The disjoint curve property

A Heegaard splitting of a closed, orientable three-manifold satisfies the disjoint curve property if the splitting surface contains an essential simple closed curve and each handlebody contains an essential disk disjoint from this curve [Thompson, 1999]. A splitting is full if it does not have the disjoint curve property. This paper shows that in a closed, orientable three-manifold all splittings of sufficiently large genus have the disjoint curve property. From this and a solution to the generalized Waldhausen conjecture it would follow that any closed, orientable three manifold contains only finitely many full splittings.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper3.abs.htm

The Geometry of R-covered foliations

We study R-covered foliations of 3-manifolds from the point of view of their transverse geometry. For an R-covered foliation in an atoroidal 3-manifold M, we show that M-tilde can be partially compactified by a canonical cylinder S^1_univ x R on which pi_1(M) acts by elements of Homeo(S^1) x Homeo(R), where the S^1 factor is canonically identified with the circle at infinity of each leaf of F-tilde. We construct a pair of very full genuine laminations transverse to each other and to F, which bind every leaf of F. This pair of laminations can be blown down to give a transverse regulating pseudo-Anosov flow for F, analogous to Thurston's structure theorem for surface bundles over a circle with pseudo-Anosov monodromy. A corollary of the existence of this structure is that the underlying manifold M is homotopy rigid in the sense that a self-homeomorphism homotopic to the identity is isotopic to the identity. Furthermore, the product structures at infinity are rigid under deformations of the foliation F through R-covered foliations, in the sense that the representations of pi_1(M) in Homeo((S^1_univ)_t) are all conjugate for a family parameterized by t. Another corollary is that the ambient manifold has word-hyperbolic fundamental group. Finally we speculate on connections between these results and a program to prove the geometrization conjecture for tautly foliated 3-manifolds

Weighted L^2-cohomology of Coxeter groups based on barycentric subdivisons

Associated to any finite flag complex L there is a right-angled Coxeter group W_L and a contractible cubical complex Sigma_L (the Davis complex) on which W_L acts properly and cocompactly, and such that the link of each vertex is L. It follows that if L is a generalized homology sphere, then Sigma_L is a contractible homology manifold. We prove a generalized version of the Singer Conjecture (on the vanishing of the reduced weighted L^2_q-cohomology above the middle dimension) for the right-angled Coxeter groups based on barycentric subdivisions in even dimensions. We also prove this conjecture for the groups based on the barycentric subdivision of the boundary complex of a simplex.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper28.abs.htm

The Current Adoption of Dry-Direct Seeding Rice (DDSR) in Thailand and Lessons Learned for Mekong River Delta of Vietnam

The paper documents the joint study trip, organized by CCAFS Southeast Asia for Vietnamese rice researchers, extension workers, as well as local decision makers, to visit Thailand in April 2018. The goal of the study trip was to observe and learn the experience of Thai farmers on the large-scale adoption process of dry-direct seeding rice (DDSR), a viable alternative to address regional scarcity of fresh water in irrigation caused by the drought and salinity intrusion in the Mekong River Delta

Optimizing a green manure-based row cropping system for organic cereal production

A row cropping system with an increase of row distance to 24 cm increased the growth of undersown cover crops and allowed 1-2 passes of interow hoeing for weed control before sowing cover crops. The three-week delay sowing time was suitable for the growth of legume species. The new system significantly improved both grain yield and grain N content of the succeeding crop compared to the traditional cropping system

Statistical Learning in Wasserstein Space

We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast these analyses as multimarginal optimal transport problems. The particular formulation allows efficient computation, ensures existence of optimal solutions, and admits a probabilistic interpretation over the space of paths (line segments). Application of the theory to the interpolation of empirical distributions, images, power spectra, as well as assessing uncertainty in experimental designs, is envisioned

Combination of undersown catch crops and row-hoeing for optimizing nitrogen supply and weed control in organic spring barley

This is an early result of a field experiment where we aimed to optimize a row cropping system for organic cereal production with the use of undersown cover crops in combination with inter-row hoeing

Maximal power output of a stochastic thermodynamic engine

Classical thermodynamics aimed to quantify the efficiency of thermodynamic engines, by bounding the maximal amount of mechanical energy produced, compared to the amount of heat required. While this was accomplished early on, by Carnot and Clausius, the more practical problem to quantify limits of power that can be delivered, remained elusive due to the fact that quasistatic processes require infinitely slow cycling, resulting in a vanishing power output. Recent insights, drawn from stochastic models, appear to bridge the gap between theory and practice in that they lead to physically meaningful expressions for the dissipation cost in operating a thermodynamic engine over a finite time window. Indeed, the problem to optimize power can be expressed as a stochastic control problem. Building on this framework of stochastic thermodynamics we derive bounds on the maximal power that can be drawn by cycling an overdamped ensemble of particles via a time-varying potential while alternating contact with heat baths of different temperature (Tc cold, and Th hot). Specifically, assuming a suitable bound M on the spatial gradient of the controlling potential, we show that the maximal achievable power is bounded by [Formula presented]. Moreover, we show that this bound can be reached to within a factor of [Formula presented] by operating the cyclic thermodynamic process with a quadratic potential