Simple coarse graining and sampling strategies for image recognition

A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased using simple strategies of coarse graining (replacing groups of images by their centroids) and stochastic sampling (using distinct sets of centroids in combination). We use the MNIST and Fashion-MNIST data sets to show that coarse graining can be used to convert a subset of training images into many fewer image centroids, with no loss of accuracy of classification of test-set images by direct (nearest-neighbor) classification. Distinct batches of centroids can be used in combination as a means of stochastically sampling configuration space, and can classify test-set data more accurately than can the unaltered training set. The approach works most naturally with multiple processors in parallel

Minimal positive design for self-assembly of the Archimedean tilings

A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of minimal positive design allows the self-assembly of networks equivalent to the 8 semiregular Archimedean tilings of the plane, structures not previously realized in simulation. This strategy consists of identifying the fewest distinct types of interparticle interaction that appear in the desired structure, and does not require enumeration of the many possible undesired structures. The resulting particles, which self-assemble into the desired networks, possess DNA-like selectivity of their interactions. Assembly of certain molecular networks may therefore require such selectivity

Large deviations in the presence of cooperativity and slow dynamics.

We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative or when its basic time scale diverges. In the first case the unbiased trajectory distribution undergoes a symmetry breaking, leading to a change in shape of the large-deviation rate function for a particular dynamical observable. In the second case the symmetry of the unbiased trajectory distribution remains unbroken. Comparison of these models suggests that singularities of the dynamical large-deviation formalism can signal the dynamical equivalent of an equilibrium phase transition but do not necessarily do so

Strong bonds and far-from-equilibrium conditions minimize errors in lattice-gas growth

We use computer simulation to study the layer-by-layer growth of particle structures in a lattice gas, taking the number of incorporated vacancies as a measure of the quality of the grown structure. By exploiting a dynamic scaling relation between structure quality in and out of equilibrium, we determine that the best quality of structure is obtained, for fixed observation time, with strong interactions and far-from-equilibrium growth conditions. This result contrasts with the usual assumption that weak interactions and mild nonequilibrium conditions are the best way to minimize errors during assembly

Sampling rare fluctuations of discrete-time Markov chains

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.Comment: Submitted along with arXiv:1709.03951 as a joint wor