Exploring Complex Dynamical Systems via Nonconvex Optimization

Cataloging the complex behaviors of dynamical systems can be challenging, even when they are well-described by a simple mechanistic model. If such a system is of limited analytical tractability, brute force simulation is often the only resort. We present an alternative, optimization-driven approach using tools from machine learning. We apply this approach to a novel, fully-optimizable, reaction-diffusion model which incorporates complex chemical reaction networks (termed "Dense Reaction-Diffusion Network" or "Dense RDN"). This allows us to systematically identify new states and behaviors, including pattern formation, dissipation-maximizing nonequilibrium states, and replication-like dynamical structures.

Finding Mirror Symmetry via Registration

Symmetry is prevalent in nature and a common theme in man-made designs. Both the human visual system and computer vision algorithms can use symmetry to facilitate object recognition and other tasks. Detecting mirror symmetry in images and data is, therefore, useful for a number of applications. Here, we demonstrate that the problem of fitting a plane of mirror symmetry to data in any Euclidian space can be reduced to the problem of registering two datasets. The exactness of the resulting solution depends entirely on the registration accuracy. This new Mirror Symmetry via Registration (MSR) framework involves (1) data reflection with respect to an arbitrary plane, (2) registration of original and reflected datasets, and (3) calculation of the eigenvector of eigenvalue -1 for the transformation matrix representing the reflection and registration mappings. To support MSR, we also introduce a novel 2D registration method based on random sample consensus of an ensemble of normalized cross-correlation matches. With this as its registration back-end, MSR achieves state-of-the-art performance for symmetry line detection in two independent 2D testing databases. We further demonstrate the generality of MSR by testing it on a database of 3D shapes with an iterative closest point registration back-end. Finally, we explore its applicability to examining symmetry in natural systems by assessing the degree of symmetry present in myelinated axon reconstructions from a larval zebrafish.

DeadNet: Identifying Phototoxicity from Label-free Microscopy Images of Cells using Deep ConvNets

Exposure to intense illumination light is an unavoidable consequence of fluorescence microscopy, and poses a risk to the health of the sample in every live-cell fluorescence microscopy experiment. Furthermore, the possible side-effects of phototoxicity on the scientific conclusions that are drawn from an imaging experiment are often unaccounted for. Previously, controlling for phototoxicity in imaging experiments required additional labels and experiments, limiting its widespread application. Here we provide a proof-of-principle demonstration that the phototoxic effects of an imaging experiment can be identified directly from a single phase-contrast image using deep convolutional neural networks (ConvNets). This lays the groundwork for an automated tool for assessing cell health in a wide range of imaging experiments. Interpretability of such a method is crucial for its adoption. We take steps towards interpreting the classification mechanism of the trained ConvNet by visualizing salient features of images that contribute to accurate classification.