scholarly journals A Two-Step Spectral Gradient Projection Method for System of Nonlinear Monotone Equations and Image Deblurring Problems

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 874 ◽  
Author(s):  
Aliyu Muhammed Awwal ◽  
Lin Wang ◽  
Poom Kumam ◽  
Hassan Mohammad
Keyword(s):  
Image Deblurring ◽  
Convergence Result ◽  
Convex Constraints ◽  
Spectral Parameters ◽  
Monotone Equations ◽  
Scalar Multiple ◽  
Separating Hyperplane ◽  
Step Algorithm ◽  
The One ◽  
Clustered Eigenvalues

In this paper, we propose a two-step iterative algorithm based on projection technique for solving system of monotone nonlinear equations with convex constraints. The proposed two-step algorithm uses two search directions which are defined using the well-known Barzilai and Borwein (BB) spectral parameters.The BB spectral parameters can be viewed as the approximations of Jacobians with scalar multiple of identity matrices. If the Jacobians are close to symmetric matrices with clustered eigenvalues then the BB parameters are expected to behave nicely. We present a new line search technique for generating the separating hyperplane projection step of Solodov and Svaiter (1998) that generalizes the one used in most of the existing literature. We establish the convergence result of the algorithm under some suitable assumptions. Preliminary numerical experiments demonstrate the efficiency and computational advantage of the algorithm over some existing algorithms designed for solving similar problems. Finally, we apply the proposed algorithm to solve image deblurring problem.

scholarly journals Homophily, heterophily and the diversity of messages among decision-making individuals

2018 ◽  
Vol 5 (4) ◽  
pp. 180027 ◽  
Author(s):  
Pouria Ramazi ◽  
James Riehl ◽  
Ming Cao
Keyword(s):  
Decision Making ◽  
Replicator Dynamics ◽  
Evolutionary Games ◽  
Cheap Talk ◽  
Convergence Result ◽  
Term Survival ◽  
Dominated Strategies ◽  
The Face ◽  
Cheap Talk Games ◽  
The One

To better understand the intriguing mechanisms behind cooperation among decision-making individuals, we study the simple yet appealing use of preplay communication or cheap talk in evolutionary games, when players are able to choose strategies based on whether an opponent sends the same message as they do. So when playing games, in addition to pure cooperation and defection, players have two new strategies in this setting: homophilic (respectively, heterophilic) cooperation which is to cooperate (respectively, defect) only with those who send the same message as they do. We reveal the intrinsic qualities of individuals playing the two strategies and show that under the replicator dynamics, homophilic cooperators engage in a battle of messages and will become dominated by whichever message is the most prevalent at the start, while populations of heterophilic cooperators exhibit a more harmonious behaviour, converging to a state of maximal diversity. Then we take Prisoner’s Dilemma (PD) as the base of the cheap-talk game and show that the hostility of heterophilics to individuals with similar messages leaves no possibility for pure cooperators to survive in a population of the two, whereas the one-message dominance of homophilics allows for pure cooperators with the same tag as the dominant homophilics to coexist in the population, demonstrating that homophilics are more cooperative than heterophilics. Finally, we generalize an existing convergence result on population shares associated with weakly dominated strategies to a broadly applicable theorem and complete previous research on PD games with preplay communication by proving that the frequencies of all types of cooperators, i.e. pure, homophilic and heterophilic, converge to zero in the face of defectors. This implies homophily and heterophily cannot facilitate the long-term survival of cooperation in this setting, which urges studying cheap-talk games under other reproduction dynamics.

scholarly journals On Peculiarities of Betatron Oscillations of Accelerated Electron Bunches in Capillary Waveguides

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mikhail Veysman
Keyword(s):  
Synchrotron Radiation ◽  
Parametric Excitation ◽  
Electron Bunch ◽  
Short Pulse ◽  
Spectral Parameters ◽  
Electron Bunches ◽  
Narrow Capillary ◽  
Parametric Resonances ◽  
Parametric Instabilities ◽  
The One

It is shown that the dynamics of electrons accelerated in narrow capillary waveguides is significantly influenced by the parametric excitation of their betatron oscillations. On the one hand, this excitation can irreversibly spoil the emittance of an accelerated electron bunch that limits the possibilities of their practical use. On the other hand, controlled parametric excitation of betatron oscillations can be used to generate short-pulse sources of synchrotron radiation. The article analyzes the regions of parametric instabilities, their dependence on the parameters of accelerated electron bunches and guiding structures, and their influence on the dynamics of accelerated electrons. The parameters of the generated synchrotron radiation are also estimated. Measurements of the spectral parameters of synchrotron radiation can serve as a tool for diagnostics of betatron oscillations and their excitation in the case of parametric resonances.

ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450007
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Lipschitz Condition ◽  
Riemannian Manifolds ◽  
Newton’S Method ◽  
Newton's Method ◽  
Geometric Model ◽  
Semilocal Convergence ◽  
Convergence Result ◽  
Numer Anal ◽  
The One

We present a semilocal convergence analysis of Newton's method for sections on Riemannian manifolds. Using the notion of a 2-piece L-average Lipschitz condition introduced in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] in combination with the weaker center 2-piece L1-average Lipschitz condition given by us in this paper, we provide a tighter convergence analysis than the one given in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] which in turn has improved the works in earlier studies such as [R. L. Adler, J. P. Dedieu, J. Y. Margulies, M. Martens and M. Shub, Newton's method on Riemannian manifolds and a geometric model for the human spine, IMA J. Numer. Anal.22 (2002) 359–390; F. Alvarez, J. Bolte and J. Munier, A unifying local convergence result for Newton's method in Riemannian manifolds, Found. Comput. Math.8 (2008) 197–226; J. P. Dedieu, P. Priouret and G. Malajovich, Newton's method on Riemannian manifolds: Covariant α-theory, IMA J. Numer. Anal.23 (2003) 395–419].

