Ergodicity and Conservativity of products of infinite transformations and their inverses

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\times T$ of the transformation with itself is ergodic, but the product $T\times T^{-1}$ of the transformation with its inverse is not ergodic. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.Comment: Added references and revised some arguments; removed old section 6; main results unchange

The Far-reaching Impacts of Coastal Flooding on Non-Highway Car Accidents in the San Francisco Bay Area

A rising global sea level and intensifying coastal flood events increase the risks of disruption of traffic networks in low-lying, coastal communities. The inundation of major traffic corridors forces commuters onto alternate routes, thus creating travel time delays, and increasing the likelihood of traffic accidents. In this study, we build on our previous work of understanding flood impacts on the transportation system by quantifying the increase in non-highway car accident rates in the San Francisco Bay Area as a result of flood-related traffic disruption in the 2020-2040 period. We simulate traffic patterns by integrating an incremental traffic assignment model with coastal flood maps that represent extreme water levels resulting from multiple potential combinations of storm surges, tides, seasonal cycles, interannual anomalies driven by large-scale climate variability such as the El Niño Southern Oscillation, and sea level rise. We partition the region into subregions and develop quadratic regression models for each subregion that relate simulated traffic volumes to historical accident rates. Our results show that the increase in accident rates is spatially extensive, reaching far beyond the areas of flooding. As the water level rises, accident rates increase in the northern and eastern regions, but decrease in the peninsula region. In contrast with travel time delays, accident rates increase substantially at low water levels, but less so at higher water levels. Our work thus suggests that, for low intensity flood events, accidents are potentially a greater concern than delays for communities

Traffic accidents and delays present contrasting pictures of traffic resilience to coastal flooding in the San Francisco Bay Area

Climate change is intensifying coastal floods and increasing the risks of traffic disruption in low-lying, coastal communities. Efforts to understand the differential impacts of traffic disruption on communities have led to the concept of traffic resilience which captures the degree to which a traffic system can recover from disruption. Existing proxies of traffic resilience are focused on quantifying travel time delays but lack the important dimension of road safety. In this study, we quantify traffic resilience in terms of the change in non-highway car and pedestrian accident rates during the 5-10 am period as a result of coastal flooding in the San Francisco Bay Area for the 2020-2040 period. We use a regional traffic model to simulate traffic patterns under a range of coastal flood water levels. We use regressions that relate traffic volumes to historical accident rates to estimate accidents rates in the presence of flooding. Our results show that the flooding of highways forces commuters onto local roads passing through residential communities, causing a spike in accident rates. Unlike delays which increase sharply at the higher water levels considered in this study, we project that region-wide peak-hour accident rates may increase substantially at lower water levels

Flood-Induced Commute Disruption in the San Francisco Bay Area and Beyond

As sea levels rise, urban traffic networks in low-lying coastal areas face an increasing risk of flood disruption and commute delays. We hypothesize that road network connectivity rather than flood exposure governs commute delays. We integrate an existing traffic model with flood maps to identify inundated roads, simulate traffic patterns, and quantify commute delays. When identifying inundated roads, we demonstrate potential biases arising from the model integration and propose appropriate refinements, such as incorporating road geometry and elevation data, and identifying small-scale topographical features like road-creek crossings. Our results for the San Francisco Bay Area show commute delays propagate far inland, creating longer commute delays for inland communities with low road network connectivity than for communities near the flood zone. We show that metric reach, a measure of road network connectivity, is a better proxy for quantifying the resilience of a community to flood-related commute delays than flood exposure