Properties of the solutions of delocalised coagulation and inception problems with outflow boundaries

Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while the spatial domain is a bounded region of $d$-dimensional space for which every point lies on exactly one streamline associated with the velocity field. The problem is formulated as a semi-linear ODE in the Banach space of bounded measures on particle position and type space. A local Lipschitz property is established in total variation norm for the propagators (generalised semi-groups) associated with the problem and used to construct a Picard iteration that establishes local existence and global uniqueness for any initial condition. The unique weak solution is shown further to be a differentiable or at least bounded variation strong solution under smoothness assumptions on the parameters of the coagulation interaction. In the case of one spatial dimension strong differentiability is established even for coagulation parameters with a particular bounded variation structure in space. This one dimensional extension establishes the convergence of the simulation processes studied in [Patterson, Stoch. Anal. Appl. 31, 2013] to a unique and differentiable limit

The Essential Facilities Doctrine Under United States Antitrust Law

The issue of essential facilities has attracted renewed attention in Europe in recent years because of the controversy between IMS Health Inc. and NDC Health Corporation, two competitors in pharmaceutical data services in Germany . . . After an extensive investigation, the European Commission (EC) ordered that IMS grant access to the 1860 brick structure on commercially reasonable terms, and the EC decision is now on appeal in the Court of First Instance in Luxembourg. One issue that emerged in that litigation is whether a decision by European authorities to grant access to the alleged essential facility, especially one whose market power derived in part from a copyright, would open a gap between European and U.S. antitrust law. In response to that contention, the authors of this piece filed a statement in the Court of First Instance describing U.S. law on the subject. We argued that the EC\u27s ruling is consistent with U.S. jurisprudence on the subject of essential facilities. The remainder of this article consists of a revised version of the Court of First Instance filing

How to Grow Strawberries in the Home Garden

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Bilinear Coagulation Equations

We consider coagulation equations of Smoluchowski or Flory type where the total merge rate has a bilinear form $\pi(y)\cdot A\pi(x)$ for a vector of conserved quantities $\pi$, generalising the multiplicative kernel. For these kernels, a gelation transition occurs at a finite time $t_\mathrm{g}\in (0,\infty)$, which can be given exactly in terms of an eigenvalue problem in finite dimensions. We prove a hydrodynamic limit for a stochastic coagulant, including a corresponding phase transition for the largest particle, and exploit a coupling to random graphs to extend analysis of the limiting process beyond the gelation time.Comment: Generalises the previous version to focus on general coagulation processes of bilinear type, without restricting to the single example of the previous version. The previous results are mentioned as motivation, and all results of the previous version can be obtained from this more general versio

Evaluating human performance modeling for system assessment: Promise and problems

The development and evaluation of computational human performance models is examined. An intention is to develop models which can be used to interact with system prototypes and simulations to perform system assessment. Currently LR is working on a set of models emulating cognitive, psychomotor, auditory, and visual activity for multiple operator positions of a command and control simulation system. These models, developed in conjunction with BBN Systems and Technologies, function within the simulation environment and allow for both unmanned system assessment and manned (human-in-loop) assessment of system interface and team interactions. These are relatively generic models with built-in flexibility which allows modification of some model parameters. These models have great potential for improving the efficiency and effectiveness of system design, test, and evaluation. However, the extent of the practical utility of these models is unclear. Initial verification efforts comparing model performance within the simulation to actual human operators on a similar, independent simulation have been performed and current efforts are directed at comparing human and model performance within the same simulation environment

Municipal Property Acquisition Patterns in a Shrinking City: Evidence for the Persistence of an Urban Growth Paradigm in Buffalo, NY

The purpose of this article is to examine municipal property acquisition patterns in shrinking cities. We use data from the City of Buffalo’s municipal property auction records to analyze the spatial distribution of properties offered for sale in its annual tax foreclosure auction. In addition to these data, we examine demolition and building permit records. Our analysis suggests that cities like Buffalo follow strategies based on an urban growth paradigm when responding to abandonment. This paradigm operates under the assumption that growth is a constant and urban development is only limited by fiscal constraints, underdeveloped systems of urban governance, environmental degradation, and resistance by anti-growth coalitions. We recommend that planners in shrinking cities de-emphasize growth based planning and focus on rightsizing strategies. These strategies are based on the assumption that growth is not a constant. Consequently, urban revitalization is concentrated in a smaller urban footprint

Mandeville\u27s Intolerance: The Contest for Souls and Sacred Sites in The Travels of Sir John Mandeville

As the first medieval text to combine the matter of the East with the matter of the Holy Land, The Travels circulated widely in over 300 manuscripts, making it an important text when studying medieval Christian attitudes toward non-Christians. Although many scholars point to The Travels as a tolerant text ahead of its time, a historicized approach reveals that Mandeville\u27s project is better understood in terms of his intolerant universalism. I argue that in casting non-Christians as proto-Christians who stand as evidence of Christianity\u27s global spiritual hegemony, the author appropriates and consumes them in service of his universalist agenda. I suggest that reading the text in terms of this intolerant universalism is a more productive approach to questions surrounding The Travels including Mandeville\u27s demonization of Jews: an exception to his generous treatment of non-Christians), his concern for the Holy Land, and his reasons for combining the matter of the Holy Land with the matter of the East