Motto: *Well, you've got to start somewhere...*

**Spring 2014, 3CR
Tue/Thu 11:00 am - 12:15 pm in PSC 803
(Cross-listed with Math 8530, Biol 8390, eligible for Neuro credit for Philosophy grad students)
**

Assistant Professor

Neuroscience Institute and

Department of Mathematics and Statistics

Georgia State University

Click the thumbnails for the full, letter-sized, PDF posters

Here is the 2014 syllabus.

- Diagram for theory-driven research framework. Note that this version already has the "conceptual model" moved out of the user's mind and into some objective framework. This is an aspirational and idealized situation. Pragramatic considerations may distort this picture considerably.
- A diagram that relates some of the many different characteristics of models. This diagram is best appreciated in the context of the following two documents.
- These documents are starting points for discussion, and we will explore the ideas further through the reading assignments.
- Here is a useful online resource for technical writing, especially the link to Purdue's OWL.
- OWL also has good exercises and information for writing in English as a Second Language and also here.
- I wrote an introduction to technical writing as well.
- Here is the
**Essay Grading Rubric**.

- Here is a java applet for reaction-diffusion pattern formation based on Turing's model for morphogenesis. Read about RD equations for pattern formation.

I strongly recommend reading the free materials
provided by the publisher of Ellner and Guckenheimer's book that we will occasionally use,
particularly the Preface and Chapter 1. More math-oriented students
can look at the later chapters too, especially Chapter 9. We will
**not** be covering mathematical details in these chapters, just
the concepts and diagrammatic structures and relationships.

Also worth looking through are several well-written wikipedia pages:

- Mathematical model
- Conceptual model
- Scientific model
- Model selection
- Mathematical and theoretical biology
- Modeling biological systems

There will be no formal examinations in the course, and no formal prerequisites (registration will be by instructor consent - please email me with your details and interests). Instead, there will be assessments such as collaborative essay assignments and in-class presentations based on reading assignments.

In this course we will ponder questions such as the following: What is the connection between (a) the ability of an F-16 fighter jet to maneuver much more nimbly than an F-4, (b) the possibility that small genetic modifications lead to large differences in phylogenetic outcome within a couple of generations, and (c) the ability of a neural circuit controlling limb motor patterns to switch an animal rapidly between locomotive gaits?

The class is intended for the non-mathematically literate, and yet we will consider non-elementary concepts from applied mathematics and modeling in the biosciences. A primary goal of this course is to increase basic literacy about modeling and simulation, and to promote future participation in collaborations with mathematicians and computational modelers. You will be motivated to appreciate that there are many insights from mathematical thinking that can improve biologists' ability to comprehend and develop complex theories of biological mechanisms, even if they lack traditional training in mathematics.

Do not mistake this class as a "superficial" approach to the modeling of complex problems. On the contrary, it will complement mathematically rigorous, traditional courses on mathematical and computational modeling by providing students with a basis for evaluating good modeling projects in the literature, and understanding their assumptions and limitations. Most traditional courses are themselves, in that sense, superficial in their treatment of these topics, and take many things for granted. It can lead to both students and professionals making poorly chosen approaches to modeling their pet phenomena. We will not try to digest or review the large literature on any given subject area, which certainly would require more time and a formal training in mathematics.

Necessarily, the tools, techniques, and skills of modeling come secondary to the idea of what a reasonable model might consist of, what assumptions need to be made, what types of data lead to what kinds of model, what kinds of representations and techniques are available, what their scopes are, and so on. These are important meta-discussions that are generally avoided in the education of math-oriented students, and is an important reason why I encourage such students to be in this class too.

We will focus on intuition and qualitative, geometric mathematical concepts. This will include ideas drawn from calculus and statistics (among other technical subjects) but a technical understanding of the math will not be assumed, nor will it be taught. This is not a remedial math course! We will discuss different biological systems that have been the subject of modeling through journal articles and book material. Among other topics, we will discuss evolutionary stable strategies in evolution and its abstract connection to the idea of attractors in brain states, small world and other kinds of structured networks in the brain, pattern formation concepts, rhythms in the nervous system. We will analyze the benefits, misconceptions, limitations, and pitfalls of modeling such systems when guided by experimental data, in terms of both the logic of mechanistic theories and their abstraction to mathematical principles.

As should now be clear from this description, students will not be learning specific computer tools in this class. Nonetheless, students will interact with some elementary, pre-packaged simulations to get some visual experience with changing parameters, and so on.

For the visit of Carson Chow from NIH, the class prepared this news item for the College web page (and a similar item linked from GSU's front page, Nov 28th 2011) and this handout for the seminar to help the Biology department's graduate student attendees.

We will use Google Docs and Google Groups to manage the collaborative writing project.

Features in GDocs are live updates as collaborators write, live chat between collaborators, records (provenance / audit trail) of edits especially in case of accidental loss of material, export options to PDF and DOC, multiple formats for materials including document text, presentation slides, and drawings.