242 research outputs found

    Chow Rings of Vector Space Matroids

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    The Chow ring of a matroid (or more generally, atomic latice) is an invariant whose importance was demonstrated by Adiprasito, Huh and Katz, who used it to resolve the long-standing Heron-Rota-Welsh conjecture. Here, we make a detailed study of the Chow rings of uniform matroids and of matroids of finite vector spaces. In particular, we express the Hilbert series of such matroids in terms of permutation statistics; in the full rank case, our formula yields the maj-exc qq-Eulerian polynomials of Shareshian and Wachs. We also provide a formula for the Charney-Davis quantities of such matroids, which can be expressed in terms of either determinants or qq-secant numbers

    Process tomography via sequential measurements on a single quantum system

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    We utilize a discrete (sequential) measurement protocol to investigate quantum process tomography of a single two-level quantum system, with an unknown initial state, undergoing Rabi oscillations. The ignorance of the dynamical parameters is encoded into a continuous-variable classical system which is coupled to the two-level quantum system via a generalized Hamiltonian. This combined estimate of the quantum state and dynamical parameters is updated by using the information obtained from sequential measurements on the quantum system and, after a sufficient waiting period, faithful state monitoring and parameter determination is obtained. Numerical evidence is used to demonstrate the convergence of the state estimate to the true state of the hybrid system.Comment: 7 pages, 2 figure

    Electronic bill presentment and payment--is it just a click away?

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    This article addresses the following questions about electronic presentment and payment (EBPP) in the business-to-consumer marketplace: Why aren't electronically presented bills always paid electronically? And, if EBPP does aid in the migration to fully electronic end-to-end payment, what are the barriers to its adoption.Payment systems ; Electronic funds transfers

    Wetting and energetics in nanoparticle etching of graphene

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    Molten metallic nanoparticles have recently been used to construct graphene nanostructures with crystallographic edges. The mechanism by which this happens, however, remains unclear. Here, we present a simple model that explains how a droplet can etch graphene. Two factors possibly contribute to this process: a difference between the equilibrium wettability of graphene and the substrate that supports it, or the large surface energy associated with the graphene edge. We calculate the etching velocities due to either of these factors and make testable predictions for evaluating the significance of each in graphene etching. This model is general and can be applied to other materials systems as well. As an example, we show how our model can be used to extend a current theory of droplet motion on binary semiconductor surfaces

    Modeling the Transition between Localized and Extended Deposition in Flow Networks through Packings of Glass Beads

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    We use a theoretical model to explore how fluid dynamics, in particular, the pressure gradient and wall shear stress in a channel, affect the deposition of particles flowing in a microfluidic network. Experiments on transport of colloidal particles in pressure-driven systems of packed beads have shown that at lower pressure drop, particles deposit locally at the inlet, while at higher pressure drop, they deposit uniformly along the direction of flow. We develop a mathematical model and use agent-based simulations to capture these essential qualitative features observed in experiments. We explore the deposition profile over a two-dimensional phase diagram defined in terms of the pressure and shear stress threshold, and show that two distinct phases exist. We explain this apparent phase transition by drawing an analogy to simple one-dimensional models of aggregation in which the phase transition is calculated analytically.Comment: 9 pages, 6 figures including Supplemental Materia

    Quantitative and qualitative assessment of exploitation of juvenile cephalopods from the Arabian Sea and Bay of Bengal and determination of minimum legal sizes

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    Using the minimum size at maturity (MSM) as a biological reference point and relatively low reproductive loads and generation times of the studied animals, the minimum legal sizes (MLS) for the Indian squid Loligo duvauceli, the pharaoh cuttlefish Sepia pharaonis and for the webfoot octopus Octopus membranaceous was fixed at 80, 115 and 45 mm Dorsal Mantle Length (DML) respectively with corresponding minimum legal weights at 25, 150 and 15 g. For L. duvauceli, during 1997-2001, 12.8% of the average catch was constituted by juveniles, the proportion being higher along the west coast. In 2002-05, the proportion of juveniles was lower at 5.3% and the total weights were also much less (1817 t as compared to 5354 t). In the case of S. pharaonis, 6.9% (2281 t) of the catch was constituted by juveniles, but the proportion was very high (22.4%) along the east coast. In O. membranaceous during 2002-04, an estimated 527 t (5.9%) of the total catch comprised of juveniles. The present Lmean in the fishery is lower than the Lopt and their difference is considerably high at 60 mm for L. duvauceli. However, in the case of S. pharaonis this difference is only 10 mm and in the case of O. membranaceous the Lmean is higher than the Lopt. If the juveniles are permitted to grow to Lmean by implementing the MLS, the estimated economic gain is to the tune of Rs. 426 crores per annum. The present study shows that harvest weights can be improved by up to 34 times and would result in higher incomes to trawl fishers
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