/G1-phase arrest. Cell cycle arrest and apoptosis-inducing effect gradually increased with increase in PPE concentration. With increasing concentration of PPE, there was significant increase in the expressions of caspase-8, caspase-3 and caspase-9, but significant decrease in Ki-67, p21ras protein (p < 0.01).Conclusion: PPE exerts pronounced inhibitory activity on the proliferation of A549 lung cancer cells. It also induces apoptosis in A549 cells, most probably by a mechanism related to Ki-67 and p21 ras protein expression, and arrest of cell cycle in G0/G1-phase.Keywords: Paris polyphylla, Antitumor activity, Lung cancer, A549 cells, p21 ras protein expression, Caspase, Cell cycle arrest, Apoptosi