Poor Participants and Even Poorer Free Riders in Nepal’s ...
Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor...
-
date post
15-Jan-2016 -
Category
Documents
-
view
217 -
download
0
Transcript of Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor...
![Page 1: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/1.jpg)
Levels in Computational Neuroscience
Reasonably good Reasonably good understanding (for our understanding (for our
purposes!) purposes!)
Poor understanding Poor understanding
Poorer understanding Poorer understanding
Very poorer Very poorer understanding understanding
![Page 2: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/2.jpg)
From neuron to network
![Page 3: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/3.jpg)
The layered structure of the first visual area, and connections to other areas (Fig. 27.10 in Kandel and Schwartz, Principles of Neural Science)
![Page 4: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/4.jpg)
The columnar organization of the monkey visual cortex (Fig. 12.6 in Shepherd, The Synaptic Organization of the Brain)
![Page 5: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/5.jpg)
Definition of the firing rate in terms of a temporal average. (Fig. 1.9, Spiking Neuron Models)
![Page 6: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/6.jpg)
Definition of the firing rate in terms of the peri-stimulus-time-histogram (PSTH) as an average over several runs of an experiment. (Fig. 1.10, Spiking Neuron Models)
![Page 7: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/7.jpg)
Definition of the firing rate as a population density.
Gerstner & Kistler Fig. 1.11
![Page 8: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/8.jpg)
Feedforward inputs to a single neuron.
Dayan and Abbott Fig. 7.81
![Page 9: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/9.jpg)
Feedforward and recurrent networks
Dayan and Abbott Fig. 7.3
![Page 10: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/10.jpg)
Dayan and Abbott Fig. 7.4
Coordinate transformations during a reaching taskTargetFixation
Gaze angle Retinal angle
Body coordinates
Objective: transform from retinal coordinates to body coordinates
![Page 11: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/11.jpg)
Tuning curves of a visually responsive neuron
in premotor cortex
Dayan and Abbott Fig. 7.5
Head fixed
Fixate on
• Body coordinates
• Response curve fixed!
• Retinal coordinates
• Curve shifts to compensate!
Head rotates
Fixation fixed
Model tuning curve
g=00g=100 g=-200
![Page 12: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/12.jpg)
Dayan and Abbott Fig. 7.6
The gaze-dependent gain modulation of visual responses of neurons in area 7a
Tuning curve
2 Gaze directions
Gaze independence!
Related to s
2D tuning function
![Page 13: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/13.jpg)
burst and an integrator neurons involved in horizontal eye positioning
Dayan and Abbott Fig. 7.7
![Page 14: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/14.jpg)
Eigenvector expansion
![Page 15: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/15.jpg)
Steady state rates – linear network
Real-valued matrix M: use real and imaginary parts
![Page 16: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/16.jpg)
Selective amplification by a linear network
Dayan and Abbott Fig. 7.8
Input: cosine with peak at = 0o + added noise
Fourier amplitude of inputs
Output: steady state
Fourier amplitude of output
= 0 component enhancedAll Fourier components present
![Page 17: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/17.jpg)
Effect of nonlinearity on amplification
Dayan and Abbott Fig. 7.8
Smoother response
Several Fourier components appear
![Page 18: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/18.jpg)
Visual information flow
Dayan and Abbott Fig.2.5
Center surround responseOriented response
![Page 19: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/19.jpg)
Visual receptive fields
Dayan and Abbott Fig. 2.25
Mathematical fit
Actual response
LGN neuron Center surround
Orientation selective
V1 neuron (simple)
![Page 20: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/20.jpg)
Hubel Wiesel model
Low response
Simple summation
Vertical response Undirected response
High response
![Page 21: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/21.jpg)
Effect of contrast
Dayan and Abbott Fig. 7.10
4 input contrast levels
Note: response is amplified but
Real responses Network amplification
not broadened
![Page 22: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/22.jpg)
Nonlinear winner-takes-all selection
Dayan and Abbott Fig. 7.12Dayan and Abbott Fig. 7.12
Input: cantered at ±900Output: Higher peak selected
![Page 23: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/23.jpg)
Associative recall
Dayan and Abbott Fig. 7.16
2 representative units Memory: units 18-31 high, others low
Memory: every 4th unit high
Nv=50, 4 patterns
Partial inputs Converged outputs
![Page 24: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/24.jpg)
Pattern recall – Hopfield model
Input Output
Time
![Page 25: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/25.jpg)
Dayan and Abbott Fig. 7.17
Excitatory-Inhibitory network Nullclines Eigenvalues
Unstable
Stable
![Page 26: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/26.jpg)
Dayan and Abbott Fig. 7.18
Excitatory-Inhibitory network Temporal behavior Stable fixed point
30msI
![Page 27: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/27.jpg)
Dayan and Abbott Fig. 7.19
Excitatory-Inhibitory network Temporal behavior Unstable fixed point –
limit cycle
50msI
![Page 28: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/28.jpg)
Dayan and Abbott Fig. 7.20
Extracellular field potential in olfactory bulb
Olfactory model I
To cortex
Excitatory
Inhibitory interneurons
Sniffs
Oscillatory neural activity
No fast oscillations
![Page 29: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/29.jpg)
Dayan and Abbott Fig. 7.16
Olfactory model II Activation functions Eigenvalues
Region of instability
![Page 30: Levels in Computational Neuroscience Reasonably good understanding (for our purposes!) Poor understanding Poorer understanding Very poorer understanding.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649d4e5503460f94a2d0e1/html5/thumbnails/30.jpg)
Dayan and Abbott Fig. 7.22
Olfactory model III
Behavior during a sniff cycle
Identity of odor determined by:
• Amplitudes and phases of oscillations
• Identity of participating mitral cells