Conditional mean dimension

We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an extension system. The conditional mean dimension for G-extensions is computed. We also exhibit some applications in dynamical embedding problems.

A Rainfall Erosivity database for Brazil from MSWEP rainfall dataset

<p>In erosion studies the behavior of rainfall is primordial, since rain is responsible for the first stage of the erosion process: the detachment of soil particles. The erosive potential of rainfall, erosivity, is considered in the universal soil loss equations (R)USLE family through the parameter R, or R factor. This factor is calculated from the rainfall erosivity index, which is the product of kinetic energy of the rain by the maximum intensity of the rain of 30 minutes of duration. As sub-hour rainfall data is not always available, there are in the literature a series of equations obtained from regression, which use monthly and annual rainfall and present a good estimate of erosivity for your study site. In Brazil, in addition to limitations regarding the temporal resolution of rainfall data, there are also spatial limitations. Monitoring stations are concentrated mostly in urbanized areas, usually near the coast. The other regions, such as agricultural and forest areas, are poorly monitored, and these areas are of great interest for monitoring erosion, not only because they are periodically exposed soil areas, but also because of the high rainfall rates that humid forests like Amazon have. MSWEP is a rainfall database that combines observed, satellite and reanalysis data. It has global coverage, temporal resolution of 3 hours, spatial 0.1º and data from 1979 to 2016. Databases like this have great potential to be used in areas such as Brazil, due to its spatial and temporal resolution. In this context, considering the relevance that the soil loss equations still present today, this work developed a rainfall erosivity database entitled REDB-BR (Rainfall Erosivity Database for Brazil). It provides the R factor in a 0.1º resolution grid, developed with 37 years of rainfall data from the MSWEP dataset. The R factor was calculated trough 73 erosivity index regression equations, which mostly uses the Modified Fournier Index (MFI), a relation between monthly precipitation and annual precipitation. Thiessen polygons were used in order to spatialize and define the areas of each equation. Over the Brazilian territory, the R factor ranges from 1.200 to 20.000 MJ mm ha-1 h-1 year-1, with the higher values in the North region, and the lowest values in the Northeast. The spatial patterns of erosivity are very similar to the climatic zones of Brazil. The R factor map takes advantage of MSWEP dataset and presents a spatial resolution very detailed to a country with continental scale such as Brazil. The database includes the equations shapefile and table, Thiessen Polygons shapefile and the R factor map in raster format, which allows more possibilities of application. The database can be accessed at <https://zenodo.org/record/4428308#.X_hxsOhKiUk>. We identified sudden changes in behavior between the delimited areas, which suggests a need for more regression equations in order to better represent the behavior of the erosivity in the Brazilian territory.</p>

Rainfall erosivity mapping over mainland China based on high density hourly rainfall records

Rainfall erosivity represents the effect of rainfall and runoff on the average rate of soil erosion. Maps of rainfall erosivity are indispensable for soil erosion assessment using the Universal Soil Loss Equation (USLE) and its successors. To improve current erosivity maps based on daily rainfall data for mainland China, hourly rainfall data from 2381 stations for the period 1951–2018 were collected to generate the R factor and the 1-in-10-year EI30 maps (available at https://dx.doi.org/10.12275/bnu.clicia.rainfallerosivity.CN.001; Yue et al., 2020). Rainfall data at 1-min intervals from 62 stations (18 stations) were collected to calculate rainfall erosivities as true values to evaluate the improvement of the new R factor map (1-in-10-year EI30 map) from the current maps. Both the R factor and 1-in-10-year EI30 decreased from the southeastern to the northwestern, ranging from 0 to 25300 MJ mm ha−1 h−1 a−1 for the R factor and 0 to 11246 MJ mm ha−1 h−1 for the 1-in-10-year EI30. New maps indicated current maps existed an underestimation for most of the southeastern areas and an overestimation for most of the middle and western areas. Comparing with the current maps, the R factor map generated in this study improved the accuracy from 19.4 % to 15.9 % in the mid-western and eastern regions, from 45.2 % to 21.6 % in the western region, and the 1-in-10-year EI30 map in the mid-western and eastern regions improved the accuracy from 21.7 % to 13.0 %. The improvement of the new R factor map can be mainly contributed to the increase of data resolution from daily data to hourly data, whereas that of new 1-in-10-year EI30 map to the increase of the number of stations from 744 to 2381. The effect of increasing the number of stations to improve the interpolation seems to be not very obvious when the station density was denser than about 10 · 103 km2 1 station.

Sensitivity for topologically double ergodic dynamical systems

<abstract><p>As a stronger form of multi-sensitivity, the notion of ergodic multi-sensitivity (resp. strongly ergodically multi-sensitivity) is introduced. In particularly, it is proved that every topologically double ergodic continuous selfmap (resp. topologically double strongly ergodic selfmap) on a compact metric space is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive). And for any given integer $ m\geq 2 $, $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ f^{m} $. Also, it is shown that if $ f $ is a continuous surjection, then $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ \sigma_{f} $, where $ \sigma_{f} $ is the shift selfmap on the inverse limit space $ \lim\limits_{\leftarrow}(X, f) $. Moreover, it is proved that if $ f:X\rightarrow X $ (resp. $ g:Y\rightarrow Y $) is a map on a nontrivial metric space $ (X, d) $ (resp. $ (Y, d') $), and $ \pi $ is a semiopen factor map between $ (X, f) $ and $ (Y, g) $, then the ergodic multi-sensitivity (resp. the strongly ergodic multi-sensitivity) of $ g $ implies the same property of $ f $.</p></abstract>

