Docstoc

PowerPoint Presentation - KAIST

Document Sample
PowerPoint Presentation - KAIST Powered By Docstoc
					           Wiring Cost
   in the Organization of
   a Biological Network
Yong-Yeol Ahn*, Beom Jun Kim, Hawoong Jeong
          KAIST, Republic of Korea



                               * yongyeol@gmail.com
2
Putting a “Neural Network Model”
      on a “Neural Network”




                    The ability to recognize patterns must be
                    crucial for surviving and mating


 • Hopfield model on C. elegans neural
   network. (Beom Jun Kim, 2004)
                 Hopfield Model
Neurons can have two states. At each time step, each
neuron’s state is determined by other neurons which have
links to it. -> The state vector falls into some attractors.


       +1
             2
  -1
        -3

             1
   +1
                          Ex)   (+1) x 2 + (-1) x (-3) + …
     Performance Measure
• By the Hebb’s rule, the Hopfield network
  can learn several patterns.

• After learning process, we try with the
  testing pattern which has some error in it.

• Does this testing pattern end up to the
  learned pattern? How much is the overlap?
                                        5
6
                 So, Why?
• If we assume that the measure is good, Possible
  other constraint is ‘wiring cost’.

• Energy consumption acts a crucial role in the
  operation of the brain. (A brain consumes more
  energy than heart, about 20% of all energy spent)

• Ganglia order in C. elegans is the global minima.
  (Cherniak1994)
The C. elegans neuronal map
                  Assumptions:

                  • Head neurons are
                  placed in the virtual
                  cylinder which wraps
                  the pharynx.

                  • Body neurons are
                  placed just below the
                  cuticle layer (because
                  of the body cavity)
Is C. elegans neural network
 optimized by wiring cost?
Two variational methods

Node Swapping
(conserving topology)




Edge Excange
(conserving positions
and degrees of all
neurons)
Optimized Network vs.
  Random Network

                The C. elegans
                network is far from
                random nework

                If we neglect the
                body-spanning links,
                It approaches toward
                the optimal network.
     Cumulative Distribution of
distance(cost) between two neurons
• Exponential
  Decay

• Three length
  scales

• Body spanning
  Links (like spinal
  cord)
  Is Clustering Coefficient
 Playing an Important Role?
• We equilibrate the
  network by rewiring
  randomly around
  given cost.

• C. elegans has much
  bigger c.c. than this
  randomly rewired
  networks.



                          12
                    Conclusion
•   We constructu the C. elegans neural network with
    geometrical information.

•   The distribution of distances between neurons in C.
    elegans neural network follows piecewise exponential
    decaying funtion.

•   Although the neural network is not optimal, it is far from
    random.

•   The performance measure (Hopfield model) does not play
    a crucial role in the organization of C. elegans neural
    network.

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:0
posted:2/15/2013
language:English
pages:13