A Linear Spline Markov Approximation Method for Random Maps with Position Dependent Probabilities

2020 ◽  
Vol 30 (03) ◽  
pp. 2050046
Author(s):  
Congming Jin ◽  
Jiu Ding
Keyword(s):  
Theoretical Analysis ◽  
Approximation Method ◽  
Chaotic Maps ◽  
Type Inequality ◽  
Markov Operator ◽  
Markov Approximation ◽  
Random Maps ◽  
Linear Spline ◽  
Finite Approximation ◽  
Better Than

We present a rigorous convergence analysis of a linear spline Markov finite approximation method for computing stationary densities of random maps with position dependent probabilities, which consist of several chaotic maps. The whole analysis is based on a new Lasota–Yorke-type inequality for the Markov operator associated with the random map, which is better than the previous one in the literature and much simpler to obtain. We also present numerical results to support our theoretical analysis.

scholarly journals The Median Solution of the Newsvendor Problem and Some Observations

2015 ◽  
Vol 6 (3) ◽  
pp. 55-60
Author(s):  
Pritibhushan Sinha
Keyword(s):  
Standard Deviation ◽  
Theoretical Analysis ◽  
Numerical Experiment ◽  
Objective Function ◽  
Optimization Problems ◽  
Newsvendor Problem ◽  
Expected Profit ◽  
Random Optimization ◽  
Better Than

Abstract We consider the median solution of the Newsvendor Problem. Some properties of such a solution are shown through a theoretical analysis and a numerical experiment. Sometimes, though not often, median solution may be better than solutions maximizing expected profit, or maximizing minimum possible, over distribution with the same average and standard deviation, expected profit, according to some criteria. We discuss the practical suitability of the objective function set and the solution derived, for the Newsvendor Problem, and other such random optimization problems.

scholarly journals Markov Approximation Method for Optimal Service Orchestration in IoT Network

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 49538-49548 ◽  
Author(s):  
Wenchen He ◽  
Shaoyong Guo ◽  
Yun Liang ◽  
Xuesong Qiu
Keyword(s):  
Approximation Method ◽  
Markov Approximation ◽  
Service Orchestration ◽  
Optimal Service

The Research of the Quality Testing Technology for Solder Paste Coating of the PCB Solder

2014 ◽  
Vol 701-702 ◽  
pp. 565-568
Author(s):  
Hao Ren ◽  
Jie Sun ◽  
Yue Feng Li
Keyword(s):  
Computer Vision ◽  
Theoretical Analysis ◽  
Detection Method ◽  
Solder Paste ◽  
Welding Quality ◽  
Quality Detection ◽  
Quality Testing ◽  
Testing Technology ◽  
Computer Vision Technology ◽  
Better Than

This paper proposed a welding quality detection method with the computer vision technology for PCB of IC chip. This method is better than the normal one by human examines in the precision and in speed. It is suitable for welding quality automatic detection in the printing process of the SMT solder paste for IC chips mount on PCB board. This method is implemented in lab. Theoretical analysis and experimental results show that the accuracy of this method is high; the capture error is small and is easy to operate.

scholarly journals Local Regularizer Improves Generalization

2020 ◽  
Vol 34 (04) ◽  
pp. 6861-6868 ◽  
Author(s):  
Yikai Zhang ◽  
Hui Qu ◽  
Dimitris Metaxas ◽  
Chao Chen
Keyword(s):  
Deep Learning ◽  
Theoretical Analysis ◽  
Experimental Evidence ◽  
Gradient Descent ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Training Algorithms ◽  
Training Methods ◽  
Theoretical Understanding ◽  
Better Than

Regularization plays an important role in generalization of deep learning. In this paper, we study the generalization power of an unbiased regularizor for training algorithms in deep learning. We focus on training methods called Locally Regularized Stochastic Gradient Descent (LRSGD). An LRSGD leverages a proximal type penalty in gradient descent steps to regularize SGD in training. We show that by carefully choosing relevant parameters, LRSGD generalizes better than SGD. Our thorough theoretical analysis is supported by experimental evidence. It advances our theoretical understanding of deep learning and provides new perspectives on designing training algorithms. The code is available at https://github.com/huiqu18/LRSGD.

scholarly journals Chaotic Fitness Dependent Optimizer for Planning and Engineering Design

2021 ◽  
Author(s):  
Hardi M. Mohammed ◽  
Tarik A. Rashid
Keyword(s):  
Chaotic Maps ◽  
Task Assignment ◽  
Swarm Optimization ◽  
Local Optima ◽  
Tent Map ◽  
Engineering Problems ◽  
Global Optima ◽  
Specific Limitation ◽  
Task Assignment Problem ◽  
Better Than

