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Depiction of the IAF model for Cell 1 and Cell 2 from [link] . We calculate the conductances and voltages for Cells 1 and 2 by [link] and [link] , respectively. v t h = - 54 m V , and w e x t = w 12 = 2 S are the weights of the synapses from the external source and Cell 1, respectively. It can be seen that in Place Field 1 ( 0 < t < 100 ), Cell 1 receives external input every 20 ms (in the form of conductance spikes), and in Place Field 2 ( 100 t < 200 ), Cell 2 receives the external input. At each external input spike, the corresponding cell fires (its voltage spikes) and gives a small amount of input to its neighboring cells. ( IAF2cellsweight.m )


To determine how the weights of the synapses change, we use an STDP model [link] . The spikes times of the pre- and post-synaptic cells are compared, and the smaller the time difference, the more the weight is adjusted. See [link] . The percentage of weight change is determined by

F ( Δ t ) = A + e Δ t / τ + , Δ t < 0 - A - e - Δ t / τ - , Δ t 0 ,

where Δ t = t p r e - t p o s t and A + and A - scale the maximal amount of change allowed when Δ t is close to 0 [link] . F ( Δ t ) is depicted in [link] .

Percentage of weight change due to STDP. This graph shows that as Δ t = t p r e - t p o s t approaches 0, the percentage of change in the weight of the synapse increases [link] . F ( Δ t ) is calculated by Equation [link] .

In our 120-cell model, we set a lower bound for the weights at 0 m V and an upper bound at 5 m V . The necessity for an upper weight bound is one of the weaknesses of the STDP model, so Andrew Wu, another member of this PFUG, has done work with other plasticity models. See the link "Mathematical Models of Hippocampal Spatial Memory".

The work with the 120-cell model is all computational. Our results show that each lap, the weight of the synapse from Cell 1 to Cell 2 ( w 12 ) increases toward a set weight bound and the weight of the synapse from Cell 2 to Cell 1 ( w 21 ) decreases to 0 as in [link] . We also see that after 4 laps around the path, the place fields start to shift backward. [link] shows that the spike time of Cell 2 decreases each lap, which is indicative of a backward shift of Cell 2's place field. See IAF120cells1stspks.m .

Weights of synapses over time. The weight of the synapse from Cell 1 to Cell 2 ( w 12 ) increases each lap (1 lap = 12,000 ms) as the weight of the synapse from Cell 2 to Cell 1 ( w 21 ) decreases each lap to 0. ( IAF120cellsSTDP.m )
Backward shift of place field of Cell 2 in m s . The rat spends 100 m s in each place field. It can be seen here that after as few as 4 laps around the track, place cell 2 starts to fire earlier and its place field shifts backwards. ( IAF120cells1stspks.m )

Model for analysis

Simple 1-cell system. Cell 1 receives input of weight w i n p at an interspike interval I .

We begin by considering only one place cell which receives input from one external source with constant weight w i n p at a set interspike interval, I , as depicted in [link] . The following equation gives the voltage v in m V of the cell at time t with n total input spikes:

τ v ' ( t ) = ( v r - v ( t ) ) + w i n p i = 1 n δ ( t - T i )

where τ = 20 m s is the membrane time constant, v r = - 70 m V is the resting potential, T is the set of input spike times, and δ ( t - T i ) is the Dirac delta function. This is a simplification of equation [link] .

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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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