The structure of gauge-invariant ideals of labelled graph C∗C^*-algebras

In this paper, we consider the gauge-invariant ideal structure of a $C^*$-algebra $C^*(E,\mathcal{L},\mathcal{B})$ associated to a set-finite, receiver set-finite and weakly left-resolving labelled space $(E,\mathcal{L},\mathcal{B})$, where $\mathcal{L}$ is a labelling map assigning an alphabet to each edge of the directed graph $E$ with no sinks. Under the assumption that an accommodating set $\mathcal{B}$ is closed under taking relative complement, it is obtained that there is a one to one correspondence between the set of all hereditary saturated subsets of $\mathcal{B}$ and the gauge-invariant ideals of $C^*(E,\mathcal{L},\mathcal{B})$. For this, we introduce a quotient labelled space $(E,\mathcal{L},[\mathcal{B}]_R)$ arising from an equivalence relation $\sim_R$ on $\mathcal{B}$ and show the existence of the $C^*$-algebra $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ generated by a universal representation of $(E,\mathcal{L},[\mathcal{B}]_R)$. Also the gauge-invariant uniqueness theorem for $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ is obtained. For simple labelled graph $C^*$-algebras $C^*(E,\mathcal{L},\bar{\mathcal{E}})$, where $\bar{\mathcal{E}}$ is the smallest accommodating set containing all the generalized vertices, it is observed that if for each vertex $v$ of $E$, a generalized vertex $[v]_l$ is finite for some $l$, then $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ is simple if and only if $(E,\mathcal{L},\bar{\mathcal{E}})$ is strongly cofinal and disagreeable. This is done by examining the merged labelled graph $(F,\mathcal{L}_F)$ of $(E,\mathcal{L})$ and the common properties that $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ and $C^*(F,\mathcal{L},\bar{\mathcal{F}})$ share

Influence of prediction approaches for spatially-dependent air pollution exposure on health effect estimation

Background: Air pollution studies increasingly estimate individual-level exposures from area-based measurements by using exposure prediction methods such as nearest monitor and kriging predictions. However, little is known about the properties of these methods for health effects estimation. This simulation study explores how two common prediction approaches for fine particulate matter (PM2.5) affect relative risk estimates for cardiovascular events in a single geographic area. Methods: We estimated two sets of parameters to define correlation structures from 2002 PM2.5 data in the Los Angeles (LA) area and selected additional parameters to evaluate different correlation features. For each structure, annual average PM2.5 was generated at 22 existing monitoring sites and 2,000 pre-selected individual locations in LA. Associated survival time until cardiovascular event was simulated for 10,000 hypothetical subjects. Using PM2.5 generated at monitoring sites, we predicted PM2.5 at subject locations by nearest monitor and kriging interpolation. Finally, relative risks (RRs) of the effect of PM2.5 on time to cardiovascular event were estimated. Results: Health effect estimates for cardiovascular events had higher or similar coverage probability for kriging compared to nearest monitor exposures. The lower mean square error of nearest monitor prediction resulted from more precise but biased health effect estimates. The difference between these approaches dramatically moderated when spatial correlation increased and geographical characteristics were included in the mean model. Conclusions: When the underlying exposure distribution has a large amount of spatial dependence, both kriging and nearest monitor predictions gave good health effect estimates. For exposure with little spatial dependence, kriging exposure was preferable but gave very uncertain estimates

The Private Housing Market Cyclical Price Dynamics

Two types of heterogeneous investors (momentum and disposition) form a unique difference model to interpret housing price dynamics. Three parameters are crucial: auto-correlation, the rate of mean reversion and the contemporaneous adjustment towards long-term equilibrium price. For Singapore, we examine the dynamic structures that oscillate and/or diverge from equilibrium. Disposition investors predominate although the interaction between momentum and disposition investors acts as a key determinant of private housing price dynamics for a given time in a specific market. Key implication is that Singapore’s private housing market is low risk, offering stable returns owing to virtually no divergence even in the speculative 1990s. The best way to invest is to consider the momentum strategy and avoid the herd behavior for profit sustainability. For policy-makers, the Singapore private housing market is over-damped in the long run. Predominating disposition investors contribute to the market mechanism, which automatically adjusts private housing market prices. It is imperative to relax government intervention in Singapore’s private housing market to enhance its efficiency