Abstract: Methods, apparatus, systems, computing devices, computing entities, and/or the like for verifying the coordination of benefits information with an end-to-end automated process. First, one or more machine-learning models generate predictions for members who are likely to have insurance with another insurer. The members identified are processed through another one or more machine learning models that generate predictions for who the likely other insurers are. Each insurer is associated with an insurer record/profile that identifies one or more application programming interface templates. The API-based eligibility request templates can be automatically populated to generate eligibility API-based eligibility requests. And in turn, eligibility responses are received and used to update corresponding member profiles and process claims accordingly.

Abstract: An analytical closed form solution to mean and variance in heat flow is obtained by solving the stochastic heat conduction equation incorporating randomness in the thermal conductivity. The method has a wide range of applications in quantifying the thermal state of the crust and in obtaining closed form expressions for subsurface heat flow structure along with its error bounds. The exact formulae employed can be used to better evaluate the thermal state for related oil and natural gas applications and also in tectonic studies and in studies related to the crystallization of minerals.

Abstract: Analytical solutions to error bounds on the temperature depth distribution have been given in this invention. Solving the one dimensional steady state heat conduction equation for different sets of boundary conditions and radiogenic heat generation and incorporating Gaussian randomness in the thermal conductivity analytical closed form solutions to the mean and variance in the temperature depth distribution have been obtained. These closed form analytical solutions of mean and variance for the temperature field for different conditions have been used to compute and display the plot and results of the temperature depth profiles along with its error bounds. Quantifying the error statistics in the system output due to errors in the system input is very essential for a better evaluation of the system behavior. Earth Scientists involved in understanding the subsurface thermal structure relevant to geodynamical studies will benefit using these findings.

Abstract: The present invention relates to obtaining the analytical closed form solution to mean and variance in heat flow by solving the stochastic heat conduction equation incorporating randomness in the thermal conductivity. The method of the present invention has a wide range of applications in quantifying the thermal State of the crust and in obtaining closed form expressions for subsurface heat flow structure along with its error bounds. The exact formulae used in the invention can be used to better evaluate the thermal state for related oil and natural gas applications and also in tectonic studies and in studies related to the crystallization of minerals.

Abstract: Analytical solutions to error bounds on the temperature depth distribution have been given in this invention. Solving the one dimensional steady state heat conduction equation for different sets of boundary conditions and radiogenic heat generation and incorporating Gaussian randomness in the thermal conductivity analytical closed form solutions to the mean and variance in the temperature depth distribution have been obtained. These closed form analytical solutions of mean and variance for the temperature field for different conditions have been used to compute and display the plot and results of the temperature depth profiles along with its error bounds. Quantifying the error statistics in the system output due to errors in the system input is very essential for a better evaluation of the system behavior. Earth Scientists involved in understanding the subsurface thermal structure relevant to geodynamical studies will benefit using these findings.