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Open Access Publications from the University of California

Scholarly Works (3 results)

  • Thesis
  • Peer Reviewed
UC Berkeley Electronic Theses and Dissertations (2023)

A dimer model is a probability distribution on the set of perfect matchings on a planar graph. In this thesis we study the two-periodic weighted dimer model on the Aztec diamond graph in what we call the mesocopic limit.

In the thermodynamic limit when the size of the graph goes to infinity while edge weights are fixed, the model exhibits three different regions characterized by the rate of decrease of correlation functions. At the center is the ordered region, where two-point correlation functions between dimers decrease exponentially. We show that in the mesoscopic scaling limit, when weights scale in the thermodynamic limit such that the size of the ordered region is of the same order as the correlation length inside the ordered region, fluctuations of the correlation functions are described by a new process. We compute asymptotics of the inverse Kasteleyn matrix for vertices in a local neighborhood in this mesoscopic limit, and use this to find the one-point correlation functions. We then conclude with an experimental study of two-point correlation functions between pairs of dimers that grow further apart in the mesoscopic limit.

    Cover page: Correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit
    • Article
    • Peer Reviewed
    UC Irvine Previously Published Works (2015)
    Changes in gene activity are essential for evolutionary diversification. Yet, elucidating the cellular behaviors that underlie modifications to adult form remains a profound challenge. We use neural crest-derived adult pigmentation of zebrafish and pearl danio to uncover cellular bases for alternative pattern states. We show that stripes in zebrafish require a novel class of thin, fast cellular projection to promote Delta-Notch signaling over long distances from cells of the xanthophore lineage to melanophores. Projections depended on microfilaments and microtubules, exhibited meandering trajectories, and stabilized on target cells to which they delivered membraneous vesicles. By contrast, the uniformly patterned pearl danio lacked such projections, concomitant with Colony stimulating factor 1-dependent changes in xanthophore differentiation that likely curtail signaling available to melanophores. Our study reveals a novel mechanism of cellular communication, roles for differentiation state heterogeneity in pigment cell interactions, and an unanticipated morphogenetic behavior contributing to a striking difference in adult form.
      Cover page: Long-distance communication by specialized cellular projections during pigment pattern development and evolution.
      • Article
      • Peer Reviewed
      UC Irvine Previously Published Works (2014)
      Pigment patterns are useful for elucidating fundamental mechanisms of pattern formation and how these mechanisms evolve. In zebrafish, several pigment cell classes interact to generate stripes, yet the developmental requirements and origins of these cells remain poorly understood. Using zebrafish and a related species, we identified roles for thyroid hormone (TH) in pigment cell development and patterning, and in postembryonic development more generally. We show that adult pigment cells arise from distinct lineages having distinct requirements for TH and that differential TH dependence can evolve within lineages. Our findings demonstrate critical functions for TH in determining pigment pattern phenotype and highlight the potential for evolutionary diversification at the intersection of developmental and endocrine mechanisms.
        Cover page: Thyroid hormone–dependent adult pigment cell lineage and pattern in zebrafish
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