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Peter Zeman

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3 papers
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3

TCS Journal 2021 Journal Article

Graph isomorphism restricted by lists

  • Pavel Klavík
  • Dušan Knop
  • Peter Zeman

The complexity of graph isomorphism (GraphIso ) is a famous problem in computer science. For graphs G and H, it asks whether they are the same up to a relabeling of vertices. In 1981, Lubiw proved that list restricted graph isomorphism (ListIso ) is NP -complete: for each u ∈ V ( G ), we are given a list L ( u ) ⊆ V ( H ) of possible images of u. After 35 years, we revive the study of this problem and consider which results for GraphIso can be modified to solve ListIso. We prove: 1) Under certain conditions, GI -completeness of a class of graphs implies NP -completeness of ListIso. 2) Several combinatorial algorithms for GraphIso can be modified to solve ListIso: for trees, planar graphs, interval graphs, circle graphs, permutation graphs, and bounded treewidth graphs. 3) ListIso is NP -complete for cubic colored graphs with sizes of color classes bounded by 8 with all lists of size at most 3.

YNIMG Journal 2018 Journal Article

Concentric radiofrequency arrays to increase the statistical power of resting-state maps in monkeys

  • Kyle M. Gilbert
  • David J. Schaeffer
  • Peter Zeman
  • Jörn Diedrichsen
  • Stefan Everling
  • Julio C. Martinez-Trujillo
  • J. Andrew Pruszynski
  • Ravi S. Menon

The close homology of monkeys and humans has increased the prevalence of non-human-primate models in functional MRI studies of brain connectivity. To improve upon the attainable resolution in functional MRI studies, a commensurate increase in the sensitivity of the radiofrequency receiver coil is required to avoid a reduction in the statistical power of the analysis. Most receive coils are comprised of multiple loops distributed equidistantly over a surface to produce spatially independent sensitivity profiles. A larger number of smaller elements will in turn provide a higher signal-to-noise ratio (SNR) over the same field of view. As the loops become physically smaller, noise originating from the sample is reduced relative to noise originating from the coil. In this coil-noise-dominated regime, coil elements can have overlapping sensitivity profiles, yet still possess only mildly correlated noise. In this manuscript, we demonstrate that inductively decoupled, concentric coil arrays can improve temporal SNR when operating in the coil-noise-dominated regime—in contrast to what is expected for the more ubiquitous sample-noise-dominated array. A small, thin, 7-channel flexible coil is developed and operated in conjunction with an existing whole-head monkey coil. The mean and maximum noise correlation between the two arrays was 5% and 23%, respectively. When the flex coil was placed over the sensorimotor cortex, the temporal SNR improved by up to 2. 3-fold in the peripheral cortex and up to 1. 3-fold at a 2- to 3-cm depth within the brain. When the flex coil was placed over the frontal eye fields, resting-state maps showed substantially elevated sensitivity to correlations in the prefrontal cortex (54%), supplementary eye fields (39%), and anterior cingulate cortex (41%). The concentric-coil topology provided a pragmatic and robust means to significantly improve local temporal SNR and the statistical power of functional connectivity maps.

YNIMG Journal 2017 Journal Article

A geometrically adjustable receive array for imaging marmoset cohorts

  • Kyle M. Gilbert
  • Joseph S. Gati
  • L. Martyn Klassen
  • Peter Zeman
  • David J. Schaeffer
  • Stefan Everling
  • Ravi S. Menon

The common marmoset (Callithrix jacchus) is an increasingly popular animal model for translational neuroscience studies, during which anatomical and functional MRI can be useful investigative tools. To attain the requisite SNR for high-resolution acquisitions, the radiofrequency coil must be optimized for the marmoset; however, relatively few custom coils have been developed that maximize SNR and are compatible with accelerated acquisitions. For the study of large populations of animals, the heterogeneity in animal size reduces the effectiveness of a “one size fits all” approach to coil sizing and makes coils tailored to individual animals cost and time prohibitive. The approach taken in this study was to create an 8-channel phased-array receive coil that was adjustable to the width of the marmoset head, thereby negating the need for tailored coils while still maintaining high SNR. Two marmosets of different size were imaged on a 9. 4-T small-animal scanner. Consistent SNR was achieved in the periphery of the brain between head sizes. When compared to a 15-channel, “one size fits all” receive coil, the adjustable coil achieved 57% higher SNR in the superior frontal and parietal cortices and 29% higher SNR in the centre of the brain. The mean geometry factor of the adjustable coil was less than 1. 2 for a 2-fold reduction factor in the left-right and anterior-posterior directions. Geometry factors were compared to the 15-channel coil to guide future designs. The adjustable coil was shown to be a practical means for anatomical and echo-planar imaging of marmoset cohorts.

v2026.09.13