2 research outputs found
Pattern Formation with a Compartmental Lateral Inhibition System
We propose a compartmental lateral inhibition system that generates
contrasting patterns of gene expression between neighboring compartments. The
system consists of a set of compartments interconnected by channels. Each
compartment contains a colony of cells that produce diffusible molecules to be
detected by the neighboring colony, and each cell is equipped with an
inhibitory circuit that reduces its production when the detected signal is
stronger. We develop a technique to analyze the steady-state patterns emerging
from this lateral inhibition system and apply it to a specific implementation.
The analysis shows that the proposed system indeed exhibits contrasting
patterns within realistic parameter ranges.Comment: 9 pages, 6 figure
Graph learning under spectral sparsity constraints
Graph inference plays an essential role in machine learning, pattern
recognition, and classification. Signal processing based approaches in
literature generally assume some variational property of the observed data on
the graph. We make a case for inferring graphs on which the observed data has
high variation. We propose a signal processing based inference model that
allows for wideband frequency variation in the data and propose an algorithm
for graph inference. The proposed inference algorithm consists of two steps: 1)
learning orthogonal eigenvectors of a graph from the data; 2) recovering the
adjacency matrix of the graph topology from the given graph eigenvectors. The
first step is solved by an iterative algorithm with a closed-form solution. In
the second step, the adjacency matrix is inferred from the eigenvectors by
solving a convex optimization problem. Numerical results on synthetic data show
the proposed inference algorithm can effectively capture the meaningful graph
topology from observed data under the wideband assumption