The Exact Mathematical Solutions of Cancer
The Exact Mathematical Solutions of Cancer

Author: Samson Taiwo Babatunde

Publisher: Independently Published

Published: 2019-05-15

Total Pages: 764

ISBN-13: 9781096752615

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About The BookWhile compiling this book, I have developed chapter 1 on 'Partial Differential Equations, Stochastic Generalization and Coordinate Systems Orthogonality for Modeling Cancer', Chapter 2 on 'Hilbert Space and Orthogonal Basis for Precise Understanding of Cancer Prognosis and Treatments via orthogonal Therapies, ' Chapter 3 on 'Adomian Decomposition, Laguerre Polynomials and Series Solution for Cancer Modeling, ' Chapter 4 on 'Partial Fraction Decomposition: Decomposing Cancer Anomalies via Nonlinear Fractional PDEs, ' Chapter 5 on 'The Harmonics: Cancer Prognosis and Treatments Using Resonant Frequencies and Harmonic Generation Imaging, ' Chapter 6 on 'The Laplace Transforms: Applications of CNT's In Cancer Prognosis and Treatments, ' Chapter 7 on 'Applications of Random Initial Values Generation in Cancer Initiation and Progression, ', Chapter 8 on 'Mathematical Models and Cancer Research, ' Chapter 9 on 'Genetic Algorithms in Cancer Research, ' Chapter 10 on 'Somatic Evolution: Harnessing Evolution in Therapeutics, ' Chapter 11 'Power Law Applications in Modeling Cancer Tumor and Metastatic Growth, ' Chapter 12 on 'Models Integration in Cancer Systems Biology and Fuzzy Imaging', Chapter 13 on 'Evolutionary Dynamics for Precise Understanding of Tumor Growth via Exponential Growth Model, ' Chapter 14 on 'Quantitative Computer Simulation for Modeling Cancer Anomalous Behavior via Nonlinear Fractional PDEs, ' Chapter 15 on 'Statistical Testing of Hypotheses in Cancer Research, ' Chapter 16 on 'Optimal Control Problems in clinical trials and Cancer Prognosis and Treatments', ' Chapter 17 on Applications of Boundary-Value Analysis of Non Fractional PDEs in Modeling Anomalous Behavior in Cancer' and Chapter 18 on 'Spectral Clustering Applications in Cancer Prognosis and Treatments via Nonlinear Stochastic PDEs'. Partial differential equation is known to be the basis of all physical problems and real world problems like CANCER can be formulated as initial-boundary value partial differential equation. It was in the year 2016, that I wrote a book entitled "Exact Solutions for Partial Differential Equations," Published in Germany. The book presents a novel and robust initial-boundary value analysis framework for partial differential equations. The EXACT analytical solutions are generated from the initial conditions and satisfied the boundary conditions of the fractional nonlinear partial differential equations.In this book, which has been written completely new, I have explored the evolutionary dynamics of cancer and the use of evolutionary and genetic PDEs equations with random initial values in cancer development and response to therapies. Cancer emerges due to an evolutionary process in the SOMATIC tissue. The fundamental laws of evolution can best be formulated as EXACT mathematical equations. Therefore, the process of cancer initiation, progression and treatment is amenable to mathematical investigation. Thus, cancer as a random biodynamical system with anomalous behavior can be modeled with exact mathematical formulation.The subject matter has been so arranged that even a layman can understand how to apply the "exact mathematical solutions" to the problems of CANCER! This book is strongly and widely recommended for in-depth references in all matter of cancer research.

An Introduction to Physical Oncology
An Introduction to Physical Oncology

Author: Vittorio Cristini

Publisher: CRC Press

Published: 2017-06-26

Total Pages: 303

ISBN-13: 1315356880

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Physical oncology has the potential to revolutionize cancer research and treatment. The fundamental rationale behind this approach is that physical processes, such as transport mechanisms for drug molecules within tissue and forces exchanged by cancer cells with tissue, may play an equally important role as biological processes in influencing progression and treatment outcome. This book introduces the emerging field of physical oncology to a general audience, with a focus on recent breakthroughs that help in the design and discovery of more effective cancer treatments. It describes how novel mathematical models of physical transport processes incorporate patient tissue and imaging data routinely produced in the clinic to predict the efficacy of many cancer treatment approaches, including chemotherapy and radiation therapy. By helping to identify which therapies would be most beneficial for an individual patient, and quantifying their effects prior to actual implementation in the clinic, physical oncology allows doctors to design treatment regimens customized to each patient’s clinical needs, significantly altering the current clinical approach to cancer treatment and improving the outcomes for patients.

Computational Biology Of Cancer: Lecture Notes And Mathematical Modeling
Computational Biology Of Cancer: Lecture Notes And Mathematical Modeling

Author: Dominik Wodarz

Publisher: World Scientific

Published: 2005-01-24

Total Pages: 266

ISBN-13: 9814481874

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The book shows how mathematical and computational models can be used to study cancer biology. It introduces the concept of mathematical modeling and then applies it to a variety of topics in cancer biology. These include aspects of cancer initiation and progression, such as the somatic evolution of cells, genetic instability, and angiogenesis. The book also discusses the use of mathematical models for the analysis of therapeutic approaches such as chemotherapy, immunotherapy, and the use of oncolytic viruses.

