arXiv subjects

Steven W. Zucker

Publications and source records attributed to Steven W. Zucker.

22 records · Page 2Linked to original sources

arXiv2016

Stagewise Learning for Sparse Clustering of Discretely-Valued Data

The performance of EM in learning mixtures of product distributions often depends on the initialization. This can be problematic in crowdsourcing and other applications, e.g. when a small number of 'experts' are diluted by a large number of noisy, unreliable participants. We develop a new EM algorithm that is driven by these experts. In a manner that differs from other approaches, we start from a single mixture class. The algorithm then develops the set of 'experts' in a stagewise fashion based on a mutual information criterion. At each stage EM operates on this subset of the players, effectively regularizing the E rather than the M step. Experiments show that stagewise EM outperforms other initialization techniques for crowdsourcing and neurosciences applications, and can guide a full EM to results comparable to those obtained knowing the exact distribution.

stat.ML↗

arXiv2013

Characterizing Ambiguity in Light Source Invariant Shape from Shading

Shape from shading is a classical inverse problem in computer vision. This shape reconstruction problem is inherently ill-defined; it depends on the assumed light source direction. We introduce a novel mathematical formulation for calculating local surface shape based on covariant derivatives of the shading flow field, rather than the customary integral minimization or P.D.E approaches. On smooth surfaces, we show second derivatives of brightness are independent of the light sources and can be directly related to surface properties. We use these measurements to define the matching local family of surfaces that can result from any given shading patch, changing the emphasis to characterizing ambiguity in the problem. We give an example of how these local surface ambiguities collapse along certain image contours and how this can be used for the reconstruction problem.

cs.CV↗

arXiv2009

Distance Maps and Plant Development #2: Facilitated Transport and Uniform Gradient

The principles underlying plant development are extended to allow a more molecular mechanism to elaborate the schema by which ground cells differentiate into vascular cells. Biophysical considerations dictate that linear dynamics are not sufficent to capture facilitated auxin transport (e.g., through PIN). We group these transport facilitators into a non-linear model under the assumption that they attempt to minimize certain {\em differences} of auxin concentration. This Constant Gradient Hypothesis greatly increases the descriptive power of our model to include complex dynamical behaviour. Specifically, we show how the early pattern of PIN1 expression appears in the embryo, how the leaf primordium emerges, how convergence points arise on the leaf margin, how the first loop is formed, and how the intricate pattern of PIN shifts during the early establishment of vein patterns in incipient leaves of Arabidopsis. Given our results, we submit that the model provides evidence that many of the salient structural characteristics that have been described at various stages of plant development can arise from the uniform application of a small number of abstract principles.

q-bio.QM↗

arXiv2009

Distance Maps and Plant Development #1: Uniform Production and Proportional Destruction

Experimental data regarding auxin and venation formation exist at both macroscopic and molecular scales, and we attempt to unify them into a comprehensive model for venation formation. We begin with a set of principles to guide an abstract model of venation formation, from which we show how patterns in plant development are related to the representation of global distance information locally as cellular-level signals. Venation formation, in particular, is a function of distances between cells and their locations. The first principle, that auxin is produced at a constant rate in all cells, leads to a (Poisson) reaction-diffusion equation. Equilibrium solutions uniquely codify information about distances, thereby providing cells with the signal to begin differentiation from ground to vascular. A uniform destruction hypothesis and scaling by cell size leads to a more biologically-relevant (Helmholtz) model, and simulations demonstrate its capability to predict leaf and root auxin distributions and venation patterns. The mathematical development is centered on properties of the distance map, and provides a mechanism by which global information about shape can be presented locally to individual cells. The principles provide the foundation for an elaboration of these models in a companion paper \cite{plos-paper2}, and together they provide a framework for understanding organ- and plant-scale organization.

q-bio.QM↗