Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC

We introduce Tempered Geodesic Markov Chain Monte Carlo (TG-MCMC) algorithm for initializing pose graph optimization problems, arising in various scenarios such as SFM (structure from motion) or SLAM (simultaneous localization and mapping). TG-MCMC is first of its kind as it unites asymptotically global non-convex optimization on the spherical manifold of quaternions with posterior sampling, in order to provide both reliable initial poses and uncertainty estimates that are informative about the quality of individual solutions. We devise rigorous theoretical convergence guarantees for our method and extensively evaluate it on synthetic and real benchmark datasets. Besides its elegance in formulation and theory, we show that our method is robust to missing data, noise and the estimated uncertainties capture intuitive properties of the data.Comment: Published at NeurIPS 2018, 25 pages with supplement

A minimal integer automaton behind crystal plasticity

Power law fluctuations and scale free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova (FK) type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer valued automaton revealing inherent discreteness of the plastic flow.Comment: 4 pages, 5 figure

Two-sided matching via balanced exchange: Tuition and worker exchanges

We introduce a new matching model to mimic two-sided exchange programs such as tuition and worker exchange, in which each firm has to avoid being a net-exporter of workers. These exchanges use decentralized markets, making it difficult to achieve a balance between exports and imports. We show that stable equilibria discourage net-exporting firms from exchange. We introduce the two-sided top-trading-cycles mechanism that is balanced-efficient, worker-strategy-proof, acceptable, and individually rational, and respects priority bylaws regarding worker eligibility. We prove that it is the unique mechanism fulfilling these objectives. Moreover, it encourages exchange, since full participation is the dominant strategy for firms

Volume changes during active shape fluctuations in cells

Cells modify their volume in response to changes in osmotic pressure but it is usually assumed that other active shape variations do not involve significant volume fluctuations. Here we report experiments demonstrating that water transport in and out of the cell is needed for the formation of blebs, commonly observed protrusions in the plasma membrane driven by cortex contraction. We develop and simulate a model of fluid mediated membrane-cortex deformations and show that a permeable membrane is necessary for bleb formation which is otherwise impaired. Taken together our experimental and theoretical results emphasize the subtle balance between hydrodynamics and elasticity in actively driven cell morphological changes.Comment: Phys. Rev. Lett. in press. 13 pages 4 figures, 9 supplementary figure