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  1. Biologically Inspired Intelligent Systems Lecture 3 Dr. Roger S. Gaborski

  2. MATLAB - transpose >> A = [1;2; 3; 4; 5] A = 1 2 3 4 5 >> B = A' B = 1 2 3 4 5

  3. >> M = rand(5) M = 0.8147 0.0975 0.1576 0.1419 0.6557 0.9058 0.2785 0.9706 0.4218 0.0357 0.1270 0.5469 0.9572 0.9157 0.8491 0.9134 0.9575 0.4854 0.7922 0.9340 0.6324 0.9649 0.8003 0.9595 0.6787 >> M1 =M>.5 M1 = 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1

  4. >> A * M1 Error using * Inner matrix dimensions must agree. >> A’ * M1 ans = 12 12 10 12 13

  5. >> A' ans = 1 2 3 4 5 >> M1 M1 = 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 A’ is 1 x 5, M1 is 5 x 5 A’ * M1  (1x5)*(5x5)  (1x5)

  6. Sign: >> n = rand([1,5])-.5 n = 0.2577 0.2431 -0.1078 0.1555 -0.3288 >> sign(n) ans = 1 1 -1 1 -1

  7. Matlab Examples • Create a matrix with 7 rows and 7 columns containing random numbers: • R = rand([7,7]) • R = • 0.7547 0.9597 0.6991 0.8407 0.2511 0.9172 0.0540 • 0.2760 0.3404 0.8909 0.2543 0.6160 0.2858 0.5308 • 0.6797 0.5853 0.9593 0.8143 0.4733 0.7572 0.7792 • 0.6551 0.2238 0.5472 0.2435 0.3517 0.7537 0.9340 • 0.1626 0.7513 0.1386 0.9293 0.8308 0.3804 0.1299 • 0.1190 0.2551 0.1493 0.3500 0.5853 0.5678 0.5688 • 0.4984 0.5060 0.2575 0.1966 0.5497 0.0759 0.4694

  8. Display matrix as an image • figure, imshow(R,'InitialMagnification','fit')

  9. Multiply every element in the matrix by 3.14 • R3 = R*3.14 • R3 = • 2.3697 3.0136 2.1951 2.6399 0.7884 2.8800 0.1694 • 0.8667 1.0688 2.7974 0.7984 1.9344 0.8975 1.6667 • 2.1343 1.8377 3.0122 2.5569 1.4861 2.3776 2.4466 • 2.0570 0.7028 1.7183 0.7647 1.1042 2.3667 2.9328 • 0.5106 2.3590 0.4353 2.9179 2.6088 1.1946 0.4079 • 0.3737 0.8010 0.4688 1.0989 1.8377 1.7830 1.7861 • 1.5649 1.5887 0.8086 0.6173 1.7261 0.2382 1.4739

  10. Display R3 figure, imshow(R3,'InitialMagnification','fit')

  11. Correctly display R3 >> figure, imshow(R3,[],'InitialMagnification','fit')

  12. Matrix multiply vs. point by point multiply >> A = [1 2;3 4] A = 1 2 3 4 >> B = [2 3; 5 6] B = 2 3 5 6 >> A*B ans = 12 15 26 33

  13. Matrix multiply vs. point by point multiply >> A = [1 2;3 4] A = 1 2 3 4 >> B = [2 3; 5 6] B = 2 3 5 6 >> A.*B ans = 2 6 15 24

  14. >> Z = zeros(7) Z = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 >> Z(3:5,3:5)=1 Z = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

  15. >> R R = 0.7547 0.9597 0.6991 0.8407 0.2511 0.9172 0.0540 0.2760 0.3404 0.8909 0.2543 0.6160 0.2858 0.5308 0.6797 0.5853 0.9593 0.8143 0.4733 0.7572 0.7792 0.6551 0.2238 0.5472 0.2435 0.3517 0.7537 0.9340 0.1626 0.7513 0.1386 0.9293 0.8308 0.3804 0.1299 0.1190 0.2551 0.1493 0.3500 0.5853 0.5678 0.5688 0.4984 0.5060 0.2575 0.1966 0.5497 0.0759 0.4694 >> R.*Z ans = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.9593 0.8143 0.4733 0 0 0 0 0.5472 0.2435 0.3517 0 0 0 0 0.1386 0.9293 0.8308 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

  16. Neuron Models • Example of a neuron model

  17. But to build even the simple neuron model we need data • How do we get information about the brain? • In humans, imaging, effects of brain damage • Primates and other creatures – imaging, electrodes

  18. New (or Improved) Data Collection Techniques • Individual neuron recordings (100’s) • New dyes to observe brain metabolism • Brain imaging (MRI, fMRI, CAT, PET, …)-http://en.wikipedia.org/wiki/Neuroimaging • Computer Simulation and Analysis • Opportunity to apply analysis and modeling techniques to gain new insights to the functioning of our brain

  19. Magnetic Resonance ImagingMRI • Visual internal structures in the body • Good at imaging soft tissue

  20. Functional MRI • Visualize neural activity • Indirect measurement • Commonly used in brain mapping • 2-3 mm resolution

  21. PET Scan (Positron Emission Tomography) • Measures emissions from radioactively labeled metabolically active chemicals • Tumors, Alzheimer’s disease cause change in metablism which can be detected by PET scans

  22. Functional MRIHearing Words and Speaking Words http://www.nia.nih.gov/NR/rdonlyres/

  23. Seeing Words and Thinking About Words http://www.nia.nih.gov/NR/rdonlyres/

  24. Functional MRI A 20-year old female drinker A 20-year old female nondrinker Response to the spatial working memory task. Brain activation is shown in bright colors. www.alcoholism2.com/

