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A crash course in Biomathematics: a tutorial

By Jorge Guerra Pires, PhD

See on CBIC 2017: tutorials.

Introduction

Biomathematics can be seen as a broad scientific area including areas such as biomechanics/systemic biology and systems biology. On the other hand, computational intelligence can be seen as a broad scientific area including artificial neural networks and evolutionary computing. On this tutorial, we shall see what is biomathematics and its ramifications, e.g. systems biology, and how they can be supported by methodologies from computational intelligence, e.g. in parameters estimations and pattern search (e.g., in gene expression). The tutorial is followed by the 1st CIBio-CBICwhich brings some key research all over the world around biomathematics with mentions to computational intelligence. 

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Public aimed

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  • From computational intelligence with no background in biomechanics;

  • Since we shall take it ease, it can be an opportunity for medical doctors and biologists to know both areas at once;

  • This course can be a nice opportunity to attract medical doctors and biologists to both areas, what I have been trying to do with biomathematics, “breaking the ice”, in previous endeavors;

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Objective(s)


Showing professionals from computational intelligence a rich source of problems to be handled and people from biomathematics and related areas a rich source of methodological tools in some cases ignored, however, that can give promising results.
 

Motivations

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In general,  a differential equation picked out of a hat 
will be insoluble
” 


It has been realized soon that biological problems tend to be more complex than physics-based problems. E.g.:

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1) they tend to be nonlinear;

2) they tend to be difficult to grasp its true dynamics;

3) they tend to be large and heterogenous.

 

Most of the models hitherto are “white box modeling”, but the question is whether we are matured enough for that, most of the approaches are reduced to special cases, being just toy models. A rich source of models is computational intelligence, which can be classified as “black box models”. They can be applied in a broad set of settings, from parameter estimation to nonlinear regression. And it has been locally exploited, those tools must be properly shared between community, and motivated properly for avoiding misconception, which largely creates myths and rejection. 
 

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On the unreasonable effectiveness of Biomathematics on life (biomedical) sciences:

A friendly discussion

Hands-on section: Optimal control in medicine and biology

Biomathematics and computational intelligence:

practical and theoretical perspectives

module 1

module 2

module 3

On this section, we shall discuss basics on biomathematics, including, but not restricted to:

  • Different "flavors";

  • Paradigms;

  • Classical problems in biomathematics;

  • Some nice references

  • Tips for someone interested in the area;

  • Some insights into biomathematics in Brazil (personal experience)

We could have chosen an almost infinite possible sequence of exercises for the hands-on section: this one was chosen based on past publication of the one responsible for the tutorial. Essentially, we show see it from simple to complicate; from classical tools to natural computing approach. See for now: Pires et al (2015) and Pires (2015).

 

We are going to play with a model in drug optimal therapy, using optimal control for designing best drug therapy. 

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On this section, we shall close the tutorial. We shall discuss several issues "on the applicability of computational intelligence in biomathematics"; c.f., Pires (2012); Pires (a2013)Pires (b2013); Pires (2014)

We start with a general discussion, then we shift to a set of selected papers on the intersection between computational intelligence and biomathematics: since there are several nice papers, that could have easily been selected, the selection is based on past research rather than a state of the art survey.

Install Matlab in you computer

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