Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure

Continuum Derrida Approach to Drift and Diffusivity in Random Media

By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the particles is controlled by molecular diffusion and a local flow field with known statistical properties. The power of the Derrida method is that it uses the equilibrium probability distribution, that exists for each {\em finite} sample, to compute asymptotic behaviour at large times in the {\em infinite} medium. In certain cases, where this equilibrium situation is associated with a vanishing microcurrent, our results demonstrate the equality of the renormalization processes for the effective drift and diffusivity tensors. This establishes, for those cases, a Ward identity previously verified only to two-loop order in perturbation theory in certain models. The technique can be applied also to media in which the diffusivity exhibits spatial fluctuations. We derive a simple relationship between the effective diffusivity in this case and that for an associated gradient drift problem that provides an interesting constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8

Dynamic Matrix Factorization with Priors on Unknown Values

Advanced and effective collaborative filtering methods based on explicit feedback assume that unknown ratings do not follow the same model as the observed ones (\emph{not missing at random}). In this work, we build on this assumption, and introduce a novel dynamic matrix factorization framework that allows to set an explicit prior on unknown values. When new ratings, users, or items enter the system, we can update the factorization in time independent of the size of data (number of users, items and ratings). Hence, we can quickly recommend items even to very recent users. We test our methods on three large datasets, including two very sparse ones, in static and dynamic conditions. In each case, we outrank state-of-the-art matrix factorization methods that do not use a prior on unknown ratings.Comment: in the Proceedings of 21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining 201

Randomized Composable Core-sets for Distributed Submodular Maximization

An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution inside the union of the representative solutions for all pieces. This technique can be captured via the concept of {\em composable core-sets}, and has been recently applied to solve diversity maximization problems as well as several clustering problems. However, for coverage and submodular maximization problems, impossibility bounds are known for this technique \cite{IMMM14}. In this paper, we focus on efficient construction of a randomized variant of composable core-sets where the above idea is applied on a {\em random clustering} of the data. We employ this technique for the coverage, monotone and non-monotone submodular maximization problems. Our results significantly improve upon the hardness results for non-randomized core-sets, and imply improved results for submodular maximization in a distributed and streaming settings. In summary, we show that a simple greedy algorithm results in a $1/3$-approximate randomized composable core-set for submodular maximization under a cardinality constraint. This is in contrast to a known $O({\log k\over \sqrt{k}})$ impossibility result for (non-randomized) composable core-set. Our result also extends to non-monotone submodular functions, and leads to the first 2-round MapReduce-based constant-factor approximation algorithm with $O(n)$ total communication complexity for either monotone or non-monotone functions. Finally, using an improved analysis technique and a new algorithm $\mathsf{PseudoGreedy}$, we present an improved $0.545$-approximation algorithm for monotone submodular maximization, which is in turn the first MapReduce-based algorithm beating factor $1/2$ in a constant number of rounds

Does Wheat Cultivar Choice Affect Crop Quality and Soil Microbial Communities in Cropping Systems?

Wheat (Triticum aestivum L.) cultivars may have differential effects on soil microbial communities and the breadmaking quality of harvested grain. We compared six Canadian spring wheat cultivars under organic and conventional management systems for yield, breadmaking quality and soil phospholipid fatty acid analysis (PLFA) profile. Yields were lower, but protein levels were higher in the organic system. Cultivars differed for quality traits, but all cultivars had acceptable levels for processing. There were small differences in PLFA profiles for cultivars in the conventional system, but none in the organic system. More significant correlations between grain quality and PLFA measures were present in the organic system. Protein levels and breadmaking quality at least equal to conventional systems can be achieved in organic systems. Wheat cultivars differed for grain quality in both organic and conventional systems, and culivars altered the soil microbial profile in conventional systems. Microbes may play a greater role in determining crop quality in organic systems than in conventional systems

Electrostatic interactions mediated by polarizable counterions: weak and strong coupling limits

We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between charged dielectric interfaces.Comment: 25 pages, 7 figure

Plan of Part of Original Setlers [sic] Lot no. 66, Holland\u27s Survey

Map depicting part of original setlers [sic] lot no. 66 Holland\u27s survey lying west of Kenduskeag Avenue and east of Kenduskeag Stream as surveyed for S. & T. Nowell, Esq.\u27s by B. S. Dean, surveyor. Scale: 1:600. Map size: 66 x 48 cm. Map is faded, making portions illegible under full-spectrum, ambient light. Map includes a compass arrow indicating north. Map is yellowed and shows foxing.https://digitalcommons.library.umaine.edu/mainebicentennial/1029/thumbnail.jp

An Extraordinary Scattered Broad Emission Line in a Type 2 QSO

An infrared-selected, narrow-line QSO has been found to exhibit an extraordinarily broad Halpha emission line in polarized light. Both the extreme width (35,000 km/sec full-width at zero intensity) and 3,000 km/sec redshift of the line centroid with respect to the systemic velocity suggest emission in a deep gravitational potential. An extremely red polarized continuum and partial scattering of the narrow lines at a position angle common to the broad-line emission imply extensive obscuration, with few unimpeded lines of sight to the nucleus.Comment: 4 pages, 1 figure, to appear in the Astrophysical Journal Letter