This page is a result of a *CNS*95*
workshop which focused on the use of computers in computational neuroscience.
We don't claim that this represents complete coverage of the topic, though
we hope that it eventually will. In fact, we don't even guarantee that
any of this makes sense right now; we thought it better to put this on
the web early than to polish it. In other words, it's like 99% of the the
other web pages out there. We expect the information it contains to be
constantly changing to reflect what's going on right now in the CN, scientific
visualization, and simulation worlds. So, if you have additions, corrections,
suggestions, complaints, cute graphics, etc., please send them to Michael
Stiber, who has volunteered to maintain this page. We're especially
interested in pointers to **your** work that are relevant (and on the
Web would be nice); please let us know from which part of this document
you'd like to link it. If you'd like information about your work included
here, but you can't put it on your own server, let us know, too, and we'll
put it on our site. Thanks go to Rich Murphey and Upi Bhalla for their
help in adding information to this page.

## What's New?

Yes, I know this page hasn't been kept up. If someone would like to claim ownership, I'll be happy to cede it. Otherwise, we shall allow this page to more-or-less gracefully transform into a historical document.

Don't like the name "NeuroGeek"? Here's a short blurb about
the trendiness of being a geek,
taken from *The Computists' Communique*
**5**(39):

It's chic to be geek. (If that doesn't rhyme, you're either a geek or
a nerd.) Keyboard-phobic executives are Out; anyone who enjoys using computers
is In. *Newsweek* says so; *Business Week* says so; and *TV
Guide* says so, in this week's review of "Dweebs". Of course,
most of us are supposed to be rich: "If I had a million for every
time I was given a wedgie... Wait! I do!" Jeff Jarvis writes, "So
don't think of them as nerds or losers; in today's society, they are the
winners. Think of them as *Friends* with real jobs, more money, more
brains... and bad wardrobes." [*TV Guide*, 10/28/95, p. 6.]

(Geeks were carnival performers who bit the heads off live chickens or snakes -- possibly from Middle Low German for "fool"...)

We're looking for cute artwork, logos, etc. to add interest and color to this page.

There's now a revision date at the end of this document, so you can "easily" check to see if this page has been recently updated.

A people section has been added, to provide pointers to people and their work of possible interest.

## Quick Index:

- What are people up to now?
- Integration algorithms
- What could people be doing that they're not?
- Analysis Tools
- Resources
- People
- Our Australian mirror site (kinda late to find this out, right?).

### What are people doing now?

- Lumped neuron models
- No spatial information available.
- A reasonable approximation.
- Fewer state variables.
- Makes building networks more feasible.
- Focus on membrane properties for incorporation into more detailed compartmental models.
- System of nonlinear odinary differential equations.
- "Direct" analytical approaches.
- 3--30 state variables.
- Compartmental models
- Nonhomgeneity of cell membrane.
- Interest in geometry.
- Interest in propagation.
- Ad hoc heuristics for compartmentalization.
- Sub-compartments for examining chemical diffusion within (electrotonic) compartments.
- PDE models: why aren't they used (more often)?
- Are they helpful or hurtful, from a conceptual standpoint?
- Could they allow separation of geometry/membrane properties from implementation issues?
- Would existing PDE integrator approaches be more or less efficient than compartmental models?
- Multi-neuron models

Why?

How?

Why?

How?

### Integration algorithms

- Euler (forward & backward).
- Runge-Kutta (4th and 5th order).
- Predictor/corrector methods.
- Crank-Nicolson, used by both Genesis and Neuron,
and described in detail in Mascagni's chapter in
*Methods in Neuronal Modeling*. - Backward differentiation with variable stepsize and order (Epsode, Bryne & Hindmarsh).
- DASSL, a BDF method with variable order (1-5) and variable step size, L. Petzold.
- ODEPACK, Hindmarsh & others.
- CVODE, Cohen & Hindmarsh.
- LAPACK by Ed Anderson, Z. Bai, Chris Bischof, Jim Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, Susan Ostrouchov, and Danny Sorensen. Also available in C by J. Demmel & Xiaoye Li
- Mixed methods, Rush & Larson

#### Testimonials, Benchmarks & Practical Experiences

**Mike
Stiber** writes his own simulators
using ODEPACK. He's especially pleased with the
ability of the {L}SODAR subpackages to simultaneously solve a system
of constraint equations, allowing easy instrumentation of the
simulation for spike detection, etc.

**Rogene M. Eichler West**
of the Neuroscience Department at the University of Minnesota says, "We
have compared DASSL (L. Petzold) to the popular Crank-Nicolson
and found that when high accuracy is requested, DASSL is 60% faster...
Our comparison was on the Rallpack set of standards..."

**Rob Butera** of
the Mathematical Research Branch, NIDDK, NIH, says, "I now use CVODE,
which is available from NETLIB.
CVODE is an extension of LSODE written entirely in C - no more mixed language
programming! I have found my code to run twice as fast as RADAU5 using
similar error tolerances and similar order methods. Artie Sherman (here
at NIH) tells me that he has found LSODE code in FORTRAN to be faster than
comparable CVODE code in C. Still, I like the convenience of not having
to hassle with mixed-language programming."

