On connectedness: a solution based on oscillatory correlation.

D L Wang

doi:10.1162/089976600300015916

Home/Archive/PubMed

PubMed · 10636935

On connectedness: a solution based on oscillatory correlation.

D L Wang

View original source ↗Export metadata ↓

Abstract

A long-standing problem in Neural Comp has been the problem of connectedness, first identified by Minsky and Papert (1969). This problem served as the cornerstone for them to establish analytically that perceptrons are fundamentally limited in computing geometrical (topological) properties. A solution to this problem is offered by a different class of neural networks: oscillator networks. To solve the problem, the representation of oscillatory correlation is employed, whereby one pattern is represented as a synchronized block of oscillators and different patterns are represented by distinct blocks that desynchronize from each other. Oscillatory correlation emerges from LEGION (locally excitatory globally inhibitory oscillator network), whose architecture consists of local excitation and global inhibition among neural oscillators. It is further shown that these oscillator networks exhibit sensitivity to topological structure, which may lay a neurocomputational foundation for explaining the psychophysical phenomenon of topological perception.

Explore related subjects

Image Processing, Computer-Assisted Models, Neurological Neural Networks, Computer Neurons Oscillometry Journal Article Research Support, U.S. Gov't, Non-P.H.S.

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

D L Wang. 2000. On connectedness: a solution based on oscillatory correlation.. https://doi.org/10.1162/089976600300015916

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2003

Nanodissection and high-resolution imaging of the Rhodopseudomonas viridis photosynthetic core complex in native membranes by AFM. Atomic force microscopy.

In photosynthesis, highly organized multiprotein assemblies convert sunlight into biochemical energy with high efficiency. A challenge in structural biology is to analyze such supramolecular complexes in native membranes. Atomic force microscopy (AFM) with high lateral resolution, high signal-to-noise ratio, and the possibility to nanodissect biological samples is a unique tool to investigate multiprotein complexes at molecular resolution in situ. Here we present high-resolution AFM of the photosynthetic core complex in native Rhodopseudomonas viridis membranes. Topographs at 10-A lateral and approximately 1-A vertical resolution reveal a single reaction center (RC) surrounded by a closed ellipsoid of 16 light-harvesting (LH1) subunits. Nanodissection of the tetraheme cytochrome (4Hcyt) subunit from the RC allows demonstration that the L and M subunits exhibit an asymmetric topography intimately associated to the LH1 subunits located at the short ellipsis axis. This architecture implies a distance distribution between the antenna and the RC compared with a centered location of the RC within a circular LH1, which may influence the energy transfer within the core complex. The LH1 subunits rearrange into a circle after removal of the RC from the core complex.

Image Processing, Computer-Assisted↗

PubMed2003

Precise 3D image alignment in micro-axial tomography.

Micro (micro-) axial tomography is a challenging technique in microscopy which improves quantitative imaging especially in cytogenetic applications by means of defined sample rotation under the microscope objective. The advantage of micro-axial tomography is an effective improvement of the precision of distance measurements between point-like objects. Under certain circumstances, the effective (3D) resolution can be improved by optimized acquisition depending on subsequent, multi-perspective image recording of the same objects followed by reconstruction methods. This requires, however, a very precise alignment of the tilted views. We present a novel feature-based image alignment method with a precision better than the full width at half maximum of the point spread function. The features are the positions (centres of gravity) of all fluorescent objects observed in the images (e.g. cell nuclei, fluorescent signals inside cell nuclei, fluorescent beads, etc.). Thus, real alignment precision depends on the localization precision of these objects. The method automatically determines the corresponding objects in subsequently tilted perspectives using a weighted bipartite graph. The optimum transformation function is computed in a least squares manner based on the coordinates of the centres of gravity of the matched objects. The theoretically feasible precision of the method was calculated using computer-generated data and confirmed by tests on real image series obtained from data sets of 200 nm fluorescent nano-particles. The advantages of the proposed algorithm are its speed and accuracy, which means that if enough objects are included, the real alignment precision is better than the axial localization precision of a single object. The alignment precision can be assessed directly from the algorithm's output. Thus, the method can be applied not only for image alignment and object matching in tilted view series in order to reconstruct (3D) images, but also to validate the experimental performance (e.g. mechanical precision of the tilting). In practice, the key application of the method is an improvement of the effective spatial (3D) resolution, because the well-known spatial anisotropy in light microscopy can be overcome. This allows more precise distance measurements between point-like objects.

Image Processing, Computer-Assisted↗

PubMed2002

On the fitting of model electron densities into EM reconstructions: a reciprocal-space formulation.

A fast method for fitting model electron densities into EM reconstructions is presented. The methodology was inspired by the molecular-replacement technique, adapted to take into account phase information and the symmetry imposed during the EM reconstruction. Calculations are performed in reciprocal space, which enables the selection of large volumes of the EM maps, thus avoiding the bias introduced when defining the boundaries of the target density.

Image Processing, Computer-Assisted↗