Neural Dynamics & Computation

Question 1

What is a dynamical system?

Answer 1

A system whose states varies over time, and is described predefined rules

Question 2

What is the significance of using oscillations / waves in biological models?

Answer 2

They correspond to periodic activity and are ubiquitous in biological systems

Question 3

What frequency are slow-delta waves in the brain?

Answer 3

0-4 Hz

Question 4

What frequency are theta waves in the brain?

Answer 4

4-8 Hz

Question 5

What frequency are alpha waves in the brain?

Answer 5

8-12 Hz

Question 6

What frequency are beta waves in the brain?

Answer 6

13-30 Hz

Question 7

What frequency are gamma waves in the brain?

Answer 7

> 40 Hz

Question 8

How can we measure brain waves

Answer 8

Invasive probes, local field potentials

Electroencephalogram

Question 9

What is a matrix?

Answer 9

Array of numbers organised in to rows and columns

Question 10

What is a vector?

Answer 10

A special type of matrix with only one row, or only one column

Question 11

What is the identity matrix?

Answer 11

Matrix of 0s with 1s down the diagonal

Question 12

What is a singular matrix?

Answer 12

A square matrix that does not have an inverse, meaning its determinant = 0

Question 13

How can we represent two linear equations as a matrix?

eg. x + 2y = 6
3x + y = 3

Answer 13

[1 2] [x] = [6]
[3 1] [y] [3]

Question 14

What is an eigen vector?

Answer 14

A vector that has its direction unchanged by a given linear transformation

Question 15

What is an eigen value?

Answer 15

The scalar quantity by which an eigen vector is multiplied by in a linear transformation (can be negative)

Question 16

How to calculate the determinant of a matrix

Answer 16

ad - bc

Question 17

How to calculate the trace of a matrix?

Answer 17

a + d

Question 18

What is the equation we can use to solve for eigen values?

Answer 18

determinant [A-lambda I] = 0

Question 19

How can you find the eigen vectors once you have an eigen value?

Answer 19

Substitute in your values of lambda and solve

Question 20

What is a derivative?

Answer 20

An expression representing the rate of change of a function relative to an independent variable

Question 21

What is a first order differential equation?

Answer 21

One where the highest power is dy/dx = y

Question 22

What is a second order differential equation?

Answer 22

One where the highest power is d^2y / d^2x

Question 23

What is a fixed point?

Answer 23

A solution for x where x’ = 0

Question 24

What is the classification of a fixed point with real and negative eigen values?

Answer 24

Stable node

Question 25

What is the classification of a fixed point with real and positive eigen values?

Answer 25

Unstable node

Question 26

What is the classification of a fixed point with real and one positive and one negative eigenvalue?

Answer 26

Saddle node

Question 27

What is the classification of a fixed point with complex and negative eigen values?

Answer 27

Stable spirals

Question 28

What is the classification of a fixed point with complex and positive eigen values?

Answer 28

Unstable spirals

Question 29

What is a phase plane?

Answer 29

Solutions of x’ = Ax as trajectories on the (x,y) plane

(A is a 2x2 matrix)

Question 30

What is the most basic way to model a neuron as an electrical circuit?

Answer 30

Capacitor - Cell membrane
Cell - Resting membrane potential
Resistor - Pooled conductance