Mathematical Theorems
Mathematical Theorems

Author: Lyudmila Alexeyeva

Publisher: BoD – Books on Demand

Published: 2020-12-09

Total Pages: 149

ISBN-13: 1838800719

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The main content of this book is related to construction of analytical solutions of differential equations and systems of mathematical physics, to development of analytical methods for solving boundary value problems for such equations and the study of properties of their solutions. A wide class of equations (elliptic, parabolic, and hyperbolic) is considered here, on the basis of which complex wave processes in biological and physical media can be simulated.The method of generalized functions presented in the book for solving boundary value problems of mathematical physics is universal for constructing solutions of boundary value problems for systems of linear differential equations with constant coefficients of any type. In the last sections of the book, the issues of calculating functions based on Padé approximations, binomial expansions, and fractal representations are considered. The book is intended for specialists in the field of mathematical and theoretical physics, mechanics and biophysics, students of mechanics, mathematics, physics and biology departments of higher educational institutions.

Dynamics Of Cancer: Mathematical Foundations Of Oncology
Dynamics Of Cancer: Mathematical Foundations Of Oncology

Author: Dominik Wodarz

Publisher: World Scientific

Published: 2014-04-24

Total Pages: 533

ISBN-13: 9814566381

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The book aims to provide an introduction to mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells. It can be used as a textbook for advanced undergraduate or graduate courses, and also serves as a reference book for researchers. The book has a strong evolutionary component and reflects the viewpoint that cancer can be understood rationally through a combination of mathematical and biological tools. It can be used both by mathematicians and biologists. Mathematically, the book starts with relatively simple ordinary differential equation models, and subsequently explores more complex stochastic and spatial models. Biologically, the book starts with explorations of the basic dynamics of tumor growth, including competitive interactions among cells, and subsequently moves on to the evolutionary dynamics of cancer cells, including scenarios of cancer initiation, progression, and treatment. The book finishes with a discussion of advanced topics, which describe how some of the mathematical concepts can be used to gain insights into a variety of questions, such as epigenetics, telomeres, gene therapy, and social interactions of cancer cells.

An Introduction to Physical Oncology
An Introduction to Physical Oncology

Author: Vittorio Cristini

Publisher: CRC Press

Published: 2017-06-26

Total Pages: 204

ISBN-13: 1466551364

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Physical oncology has the potential to revolutionize cancer research and treatment. The fundamental rationale behind this approach is that physical processes, such as transport mechanisms for drug molecules within tissue and forces exchanged by cancer cells with tissue, may play an equally important role as biological processes in influencing progression and treatment outcome. This book introduces the emerging field of physical oncology to a general audience, with a focus on recent breakthroughs that help in the design and discovery of more effective cancer treatments. It describes how novel mathematical models of physical transport processes incorporate patient tissue and imaging data routinely produced in the clinic to predict the efficacy of many cancer treatment approaches, including chemotherapy and radiation therapy. By helping to identify which therapies would be most beneficial for an individual patient, and quantifying their effects prior to actual implementation in the clinic, physical oncology allows doctors to design treatment regimens customized to each patient’s clinical needs, significantly altering the current clinical approach to cancer treatment and improving the outcomes for patients.

Proceedings of International Conference on Trends in Computational and Cognitive Engineering
Proceedings of International Conference on Trends in Computational and Cognitive Engineering

Author: Phool Singh

Publisher: Springer Nature

Published: 2020-09-30

Total Pages: 372

ISBN-13: 9811554145

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This book presents various computational and cognitive modeling approaches in the areas of health, education, finance, theenvironment, engineering, commerce and industry. Gathering selected conference papers presented atthe International Conference on Trends in Computational and Cognitive Engineering (TCCE), it sharescutting-edge insights and ideas from mathematicians, engineers, scientists and researchers anddiscusses fresh perspectives on problem solving in a range of research areas.

Mathematical Methods for Cancer Evolution
Mathematical Methods for Cancer Evolution

Author: Takashi Suzuki

Publisher: Springer

Published: 2017-06-20

Total Pages: 144

ISBN-13: 9789811036705

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The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools.The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.

Mathematical Intelligence
Mathematical Intelligence

Author: Junaid Mubeen

Publisher: Profile Books

Published: 2022-06-02

Total Pages: 226

ISBN-13: 1782837957

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There's so much talk about the threat posed by intelligent machines that it sometimes seems as though we should surrender to our robot overlords. But Junaid Mubeen isn't ready to throw in the towel just yet. As far as he is concerned, we have the creative edge over machines, because of a remarkable system of thought that humans have developed over the millennia. It's familiar to us all, but often badly taught in schools and misrepresented in popular discourse - maths. Computers are, of course, brilliant at totting up sums, pattern-seeking and performing mindless tasks of, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical superpowers.