6 Matching Annotations
  1. Dec 2022
  2. Aug 2020
  3. May 2020
  4. Jan 2020
    1. What does it mean for a matrix UUU to be unitary? It’s easiest to answer this question algebraically, where it simply means that U†U=IU^\dagger U = IU†U=I, that is, the adjoint of UUU, denoted U†U^\daggerU†, times UUU, is equal to the identity matrix. That adjoint is, recall, the complex transpose of UUU:

      Starting to get a little bit more into linear algebra / complex numbers. I'd like to see this happen more gradually as I haven't used any of this since college.

  5. Sep 2018
    1. Whilespatial biases may contribute to these findings,asnodes belonging to the same module tend to be anatomically colocalized [7,8],they cannot explain these effects entirely [94,95].

      Very nice review. Please note the reference [94] (Pantazatos et al.) is misplaced because they did not argue that spatial biases cannot entirely explain the putative links between CGE and functional segregation. Instead, they argued there was insufficient evidence in the original Richiardi et al. study linking elevated CGE with resting state functional networks, and that spatial biases may in fact entirely account for their findings. To describe the debate/exchange more accurately, I would suggest replacing the below sentence

      “While spatial biases may contribute to these findings, as nodes belonging to the same module tend to be anatomically colocalized [7,8], they cannot explain these effects entirely [94,95].”

      with the below paragraph:

      “Spatial biases may contribute to these findings, as nodes belonging to the same module tend to be anatomically colocalized [7,8]. Pantazatos et al. argued that these findings are entirely explained by spatial biases [94]. They showed that elevated CGE, as defined in the original Richiardi et al. study, falls monotonically as longer distance edges are removed. Moreover, they showed that 1,000 sets of randomly spaced modules all have significantly high CGE when using the same null distribution defined in the original Richiardi et al. analyses. Therefore, elevated CGE is not specifically related to functional segregation as defined by resting state functional networks, which is in direct contradiction to the main conclusion of the original Richiardi et al. study. Since randomly placed modules do not align (spatially) with any distributed pattern of functional segregation, the finding of elevated CGE may instead be attributed entirely to anatomical colocalization of the nodes within each module. In their rebuttal to [94], Richiardi et al. argue spatial biases cannot explain their findings entirely [95]. However, the authors do not offer an explanation for significantly high CGE observed for randomly spaced sets of modules, other than to note that nodes tend to be closer on average compared to when modules are defined by resting state fMRI. Future work is required to dissociate the effects of spatially proximity on relationships between CGE and spatially distributed functional networks.”

  6. Feb 2018