Parameter Estimation and Measurement of Social Inequality in a Kinetic Model for Wealth Distribution

This paper deals with the modeling of wealth distribution considering a society with non-constant population and non-conservative wealth trades. The modeling approach is based on the kinetic theory of active particles, where individuals are distinguished by a scalar variable (the activity) which expresses their social state. A qualitative analysis of the model focusing on asymptotic behaviors and measurement of inequality through the Gini coefficient is presented. Finally, some specific case-studies are proposed in order to carry out numerical experiments to validate our model, characterize societies and investigate emerging behaviors.

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ON THE MODELING OF MIGRATION PHENOMENA ON SMALL NETWORKS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202512500558 ◽

2013 ◽

Vol 23 (03) ◽

pp. 541-563 ◽

Cited By ~ 30

Author(s):

D. KNOPOFF

Keyword(s):

Probability Distribution ◽

Existence And Uniqueness ◽

Nonlinear Ordinary Differential Equations ◽

Discrete Probability ◽

Welfare Policies ◽

Social State ◽

Active Particles ◽

The Social ◽

Scalar Variable ◽

Uniqueness Of The Solution

This paper deals with the modeling of migration phenomena in a small network of nations, with the aim of investigating the influence that the wealth and the welfare policies have on this phenomena. The modeling approach is based on the kinetic theory of active particles, while individuals over the network are distinguished by a scalar variable (the activity) which expresses their social state. The dynamics is induced both by the communication of individuals over the network and by the welfare policy within each nation, which is expressed in terms of competitive and altruistic interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear ordinary differential equations. The existence and uniqueness of the solution is discussed and some specific case-studies are proposed in order to carry out simulations and to investigate the emerging behaviors.

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FROM THE MODELING OF THE IMMUNE HALLMARKS OF CANCER TO A BLACK SWAN IN BIOLOGY

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202512500650 ◽

2013 ◽

Vol 23 (05) ◽

pp. 949-978 ◽

Cited By ~ 59

Author(s):

ABDELGHANI BELLOUQUID ◽

ELENA DE ANGELIS ◽

DAMIAN KNOPOFF

Keyword(s):

Immune System ◽

Kinetic Theory ◽

Biological Function ◽

Early Stage ◽

Black Swan ◽

Mathematical Approach ◽

Hallmarks Of Cancer ◽

Active Particles ◽

Scalar Variable ◽

Large Systems

This paper deals with the modeling of the early stage of cancer phenomena, namely mutations, onset, progression of cancer cells, and their competition with the immune system. The mathematical approach is based on the kinetic theory of active particles developed to describe the dynamics of large systems of interacting cells, called active particles. Their microscopic state is modeled by a scalar variable which expresses the main biological function. The modeling focuses on an interpretation of the immune-hallmarks of cancer.

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Constrained Parameter Estimation for a Mechanistic Kinetic Model of Cobalt–Hydrogen Electrochemical Competition during a Cobalt Removal Process

Entropy ◽

10.3390/e23040387 ◽

2021 ◽

Vol 23 (4) ◽

pp. 387

Author(s):

Yiting Liang ◽

Yuanhua Zhang ◽

Yonggang Li

Keyword(s):

Parameter Estimation ◽

Kinetic Model ◽

Model Parameters ◽

Hydrogen Ions ◽

Removal Process ◽

Cobalt Removal ◽

Estimation Scheme ◽

Zinc Hydrometallurgy ◽

The Impact ◽

Parameter Estimation Scheme

A mechanistic kinetic model of cobalt–hydrogen electrochemical competition for the cobalt removal process in zinc hydrometallurgical was proposed. In addition, to overcome the parameter estimation difficulties arising from the model nonlinearities and the lack of information on the possible value ranges of parameters to be estimated, a constrained guided parameter estimation scheme was derived based on model equations and experimental data. The proposed model and the parameter estimation scheme have two advantages: (i) The model reflected for the first time the mechanism of the electrochemical competition between cobalt and hydrogen ions in the process of cobalt removal in zinc hydrometallurgy; (ii) The proposed constrained parameter estimation scheme did not depend on the information of the possible value ranges of parameters to be estimated; (iii) the constraint conditions provided in that scheme directly linked the experimental phenomenon metrics to the model parameters thereby providing deeper insights into the model parameters for model users. Numerical experiments showed that the proposed constrained parameter estimation algorithm significantly improved the estimation efficiency. Meanwhile, the proposed cobalt–hydrogen electrochemical competition model allowed for accurate simulation of the impact of hydrogen ions on cobalt removal rate as well as simulation of the trend of hydrogen ion concentration, which would be helpful for the actual cobalt removal process in zinc hydrometallurgy.

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An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

International Journal of Applied Mathematics and Computer Science ◽

10.2478/amcs-2013-0010 ◽

2013 ◽

Vol 23 (1) ◽

pp. 117-129 ◽

Cited By ~ 2

Author(s):

Jiawen Bian ◽

Huiming Peng ◽

Jing Xing ◽

Zhihui Liu ◽

Hongwei Li

Keyword(s):

Parameter Estimation ◽

Convergence Rate ◽

Efficient Algorithm ◽

Numerical Experiments ◽

Additive Noise ◽

Mean Squared Errors ◽

Least Squares Estimators ◽

The Mean ◽

Newton Raphson ◽

Raphson Algorithm

This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton-Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton- Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.

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