  25. PET Scan 20 Year Old 80 Year Old http://www.nia.nih.gov/NR/rdonlyres/

  26. PET Scan of Normal Brain and Alzheimer's Disease Brain http://www.nia.nih.gov/NR/rdonlyres/

  27. Real Neurons Outline of how real neurons function www.alanturing.net/

  28. How Do Real Neurons ‘Operate’ ? http://ei.cs.vt.edu/~history/NEURLNET.HTML

  29. A Careful Examination of Neurons and the Flow of Information • BACKGROUND INFORMATION: Three factors influence the flow of ions into and out of neurons: • Charge • Diffusion • Concentration

  30. Charge • Recall, like charges repel (both positive or both negative), opposite charges attract (positive and negative) • Ions are charged - Number of electrons do not equal number of protons • Sodium, Na+ • Potassium, K+ • Chloride, Cl- • Bicarbonate HCO3- • Protein-

  31. Diffusion • Diffusion – random movement of ions or molecules from a high concentration to a low concentration • Illustration: • Place a drop of red dye into a container of clean water • The red dye will distribute itself equally moving from a high concentration to areas of low concentration

  32. Concentration Gradient • Concentration Gradient – the difference in concentration of a material between two spatial regions • Voltage Gradient- when a salt solution composed of positive and negative ions is poured into a glass of water • Ions move down a voltage gradient from area of high charge to an area of low charge • Positive and negative ions distribute themselves equally (electrostatic gradient)

  33. Cell Membrane V -+ +- -+ +- -+ -+ +- -+ +- -+ -+ + -+ + -+ - - - Add salt to contain of water with a barrier (cell Membrane). Ions cannot pass through Membrane now has holes so that only Cl- ions can pass. After a period of time Cl- ions will diffuse to right hand side. Cl- is not equally distributed because some are attracted to positive charges sodium, Na+ resultingin a Voltage difference across the membrane

  34. Axon • Assume axon is modeled by a cylinder. • The walls of the cylinder is the membrane. • This membrane contains ion channels that when open allow specific ions to pass

  35. Action Potential Image from: http://scienceblogs.com/clock/2006/06/bio101_lecture_6_physiology_re.php

  36. Resting Potential • The unequal distribution of positively and negatively charged ions across the membrane results in a voltage potential • Resting potential is typically -70mv, but can vary for different neurons

  37. Action Potential • The action potential is a rapid change of the membrane potential caused by the opening and closing of ion channels • At the start of an action potential the sodium channels open • What will the voltage difference between the inside and the outside of the axon have on the sodium ions?

  38. Action Potential • At the start of an action potential the sodium channels open • What will the voltage difference between the inside and the outside of the axon have on the sodium ions? • The positively charged sodium ions will move to the inside (opposite charges attract) • As more positive ions enter the axon it becomes more positively charged

  39. Movement of Action Potential Down the Axon • You can think of the action potential being generated by the flow of ions crossing the membrane as first the sodium channel opens, then closes and the potassium channel opens, then closes • This sequence of opening and closing of channels flows down the length of the axon resulting in the action potential flowing down the length of the axon

  40. http://faculty.washington.edu/chudler/ap.html

  41. Action Potential • http://www.dnatube.com/video/1105/Action-potential • http://www.dnatube.com/video/28972/A-Look-at-the-Action-Potential

  42. Pre-Synaptic and Post-Synaptic Neurons • The action potential travels down the axon from the cell body to the synapse (pre-synaptic neuron) • At the synapse the electrical signal is converted to a chemical signal • The chemical signal is propagated to the post-synapse neuron’s dendrite (Dendrites extend from the post-synaptic cell body and receive inputs from other pre-synaptic neurons through connections called synapses) • Neurons also communicate with muscle cells through chemical synapses

  43. http://en.wikipedia.org/wiki/Image:SynapseIllustration.png

  44. Action Potential and Synapse • http://www.youtube.com/watch?v=HnKMB11ih2o&feature=fvwp • http://www.youtube.com/watch?v=U0NpTdge3aw&feature=endscreen&NR=1 • http://www.youtube.com/watch?v=ifD1YG07fB8 • http://www.youtube.com/watch?v=9nUY6o-LCWY&NR=1 • http://www.youtube.com/watch?v=LT3VKAr4roo&feature=related

  45. Neurotransmitters • There are more than 25 known neurotransmitters • The combination of neurotransmitter and receptor either excites or inhibits the post-synaptic cell

  46. SUMMARY:Action Potential Generation • Step 1: Synaptic terminal receives action potential from its neuron • Step 2: Neurotransmitter (chemical) is released which crosses the synaptic cleft • Step 3: Results in depolarization in post-synaptic neuron by opening ion channels

  47. Action Potential Generation • Step 4: Summation of a sufficient number of depolarizations within the time constant of the receiving neuron (20-30 ms) produces sufficient depolarization that the neuron fires an action potential • 5000-20000 inputs per neuron

  48. Summary • Neuron: • Computational element • Sums inputs within a time constant • When sum of excitatory-inhibitory inputs exceed a threshold an action potential is produced which propagates down the neuron’s axon to all of its outputs

  49. Abstraction • Make simplifications to a system without loosing important features we want to understand • Study problem at various levels and make connections between different levels to explain how low level factors can (biochemical processes in a single neuron) influence large scale systems, such as behavior

  50. Light and Switch Example • What does an electrician need to model? • What would a light bulb designer need to model Need enough information model system you are trying to understand