scholarly journals Hyperbolastic Models from a Stochastic Differential Equation Point of View

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1835
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Francisco Torres-Ruiz
Keyword(s):  
Differential Equation ◽  
Simulated Data ◽  
Real Data ◽  
Point Of View ◽  
Likelihood Method ◽  
Numerical Resolution ◽  
The Family ◽  
The Common ◽  
Linear Differential ◽  
Mean Function

A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of this, and by adding a multiplicative noise to said ordinary differential equation, a diffusion process may be associated with each curve whose mean function is said curve. The inference in the resulting processes is presented jointly, as well as the strategies developed to obtain the initial solutions necessary for the numerical resolution of the system of equations resulting from the application of the maximum likelihood method. The common perspective presented is especially useful for the implementation of the necessary procedures for fitting the models to real data. Some examples based on simulated data support the suitability of the development described in the present paper.

scholarly journals The Generalized Additive Weibull-G Family of Distributions

2017 ◽  
Vol 6 (5) ◽  
pp. 65 ◽  
Author(s):  
Amal S. Hassan ◽  
Saeed E. Hemeda ◽  
Sudhansu S. Maiti ◽  
Sukanta Pramanik
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Random Variable ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Data Sets ◽  
New Family ◽  
The Family ◽  
Generated Family ◽  
Family Of Distributions

In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.

New formula for solution of one class of linear differential equations of the second order with the variable coefficients

2020 ◽  
Vol 8 (3) ◽  
pp. 61-68
Author(s):  
Avyt Asanov ◽  
Kanykei Asanova
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Variable Coefficients ◽  
Second Order ◽  
Linear Differential Equations ◽  
Common Solution ◽  
The Common ◽  
Linear Differential ◽  
New Formula

Exact solutions for linear and nonlinear differential equations play an important rolein theoretical and practical research. In particular many works have been devoted tofinding a formula for solving second order linear differential equations with variablecoefficients. In this paper we obtained the formula for the common solution of thelinear differential equation of the second order with the variable coefficients in themore common case. We also obtained the new formula for the solution of the Cauchyproblem for the linear differential equation of the second order with the variablecoefficients.Examples illustrating the application of the obtained formula for solvingsecond-order linear differential equations are given.Key words: The linear differential equation, the second order, the variablecoefficients,the new formula for the common solution, Cauchy problem, examples.

Photobleaching/Photoblinking Differential Equation Model for Fluorescence Microscopy Imaging

2013 ◽  
Vol 19 (5) ◽  
pp. 1110-1121 ◽  
Author(s):  
J. Miguel Sanches ◽  
Isabel Rodrigues
Keyword(s):  
Signal To Noise Ratio ◽  
Temporal Correlation ◽  
Real Data ◽  
Equation Model ◽  
Point Of View ◽  
Microscopy Imaging ◽  
Observation Process ◽  
The Common ◽  
Model Improvement

AbstractFluorescence images present low signal-to-noise ratio (SNR), are corrupted by a type of multiplicative noise with Poisson distribution, and are affected by a time intensity decay due to photoblinking and photobleaching (PBPB) effects. The noise and the PBPB effects together make long-term biological observation very difficult. Here, a theoretical model based on the underlying quantum mechanic physics theory of the observation process associated with this type of image is presented and the common empirical weighted sum of two decaying exponentials is derived from the model. Improvement in the SNR obtained in denoising when the proposed method is used is particularly important in the last images of the sequence where temporal correlation is used to recover information that is sometimes faded and therefore useless from a visual inspection point of view. The proposed PBPB model is included in a Bayesian denoising algorithm previously proposed by the authors. Experiments with synthetic and real data are presented to validate the PBPB model and to illustrate the effectiveness of the model in denoising and reconstruction results.

scholarly journals Genetic parameters for weight, morphometry and oviposition of Africanized honeybee queens using simulated data

2020 ◽  
Vol 72 (5) ◽  
pp. 1959-1964
Author(s):  
E.H. Martins ◽  
G. Tarôco ◽  
G.A. Rovadoscki ◽  
M.H.V. Oliveira ◽  
G.B. Mourão ◽  
...  
Keyword(s):  
Variance Components ◽  
Genetic Parameters ◽  
Genetic Correlations ◽  
Simulated Data ◽  
Real Data ◽  
Biological Data ◽  
Likelihood Method ◽  
Phenotypic Correlations ◽  
Genetic Evaluations ◽  
The Impact

