The mean exit time escaping basin of attraction in the presence white noise is practical importance various scientific fields. In this work, we propose a strategy to control general stochastic dynamical systems achieve desired value based on quasipotential concept and machine learning. Specifically, develop neural network architecture compute global function. Then design systematic iterated num...

Abstract We propose a method to carry out an inequality assessment in dynamic and cross-sectional framework, by applying the version of suitable index, such as Gini coefficient, function time. use our methodology setup where optimal value functions is individuals’ income flows while initial conditions characterize their level wealth. When Hamilton–Jacobi–Bellman system equations can be solved c...

We present a consistent and comprehensive treatise on the foundations of the extended HamiltonLagrange formalism—where the dynamical system is parameterized along a general system evolution parameter s, and the time t is treated as a dependent variable t(s) on equal footing with all other configuration space variables q(s). In the action principle, the conventional classical action L dt is then...

We analyze a mean-field game model proposed by economists R.E. Lucas and B. Moll (2014) to describe economic systems where production is based on knowledge growth diffusion. This reduces PDE system backward Hamilton-Jacobi-Bellman equation coupled with forward KPP-type nonlocal reaction term. study the existence of traveling waves for this system, obtaining both critical supercritical waves. In...

 Background: Frozen shoulder is resulting in limb disability and reduction of quality of life but the factors associated with patients’ disability and quality of life is not clear. To assess pain, disability, the quality of life and factors associated with them in patients suffering from frozen shoulder.  Methods: We enrolled 120 patients (37 men and 83 women) with phase-II idiopathic frozen sh...

In this paper we present a volumetric approach for quantitatively studying white matter connectivity from diffusion tensor magnetic resonance imaging (DT-MRI). The proposed method is based on a minimization of path cost between two regions, defined as the integral of local costs that are derived from the full tensor data along the path. We solve the minimal path problem using a Hamilton-Jacobi ...

Hamilton

We consider an optimal feedback control approach for multiple nonholonomic vehicles to achieve a distance-based formation with their neighbors using only local observations. Beginning with a non-optimal feedback control for collision-free flocking, each agent determines an additive correction term to its nonoptimal control from an elliptic Hamilton-Jacobi-Bellman equation so that its actions ar...