Stability of Stationary and Minimum Points

1998 ◽  
pp. 232-245
Author(s):  
Donald H. Hyers ◽  
George Isac ◽  
Themistocles M. Rassias
Keyword(s):  
Minimum Points

scholarly journals Lower Bounds for Cover-Free Families

10.37236/5202 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Ali Z. Abdi ◽  
Nader H. Bshouty
Keyword(s):  
Lower Bounds ◽  
Cover Free Families ◽  
Minimum Points

Let ${\cal F}$ be a set of blocks of a $t$-set $X$. A pair $(X,{\cal F})$ is called an $(w,r)$-cover-free family ($(w,r)-$CFF) provided that, the intersection of any $w$ blocks in ${\cal F}$ is not contained in the union of any other $r$ blocks in ${\cal F}$.We give new asymptotic lower bounds for the number of minimum points $t$ in a $(w,r)$-CFF when $w\le r=|{\cal F}|^\epsilon$ for some constant $\epsilon\ge 1/2$. 

FINDING MULTIPLE LOCAL MINIMA USING CHAOTIC JUMP

1998 ◽  
Vol 07 (01) ◽  
pp. 105-115 ◽  
Author(s):  
CHANGKYU CHOI ◽  
JU-JANG LEE
Keyword(s):  
Search Algorithm ◽  
Gaussian Function ◽  
Search Space ◽  
Planning Problem ◽  
Local Minima ◽  
Chaotic Motions ◽  
Quality Function ◽  
Unstructured Search ◽  
Free Search ◽  
Minimum Points

In this paper, the local minima free search algorithm using chaos is proposed for an unstructured search space. The problem is that given the quality function, find the value of a configuration that minimizes the quality function. The proposed algorithm started basically from the gradient search technique but at the prescribed points, that is, local minimum points, which are to be automatically detected the chaotic jump is introduced by the dynamics of a chaotic neuron. Chaotic motions are mainly because of the Gaussian function having a hysteresis as a refractoriness. In order to enhance the probability of finding the global minimum, a parallel search strategy is also given. The validity of the proposed method wil be verified in simulation examples of the function minimization problem and the motion planning problem of a mobile robot.

Diagonal non-semicontinuous variational problems

2018 ◽  
Vol 24 (4) ◽  
pp. 1333-1343
Author(s):  
Sandro Zagatti
Keyword(s):  
Sobolev Spaces ◽  
Hessian Matrix ◽  
Variational Problems ◽  
Convex Envelope ◽  
Minimum Problem ◽  
Unique Minimizer ◽  
Special Case ◽  
Minimum Points

We study the minimum problem for non sequentially weakly lower semicontinuos functionals of the form F(u)=∫If(x,u(x),u′(x))dx, defined on Sobolev spaces, where the integrand f:I×ℝm×ℝm→ℝ is assumed to be non convex in the last variable. Denoting by f̅ the lower convex envelope of f with respect to the last variable, we prove the existence of minimum points of F assuming that the application p↦f̅(⋅,p,⋅) is separately monotone with respect to each component pi of the vector p and that the Hessian matrix of the application ξ↦f̅(⋅,⋅,ξ) is diagonal. In the special case of functionals of sum type represented by integrands of the form f(x, p, ξ) = g(x, ξ) + h(x, p), we assume that the separate monotonicity of the map p↦h(⋅, p) holds true in a neighbourhood of the (unique) minimizer of the relaxed functional and not necessarily on its whole domain.

An Optimized BP Neural Network Based on DS Evidential Reasoning on Heart Disease Prediction

2012 ◽  
Vol 263-266 ◽  
pp. 3342-3347
Author(s):  
Nan Nan Xie ◽  
Fei Yan Chen ◽  
Kuo Zhao ◽  
Liang Hu
Keyword(s):  
Neural Network ◽  
Heart Disease ◽  
Bp Neural Network ◽  
Recognition Rate ◽  
Evidential Reasoning ◽  
Self Organization ◽  
Uncertain Information ◽  
Data Set ◽  
Time Prediction ◽  
Minimum Points

BP neural network is a widely used neural network, with advantages as adaptability, fault tolerance and self-organization. However, BP neural network is difficult to determine the network structure, and easy to fall into local minimum points. In this paper, an optimized BP neural network was proposed based on DS, he advantages of DS Evidential Reasoning on uncertain information are used to improve the recognition rate and credibility of BP. Experiments on Heart Disease Data set shows the proposed method have good performance on run time, prediction accuracy and robustness.

scholarly journals CRITERIA OF BELLY BACON DESIRABILITY. III. WITHIN-BELLY VARIANCE IN CHEMICAL AND PHYSICAL CHARACTERISTICS

1975 ◽  
Vol 55 (4) ◽  
pp. 661-672 ◽  
Author(s):  
H. T. FREDEEN ◽  
A. H. MARTIN ◽  
J. G. McANDREWS
Keyword(s):  
Specific Gravity ◽  
Cross Section ◽  
Variance Component ◽  
Regression Analyses ◽  
Components Of Variance ◽  
Coefficients Of Variation ◽  
Percent Protein ◽  
Accuracy Of Prediction ◽  
Weight Regression ◽  
Minimum Points

Within-belly variation (four cross-section rashers per belly) was substantially greater than the variation between bellies (n = 730) for the physical dimensions of width of rasher and depth at maximum and minimum points. Ratios among these variables has large coefficients of variation and their between-belly components of variance were negative. Correlations among measurements, both within and between rashers were small, indicating limited potential for predicting variance in any one physical dimension from knowledge of another. However, variation in width and depth measurements was associated with variation in the carcass measurements of backfat and carcass weight. Regression analyses identified carcass backfat as an important contributor to within-rasher variance in composition traits (percent fat, percent protein, lean ratios, photo grade). Accuracy of prediction was improved by enlarging the regression equation to include specific gravity of the belly, but was not influenced by either sex or weight of carcass. Variance component analyses identified a larger within-belly component for percent fat than for percent protein and, for both traits, the within-belly component was greater for castrates than for gilts. Individual pig differences contributed little to the between-belly variance for percent fat after consideration of backfat and weight. It was concluded that composition is the only aspect of belly bacon desirability that is amenable to prediction from measurements made on the carcass or the belly, that potential fat–lean ratio can be predicted from knowledge of carcass backfat, and that the accuracy of estimation can be further improved by adding specific gravity to the estimation equation.

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