Using Entropy Penalty Term for Improving the Generalization Ability of Multilayer Feedfoward Networks *

Generalization ability is a major problem encountered when using neural networks to find the structures in noisy data sets. Controlling the network complexity is a common method to solve this problem. In this paper, however, a novel additive penalty term which represents the features extracted by hidden units is introduced to eliminate the overtraining of multilayer feedfoward networks. Computer simulations demonstrate that by using this unsupervised fashion penalty term, the generalization ability is greatly improved.

A Novel Derivation of Black Hole Entropy in all Dimensions from Truly Point Mass Sources

It is explicitly shown how the Schwarzschild Black Hole Entropy (in all dimensions) emerges from truly point mass sources at r=0due to a non-vanishing scalar curvature involving the Dirac delta distribution. In order to achieve this, one is required to extend the domain of r to negative values −∞≤r≤+∞. It is the density and anisotropic pressure components associated with the point mass delta function source at the origin r=0which furnish the Schwarzschild black hole entropy in all dimensions D≥4after evaluating the Euclidean Einstein-Hilbert action. Two of the most salient results are i) that the observed spacetime dimension D=4is precisely singled out from all the other dimensions when the strong and weak energy conditions are met, and ii) the point mass source described in this work is not the result of a spherically symmetric gravitational collapse of a star as described by the Oppenheimer-Snyder model because we are not neglecting the pressure. As usual, it is required to take the inverse Hawking temperature βHas the length of the circle Sβ1obtained from a compactification of the Euclidean time in thermal field theory which results after a Wick rotation, it=τ, to imaginary time. This approach can be generalized to the Reissner-Nordstrom and Kerr-Newman metrics. The physical implications of this finding warrant further investigation since it suggests a profound connection between the notion of gravitational entropy and spacetime singularities.

Approximate entropy and support vector machines for electroencephalogram signal classification

The automatic detection and identification of electroencephalogram waves play an important role in the prediction, diagnosis and treatment of epileptic seizures. In this study, a nonlinear dynamics index–approximate entropy and a support vector machine that has strong generalization ability were applied to classify electroencephalogram signals at epileptic interictal and ictal periods. Our aim was to verify whether approximate entropy waves can be effectively applied to the automatic real-time detection of epilepsy in the electroencephalogram, and to explore its generalization ability as a classifier trained using a nonlinear dynamics index. Four patients presenting with partial epileptic seizures were included in this study. They were all diagnosed with neocortex localized epilepsy and epileptic foci were clearly observed by electroencephalogram. The electroencephalogram data form the four involved patients were segmented and the characteristic values of each segment, that is, the approximate entropy, were extracted. The support vector machine classifier was constructed with the approximate entropy extracted from one epileptic case, and then electroencephalogram waves of the other three cases were classified, reaching a 93.33% accuracy rate. Our findings suggest that the use of approximate entropy allows the automatic real-time detection of electroencephalogram data in epileptic cases. The combination of approximate entropy and support vector machines shows good generalization ability for the classification of electroencephalogram signals for epilepsy.

Quantum Extensions to the Einstein Field Equations

This paper proposes an extension to the Einstein Field Equations by integrating quantum informational measures, specifically entanglement entropy and quantum complexity. These modified equations aim to bridge the gap between general relativity and quantum mechanics, offering a unified framework that incorporates the geometric properties of spacetime with fundamental aspects of quantum information theory. The theoretical implications of this approach include potential resolutions to longstanding issues like the black hole information paradox and new perspectives on dark energy. The paper presents modified versions of classical solutions such as the Schwarzschild metric and Friedmann equations, incorporating quantum corrections. It also outlines testable predictions in areas including gravitational wave propagation, black hole shadows, and cosmological observables. We propose several avenues for future research, including exploring connections with other quantum gravity approaches designing experiments to test the theory’s predictions. This work contributes to the ongoing exploration of quantum gravity, offering a framework that potentially unifies general relativity and quantum mechanics with testable predictions.

Re-examination of Fundamental Concepts of Heat, Work, Energy, Entropy, and Information Based on NGST

In order to use the framework of general system theory(GST)to unify the three mechanics subjects of classical mechanics,quantum mechanics,and relativistic mechanics,a new general system theory(NGST)is developed based on a new ontology of ether and minds as the fundamental existences in the world.Based on this new ontology,many fundamental concepts have been detected to be ambiguously defined nowadays and particularly lack of ontological support.In our previous work,some of the fundamental concepts such as universe,world,time,space,matter,ether,mind,life,field,force have been redefined.The purpose of this paper is to clarify the concepts of energy,heat,work,entropy,and information in our NGST.This is an important and necessary step in the development of the NGST.

