Mathematical modeling of the learning curve and its practical applications / Igor I. Stepanov and Charles I. Abramson.

Format:

Book

Author/Creator:

Stepanov, Igor I., author.

Abramson, Charles I., author.

Series:

Mathematics research developments series.

Mathematics research developments

Language:

English

Subjects (All):

Learning curve (Psychometrics).

Learning--Mathematical models.

Learning.

Physical Description:

1 online resource (276 pages)

Place of Publication:

New York : Nova Science Publishers, [2022]

Summary:

"This book provides a detailed description of the application of mathematical learning curve modeling to analyze the state of learning and memory in humans and animals. The purpose of the book is to enable the readers to apply the knowledge gained in their own research on learning and memory. The authors hope that the readers may achieve success in this field of knowledge, expand and advance mathematical modeling of the learning curve, and that this book may aid in this process. For this, the authors have developed their own mathematical model based on the systems theory and proved its advantage in relation to those previously proposed. The authors developed MS Windows application "Learning Curve Modeling Tool" to help the reader modeling the learning curve from raw learning data in the California Verbal Learning Test, the Rey Auditory Verbal Learning Test, and other similar memory tests. Moreover, the book describes in detail the Windows and Android application "Memory Monitoring Tool", developed by the authors, which is suited well for mathematical modeling of the learning curves. The application aims to reveal initial signs of memory impairment. Besides, the section APPENDIX A describes a Web application - "Learning curve simulator" - developed by the authors for helping readers to get started with practically modeling the learning curve and testing their memory. This application is included in the book. The book will be useful for undergraduate students, graduate students, advanced graduate students, and professors, especially for professors who work on learning in both humans and animals, and those interested in the memory of marijuana users, alcoholics, and those suffering from diabetes and multiple sclerosis, as well as other neurological and psychological diseases and their neurological complications including those after COVID-19"-- Provided by publisher.

Contents:

Intro

Contents

Preface

Acknowledgments

Chapter 1

Mathematical Models of the Learning Curves

Basic Concepts of Regression Models

Types of the Regression Models

Fitting a Learning Curve Model

Empirical Mathematical Functions

A Hyperbolic Function

An Arc Cotangent Function

A Logarithmic Function

An Error Function

Differential Equations

Logistic Differential Equations

Rational Equations

Memory Model of Hull

Rescorla-Wagner's Model

Rescorla-Wagner's Model as a Difference Equation

Rescorla-Wagner's Model as a Function of Trials

Stochastic Models

The System Analysis Approach to Learning Curve Modeling

The Transitional Process in the First Order Linear System

The Time Constant

The Authors' Model Based on the First Order Transfer Function

Description of the Model

Comparison of the Model's Coefficients

Comparison of the Authors' Model with Other Models

Chapter 2

Modeling the Learning Curves in Animals

Learning Curves in Land Snail, Helix Pomatia

Learning Curves in Honeybees, Apis Mellifera L., Exposed to Pesticides

Confirm®2F

Dimilin®

Learning Curves in Rats Trained in a 3-Arm Radial Maze

Method

Results

Wistar Group

Albino Group

Chapter 3

The CVLT Learning Curves in Patients with Type 2 Diabetes Mellitus (T2DM)

Averaged Learning Curves over the Group of Healthy Participants and the Group of Patients with T2DM

Individual Learning Curves for Patients with T2DM

Definition of Extreme Values of B2 and B4

Correction B2/B4 Outliers

Extremely High B4 Value after Correction

Comparison of the Model's Coefficients versus CVLT Learning Curve Standard Measures

Chapter 4

The CVLT-II Learning Curves in Patients with Multiple Sclerosis

Averaged Learning Curves over Healthy Participants and MS Patients.

Short- and Long-Term Memory Levels in Women

Short-Term Memory Levels (Coefficient B3) in Women

Discrimination between Cluster 1 and Cluster 2 by B3

Discrimination between Cluster 2 and Cluster 3 by B3

Discrimination between Cluster 3 and Cluster 4 by B3

Discrimination between Cluster 4 and Cluster 5 by B3

Discrimination between Cluster 5 and Cluster 6 by B3

Long-Term Memory Levels (Coefficient B4) in Women

Discrimination between Cluster 1 and Cluster 2 by B4

Discrimination between Cluster 2 and Cluster 3 by B4

Discrimination between Cluster 3 and Cluster 4 by B4

Discrimination between Cluster 4 and Cluster 5 by B4

Discrimination between Cluster 5 and Cluster 6 by B4

Short- and Long-Term Memory Levels in Men

Short-Term Memory Levels (Coefficient B3) in Men

Long-Term Memory Levels (Coefficient B4) in Men

The Tables with Cut-Off Values of the Coefficients B3 and B4

Levels of Memory with Cut-Off Values

Levels of Short- and Long-Term Memory in MS Patients

Chapter 5

Modeling the CVLT-C Learning Curves

Learning Curves in Typically Developing Children

Memory Levels in Children

Short- and Long-Term Memory Levels in Girls

Short- and Long-Term Memory Levels in Boys

Levels of Short- and Long-Term Memory in Children with THI

Chapter 6.

Modification of a Free-Recalled Memory Test for Modeling the Learning Curve

The Authors' Free-Recall Memory Test

Memory Assessment in Patients with Cerebrovascular Disease

Participants

Control Group, Women

Control Group, Men

CVD Group, Women

CVD Group, Men

Chapter 7

Computer Applications for Modeling the Learning Curve, Developed by the Authors

The Learning Curve Modeling Tool

How to Run LCMT

The Main Window

Results of Modeling

Memory Levels Tables

The Computerized Free-Recalled Memory Test

The Computerized Free-Recalled Memory Test for Windows

Main Window

User Account

Start Test

Show Results

Modeling the Individual Learning Curve

Modeling the Averaged Learning Curve

Comparison Learning Curves

Comparison of Individual Learning Curves

Comparison of Averaged Learning Curves

Memory Monitoring with the MMT over Several Months

Use the MMT for Rehabilitation and Training Purposes

The Memory Monitoring Tool Version for Mobile Devices

Main Screen

Start a New Test

Modeling the Learning Curve

Recalled Numbers Analysis

Comparison of Two Tests

Comparison of Two Groups of Tests

Chapter 8

Conclusion

Choosing the Optimal Mathematical Model

Modeling the Learning Curves in Humans

Modification of a Free-Recalled Memory Test for Modeling the Learning Curve

Appendix

The Main Page

Modeling the Learning Curve with Data Entered by the User

The Memory Test

References

About The Authors

Index

Blank Page.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Stepanov, Igor Igorevich Mathematical Modeling of the Learning Curve and Its Practical Applications

ISBN:

9781685078515