What are atoms in the ising model of magnetism and what two variables control their behavior?
atoms are locations on a two-dimensional grid. They are controlled by the temperature of the magnet & the external magnetic field. Lower temperature -> more aligned spins, The external field could be caused by another magnet.
How does the emergent property of lasers occur (synergetics)? What is the order parameter and enslavement?
Increased energy -> transition from unsynchronized (regular) to powerful coherent light. order parameter = the coherent laser light wave that emerges. The individual atoms move in a manner consistent with this emergent property = Enslavement.. Motion of the atoms contributes to the formation of the order parameter (laser light wave). + the laser light wave dominates the movement of the individual atoms = cyclical cause-and-effect relationship/strong emergence
What did synergetics originate in?
in Haken’s work on lasers.
What is the curie point?
The temperature at which the magnet loses its magnetic force .
What is The Boltzmann entropy is a function of?
the number of ways (W) in which a particular macrostate can be realized.
What are glauber dynamics and why are they useful to model magnetism?
A technique that updates the spin states in a system based on energy differences and temperature, guiding it toward equilibrium. The normalization constant falls out of the equation. In this way we can simulate Ising systems with much larger than 20.
What do the two equations of the ising function define?
- H(x) -> the energy of a given state vector x
- P(X = x) The probability of a certain state
How can the mean field behavior of a fully connected Ising network (also called the Curie—Weiss model), be described?
.
A cusp
* external field = normal variable.
* Temperature = splitting variable.
* The relationship to self-organization is that when we cool a hot magnet, at some threshold the spins begin to align and soon are all 1 or -1 . This is the pitchfork bifurcation, creating order out of disorder.
What is the mean field behavior?
The emergent behavior of a magnet. The mean field behavior is the average magnetic field produced by all spins
What are dissipative systems (chemistry)?.
systems far from thermodynamic equilibrium (due to high energy input) in which complex, sometimes chaotic, structures form due to long-range correlations between interacting particles.
Explain the idea of “local entropy”
Stengers and Prigogine (1978) argued that while entropy indeed increases in closed systems, the process of self-organization in open systems can create ordered structures, resulting in a net decrease in what they referred to as “local entropy
What does The second law of thermodynamics state?
that the total entropy of an isolated system always increases over time and never decreases, meaning that spontaneous processes in nature tend to move toward a state of increasing disorder or randomness.
What does the theory of punctuated equilibria propose(biology)?
that species undergo long periods of stability interrupted by relatively short bursts of rapid evolutionary change
What are irreversible transitions and what does this say about catastrophes?
Irreversible transitions refer to changes in a system that cannot be reversed by simply reversing the conditions that caused the change, often resulting in a permanent change in the state or structure of the system (e. Frying an egg). While the catastrophe models we previously discussed exhibited symmetrical transitions (sudden jumps in the business card are symmetric), Prigogine’s research revealed that this symmetry does not always hold true
What idea did Kaufmann introduce (biology)?
the concept of self-organization into evolutionary theory. He argues that the small incremental steps in neo-Darwinistic processes cannot fully explain natural evolution.
What is a hypercycle?
A hypercycle is a network of self-replicating molecules or entities that mutually support each other’s production, leading to an increase in complexity and stability beyond what individual entities could achieve alone.
What is a cellular automaton (CA) (usually)?
It is usually a two-dimensional grid of cells, where cells interact with their neighbors, as in the 2D Ising model, but this can be generalized to more or less dimensions.
What is the difference between feedforward and reccurent neural networks?
Feedforward = process information in a single forward pass. recurrent =directed cycles, allowing them to capture temporal dependencies.
Conway’s game of life: For each cell, the next state for all cells is computedgiven the states of its neighbors,. What is this called?
synchronous updating
What is backpropagation?
A mechanism to update specific connections such that this mismatch or error is minimized over time.
Describe the general or unrestricted Boltzmann machine
- a recurrent unsupervised model.
- Basically an ising model where the connections between nodes have continuous values..
Training phase: - edge weights are updated according to the Hebb rule
Test phase: - present partial states by setting some (not all) nodes to the values of a particular learned input pattern
- By the Glauber dynamics, we update the remaining states that should take on the values belonging to the pattern - This pattern completion task is typical for ANNs.
What is the difference between general/unrestricted and restricted Boltzmann machines?
- General = any node can be connected to any other node and each node is an input node.
- RBM = nodes are organized in layers, with connections between layers but not within layers. (much more popular because of its computational efficiency)
What are Genetic algorithms?
a class of optimization algorithms inspired by the process of natural selection, where solutions to a problem evolve over generations
What is The Elo rating system?
A self-organizing method of calculating the relative skill levels of players in head-to-head games based on the results of their games.
