Abstract: A solution to the optimal power flow (OPF) problem for electrical generation and distribution systems utilizes a re-configuration of the OPF problem that allows for a simplified analysis and resolution of a network-based OPF problem in a minimal number of iterations. The standard mixed integer quadratic problem (MIQP) definition is be reconfigured, using the chain rule, to a relatively compact linear system of six equations with six unknowns (the smallest reducible (atomic) problem). Advantageously, the reduction in the complexity of the problem does not require any assumptions and yields a solution equivalent to the original problem.

Abstract: A method of approximating a solution of a stochastic state estimation (SSE) model of an electric grid, includes choosing (70) starting anchor points in an SSE model of an electric grid, relaxing (71) constraints of an SSE objective function to solve for a feasible solution of the SSE model, calculating (72) updated dual variables and infeasibility reduction directions from the feasible solution, generating (73) a linear cut for the chosen starting anchor points, choosing (74) a step size toward the reduction directions, and updating (75) the anchor points through branching by making the chosen step, wherein each anchor point defines a rectangle that at least partially covers a feasible solution set of the SSE model and the set of rectangles covering the feasible solution set of the SSE model define an approximate solution of the SSE model of said electric grid.

Abstract: A method and system for generating a patient specific anatomical heart model is disclosed. Volumetric image data, such as computed tomography (CT), echocardiography, or magnetic resonance (MR) image data of a patient's cardiac region is received. Individual models for multiple heart components, such as the left ventricle (LV) endocardium, LV epicardium, right ventricle (RV), left atrium (LA), right atrium (RA), mitral valve, aortic valve, aorta, and pulmonary trunk, are estimated in said volumetric cardiac image data. A multi-component patient specific anatomical heart model is generated by integrating the individual models for each of the heart components. Fluid Structure Interaction (FSI) simulations are performed on the patient specific anatomical model, and patient specific clinical parameters are extracted based on the patient specific heart model and the FSI simulations. Disease progression modeling and risk stratification are performed based on the patient specific clinical parameters.

Abstract: A method for optimizing operational settings for a plurality of energy devices includes representing each of the plurality of energy devices in terms of a set of decision variables and operational parameters. The decision variables and operational parameters are constrained based on operational conditions and interrelationship within the plurality of energy devices. A two-tiered model of the plurality of energy devices is generated wherein a top tier of the model represents interaction of various sub-models and a bottom tier of the model includes a set of the sub-models that form the top tier, each sub-model representing detailed operation of the plurality of energy devices. The two-tiered model is optimized to provide either a schedule of operation for the plurality of energy devices or real-time control for the plurality of energy devices.

Abstract: A solution to the optimal power flow (OPF) problem for electrical generation and distribution systems utilizes a re-configuration of the OPF problem that allows for a simplified analysis and resolution of a network-based OPF problem in a minimal number of iterations. The standard mixed integer quadratic problem (MIQP) definition is be reconfigured, using the chain rule, to a relatively compact linear system of six equations with six unknowns (the smallest reducible (atomic) problem). Advantageously, the reduction in the complexity of the problem does not require any assumptions and yields a solution equivalent to the original problem.

Abstract: A method for optimizing operational settings for a plurality of energy devices includes representing each of the plurality of energy devices in terms of a set of decision variables and operational parameters. The decision variables and operational parameters are constrained based on operational conditions and interrelationship within the plurality of energy devices. A two-tiered model of the plurality of energy devices is generated wherein a top tier of the model represents interaction of various sub-models and a bottom tier of the model includes a set of the sub-models that form the top tier, each sub-model representing detailed operation of the plurality of energy devices. The two-tiered model is optimized to provide either a schedule of operation for the plurality of energy devices or real-time control for the plurality of energy devices.

Abstract: A method and system for generating a patient specific anatomical heart model is disclosed. Volumetric image data, such as computed tomography (CT), echocardiography, or magnetic resonance (MR) image data of a patient's cardiac region is received. Individual models for multiple heart components, such as the left ventricle (LV) endocardium, LV epicardium, right ventricle (RV), left atrium (LA), right atrium (RA), mitral valve, aortic valve, aorta, and pulmonary trunk, are estimated in said volumetric cardiac image data. A multi-component patient specific anatomical heart model is generated by integrating the individual models for each of the heart components. Fluid Structure Interaction (FSI) simulations are performed on the patient specific anatomical model, and patient specific clinical parameters are extracted based on the patient specific heart model and the FSI simulations. Disease progression modeling and risk stratification are performed based on the patient specific clinical parameters.