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Multifractal scaling behavior of long‐term records of daily runoff time series in 32 subwatersheds covering a wide range of sizes was examined. These subwatersheds were associated with four agricultural watersheds with different climates and topography. The empirical moment scaling curves obtained using the trace moment method showed that the runoff time series exhibited a multifractal behavior, which was valid over a time scale range from one day to about three years. The multi‐fractal scaling of the runoff time series was well described by the Universal Multifractal Model. The spectral analysis (β < 1) and the order of fractional integration (H ⋍; 0) indicated that the runoff time series were conservative. The multifractal parameters, α (multifractal index) and C1 (co‐dimension), were reasonably close to each other for subwatersheds within each of the watersheds and were generally similar among the four watersheds. The α values of the four watersheds were 1.10 ± 0.13, 1.61 ± 0.06,1.61 ± 0.24, and 1.63 ± 0.19. The C1 values of four watersheds were 0.19 ± 0.01, 0.17 ± 0.01, 0.17 ± 0.04, and 0.11 ± 0.02. The multifractal analyses provided useful insight into the runoff time series, especially the occurrence and distribution of extreme events.

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Many studies have incorporated various scale‐dependent dispersivity functions into the convection–dispersion equation (CDE). For a given function, there are different ways of specifying the dispersivity values in the discretized subdomains of a numerical solution. These ways would depend on how the function's time or space variable is built into the numerical scheme and on how the different ways may be interrelated. No study has addressed how these different ways may affect resulting breakthrough curves (BTCs) or their applicability to solute transport problems. In this study, five ways were specified and designated as local time, average time, apparent time, local distance, or apparent distance dependent dispersivity in the numerical scheme. The main objective was to demonstrate relationships among these ways by assuming that dispersion in the scale‐dependent CDE was quasi‐Fickian and implicitly based on an estimation of the first moment of the BTC at the given location. How these ways affected calculated BTCs was numerically tested using generalized linear and power scale–dependent dispersivity functions for a one‐dimensional problem with initial solute distribution represented as a Dirac delta function. For either type of function, differences were obvious in BTCs obtained for solute transport conditions with small apparent Peclet numbers using the alternative ways of specifying scale‐dependent dispersivity in the numerical scheme. The differences decreased with increasing apparent Peclet number. The numerical test results also showed that the derived relationships were not applicable for numerically calculating the spatial solute distribution at a given time. These test results were expected to be generally applicable because any other initial‐value solute transport problem can be solved as a superposition of this test problem.

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Objective At present, there is no consensus on the relationship between diabetic nephropathy (DN) and diabetic retinopathy (DR), and there is a lack of imaging data to prove the correlation between them. Therefore, we aimed to investigate the common risk factors for DN and DR in patients with type 2 diabetes and used Emission Computed Tomography(ECT) imaging technology and clinical test criteria to assess the correlation between DR and DN.Purpose The convolutional neural network was employed to observe and detect pathological changes in DR and DN images. And further analyze the correlation between DR and DN through clinical test data.Results In this study, we discovered that with the aggravation of DR, SCR, BUN and ACR gradually increased while GFR decreased. The incidence of DN in the non-DR, mild-NPDR, moderate-NPDR, severe-NPDR and PDR groups was 4.17%, 28.33%, 55%, 75.83% and 91.67%, respectively. Multivariate linear regression analysis showed that duration of T2D, smoking, HbA1c, TC, TG, HDL-c, LDL-c, UAlb, Scr, BUN, UAlb, ACR, GFR, ACR and GFR were independent risk factors for DR. Renal dynamic ECT imaging analysis demonstrated that with the aggravation of DR, renal blood flow perfusion gradually decreased, thus resulting in a decrease in renal filtration function. In T2D patients, DR and DN show a linear aggravation relationship, and hypercholesterolemia and renal dysfunction are common risk factors for DR and DN.Conclusion The convolutional neural network provides a more accurate, efficient and easier way to analyze DR and DN images. Early screening of the renal function index in DR patients using ECT imaging technology will help to identify and prevent DN as early as possible.

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