In this paper we present two unconditionally energy stable finite difference schemes for the Modified Phase Field Crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic Phase Field Crystal (PFC) model can be viewed as a special case. The first is a convex splitting scheme based on an appropriate decomposition of the discrete energy and is first orde...

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. In general, a large number of parameters are required to represent the Volterra kernels, although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions, such as the Kautz basis. Aiming at optimizing the poles that fully parameter...

Abstract We propose a categorical semantics of gradient-based machine learning algorithms in terms lenses, parametric maps, and reverse derivative categories. This foundation provides powerful explanatory unifying framework: it encompasses variety gradient descent such as ADAM, AdaGrad, Nesterov momentum, well loss functions MSE Softmax cross-entropy, shedding new light on their similarities di...

We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and noninvertible. We separate those properties which rely solely on algebraic structures from those that require some topological arguments, in order to lay a f...

We discsus Hinton’s (1989) relative payoff procedure (RPP), a static reinforcement learning algorithm whose foundation is not stochastic gradient ascent. We show circumstances under which applying the RPP is guaranteed to increase the mean return, even though it can make large changes in the values of the parameters. The proof is based on a mapping between the RPP and a form of the expectation-...

We discuss Hinton’s (1989) relative payoff procedure (RPP), a static reinforcement learning algorithm whose foundation is not stochastic gradient ascent. We show circumstances under which applying the RPP is guaranteed to increase the mean return, even though it can make large changes in the values of the parameters. The proof is based on a mapping between the RPP and a form of the expectation-...

A GREAT DEAL OF UNCERTAINTY exists regarding the effectiveness of safety incentive programs in construction. Most research on incentives involves case studies and theoretical analyses of their advantages and disadvantages. Using primary survey data from construction firms and craftworkers, this article examines the impact of incentives on the safety performance of U.S. construction firms. The s...

post failure analysis of massive structure infers that soil-structure interaction (ssi) is a crucial phenomena influencing seismic response of massive structures. cable-stayed bridge’s popularity and numbers are increasing now-a-days because of economical longer span & aesthetic good look. the current paper examines the effect of depth of foundation on seismic response of cable-stayed bridg...

In this study, the vibration behavior of functional graded (FG) circular and annular nanoplate embedded in a Visco-Pasternak foundation and coupled with temperature change is studied. The effect of in-plane pre-load and temperature change are investigated on the vibration frequencies of FG circular and annular nanoplate. To obtain the vibration frequencies of the FG circular and annular nanopla...