Detecting Areas Vulnerable to Flooding Using Hydrological-Topographic Factors and Logistic Regression

As a result of rapid urbanization and population movement, flooding in urban areas has become one of the most common types of natural disaster, causing huge losses of both life and property. To mitigate and prevent the damage caused by the recent increase in floods, a number of measures are required, such as installing flood prevention facilities, or specially managing areas vulnerable to flooding. In this study, we presented a technique for determining areas susceptible to flooding using hydrological-topographic characteristics for the purpose of managing flood vulnerable areas. To begin, we collected digital topographic maps and stormwater drainage system data regarding the study area. Using the collected data, surface, locational, and resistant factors were analyzed. In addition, the maximum 1-h rainfall data were collected as an inducing factor and assigned to all grids through spatial interpolation. Next, a logistic regression analysis was performed by inputting hydrological-topographic factors and historical inundation trace maps for each grid as independent and dependent variables, respectively, through which a model for calculating the flood vulnerability of the study area was established. The performance of the model was evaluated by analyzing the receiver operating characteristics (ROC) curve of flood vulnerability and inundation trace maps, and it was found to be improved when the rainfall that changes according to flood events was also considered. The method presented in this study can be used not only to reasonably and efficiently select target sites for flood prevention facilities, but also to pre-detect areas vulnerable to flooding by using real-time rainfall forecasting.

Morita’s trace maps on the group of homology cobordisms

Morita introduced in 2008 a [Formula: see text]-cocycle on the group of homology cobordisms of surfaces with values in an infinite-dimensional vector space. His [Formula: see text]-cocycle contains all the “traces” of Johnson homomorphisms which he introduced 15 years earlier in his study of the mapping class group. In this paper, we propose a new version of Morita’s [Formula: see text]-cocycle based on a simple and explicit construction. Our [Formula: see text]-cocycle is proved to satisfy several fundamental properties, including a connection with the Magnus representation and the LMO homomorphism. As an application, we show that the rational abelianization of the group of homology cobordisms is non-trivial. Besides, we apply some of our algebraic methods to compare two natural filtrations on the automorphism group of a finitely-generated free group.