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When rheological models of polymer blends are used for inverse modeling, they can characterize polymer mixtures from rheological observations. This requires repeated evaluation of potentially expensive rheological models. We explored surrogate models based on Gaussian processes (GP-SM) as a cheaper alternative for describing the rheology of polydisperse binary blends. We used the time-dependent diffusion double reptation (TDD-DR) model as the true model; it takes a 5-dimensional input vector specifying the binary blend as input and yields a function called the relaxation spectrum as output. We used the TDD-DR model to generate training data of different sizes $n=30-1600$, via Latin hypercube sampling. The optimal values of the GP-SM hyper-parameters, assuming a separable covariance kernel, were obtained by maximum likelihood estimation. The GP-SM interpolates the training data by design and offers reasonable predictions of relaxation spectra with uncertainty estimates. In general, the accuracy of GP-SMs improves as the size of the training data $n$ increases, as does the cost for training and prediction. The optimal hyper-parameters were found to be relatively insensitive to $n$. Finally, we considered the inverse problem of inferring the structure of the polymer blend from a synthetic dataset generated using the true model. Surprisingly, the solution to the inverse problem obtained using GP-SMs and TDD-DR was qualitatively similar. GP-SMs can be several orders of magnitude cheaper than expensive rheological models, which provides a proof-of-concept validation for using GP-SMs for inverse problems in polymer rheology.

We combine a theoretical model and a quantitative modeling chain based on a bio-economic model and a hydrological model in order to assess the marginal damage related to the nitrate concentration in an aquifer. The fundamental concept is to take the steady state level resulting from a social planner’s optimization program as the target level of nitrate concentration. The interest of doing this is three-fold: (i) we characterize the social value of damage related to the targeted nitrate concentration; which (ii) leads us to design the optimal path consistent with the target; and (iii) we can in turn assess welfare losses arising when the tax path deviates from the optimal one.

Signature authentication with static and dynamic features of signature has been studied for decades, in this paper a novel and new method based on estimating elasticity and viscoelasticity characteristics of the muscles and tendons of index finger of the right hand was presented and the angles between the finger knuckles were collected by data collection glove and the location of digital pen tip on sensitive pad is stored in computer too. With NMC model and writing required mathematical equations and inverse modeling, physiological characteristics of muscles and tendons of right hand were estimated by LMS criteria. This approach has been applied on 30 right-hand persons that of each individual 5 genuine signature and some ordinary forgers to counterfeit genuine signature only by seeing the shape of original signature. 93.4% forgery signatures could have been recognized from genuine and only 6.6% could not have been detected. For verification, we used 5-fold cross-validation, with mean of EER$=$ 3.57 and standard deviation of EER$=$ 0.736. Therefore, we identified the physiological viscoelasticity and elasticity of muscles and tendons of hand as a new biometric.

A novel hybrid model for predicting medium- to long-term morphodynamic responses of estuaries is developed using a hybrid approach between top-down and bottom-up models. The model is based on a two-dimensional diffusion formulation. Effects of non-diffusive processes on medium- to long-term estuary morphology are modeled by a source function in the governing equation. The source function is determined by solving an inverse problem using historical bathymetry data. The model is then applied to predict future evolution of morphology of the Humber Estuary, UK. Comparison of predicted morphologies with measured values shows that despite the simplified dynamics of the morphological processes used, the model provides encouraging predictions of future morphological changes of the Humber Estuary.