Model Construction and CA Flashcards
Describe the steps of using mathematical models
to explain biological data
- Collect biological facts, and define the
question (e.g. tumour radius growth data) - Define the conceptual model (e.g. cell division, starvation, apoptosis)
- Formulate the mathematical model (e.g. N(t) = N_0 * e^rt)
- Define/write the model implementation (e.g. in python, c++,pen)
- Define visualisations and observables (e.g. plot radius “r”)
- Run model simulations
- Model falsification: find conditions for which the model does not work
- Repeat and improve with the obtained knowledge until happy
What is Eden Growth?
A stochastic cellular automata model where cells divide into adjacent site if space is available. A spatial model of colony growth.
Eden growth produces “rough” (fractal) boundaries which allow for faster invasion and more access to nutrients than smooth
boundaries
What kind of growth is Eden growth?
Linear (until carying capacity is reached)
unlike the logistic growth which is exponential
Describe a finite-state-automaton
It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSA can change from one state to another in response to some inputs; the change from one state to another is called a transition. An FSA is defined by 5 elements: a set of possible states (S), set of initial state(s_0), set of inputs (Σ), that trigger each transition following a stat-transition function δ and a final set of states F
What are the two types of finite-state-automata?
Deterministic and probabalistic
What is a cellular automaton?
A CA consists of a lattice of finite-state-automatons. Adjacent sites (“cells”) are coupled to one another, with Σ = S input updates at fixed clock ticks on the adjacent cells.
What are the two main types of adjacency neighbourhood in a 2D CA?
Van Neumann and Moore
Describe Conway’s Game of Life
An example of a Turing complete CA
Describe the 4 Wolfram classes of CA behaviour
Class 1: Converges onto uniform state
Class 2: Converges onto repetitive or stable
state
Class 3: Converges onto “random” state
Class 4: There are both randomness and repetitive patterns, combining Class 2 and Class 3. Example: Conway’s GoL
What kind of rule describes the following final pattern?
A voting (majority) rule ( synch, moore neighbourhood)
Describe the voting rule!
What is the following pattern result of?
Voting rule after just a couple of simulation steps (synch)
What is the following pattern the result of?
Probabalistic synch voting rule with probability for update p = 0.7 <=> probability for flip (1-p) = 0.3
What rule?
Probabalistic synch voting rule with p = 0.5
What rule?
Probabalistic synch voting rule with p=0.1
What rule?
Probabalistic voting rule synch with p = 0.9
This is the result of probabalistic voting rule with p = 0.5. Is this simulation synch or asynch
asynch
This is the result of probabalistic voting rule with p = 0.5. Is this simulation synch or asynch
synch, this flashy pattern is more of a result of synchronicity
What Wolfram class is the 1D system described by this kinetogram
4
What Wolfram class is the 1D system described by this kinetogram
2
