Hydrologic Similarity Based on Width Function and Hypsometry: An Unsupervised Learning Approach

In ungauged or data-scarce watersheds, systematic analyses of a set of proximate watersheds (for example, selected based on locational proximity or similarity in climate, morphometry, lithology, soils, and vegetation) have been shown to lend significant insights regarding hydrologic response and prediction. Current approaches often rely on: (a) statistical regression models that use measurable watershed attributes, such as area, slope, and stream length; and (b) comparative hydrology that considers watershed characteristics to assess hydrologic similarity to select analogous gauged watersheds as proxies. Newer conceptions regarding hydrologic similarity focus on hydrologic response and therefore emphasize the use of dynamical measures of the stream network and watershed terrain. For example, the width function and hypsometric curve can be readily estimated using the available global digital terrain datasets and represented as functional forms involving a small set of parameters, thus achieving significant data reduction. In this study, a new approach to hydrological similarity in watersheds, one that utilizes these functional forms to identify dynamically similar watersheds, is presented. Dissimilarity matrices are created based on divergence measures, and watersheds are classified using hierarchical clustering. The joint analysis of watershed width functions and hypsometric curves allows for the classification of watersheds into a reduced number of dynamically-similar groups. An illustrative case study for the Narmada River, with 72 sub-watersheds, is presented.

Medial Representation Based Font Recognition Method

In this article, a method of font recognition based on the medial representation, integrated into the font recognition system based on a digital image of text is described. This system searches for similar fonts, ordered by similarity, to the font shown in the user-entered text image. The system is based on solving two machine learning problems: text recognition on an image and font recognition on a text image. To solve the first problem, we use the concept of a mathematical model of a grapheme based on a continuous medial representation of a symbol. The solution to the font recognition problem is based on the concept of the morphological width of the figure, which is also closely related to the medial representation. We propose a method for using the morphological width function to find the most similar fonts from a known database. The experiments show high accuracy of searching for the most similar fonts. For a database consisting of 2543 fonts, the accuracy is 0.991 according to the metric top@5 for correctly recognized text in the font size of 100 pixels in the image.

Predictions for the FAST telescope’s CRAFTS extragalactic H i survey

ABSTRACT The Five-hundred-meter Aperture Spherical radio Telescope (FAST) has started the Commensal Radio Astronomy FasT Survey (CRAFTS). In this paper, we use the technical parameters of FAST derived from commissioning observations to simulate the completeness function for extragalactic H i survey of CRAFTS, H i galaxies from two kinds of mock catalogues are selected. One is generated by Monte Carlo simulation based on the interpolated mass–velocity width function of the ALFALFA $100{{\ \rm per\ cent}}$ (a.k.a. α.100) catalogue. The other is constructed by semi-analytical N-body simulation based on the ΛCDM model. Our results suggest that a two-pass CRAFTS extragalactic H i survey will be able to detect nearly 4.8 × 105 galaxies, from which the ‘faint end’ slope of the H i mass function (HIMF) can be recovered to $\mathrm{10^{7}\, M_{\odot }}$ and the ‘knee mass’ of the HIMF can be measured to a redshift of 0.1. Considering the radio frequency interference status and sensitivity limitation, CRAFTS will be efficient in detecting H i galaxies at redshifts below 0.1, which implies a tremendous potential in exploring the galaxy interactions in different environments and the spatial distribution of H i galaxies in the local universe.

The width of the solitary wave in dusty plasma

The Sagdeev potential method is employed to compute the width of the ion-acoustic solitary wave propagated in a dusty plasma containing three components (dust–ion–electron). The results indicate that the width is a continuous function over the allowable ranges of plasma parameters. The complexity of the resulting equations is an obstacle to the expression of the width function in an explicit form in terms of the parameters. Thus, computer algebra is needed to plot the graph of the width function versus the parameters, which helps us to understand the width changes as the parameters change.

Dynamic Characteristics of Electrostatically Actuated Shape Optimized Variable Geometry Microbeam

We mainly analyze the dynamic characteristics of electrostatically actuated shape optimized variable geometry microbeam. A nonlinear dynamic model considering midplane stretching, electrostatic force, and electrical field fringing effects is developed. Firstly, we study the static responses of the optimized microbeams under DC polarization voltage. The generalized differential quadrature method (GDQM) is used. Secondly, the dynamic responses of the shape optimized microbeams driven by DC and AC voltages are investigated using GDQM in conjunction with Levenberg-Marquardt optimization method. The results show that the more gradual change in width, the larger the resonant frequency and the maximum amplitude at resonance. Then we further discuss in detail how do the maximum width, midsection width, and curvature of the width function affect the frequency response of the microbeams. We find that the amplitude and resonant frequency of the dynamic response are not monotonically increasing as the curvature of the width function increases and there exists a critical curvature. This analysis will be helpful in the optimal design of MEMS actuators. Finally, for more consideration, different residual stress, squeeze-film damping, and fringing effect models are introduced into the governing equation of motion and we compare the corresponding dynamic response.

Prediction of direct runoff hydrographs utilizing stochastic network models: a case study in South Korea

In this study, we combine stochastic network models that reproduce the actual width function and the width function based instantaneous unit hydrograph (WFIUH) that directly makes use of a width function and converts it into runoff hydrographs. We evaluated the stochastic network models in terms of reproducing the actual width function and also the robustness of the semi-distributed model (WFIUH) in application to a test watershed in South Korea. The stochastic network model has an advantage that it replicates width functions of actual river networks, whereas the WFIUH has an advantage that the parameter values are physically determined, which can be potentially advantageous in prediction of ungauged basins. This study demonstrates that the combination of the Gibbsian model and the WFIUH is able to reproduce runoff hydrographs not just for the case of uniform rainfall over the test catchment but also for moving storms. Therefore, results of this study indicate that the impact of spatial and temporal rainfall variation on runoff hydrographs can be evaluated by the suggested approach in ungauged basins even without detailed knowledge of river networks. Once the regional similarity in river network configuration is identified, the proposed approach can be potentially utilized to estimate the runoff hydrographs for ungauged basins.

Grinding Hyperboloid Part by Bending Method

In view of the machining difficult problem of hyperboloid, a new method is presented that high speed lapping hyperboloid parts using the bended lapping tool, and the principle of high speed lapping by the bending method is discussed. The mathematical model of bended lapping tool has been established using mechanics and higher mathematics, and the expression of width function of lapping tool is deduced. Analysis of the calculating example indicated that this method is possible to design the needed lapping tool. The bending experiment of lapping tool has confirmed the feasibility using this method, the biggest error of face shape was 1.0038μm, the face shape precision can satisfy the majority part request.