Optimal transport: Fast probabilistic approximation with exact solvers.

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances on finite spaces. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including state-of-the-art solvers and entropically penalized versions. It is based on averaging the exact distances between empirical measures generated from independent samples from the original measures and can easily be tuned towards higher accuracy or shorter computation times. To this end, we give non-asymptotic deviation bounds for its accuracy in the case of discrete optimal transport problems. In particular, we show that in many important instances, including images (2D-histograms), the approximation error is independent of the size of the full problem. We present numerical experiments that demonstrate that a very good approximation in typical applications can be obtained in a computation time that is several orders of magnitude smaller than what is required for exact computation of the full problem

Transformation Equivariant Boltzmann Machines

Abstract. We develop a novel modeling framework for Boltzmann machines, augmenting each hidden unit with a latent transformation assignment variable which describes the selection of the transformed view of the canonical connection weights associated with the unit. This enables the inferences of the model to transform in response to transformed input data in a stable and predictable way, and avoids learning multiple features differing only with respect to the set of transformations. Extending prior work on translation equivariant (convolutional) models, we develop translation and rotation equivariant restricted Boltzmann machines (RBMs) and deep belief nets (DBNs), and demonstrate their effectiveness in learning frequently occurring statistical structure from artificial and natural images

Multivitamins, Individual Vitamin and Mineral Supplements, and Risk of Diabetes Among Older U.S. Adults

OBJECTIVE: Understanding the relationship between multivitamin use and diabetes risk is important given the wide use of multivitamin supplements among U.S. adults. RESEARCH DESIGN AND METHODS: We prospectively examined supplemental use of multivitamins and individual vitamins and minerals assessed in 1995–1996 in relation to self-reported diabetes diagnosed after 2000 among 232,007 participants in the National Institutes of Health–American Association of Retired Persons Diet and Health Study. Multivitamin use was assessed by a food-frequency questionnaire at baseline. Odds ratios (ORs) and 95% CIs were calculated by logistic regression models, adjusted for potential confounders. In total, 14,130 cases of diabetes diagnosed after 2000 were included in the analysis. RESULTS: Frequent use of any multivitamins was not associated with risk of diabetes after adjustment for potential confounders and uses of individual supplements. Compared with nonusers of any multivitamins, the multivariate ORs among users were 1.07 (95% CI 0.94–1.21) for taking vitamins less than once per week, 0.97 (0.88–1.06) for one to three times per week, 0.92 (0.84–1.00) for four to six times per week, and 1.02 (0.98–1.06) for seven or more times per week (P for trend = 0.64). Significantly lower risk of diabetes was associated with the use of vitamin C or calcium supplements. The multivariate ORs comparing daily users with nonusers were 0.91 (0.86–0.97) for vitamin C supplements and 0.85 (0.80–0.90) for calcium supplements. Use of vitamin E or other individual vitamin and mineral supplements were not associated with diabetes risk. CONCLUSIONS: In this large cohort of U.S. older adults, multivitamin use was not associated with diabetes risk. The findings of lower diabetes risk among frequent users of vitamin C or calcium supplements warrant further evaluations

Multi-quasiparticle gamma-band structure in neutron-deficient Ce and Nd isotopes

The newly developed multi-quasiparticle triaxial projected shell-model approach is employed to study the high-spin band structures in neutron-deficient even-even Ce- and Nd-isotopes. It is observed that gamma-bands are built on each intrinsic configuration of the triaxial mean-field deformation. Due to the fact that a triaxial configuration is a superposition of several K-states, the projection from these states results in several low-lying bands originating from the same intrinsic configuration. This generalizes the well-known concept of the surface gamma-oscillation in deformed nuclei based on the ground-state to gamma-bands built on multi-quasiparticle configurations. This new feature provides an alternative explanation on the observation of two I=10 aligning states in 134Ce and both exhibiting a neutron character.Comment: 15 pages, 9 figures, accepted by Nucl. Phys.

Dynamic Mechanisms of Cell Rigidity Sensing: Insights from a Computational Model of Actomyosin Networks

Cells modulate themselves in response to the surrounding environment like substrate elasticity, exhibiting structural reorganization driven by the contractility of cytoskeleton. The cytoskeleton is the scaffolding structure of eukaryotic cells, playing a central role in many mechanical and biological functions. It is composed of a network of actins, actin cross-linking proteins (ACPs), and molecular motors. The motors generate contractile forces by sliding couples of actin filaments in a polar fashion, and the contractile response of the cytoskeleton network is known to be modulated also by external stimuli, such as substrate stiffness. This implies an important role of actomyosin contractility in the cell mechano-sensing. However, how cells sense matrix stiffness via the contractility remains an open question. Here, we present a 3-D Brownian dynamics computational model of a cross-linked actin network including the dynamics of molecular motors and ACPs. The mechano-sensing properties of this active network are investigated by evaluating contraction and stress in response to different substrate stiffness. Results demonstrate two mechanisms that act to limit internal stress: (i) In stiff substrates, motors walk until they exert their maximum force, leading to a plateau stress that is independent of substrate stiffness, whereas (ii) in soft substrates, motors walk until they become blocked by other motors or ACPs, leading to submaximal stress levels. Therefore, this study provides new insights into the role of molecular motors in the contraction and rigidity sensing of cells

Sarcomeric Pattern Formation by Actin Cluster Coalescence

Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells