The Novikov conjecture and extensions of coarsely embeddable groups

Let $1 \to N \to G \to G/N \to 1$ be a short exact sequence of countable discrete groups and let $B$ be any $G$-$C^*$-algebra. In this paper, we show that the strong Novikov conjecture with coefficients in $B$ holds for such a group $G$ when the normal subgroup $N$ and the quotient group $G/N$ are coarsely embeddable into Hilbert spaces. As a result, the group $G$ satisfies the Novikov conjecture under the same hypothesis on $N$ and $G/N$.Comment: 40 page

The Novikov Conjecture and Extensions of Coarsely Embeddable Groups

This dissertation can be said to consider the Novikov conjecture for an extension of coarsely embeddable groups. The first part of the dissertation is about defining a $C^*$-algebra associated with an extension of coarsely embeddable groups. This $C^*$-algebra comes with an action of the extension group, and we explore the properties of this action. We then construct twisted Roe algebras and twisted localization algebras associated with the extension, and develop a framework to compute their $K$-theory. In the second part of this dissertation, we define and study the Bott map from the suspension of the localization algebra to the twisted localization algebra and the Bott map from the suspension of the Roe algebra to the twisted Roe algebra associated with the extension group. We show that the Bott map between localization algebras induces an isomorphism on $K$-theory. It follows that the strong Novikov conjecture with coefficients in any $C^*$-algebra holds for a group $G$ when a normal subgroup $N$ of $G$ and the quotient group $G/N$ are coarsely embeddable into Hilbert spaces. As a result, the group $G$ satisfies the Novikov conjecture under the same hypothesis on $N$ and $G/N$

The coarse Baum-Connes conjecture for certain extensions and relative expanders

Let $\left( 1\to N_n\to G_n\to Q_n\to 1 \right)_{n\in \mathbb{N}}$ be a sequence of extensions of finitely generated groups with uniformly finite generating subsets. We show that if the sequence $\left( N_n \right)_{n\in \mathbb{N}}$ with the induced metric from the word metrics of $\left( G_n \right)_{n\in \mathbb{N}}$ has property A, and the sequence $\left( Q_n \right)_{n\in \mathbb{N}}$ with the quotient metrics coarsely embeds into Hilbert space, then the coarse Baum-Connes conjecture holds for the sequence $\left( G_n \right)_{n\in \mathbb{N}}$, which may not admit a coarse embedding into Hilbert space. It follows that the coarse Baum-Connes conjecture holds for the relative expanders and group extensions exhibited by G. Arzhantseva and R. Tessera, and special box spaces of free groups discovered by T. Delabie and A. Khukhro, which do not coarsely embed into Hilbert space, yet do not contain a weakly embedded expander. This in particular solves an open problem raised by G. Arzhantseva and R. Tessera \cite{Arzhantseva-Tessera 2015}

Research Directions and Projects In an Institute of Developmental Psychology in China

We are a team who maintained to focus on 3 fields in people’s mental health recent years: marriage and family research and therapy, mental health of middle and primary school students, and internet addiction in youth. In every field, we focus on both fundamental research and clinical practice. We aim to explore mechanisms using survey, observation and cognitive neuroscience methods (fMRI), and develop prediction and intervention projects based on research, to improve people’s life and policies

Coarse embeddings at infinity and generalized expanders at infinity

We introduce a notion of coarse embedding at infinity into Hilbert space for metric spaces, which is a weakening of the notion of fibred coarse embedding and a far generalization of Gromov's concept of coarse embedding. It turns out that a residually finite group admits a coarse embedding into Hilbert space if and only if one (or equivalently, every) box space of the group admits a coarse embedding at infinity into Hilbert space. Moreover, we introduce a concept of generalized expander at infinity and show that it is an obstruction to coarse embeddability at infinity.Comment: 20 page

Orthogonal printing of uniform nanocomposite monolayer and oriented organic semiconductor crystals for high-performance nano-crystal floating gate memory