Abstract Fitness Dependent Optimizer (FDO) is a recent metaheuristic algorithm that mimics the reproduction behavior of the bee swarm in finding better hives. This algorithm is similar to Particle Swarm Optimization (PSO) but it works differently. The algorithm is very powerful and has better results compared to other common metaheuristic algorithms. This paper aims at improving the performance of FDO, thus, the chaotic theory is used inside FDO to propose Chaotic FDO (CFDO). Ten chaotic maps are used in the CFDO to consider which of them are performing well to avoid local optima and finding global optima. New technic is used to conduct population in specific limitation since FDO technic has a problem to amend population. The proposed CFDO is evaluated by using 10 benchmark functions from CEC2019. Finally, the results show that the ability of CFDO is improved. Singer map has a great impact on improving CFDO while the Tent map is the worst. Results show that CFDO is superior to GA, FDO, and CSO. Both CEC2013 and CEC2005 are used to evaluate CFDO. Finally, the proposed CFDO is applied to classical engineering problems, such as pressure vessel design and the result shows that CFDO can handle the problem better than WOA, GWO, FDO, and CGWO. Besides, CFDO is applied to solve the task assignment problem and then compared to the original FDO. The results prove that CFDO has better capability to solve the problem.

Algebraically inspired results on convex functions and bodies

2016 ◽  
Vol 18 (06) ◽  
pp. 1650027 ◽  
Author(s):  
Liran Rotem
Keyword(s):  
Convex Functions ◽  
Final Section ◽  
Polar Body ◽  
Convex Bodies ◽  
Type Inequality ◽  
Dual Function ◽  
Minkowski Addition ◽  
Geometric Means ◽  
Better Than

We show how algebraic identities, inequalities and constructions, which hold for numbers or matrices, often have analogs in the geometric classes of convex bodies or convex functions. By letting the polar body [Formula: see text] or the dual function [Formula: see text] play the role of the inverses “[Formula: see text]” and “[Formula: see text]”, we are able to conjecture many new results, which often turn out to be correct. As one example, we prove that for every convex function [Formula: see text] one has [Formula: see text] where [Formula: see text]. We also prove several corollaries of this identity, including a Santal type inequality and a contribution to the theory of summands. We proceed to discuss the analogous identity for convex bodies, where an unexpected distinction appears between the classical Minkowski addition and the more modern 2-addition. In the final section of the paper we consider the harmonic and geometric means of convex bodies and convex functions, and discuss their concavity properties. Once again, we find that in some problems the 2-addition of convex bodies behaves even better than the Minkowski addition.

Design and analysis of radially tapered disc springs with parabolically varying thickness

2007 ◽  
Vol 221 (2) ◽  
pp. 151-158 ◽  
Author(s):  
P K Saini ◽  
P Kumar ◽  
P Tandon
Keyword(s):  
Theoretical Analysis ◽  
Linear Profile ◽  
Thickness Profile ◽  
Varying Thickness ◽  
As Stress ◽  
Better Than

A theoretical analysis on Belleville spring with parabolically varying thickness is presented in this study. The analysis aims at modifying the thickness profile of radially tapered Belleville spring in order to increase the span of null slope zone in its stiffness curve, which is beneficial in some regulation processes. The expression for linearly varying thickness used by Rosa et al. is modified to incorporate a curvature factor and the corresponding load as well as stress equations are derived using the hypothesis of Almen-Laszlo. On the basis of this analysis, it is found that a spring with convex parabolic thickness profile serves better than an equally tapered spring with linear profile in regulation processes.

scholarly journals On refinements of some integral inequalities for differentiable prequasiinvex functions

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4377-4385
Author(s):  
Serap Özcan
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Right Hand ◽  
The Right ◽  
New Inequalities ◽  
Better Than

In this paper, using the new and improved form of H?lder?s integral inequality called H?lder-??can integral inequality, some new inequalities of the right-hand side of Hermite-Hadamard type inequality for prequasiinvex functions are established. The results obtained are compared with the known results. It is shown that the results obtained in this paper are better than those known ones.

scholarly journals Improved RC6 Algorithm using Two Types of Chaos Maps

2019 ◽  
Vol 9 (1) ◽  
pp. 2856-2860
Keyword(s):  
Chaotic Maps ◽  
Scheduling Algorithm ◽  
Advanced Encryption Standard ◽  
Key Generation ◽  
Key Length ◽  
Key Scheduling ◽  
Better Than

RC6 (Rivest cipher 6) is keyblock chipher which consider symmetric imitative from RC5. It was intended to encounter the needs competition of the Advanced Encryption Standard (AES) . The aim of this work is to add new security layer to RC6 (Rivest Cipher 6) algorithm, because there is some insufficiency in the Key Scheduling Algorithm (KSA) of RC6. This paper presents improved RC6 (IRC6) key generation based on two types of chaotic maps (Chebyshev,2d logistic) to generate N key to N users. The results prove that the average secrecy of IRC6 is better than of traditional RC6, in which: for 32 bits’ key length, and 256 bits’ plaintext size, the average secrecy of IRC6 is (0.536 - 3.907) while for RC6 is (0.254 constant).

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