A four-node membrane element model with bending modification for one-step algorithm for bus rollover impact

2015 ◽  
Vol 32 (3) ◽  
pp. 607-620 ◽  
Author(s):  
Jingxin Na ◽  
Tong Wang ◽  
Changfeng Wu ◽  
Yakun Yan
Keyword(s):  
Engineering Application ◽  
Element Model ◽  
Bending Moments ◽  
Membrane Element ◽  
Computational Accuracy ◽  
Content Type ◽  
One Step ◽  
Internal Forces ◽  
Step Algorithm ◽  
The One

Purpose – The purpose of this paper is to propose a new four-node membrane element model with bending modification based on the equilibrium principle of element nodal internal forces and bending moments for the application of the one-step algorithm for bus rollover collision. And it can be concluded whether the proposed four-node membrane element model has practical value in engineering application or not. Design/methodology/approach – Based on the equilibrium principle of element nodal internal forces and bending moments, the paper puts forward a four-node membrane element model with bending modification. A case study on the rollover of a typical bus body section is carried out by using the one-step algorithm for bus rollover collision to verify the effectiveness of the proposed element model. Findings – For the simulation of bus rollover collision, the computational accuracy can be guaranteed, meanwhile, the calculated amount is much smaller than the shell element, and computational efficiency is improved significantly. Originality/value – The proposed four-node membrane element model is used for the simulation of bus rollover collision for the first time. It holds the advantage of high computational efficiency of membrane element, and the computational accuracy is improved as well. In conclusion, it has some practical value in engineering application.

ADAPTIVE AND DOUBLY-EXPEDITED ONE-STEP CONSENSUS IN BYZANTINE ASYNCHRONOUS SYSTEMS

2011 ◽  
Vol 21 (04) ◽  
pp. 461-477 ◽  
Author(s):  
NAZREEN BANU ◽  
TAISUKE IZUMI ◽  
KOICHI WADA
Keyword(s):  
Asynchronous Systems ◽  
Actual Number ◽  
Consensus Algorithms ◽  
One Step ◽  
Step Algorithm ◽  
The One

It is known that Byzantine consensus algorithms guarantee a one-step decision only in favorable situations, for instance when all processes propose the same value. Also, no one-step algorithm can support a two-step decision. In this paper, we present a novel generic one-step Byzantine algorithm, called DEX, that circumvents these impossibilities using the condition-based approach. Algorithm DEX has two distinguished features, adaptiveness and double-expedition property. Adaptiveness makes the algorithm sensitive only to the actual number of failures so that it provides fast termination for a large number of inputs when there are fewer failures (a common case in practice). The feature double-expedition property facilitates the two-step decision in addition to the one-step decision. To the best of our knowledge, the double-expedition property is a new concept introduced by this paper, and DEX is the first algorithm having such a feature. Besides, we show that our algorithm is optimal in terms of the number of processes for one-step consensus.

scholarly journals An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Gaohang Yu ◽  
Shanzhou Niu ◽  
Jianhua Ma ◽  
Yisheng Song
Keyword(s):  
Nonlinear Systems ◽  
Large Scale ◽  
Signal Reconstruction ◽  
Correction Method ◽  
Merit Function ◽  
Convergence Result ◽  
Image Deconvolution ◽  
Practical Applications ◽  
Monotone Equations ◽  
Adaptive Prediction

Combining multivariate spectral gradient method with projection scheme, this paper presents an adaptive prediction-correction method for solving large-scale nonlinear systems of monotone equations. The proposed method possesses some favorable properties: (1) it is progressive step by step, that is, the distance between iterates and the solution set is decreasing monotonically; (2) global convergence result is independent of the merit function and its Lipschitz continuity; (3) it is a derivative-free method and could be applied for solving large-scale nonsmooth equations due to its lower storage requirement. Preliminary numerical results show that the proposed method is very effective. Some practical applications of the proposed method are demonstrated and tested on sparse signal reconstruction, compressed sensing, and image deconvolution problems.

General Square Lattice Vertex Models

2019 ◽  
pp. 430-453
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Square Lattice ◽  
Vertex Model ◽  
Transfer Matrices ◽  
Spectral Parameters ◽  
Vertex Models ◽  
Integrable Quantum ◽  
Special Cases ◽  
Mechanical Models ◽  
The One ◽  
Ice Model

Vertex models more general than the ice model are possible and often have physical applications. The square lattice admits the general sixteen-vertex model of which the special cases, the eight- and the six-vertex model, are the most relevant and physically interesting, in particular through their connection to the one-dimensional integrable quantum mechanical models and the Bethe ansatz. This chapter introduces power- ful tools to examine vertex models, including the R- and L-matrices to encode the Boltzmann vertex weights and the monodromy and transfer matrices, which encode the integrability of the vertex models (i.e. that transfer matrices of different spectral parameters commute). This integrability is ultimately expressed in the Yang–Baxter relations.

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