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This report summarizes work done as part of the Hippocampus Neuroscience PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs, Faculty, Undergraduates and Graduate students formed round the study of a common problem.This module reproduces the work of A Lansner and E Fransen's "Modelling Hebbian cell assemblies comprised of cortical neurons". This work was studied in the Rice University VIGRE class CAAM 499 in the Fall of 2007.


One hypothesis on how ideas are structured in the brain is that groups of cells form a unit called a cell assembly. The cells within the assembly are connected with strong excitatory synapses. Thus, when enough activity occurs in the neurons within the assembly, then the entire assembly will have the ability to activate. An active assembly would meet the definition that the cells within the assembly are firing at a high rate in the same time frame. Successions of assembly activation could be the basis of how to form thoughts and give a mental representation for different concepts. This idea was introduced by Donald Hebb in The Organization of Behavior . The assembly will eventually shut down if the source of stimulation ceases or a competing assembly can provide inhibition. This theory can be extended to explain how learning occurs and possible phenomena such as perspective-rivalry. For instance, in optical illusions, such as the nectar cube shown below, there are two different possible interpretations of the perspective. It is possible that two different assemblies represent the different perspectives. In order to switch perspectives one must shut down the current perspective assembly and activate the alternate perspective. There could also be a hierarchy of assemblies. Sub-assemblies could give rise to larger assemblies. Due to synaptic plasticity different sub-assemblies that are activated in similar orders through repetition allows new larger Assemblies to form. If sufficient clues that are represented by smaller sub-assemblies are activated, the brain will be able to activate the larger assembly.

The Neckar Cube has two possible perspectives. Cell Assembly rivalry could be responsible for competing interpretations.

Module goal

To get some insight on whether this is plausible we want to construct biologically accurate computational models and test assembly activation and inhibition. This module will follow the paper Modeling Hebbian cell assemblies comprised of cortical neurons , by A Lanser and E Fransen. It will show how to reproduce the results contained in the paper and the mathematics involved.

Here is a brief summary of what is ahead:

1.) Go over the neuron models and the different ion channels.

2.) Show how synaptic input is modeled.

3.) Show how differential equations are solved with time stepping.

4.) Show how patterns which represent different assemblies are used to "train" a network and produce weights.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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