General Entropy Model of Line Segments Uncertainty in GIS

Spatial data uncertainty can directly affect the quality of digital products and GIS-based decision making. On the basis of the characteristics of randomicity of positional data and fuzziness of attribute data, taking entropy as a measure, the stochastic entropy model of positional data uncertainty and fuzzy entropy model of attribute data uncertainty are proposed. As both randomic-ity and fuzziness usually simultaneously exist in linear segments, their omnibus effects are also investigated and quantified. A novel uncertainty measure, general entropy, is presented. The general entropy can be used as a uniform measure to quantify the total un-certainty caused by stochastic uncertainty and fuzzy uncertainty in GIS.

提高前馈神经网络泛化能力的新算法

利用神经网络提取含噪数据的特征时，如何提高泛化能力是亟需解决的重要问题。通常的解决方法是通过结构优化和正则化来控制网络的复杂性。本文从熵函数的概念出发，提出了一项新的加性惩罚因子以消除过训练现象，从而有效的提高网络的泛化能力。

Estimating Weibull Parameters Using Least Squares and Multilayer Perceptron vs. Bayes Estimation

The Weibull distribution is regarded as among the finest in the family of failure distributions.One of the most commonly used parameters of the Weibull distribution(WD)is the ordinary least squares(OLS)technique,which is useful in reliability and lifetime modeling.In this study,we propose an approach based on the ordinary least squares and the multilayer perceptron(MLP)neural network called the OLSMLP that is based on the resilience of the OLS method.The MLP solves the problem of heteroscedasticity that distorts the estimation of the parameters of the WD due to the presence of outliers,and eases the difficulty of determining weights in case of the weighted least square(WLS).Another method is proposed by incorporating a weight into the general entropy(GE)loss function to estimate the parameters of the WD to obtain a modified loss function(WGE).Furthermore,a Monte Carlo simulation is performed to examine the performance of the proposed OLSMLP method in comparison with approximate Bayesian estimation(BLWGE)by using a weighted GE loss function.The results of the simulation showed that the two proposed methods produced good estimates even for small sample sizes.In addition,the techniques proposed here are typically the preferred options when estimating parameters compared with other available methods,in terms of the mean squared error and requirements related to time.

Thermodynamic effects of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle

The thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter is investigated.We calculate the analytical expresses of corresponding thermodynamic variables,e.g.,the Hawking temperature,entropy of the black hole.In addition,we derive the heat capacity to analyze the thermal stability of the black hole.We also compute the rate of emission in terms of photons through tunneling.By numerical method,an obvious phase transition behavior is found.Furthermore,according to the general uncertainty principle,we study the quantum corrections to these thermodynamic quantities and obtain the quantum-corrected entropy containing the logarithmic term.Lastly,we investigate the effects of the magnetic charge g,the dark matter parameter k and the generalized uncertainty principle parameterαon the thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle.

Generalized Truncated Fréchet Generated Family Distributions and Their Applications

Understanding a phenomenon from observed data requires contextual and efficient statistical models.Such models are based on probability distributions having sufficiently flexible statistical properties to adapt to a maximum of situations.Modern examples include the distributions of the truncated Fréchet generated family.In this paper,we go even further by introducing a more general family,based on a truncated version of the generalized Fréchet distribution.This generalization involves a new shape parameter modulating to the extreme some central and dispersion parameters,as well as the skewness and weight of the tails.We also investigate the main functions of the new family,stress-strength parameter,diverse functional series expansions,incomplete moments,various entropy measures,theoretical and practical parameters estimation,bivariate extensions through the use of copulas,and the estimation of the model parameters.By considering a special member of the family having the Weibull distribution as the parent,we fit two data sets of interest,one about waiting times and the other about precipitation.Solid statistical criteria attest that the proposed model is superior over other extended Weibull models,including the one derived to the former truncated Fréchet generated family.

