The mixed Tate property of reductive groups

This thesis is concerned with the mixed Tate property of reductive algebraic groups $G$, which in particular guarantees a Chow Kunneth property for the classifying space $BG$. Toward this goal, we first refine the construction of the compactly supported motive of a quotient stack. In the first section, we construct the compactly supported motive $M^c(X)$ of an algebraic space $X$ and demonstrate that it satisfies expected properties, following closely Voevodsky's work in the case of schemes. In the second section, we construct a functorial version of Totaro's definition of the compactly supported motive $M^c([X/G])$ for any quotient stack $[X/G]$ where $X$ is an algebraic space and $G$ is an affine group scheme acting on it. A consequence of functoriality is a localization triangle for these motives. In the third section, we study the mixed Tate property for the classical groups as well as the exceptional group $G_2$. For these groups, we demonstrate that all split forms satisfy the mixed Tate property, while exhibiting non-split forms that do not. Finally, we prove that for any affine group scheme $G$ and normal split unipotent subgroup $J$ of $G$, the motives $M^c(BG)$ and $M^c(B(G/J))$ are isomorphic.Comment: The author's doctoral thesi

Contextual Centrality: Going Beyond Network Structures

Centrality is a fundamental network property which ranks nodes by their structural importance. However, structural importance may not suffice to predict successful diffusions in a wide range of applications, such as word-of-mouth marketing and political campaigns. In particular, nodes with high structural importance may contribute negatively to the objective of the diffusion. To address this problem, we propose contextual centrality, which integrates structural positions, the diffusion process, and, most importantly, nodal contributions to the objective of the diffusion. We perform an empirical analysis of the adoption of microfinance in Indian villages and weather insurance in Chinese villages. Results show that contextual centrality of the first-informed individuals has higher predictive power towards the eventual adoption outcomes than other standard centrality measures. Interestingly, when the product of diffusion rate $p$ and the largest eigenvalue $\lambda_1$ is larger than one and diffusion period is long, contextual centrality linearly scales with eigenvector centrality. This approximation reveals that contextual centrality identifies scenarios where a higher diffusion rate of individuals may negatively influence the cascade payoff. Further simulations on the synthetic and real-world networks show that contextual centrality has the advantage of selecting an individual whose local neighborhood generates a high cascade payoff when $p \lambda_1 < 1$. Under this condition, stronger homophily leads to higher cascade payoff. Our results suggest that contextual centrality captures more complicated dynamics on networks and has significant implications for applications, such as information diffusion, viral marketing, and political campaigns

Contextual Centrality: Going Beyond Network Structures

Centrality is a fundamental network property which ranks nodes by their structural importance. However, structural importance may not suffice to predict successful diffusions in a wide range of applications, such as word-of-mouth marketing and political campaigns. In particular, nodes with high structural importance may contribute negatively to the objective of the diffusion. To address this problem, we propose contextual centrality, which integrates structural positions, the diffusion process, and, most importantly, nodal contributions to the objective of the diffusion. We perform an empirical analysis of the adoption of microfinance in Indian villages and weather insurance in Chinese villages. Results show that contextual centrality of the first-informed individuals has higher predictive power towards the eventual adoption outcomes than other standard centrality measures. Interestingly, when the product of diffusion rate $p$ and the largest eigenvalue $\lambda_1$ is larger than one and diffusion period is long, contextual centrality linearly scales with eigenvector centrality. This approximation reveals that contextual centrality identifies scenarios where a higher diffusion rate of individuals may negatively influence the cascade payoff. Further simulations on the synthetic and real-world networks show that contextual centrality has the advantage of selecting an individual whose local neighborhood generates a high cascade payoff when $p \lambda_1 < 1$. Under this condition, stronger homophily leads to higher cascade payoff. Our results suggest that contextual centrality captures more complicated dynamics on networks and has significant implications for applications, such as information diffusion, viral marketing, and political campaigns

Contextual centrality: going beyond network structure

Centrality is a fundamental network property that ranks nodes by their structural importance. However, the network structure alone may not predict successful diffusion in many applications, such as viral marketing and political campaigns. We propose contextual centrality, which integrates structural positions, the diffusion process, and, most importantly, relevant node characteristics. It nicely generalizes and relates to standard centrality measures. We test the effectiveness of contextual centrality in predicting the eventual outcomes in the adoption of microfinance and weather insurance. Our empirical analysis shows that the contextual centrality of first-informed individuals has higher predictive power than that of other standard centrality measures. Further simulations show that when the diffusion occurs locally, contextual centrality can identify nodes whose local neighborhoods contribute positively. When the diffusion occurs globally, contextual centrality signals whether diffusion may generate negative consequences. Contextual centrality captures more complicated dynamics on networks than traditional centrality measures and has significant implications for network-based interventions

Contextual centrality: going beyond network structure

© 2020, The Author(s). Centrality is a fundamental network property that ranks nodes by their structural importance. However, the network structure alone may not predict successful diffusion in many applications, such as viral marketing and political campaigns. We propose contextual centrality, which integrates structural positions, the diffusion process, and, most importantly, relevant node characteristics. It nicely generalizes and relates to standard centrality measures. We test the effectiveness of contextual centrality in predicting the eventual outcomes in the adoption of microfinance and weather insurance. Our empirical analysis shows that the contextual centrality of first-informed individuals has higher predictive power than that of other standard centrality measures. Further simulations show that when the diffusion occurs locally, contextual centrality can identify nodes whose local neighborhoods contribute positively. When the diffusion occurs globally, contextual centrality signals whether diffusion may generate negative consequences. Contextual centrality captures more complicated dynamics on networks than traditional centrality measures and has significant implications for network-based interventions