Fig. 5: Design of self-assembly phase diagrams to solve pattern recognition problems.
From: Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly
a, Phase diagram shows desired outcomes of kinetically controlled self-assembly in different regions of N = 917 dimensional concentration space (2D schematic shown). Each grayscale image represents a vector of tile concentrations. b, θ specifies which pixel location corresponds to which tile. c, Given a map θ, any image can be converted to a tile concentration vector by associating the grayscale value of pixel location n with the concentration of the corresponding tile i = θ(n). We compute the loss for a given pixel-to-tile map θ using simulations to estimate the nucleation rates of desired and undesired structures for each image and summing over a training set. Stochastic optimization in θ space gives a putative optimal θopt that we used for experiments. d, Images used for training. e, Extra images used to test generalization power. Sources and names of individuals are from left to right as follows in d (for details, see Supplementary Information section 2.7). In a, c and e, some of the images are also shown, credits are as for d. d, Top row, D. Hodgkin, Keystone/Getty Images; J. Hopfield, Princeton University; Horse, Pixabay. Second row: Hazelnuts, Pixabay; Harom, MNIST; H, EMNIST. Third row: A. Avogadro, C. Sentier/University of Pennsylvania; L. Abbott, himself; Anchovy, NOAA/NMFS/SEFSC Pascagoula Laboratory. Fourth row: Apples, M. Shemesh; Aon, MNIST; A, EMNIST. Fifth row: E. Mitscherlich, William Sharpe/Smithsonian Institute; M.-B. Moser, BI Basmo/Kavli Institute of Systems Neuroscience; Mockingbird, Pixabay. Sixth row: Magnolia, D. Richardson; Mbili, MNIST; M, EMNIST.