The Influence of Demoiselle Aircraft on Light and General Aviation Design

In 1907, aviation pioneer Santos-Dumont had the idea of building a very light airplane. He designed and built the SD 19, the Demoiselle, an aircraft with a 6 meter wing span and a 24 HP engine of his own design. The Demoiselle was very successful in flying and, became very popular and its development continued as SD20, SD21 and SD22 （his last airplane）. The influence of the Demoiselle on design principles of light aircraft and general aviation were studied in this work, using statistical entropy, The designs number 20 and 22 may be considered dominant and influenced the design principles of light aircraft and general aviation.

Structural Dynamics in Biology: A Bridge Given by Implicit Vibratory Crossed Models

This article proposes a synthesis and contribution at three levels: generation of dynamic equations of shell structures interacting with fluids, reduction of implicit resolution, and cross-applications to aerospace tanks and living systems. The synthesis of the equations is proposed around the four principles of thermodynamics at the level of discrete, structural and digitized systems. The implicit approach envisages an innovative analysis in terms of condensation and digitization, with in particular a perspective towards singular and integral methods. Some illustrations are proposed, in the field of performed research models and also in the fields of educational applications in biodynamics. The proposed bridge links, on one hand, the analytical Lagrange-Feynman’s approach, and on the other hand experimental results obtained in laboratory and numerical experiments obtained with multiphysics software. Finally, the realized models concern conservative and dissipative models for the active and passive control of complex systems, in a unified approach.

Flat Space Cosmology as a Model of Light Speed Cosmic Expansion—Implications for the Vacuum Energy Density

Cosmologists have long ignored a stipulation by quantum field theorists that the vacuum pressure p corresponding to the zero-state vacuum energy must always be equal in magnitude to the vacuum energy density ρ(i.e., p=ρ). Although general relativity stipulates the additional condition of proportionality between the vacuum gravitational field and (ρ+3p), the equation of state for the cosmic vacuum must fulfill both relativistic and quantum stipulations. This paper fully integrates Flat Space Cosmology (FSC) into the Friedmann equations containing a cosmological term, with interesting implications for the nature of dark energy, cosmic entropy and the entropic arrow of time. The FSC vacuum energy density is shown to be equal to the cosmic fluid bulk modulus at all times, thus meeting the quantum theory stipulation of (p=ρ). To date, FSC is the only viable dark energy cosmological model which has fully-integrated general relativity and quantum features.

The Entropies Evaluation of the High-entropy System and its Determination of Operating Entropy

This article applies the basic principles of the general and special entropy, puts forward the concept of High\|entropy system and its entropies. Sometimes, the entropy functions have been defined, and their mathematical models have been constructred, and methods of quantification. Specially. Taking the Mining System as an example, the quantification method of the operating entropy is given under the synthetic action of the man\|made entropy, machine entropy, natural entropy and environmnet entropy. Therefore it enriches the theoretical and applied systems of the general and special entropy.

WEAKLY ALMOST PERIODIC POINT AND ERGODIC MEASURE

Let X be a compact metric space and f: X→X be continuous.This pape introduces the notion of weakly almost periodic point, which is a generalization of the notion of almost periodic point, proves that each of f-invariant ergodic measures can be generated by a weakly almost periodic point of f and gives some equivalent conditions for that f has an invariant ergodic measure whose support is X and ones for that f has no non-atomic invariant ergodic measure, the latter is a generalization of the Blokh’s work on self-maps of the interval. Also two formulae for calculating the togological entropy are obtained.

The effects of China’s VAT enlargement reform on the income redistribution of urban households

Using the 2007 input-output data and 2012 household survey data,this paper estimated the overall VAT and business tax burden of urban households in China on basis of the statutory tax rates,and then studied the redistribution effects of China’s recent VAT enlargement reform.We found that this reform improved the redistribution effects of VAT and business tax mainly through lowering the average tax burden and reducing the inequality within the bottom-income group,but the inequality among different income groups was not reduced considerably.Based on a simulation analysis,we finally suggested the reduction of applicable rates on necessities to improve the redistribution effects of VAT more effectively.

Statistical Inference of Exponentiated Moment Exponential Distribution Based on Lower Record Values

Based on lower record values,we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means,variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution(EMED),a new extension of moment exponential distribution,recently introduced by Hasnain(Exponentiated moment exponential distribution.Ph.D.Thesis,2013).Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED.Finally,we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters.We have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values.Monte Carlo simulations are performed to compare the performances of the proposed methods,and a data set has been analyzed for illustrative purposes.