ABSTRACT This study aimed to estimate genetic parameters for simulated data of body weight (BW), abdominal width (AW), abdominal length (AL), and oviposition. Simulation was performed based on real data collected at apiaries in the region of Campo das Vertentes, Minas Gerais, Brazil. Genetic evaluations were performed using single- and two-trait models and (co)variance components were estimated by the restricted maximum likelihood method. The heritability for BW, AW, AL and oviposition were 0.54, 0.47, 0.31 and 0.66, respectively. Positive genetic correlations of high magnitude were obtained between BW and AW (0.80), BW and oviposition (0.69), AW and oviposition (0.82), and AL and oviposition (0.96). The genetic correlations between BW and AL (0.11) and between AW and AL (0.26) were considered moderate and low. In contrast, the phenotypic correlations were positive and high between BW and AW (0.97), BW and AL (0.96), and AW and AL (0.98). Phenotypic correlations of low magnitude and close to zero were obtained for oviposition with AL (0.02), AW (-0.02), and BW (-0.03). New studies involving these characteristics should be conducted on populations with biological data in order to evaluate the impact of selection on traits of economic interest.

Beautiful Fractals as a Crystal Ball for Financial Markets? - Investment Decision Support System Based on Image Recognition Using Artificial Intelligence

2020 ◽  
Vol 14 (2) ◽  
pp. 27-44
Author(s):  
Benjamin M. Abdel-Karim
Keyword(s):  
Machine Learning ◽  
Financial Markets ◽  
Image Recognition ◽  
Fractal Geometry ◽  
Stock Price ◽  
Simulated Data ◽  
Real Data ◽  
Point Of View ◽  
Training Data ◽  
Theoretical Point

The work by Mandelbrot develops a basic understanding of fractals and the artwork of Jackson Pollok to reveal the beauty fractal geometry. The pattern of recurring structures is also reflected in share prices. Mandelbrot himself speaks of the fractal heart of the financial markets. Previous research has shown the potential of image recognition. This paper presents the possibility of using the structure recognition capability of modern machine learning methods to make forecasts based on fractal course information. We generate training data from real and simulated data. These data are represented in images to train a special artificial neural network. Subsequently, real data are presented to the network for use in predicting. The results show that the forecast of time series based on stock price illustration, compared to a benchmark, delivers promising results. This paper makes two essential contributions to research. From a theoretical point of view, fractal geometry shows that it can serve as a means of legitimation for technical analysis. From a practical point of view, highly developed methods from the field of machine learning are able to recognize patterns in data through appropriate data transformation, and that models such as random walk have an informational content that can be used to train machine learning models.

scholarly journals Adjoint differential equations

1927 ◽  
Vol 117 (776) ◽  
pp. 201-208
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Infinite Number ◽  
Adjoint Equation ◽  
Linear Equations ◽  
Point Of View ◽  
General Interest ◽  
Linear Difference Equations ◽  
Linear Differential

1. That adjoint differential equations have an analogue in the theory of linear difference equations seems to have been first observed by Bortolotti. The relation is essentially that of a matrix ǁ a rs ǁ to its transposed matrix ǁ a sr ǁ. It seems desirable, from this point of view, to carry out the transition from difference to differential equations, and thus prove that the analogy is a real one. This is done in Art. 2. There are further consequences of general interest. A set of linear equations corresponds to a differential equation and its boundary conditions, and thus we can find an interpretation of the adjoint boundary conditions introduced by Birkhoff into the theory of linear differential equations (Arts. 3-6). The relation between the two Green’s functions, implicit in Birkhoff’s work, then becomes evident (Art. 7). 2. We first prove that if the equations a r 1 y 1 + a r 2 y 2 + ... + a rn y n = fr ( r = 1 to n ) (1) are so constituted that they merge into the differential equation L ( y ) Ξ a m d m y / dx m . . . + a 1 dy / dx + a o y = f (2) by passing to an infinite number of infinitesimally spaced unknowns, the transposed equations a 1 r z 1 + a 2 r z 2 + ... + a nr z n = g r (3) merge into the adjoint equation M ( z ) Ξ (—) m d m / dx m ( a m z ) + ... - d / dx ( a 1 z ) + a o z = g .(4)

scholarly journals Alpha-Power Exponentiated Inverse Rayleigh distribution and its applications to real and simulated data

