It is well known that for laminated composite plates a Levy-type solution exists only for cross-ply and antisymmetric angle-ply laminates. Numerous investigators have used the Levy method to solve the governing equations of various equivalent single-layer plate theories. It is the intension of the present study to introduce a method for analytical solutions of laminated composite plates with ar...

Abstract With the increased focus on quantum circuit learning for near-term applications devices, in conjunction with unique challenges presented by cost function landscapes of parametrized circuits, strategies effective training are becoming increasingly important. In order to ameliorate some these challenges, we investigate a layerwise strategy circuits. The depth is incrementally grown durin...

We propose a hierarchy of classes of functions that corresponds to the hierarchy of randomness notions. Each class of functions converges at the corresponding random points. We give various characterizations of the classes, that is, characterizations via integral tests, L-computability and layerwise computability. Furthermore, the relation among these classes is formulated using a version of So...

This work presents a new algorithm for training recurrent neural networks (although ideas are applicable to feedforward networks as well). The algorithm is derived from a theory in nonconvex optimization related to the diffusion equation. The contributions made in this work are two fold. First, we show how some seemingly disconnected mechanisms used in deep learning such as smart initialization...

We present experimental results on dense corn-starch suspensions as examples of non-Brownian, nearly hard particles that undergo continuous and discontinuous shear thickening (DST) at intermediate and high densities, respectively. Our results offer strong support for recent theories involving a stress-dependent effective contact friction among particles. We show, however, that in the DST regime...

For Markov chain Monte Carlo methods, one of the greatest discrepancies between theory and system is the scan order — while most theoretical development on the mixing time analysis deals with random updates, real-world systems are implemented with systematic scans. We bridge this gap for models that exhibit a bipartite structure, including, most notably, the Restricted/Deep Boltzmann Machine. T...

Article history: Available online 6 February 2010

Abstract In this paper, a beam theory for predicting limit point buckling and bifurcation of shallow arches composed two layers flexibly bonded is presented. The flexibility layer bond results in interlayer slip, which significantly affects the critical transverse loads. presented based on layerwise assumption Euler–Bernoulli linear behavior interlayer. After establishing equilibrium equations ...

   The main purpose of the present investigation is to analyze more comprehensively the size-dependent nonlinear free vibration response of multilayer functionally graded graphene platelet-reinforced composite (GPLRC) nanobeams. As a consequence, both of the hardening stiffness and softening stiffness of size effect are taken into consideration by implementation of the nonlocal str...