Narrow Results

Backpropagation, which is frequently used in Neural Network training, often takes a great deal of time to converge on an acceptable solution. Momentum is a standard technique that is used to speed up convergence and maintain generalization performance. In this paper we present the Windowed Momentum algorithm, which increases speedup over Standard Momentum. Windowed Momentum is designed to use a fixed width history of recent weight updates for each connection in a neural network. By using this additional information, Windowed Momentum gives significant speedup over a set of applications with same or improved accuracy. Windowed Momentum achieved an average speedup of 32% in convergence time on 15 data sets, including a large OCR data set with over 500,000 samples. In addition to this speedup, we present the consequences of sample presentation order. We show that Windowed Momentum is able to overcome these effects that can occur with poor presentation order and still maintain its speedup advantages.

Recently, Byun and Lee [On weighted W^2,p estimates for elliptic equations with BMO coefficients in nondivergence form, Internat. J. Math.26 (2015), Article ID: 1550001, 28pp.] proved that

In this paper, group consensus of second-order multi-agent systems with nonlinear dynamics is investigated. First, we design the distributed protocols for achieving group consensus, in which the strengths of the interactions among the agents are enhanced through tuning the coupling strengths. Further, taking the difference of the edges among agents into account, edge-based distributed protocols through tuning coupling weights of a fraction of edges are designed. Remarkably, only the edges of spanning tree in each group are pinned and the coupling strengths or weights of pinned edges are enhanced according to the updated laws. Both the types of distributed protocols are proved analytically and verified by numerical illustrations.

In this paper, two new second-order voltage-mode universal filters are proposed. Both of the proposed filters use only two differential voltage current conveyors (DVCCs), four resistors and two grounded capacitors which are advantageous from integrated circuit technology point of view. They can simultaneously provide second-order low-pass, high-pass, band-pass, notch and all-pass responses. They offer orthogonal control of angular resonance frequency and quality factor. However, they have a single matching condition for only all-pass responses. A number of simulations based on SPICE program are accomplished in order to demonstrate the performance of both filters.

In this paper, a new second-order current-mode universal filter using only two plus-type differential voltage current conveyors, three resistors and two grounded capacitors is proposed. The proposed circuit with two identical inputs and three outputs can simultaneously provide second-order high output impedance low-pass, band-pass and notch filter responses. Also, it can realize high-pass and all-pass filter responses with interconnection of relevant output currents. It can be easily tuned electronically. It can be operated properly at high frequencies. A number of simulations based on SPICE program and an experimental test are achieved in order to demonstrate the performance of the proposed filter.

In this paper, a new voltage-mode (VM) multifunction filter including only two grounded capacitors, three resistors, and two current feedback operational amplifiers is introduced. This filter with one high input impedance and two low output impedances can simultaneously provide band-pass filter (BPF) and low-pass filter (LPF) responses with an adjustable gain. A universal VM filter topology with three inputs and one output generating high-pass filter (HPF), BPF, LPF, notch filter, and all-pass filter (APF) responses is obtained from the multifunction one. It has the same number of active and passive elements as the multifunction and a low output impedance. Sensitivities of both introduced filters are low enough. However, the APF of the introduced universal filter has a passive element-matching problem. As an example, parasitic impedance effects are considered for the LPF of the universal filter, while non-ideal gain analyses are given for the HPF. To see how the introduced universal filter works, countless simulations are performed through the SPICE (Simulation Program with Integrated Circuit Emphasis) program in which 0.13 $\mu$m IBM CMOS technology parameters are utilized. DC supply voltages are selected as ± 0.9 V. Also, several experiments using commercially available AD844s with ± 10 V supply voltages are carried out to see the performance.

How to develop efficient numerical schemes while preserving energy stability at the discrete level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper, we develop a set of first- and second-order temporal approximation schemes based on a novel “Invariant Energy Quadratization” approach, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to well-posed linear systems with a linear symmetric, positive definite at each time step. We prove that the developed schemes are unconditionally energy stable and present various 2D and 3D numerical simulations to demonstrate the stability and the accuracy of the schemes.

In this paper, we establish a new hydrodynamically coupled phase-field model for three immiscible fluid components system. The model consists of the Navier–Stokes equations and three coupled nonlinear Allen–Cahn type equations, to which we add nonlocal type Lagrange multipliers to conserve the volume of each phase accurately. To solve the model, a linear and energy stable time-marching method is constructed by combining the stabilized-Invariant Energy Quadratization (S-IEQ) approach and the projection method. The well-posedness of the scheme and its unconditional energy stability are rigorously proved. Several numerical simulations in 2D and 3D are carried out, including spinodal decomposition, dynamical deformations of a liquid lens and rising liquid drops, to validate the model and demonstrate the efficiency and energy stability of the proposed scheme, numerically.

In this paper, we introduce the definition of $(G,{\alpha }_f)$-bonvex/$(G,{\alpha }_f)$-pseudobonvex functions and to show the existence of such functions, we construct nontrivial numerical examples. In the next section, we formulate a pair of second-order symmetric dual model in optimization problem and proved the duality results under $(G,{\alpha }_f)$-bonvexity/$(G,{\alpha }_f)$-pseudobonvexity assumptions. Further, we also construct nontrivial concrete examples which justifying definitions as well as the weak duality theorem presented in the paper.

The main purpose of this work is to study the existence of solutions for a perturbed second-order evolution inclusion involving time-dependent subdifferential operators. Under suitable conditions on the set-valued perturbation, the main result of the paper is proved in the context of a separable Hilbert space. A second-order evolution quasi-variational inequality is also investigated.

We establish sufficient conditions for oscillation of second-order nonlinear impulsive differential equations by using the integral averaging technique. In particular, we extend Philos-type oscillation criteria to impulsive differential equations.