Inkjet printing is of great interest in the preparation of optoelectronic and microelectronic devices due to its low cost, low process temperature, versatile material compatibility, and ability to precisely manufacture multi-layer devices on demand. However, interlayer solvent erosion is a typical problem that limits the printing of organic semiconductor devices with multi-layer structures. In this study, we proposed a solution to address this erosion problem by designing polystyrene-block-poly(4-vinyl pyridine)-grafted Au nanoparticles (Au@PS-b-P4VP NPs). With a colloidal ink containing the Au@PS-b-P4VP NPs, we obtained a uniform monolayer of Au nano-crystal floating gates (NCFGs) embedded in the PS-b-P4VP tunneling dielectric (TD) layer using direct-ink-writing (DIW). Significantly, PS-b-P4VP has high erosion resistance against the semiconductor ink solvent, which enables multi-layer printing. An active layer of semiconductor crystals with high crystallinity and well-orientation was obtained by DIW. Moreover, we developed a strategy to improve the quality of the TD/semiconductor interface by introducing a polystyrene intermediate layer. We show that the NCFG memory devices exhibit a low threshold voltage (100 cycles), and long-term retention (>10 years). This study provides universal guidance for printing functional coatings and multi-layer devices

Ideology in the Era of Xi Jinping

Publisher Copyright: © 2018, The Author(s).After 1978, Maoism as a living mass ideological and social force in the People’s Republic of China largely died away. The Party state’s legitimacy since that time has been based on a new pillar of economic competence and the delivery of tangible economic gains. But China is still a place where, at least within the political elite, there is an identifiable ideology and associated language that links the aims of a political force, the Communist Party of China, with national prosperity, historic rejuvenation, and the delivery of the political goals promised when the Communist Party was founded almost a century ago – modernity in Chinese society. Ideology has not disappeared in this interpretation. It has just become more concealed, more nuanced, and in some spaces more flexible. For Chinese contemporary leaders, ideology is partly a body of practices, beliefs, and language which have been bequeathed to them by previous leaders, and which show that they are part of the same historic movement that runs from 1921 to 1949, and through 1978 until today. This body of practices is aimed at maintaining a sustainable system of one party rule, as well as an assertion of discipline and control in the core tactical spaces of political power. Under Xi, a group of twelve keywords maps out the discursive space that matters to the CPC today. These terms exemplify the ways in which the contemporary CPC is willing to use ideas from diverse sources, either from its own past, or from classical Chinese thinking, as a means of achieving emotional as well as intellectual impact, and to assist in the delivery of the major Party goal of the twenty-first century – the creation of a great nation with the CPC at the heart of its governance. Underlying the keywords and the ideological space they define is the larger notion of the Party, not just attending to material but also spiritual needs – and creating not just a wealthy country, but also a spiritual socialist civilization.publishersversionPeer reviewe

The association between dietary inflammatory index and cognitive function in adults with/without chronic kidney disease

Background and aimsCognitive impairment (CI) is a prevalent condition in patients with chronic kidney disease (CKD), who face an elevated risk of developing cognitive decline. The fundamental mechanism underlying CI is linked to chronic inflammation, which can be gauged by the Dietary Inflammatory Index (DII). The DII is categorized into anti-inflammatory diets with lower scores and pro-inflammatory diets with higher scores. Specifically, pro-inflammatory diets may contribute to chronic inflammation. However, the correlation between the inflammatory potential of diet and cognitive function in patients with CKD has not been explored. This study aims to investigate the connection between the inflammatory potential of diet and cognitive function in individuals with or without chronic kidney disease.MethodsData from the 2011–2012 and 2013–2014 National Health and Nutrition Examination Survey (NHANES) were utilized. Participants under the age of 60 or lacking DII, CI, CKD, and other essential data were excluded. DII was computed based on a 24-h dietary recall interview for each participant. Cognitive performance was evaluated using three cognitive tests: the Consortium to Establish a Registry for Alzheimer’s Disease (CERAD) test, the Animal Fluency Test (AFT), and the Digital Symbol Substitution Test (DSST). Logistic regression analysis and subgroup analysis were conducted to assess the independent relationship between DII score and CI in the CKD and non-CKD populations.ResultsThe study included a total of 2069 subjects, with CI prevalence ranging from 21.4 to 23.5%. Multiple regression models showed that after adjusting for all covariates of the three cognitive function tests, higher DII scores were significantly associated with increased risk of CI (CERAD OR = 1.18, 95% CI: 1.1 ~ 1.26, AFT OR = 1.15, 95% CI: 1.08 ~ 1.23, DSST OR = 1.19, 95% CI: 1.11 ~ 1.28). Subgroup analysis indicated that the effect of DII score on CI remained consistent in all subgroups (p > 0.05).ConclusionHigher DII scores were associated with an increased risk of cognitive impairment in people with or without CKD, suggesting that consuming a pro-inflammatory diet may contribute to the impairment of the cognitive function