A stochastic optimal energy management strategy considering battery health for hybrid electric bus

The problem of battery health coupled with energy management brings a considerable challenge to the hybrid electric bus. To address this challenge, three contributions are made to realize optimal energy management control while prolonging battery life. First, a semi-empirical aging model of lithium iron phosphate battery is built and identified by the data fitting method, based on the battery cycling test. Besides, a severity factor map is constructed by employing the proposed aging model to characterize the relative aging of the battery under different operating conditions. Second, to make the driver demand torque more appropriate for statistical prediction, a Markov chain is formulated to predict driving behavior and also a stochastic vehicle mass estimation method is proposed to assist the prediction of required torque. Then, a stochastic multi-objective optimization problem is formulated by taking the severity factor map as a battery degradation criterion, where minimized battery degradation and fuel consumption can be simultaneously realized. Finally, a stochastic model predictive control strategy that considers battery health is established. Both simulation and hardware-in-loop tests are performed. The results demonstrate that fuel economy and battery degradation can be improved by 16.73% and 13.8% compared with rule-based strategy, respectively.

Suitability assessment for siting water harvesting ponds

This paper represents test results of methodology for identifying suitable sites for the water harvesting pondusing the "Multi-Criteria Analysis" in Geographical Information System. In order to do this, the objectives ofthe identification of harvesting sites were (i)to estimate constraint map (ii) to identify the multi-factor map and(iii) to measure the overall value of the suitability. According to the results of the assessment of the waterharvesting suitability, 10.23%or 173736 hectares area of Erdenetsagaan soum of Sukhbaatar aimag(province)are suitable, and 22.71% or 385534 ha area is moderately suitable, and 33.29%or 565198 ha land is limited forpond construction and 33.78% or 573532 ha territory is unsuitable for water harvesting.

The Category of Ordered Bratteli Diagrams

A category structure for ordered Bratteli diagrams is proposed in which isomorphism coincides with the notion of equivalence of Herman, Putnam, and Skau. It is shown that the natural one-to-one correspondence between the category of Cantor minimal systems and the category of simple properly ordered Bratteli diagrams is in fact an equivalence of categories. This gives a Bratteli–Vershik model for factor maps between Cantor minimal systems. We give a construction of factor maps between Cantor minimal systems in terms of suitable maps (called premorphisms) between the corresponding ordered Bratteli diagrams, and we show that every factor map between two Cantor minimal systems is obtained in this way. Moreover, solving a natural question, we are able to characterize Glasner and Weiss’s notion of weak orbit equivalence of Cantor minimal systems in terms of the corresponding C*-algebra crossed products.

Comparative analysis of the internal and external outlines of wings for an outline-based geometric morphometric approach to distinguish three Aedes mosquitoes (Diptera: Culicidae) in Thailand

Aedes mosquitoes belong to a subgenus of Stegomyia (Diptera: Culicidae), which are dengue and chigunkunya vectors, including Aedes aegypti, Ae. albopictus, and Ae. scutellaris, and have a worldwide distribution in tropical and subtropical regions. Species identification of mosquitoes is challenging yet necessary to select appropriate control methods for each species. In this study, we have analyzed the different wing components for identification to find the optimal outline for Aedes mosquito analysis by an outline-based GM approach. Two internal and external outlines of the wing were considered for Aedes species identification in this study. A total of 90 Aedes wings were analysed, divided into 30 wings per species (Ae. aegypti, Ae. albopictus, and Ae. scutellaris). The results showed that the mean size of Ae. albopictus had the largest wings, followed by Ae. Aegypti, and Ae. scutellaris, respectively, in all the internal and external outlines. While, the shape analysis in the three outlines were expressed by the factor map, the statistical difference and cross-validated classification scores indicated the ability of the outline-based GM approach to distinguish species of Aedes mosquitoes. The external outline has a relatively good range of cross-validated classification scores compared to the other internal outlines. The results of this research reveal the suitability of this external outline to identify species of Aedes vectors in Thailand.

On Structural Entropy and Spatial Filling Factor Analysis of Colonoscopy Pictures

Colonoscopy is the standard device for diagnosing colorectal cancer, which develops from little lesions on the bowel wall called polyps. The Rényi entropies-based structural entropy and spatial filling factor are two scale- and resolution-independent quantities that characterize the shape of a probability distribution with the help of characteristic curves of the structural entropy–spatial filling factor map. This alternative definition of structural entropy is easy to calculate, independent of the image resolution, and does not require the calculation of neighbor statistics, unlike the other graph-based structural entropies.The distant goal of this study was to help computer aided diagnosis in finding colorectal polyps by making the Rényi entropy based structural entropy more understood. The direct goal was to determine characteristic curves that can differentiate between polyps and other structure on the picture. After analyzing the distribution of colonoscopy picture color channels, the typical structures were modeled with simple geometrical functions and the structural entropy–spatial filling factor characteristic curves were determined for these model structures for various parameter sets. A colonoscopy image analying method, i.e., the line- or column-wise scanning of the picture, was also tested, with satisfactory matching of the characteristic curve and the image.