Deep and superficial amygdala nuclei projections revealed in vivo by probabilistic tractography

Copyright © 2011 Society for Neuroscience and the authors. The The Journal of Neuroscience uses a Creative Commons Attribution-NonCommercial-ShareAlike licence: http://creativecommons.org/licenses/by-nc-sa/4.0/.Despite a homogenous macroscopic appearance on magnetic resonance images, subregions of the amygdala express distinct functional profiles as well as corresponding differences in connectivity. In particular, histological analysis shows stronger connections for superficial (i.e., centromedial and cortical), compared with deep (i.e., basolateral and other), amygdala nuclei to lateral orbitofrontal cortex and stronger connections of deep compared with superficial, nuclei to polymodal areas in the temporal pole. Here, we use diffusion weighted imaging with probabilistic tractography to investigate these connections in humans. We use a data-driven approach to segment the amygdala into two subregions using k-means clustering. The identified subregions are spatially contiguous and their location corresponds to deep and superficial nuclear groups. Quantification of the connection strength between these amygdala clusters and individual target regions corresponds to qualitative histological findings in non-human primates, indicating such findings can be extrapolated to humans. We propose that connectivity profiles provide a potentially powerful approach for in vivo amygdala parcellation and can serve as a guide in studies that exploit functional and anatomical neuroimaging.The Wellcome Trust, a Max Planck Research Award and Swiss National Science Foundation

Making Laplacians commute

In this paper, we construct multimodal spectral geometry by finding a pair of closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are jointly diagonalizable and hence have the same eigenbasis. Our construction naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of applications in dimensionality reduction, shape analysis, and clustering, demonstrating that our method better captures the inherent structure of multi-modal data

Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM

We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of Cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compressed using steerable principal component analysis (PCA) such that rotating an image is equivalent to phase shifting the expansion coefficients. Thus we are able to extend the theory of bispectrum of 1D periodic signals to 2D images. The randomized PCA algorithm is then used to efficiently reduce the dimensionality of the bispectrum coefficients, enabling fast computation of the similarity between any pair of images. The nearest neighbors provide an initial classification of similar viewing angles. In this way, rotational alignment is only performed for images with their nearest neighbors. The initial nearest neighbor classification and alignment are further improved by a new classification method called vector diffusion maps. Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than reference-free alignment with rotationally invariant K-means clustering, MSA/MRA 2D classification, and their modern approximations