### What could people be doing that they're not?

- PDE solvers.
- Variable spatial stepsize (dynamic recompartmentalization).
- Non-global time (each compartment with its own time & stepsize).
- Higher-order integration methods.
- Each compartment/neuron with its own integrator "instance"?
- Mixed discrete/continuous methods.
- Parallel machines.

### Analysis Tools (non-commercial starred)

- Mathtools.net portal Free scientific portal for MATLAB/MIDEVA m-files and toolboxes, and Excel/Java/Fortran/C++ resources and links. *
- Mathtools.com Complementary products for MATLAB, like MIDEVA (fast MATLAB replacement), MATCOM (Compiler for MATLAB), Visual MATCOM (integrate m-files into Visual C++) and others, all available for download.
- DSTool Poincaré sections, bifurcation diagrams *
- PyDSTool, developed
in collaboration with one of the original DSTool developers.
It is not entirely meant to replace DSTool. It is an "open" rather than
"closed" working environment, and it also contains some very
pro-neuro-modelling features such as a template kit for compartmental
modelling, support for mixed discrete/continuous models (#6 on the list
above) and stiff integrators that
*partially*support multiple time-scale integration (#3 on the list above), contination/bifurcation analysis, and dimension analysis tools for time-series data. - Phaseplane/XPP/XPPAUT: G. Bard Ermentrout
- AUTO
- KAOS *
- Ye Olde Spreadsheet
- MATLAB
- Mathematica
- Maple
- S-PLUS data analysis system
- OCTAVE (MATLAB-ish) *
- MuPAD computer algebra system *
- See also Applied Chaos Laboratory's list

A graphical software package for the analysis of dynamical systems. Includes an interface to AUTO

Probably the most popular program for bifurcation analysis of ODEs. The author states about the latest version: "To get a copy of AUTO94, people can send email to me at doedel@ama.caltech.edu. So far I have installed about 20-30 copies. I want to start slowly, in case there are some remaining bugs and portability problems."

### Resources

- Neural simulators
- Code, data, and information repositories
- Netlib
- Statlib
*Numerical Recipes*code- IMSL
- Guide to Available Mathematical Software
- The Geometry Center, the National Science and Technology Research Center for Computation and Visualization of Geometric Structures
- MGNet, a repository for information related to the multigrid, multilevel, and domain decomposition methods for PDEs.
- References
- Zwillinger,
*Handbook of Differential Equations* *Numerical Recipes**Methods in Neuronal Modeling*, Koch & Segev, eds., MIT Press, 1989.- McGregor's book
*The Book of Genesis*- TINS article
- Oran & Boris,
*Reactive/Diffusion Equations* - Nonlinear science e-print archive
- MSRI mathematics e-print archive
- Electronic Journal of Differential Equations
- E. Hairer and G. Wanner, Solving ODEs (II). Stiff and Differential-Algebraic Problems, Springer-Verlag, 1990.
- A.M. Zador and B. A. Pearlmutter, "Efficient Computation of Sparse Elements of the Inverse of a Generalized Tridiagonal Matrix". A slightly older version is available as a more official technical report,A.M. Zador and B. A. Pearlmutter "Efficient Computation of Sparse Elements of the Inverse of a Sparse Near-Tridiagonal Matrix with Application to the Nerve Equation", Technical Report OGI-CSE-93-003, Oregon Graduate Institute, dept of CSE, March 1993.

Edited by Jack Dongarra and Eric Grosse. Contains an enormous quantity of numerical code, including many differential equation solvers, optimization, approximation, graphics, parallel computation, etc. Most code written in FORTRAN (you always wanted to convert large programs from FORTRAN to C, right?).

Maintained by Mike Meyer. Another large repository, containing statistical software, datasets, and information.

Developed by staff of the Applied and Computational Mathematics Division and the Scientific Computing Environments Division within the Computing and Applied Mathematics Laboratory of the National Institute of Standards and Technology. A virtual repository of mathematical and statistical software components; you can search for software according to what problem it solves, package name, or module name. Includes extensive pointers to many other sources of math software and related information.

#### Testimonials, Benchmarks & Practical Experiences

**Rogene M. Eichler West**
of the Neuroscience Department at the University of Minnesota says, "We
wrote a simulator using LAPACK routines and found
that it performs 2.5 times faster than either Genesis
or Neuron (for a fixed level of accuracy) on both
the Rallpack standards and a few other tests." He goes on to note
that, typically, any special-purpose simulator will be faster than one
meant to be both general-purpose and reasonably easy to use, so pure performance
is only one metric. A technical report on all these performance comparisons
(and others) will be available soon.

"Also, a technical report available now is: 'A Renumbering Method to Decrease Matrix Banding in Equations Describing Branched Neuron-like Structures', R. M. Eichler West and G. L. Wilcox, Minnesota Supercomputer Institute Research Report UMSI 95/167, August 1995. (To be submitted to Journal of Computational Neuroscience). This would be of interest to folks using morphometrically realistic compartmental models."

### People

- Rob Butera, Mathematical Research Branch, NIDDK , National Institutes of Health, USA.
- Rogene M. Eichler West, Neuroscience Department, University of Minnesota.
- Eric Loeb, MIT AI Lab, who's thesis "focussed not on how to do the modelling (of muscles and spinal cord) but what to do with those models".
- Terence D. Sanger.
- Michael Stiber, Computing & Software Systems Program, University of Washington, Bothell.