What are examples of undirected acyclic graphs?
- one with nodes on a line (but not a circle).
What types of graphs are trees and forests?
- Trees = Connected undirected acyclic graphs
- forests = partially unconnected undirected acyclic graphs
What are DAGs? (2 examples)
Directed acyclic graphs, e.g family trees and citation networks,
What is a preferential attachment network?
- “scale-free,”
- degree distribution that follows power law
- some nodes have many links but most just have a few
Why are preferential attachment networks often called complex?.
because they exhibit nontrivial structural patterns.
What does it mean that a network is scale-free, and what are such networks particularly useful for studying?
- the degree distribution looks the same no matter the scale.
Useful for studying - the robustness and vulnerability of networks to targeted attacks on highly connected nodes: Removing hubs with high connectivity potentially split the network into disconnected components and impede the network’s functionality. Because most nodes in the network have a small degree (few connections), randomly removing nodes tends not to disrupt the network’s overall structure.
What is the HSBM?
- hierarchical/nested stochastic block model (HSBM).
- extension of the SBM concept: clusters are nested within larger clusters, which in turn are part of even larger clusters in a continuous sequence resembling fractals.
What is “the emergence of a giant component”, how does this occur and what is the implication?
- prominent (second-order) phase transition in network theory
(1) start with a completely unconnected network
(2) randomly add links.
-> many small unconnected clusters at first,
-> then a giant component appears.
This happens when about n/2 links have been added. - Implication: randomly connected networks with a sufficient number of links are almost always connected networks.
What 3 aspects of dynamics can we distinguish between?
- dynamics on node values (e.g., Lotka—Volterra models),
- link values (connection strength in neural networks),
- cases where the structure of the network is dynamic (e.g giant component)
(These types of dynamics also coexist and interact)
What do Latent variables represent in statistical modeling?
unobservable/underlying factors that cannot be directly measured or observed.
Where do the statistical tools for analyzing latent variables come from?
- modern test theory
- structural equation modeling (SEM)
What is the main motivation for the network approach in psychology?
underlying common causes (latent variables) are unsatisfactory if they cannot be identified independently of the observed relationships they are supposed to explain.
What is the Cattell-Horn-Carroll (CHC) model?
- a g-model/factor model of intelligence (often called “the standard model”)
- test scores load on subfactors such as visual processing (Gv) and fluid reasoning (Gf)
- subfactors are correlated
- These latent correlations are explained by the general, higher-order factor g
Reflective vs formative interpretations of the factor model?
- Reflective = the latent factor is a common cause for the observations. e.g temperature -> e.g different thermometers
- Formative = factor is not a common cause - just an index (e.g., an economic index) that summarizes the state of many interacting components (e.g companies)
How does interventions affect formative and reflective models differently?
In a reflective model, intervening on on one x (e.g thermometer) will only change that particular x because each x has no outgoing connections. In the formative case, only interventions on the x can have an overall effect.
What is the mutualism model and what is the basic idea behind it?
- an alternative model that is consistent with the formative interpretation of the factor model.
The idea is: - cognitive system consists of many functions that develop over time in an autocatalytic process based on experience and training
- but also due to weak positive reciprocal interactions between developing cognitive function
- These mutualistic interactions can create correlations that are typically associated with factor models.
Examples of mutualistic interactions between cognitive functions?
- between STM and cognitive strategies, * language and cognition (syntactic and semantic bootstrapping),
- cognition and metacognition
- action and perception
- performance and motivation
What is the difference between a competitive and a mutualistic lotka-volterra model?
competitive = M (interaction matrix) contains mostly negative values
* limit cycles and other nonlinear phenomena may occur
Mutualistic = positive M
* either convergence to a positive state or exponential growth. (This exponential growth is an unfortunate aspect of the Lotka—Volterra mutualism model)
What is a limitation of the mutalism models?
only the activation of nodes is updated. The weight and structure of the network are fixed.
What is the Fortuin—Kasteleyn model and what can it explain in terms of intelligence?
- a generalization of the Ising model,
- both nodes and links are random variables.
- whenever two abilities are connected, they are necessarily in the same state (i.e either both present or both absent)
- It provides a parsimonious explanation of the positive manifold and hierarchical factor structure of intelligence.
What is resilience in dynamic terms and which states have lower/higher resilience?
- The ability of a system to recover from perturbations and maintain its current equilibrium.
- The Metastable states (E.g a less deep minimum) have less resilience than the globally stable state
How does resilience relate to healthy and unhealthy states?
associated not with the healthy or unhealthy state but with the stability of these states
How do perturbations differ from interventions and how does that relate to resilience?
- Interventions change the equilibrium landscape to allow a sustainable change to a healthy state.
- Perturbations (a brief intervention or a positive or negative event) can have a permanent or temporary effect, depending on which state is more resilient.
What are connectionist models of attitudes and in which framework were these developed?
- attitude units (e.g., beliefs) form a connected network
- Their activations (usually between 1 and -1) are updated based on the weighted sum of internal inputs from other units and an external input - according to either the delta rule (supevised learning rule) or the hebb rule
- Developed in the parallel distributed processing (PDP) framework,