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245253
Author(s):  
Muhammad Ali ◽  
Alamgir Khalil ◽  
Muhammad Ijaz ◽  
Noor Saeed
Keyword(s):  
Residual Life ◽  
Probability Distributions ◽  
Simulated Data ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Strength Parameter ◽  
Data Sets ◽  
Alpha Power ◽  
Mean Waiting Time

The main goal of the current paper is to contribute to the existing literature of probability distributions. In this paper, a new probability distribution is generated by using the Alpha Power Family of distributions with the aim to model the data with non-monotonic failure rates and provides a better fit. The proposed distribution is called Alpha Power Exponentiated Inverse Rayleigh or in short APEIR distribution. Various statistical properties have been investigated including they are the order statistics, moments, residual life function, mean waiting time, quantiles, entropy, and stress-strength parameter. To estimate the parameters of the proposed distribution, the maximum likelihood method is employed. It has been proved theoretically that the proposed distribution provides a better fit to the data with monotonic as well as non-monotonic hazard rate shapes. Moreover, two real data sets are used to evaluate the significance and flexibility of the proposed distribution as compared to other probability distributions.

The Heiress-at-Law: English Real Property Law from a New Point of View

1990 ◽  
Vol 8 (2) ◽  
pp. 273-296 ◽  
Author(s):  
Eileen Spring
Keyword(s):  
Thirteenth Century ◽  
Common Law ◽  
Point Of View ◽  
Property Law ◽  
Main Subject ◽  
Real Property ◽  
Long Run ◽  
The Family ◽  
The Common

By the common law rules of inheritance women in English landed society fell into two classes. Some were altogether excluded from inheriting; others were entitled to succeed to the family estate. The woman thus entitled, the heiress-at-law, is clearly a figure due historical attention. Yet she has never been singled out for long-term consideration. Where she has been the main subject, discussion has always been chronologically limited, and her history has not been carried any distance through the course of legal changes that are relevant to it. Usually she has been discussed as but part of the family, and attention has been focussed largely on eldest sons and their relations with younger children, with younger sons or with daughters not heiresses, as the case may be. To focus on the heiress and to follow her history over the long run, from the thirteenth century to the eighteenth, is the purpose of this article.

scholarly journals Migration of a Population

2020 ◽  
Vol 1 (1) ◽  
pp. 15-20
Author(s):  
A.N. Volobuev
Keyword(s):  
Differential Equation ◽  
Natural Selection ◽  
Linear Differential Equation ◽  
Migration Velocity ◽  
Point Of View ◽  
Average Area ◽  
Primitive People ◽  
Linear Differential ◽  
Migratory Process ◽  
Alternation Of Generations

On the basis of Hardy – Weinberg law the problem of migration from the genetic point of view is considered. It is proved the linear differential equation of migratory process of a panmictic population. The phase of the solution of this equation is investigated. On the basis of the carried out analysis the dependence of migration velocity of a population on average time of alternation of generations is found. It is shown that migration of primitive people from Africa to Europe needed alternation the several hundred generations. The dependence of migration velocity of a population on the average area developed by a population for year is investigated. Lacks of the carried out analysis owing to absence of the account of natural selection and inbreeding are marked.

scholarly journals Strong consistency of local linear estimation of a conditional density function under random censorship

2020 ◽  
Vol 9 (3) ◽  
pp. 513-529
Author(s):  
Abdelkader Benkhaled ◽  
Fethi Madani ◽  
Salah Khardani
Keyword(s):  
Strong Consistency ◽  
Computational Study ◽  
Almost Sure Convergence ◽  
Simulated Data ◽  
Real Data ◽  
Point Of View ◽  
Conditional Density ◽  
Linear Estimation ◽  
Local Linear ◽  
Local Linear Estimation

Abstract In this paper, we study nonparametric local linear estimation of the conditional density of a randomly censored scalar response variable given a functional random covariate. We establish under general conditions the pointwise almost sure convergence with rates of this estimator under $$\alpha $$ α -mixing dependence. Finally, to show interests of our results, on the practical point of view, we have conducted a computational study, first on a simulated data and, then on some real data concerning Kidney transplant data.

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