An improved method for solving quasilinear convection diffusion problems on a coarse mesh

A method is developed for solving quasilinear convection diffusion problems starting on a coarse mesh where the data and solution-dependent coefficients are unresolved, the problem is unstable and approximation properties do not hold. The Newton-like iterations of the solver are based on the framework of regularized pseudo-transient continuation where the proposed time integrator is a variation on the Newmark strategy, designed to introduce controllable numerical dissipation and to reduce the fluctuation between the iterates in the coarse mesh regime where the data is rough and the linearized problems are badly conditioned and possibly indefinite. An algorithm and updated marking strategy is presented to produce a stable sequence of iterates as boundary and internal layers in the data are captured by adaptive mesh partitioning. The method is suitable for use in an adaptive framework making use of local error indicators to determine mesh refinement and targeted regularization. Derivation and q-linear local convergence of the method is established, and numerical examples demonstrate the theory including the predicted rate of convergence of the iterations.Comment: 21 pages, 8 figures, 1 tabl

General Network Effects and Welfare

Abstract. (In)direct network effects arise frequently in economic models but, for rea-sons of analytical tractability, are often assumed to be linear. Here, we examine the general non-linear case with two platforms. We establish the conditions characterising equilibria and show that welfare changes can be related in a simple, intuitive way to the degree of diminishing returns of the network effects function

What am I? Virtual Machines and the Mind/Body Problem

When your word processor or email program is running on your computer, this creates a "virtual machine” that manipulates windows, files, text, etc. What is this virtual machine, and what are the virtual objects it manipulates? Many standard arguments in the philosophy of mind have exact analogues for virtual machines and virtual objects, but we do not want to draw the wild metaphysical conclusions that have sometimes tempted philosophers in the philosophy of mind. A computer file is not made of epiphenomenal ectoplasm. I argue instead that virtual objects are "supervenient objects". The stereotypical example of supervenient objects is the statue and the lump of clay. To this end I propose a theory of supervenient objects. Then I turn to persons and mental states. I argue that my mental states are virtual states of a cognitive virtual machine implemented on my body, and a person is a supervenient object supervening on his cognitive virtual machine

The Control of Porting in Two-Sided Markets

A sizable literature has grown up in recent years focusing on two-sided markets in which economies of scale combined with complementarities between a platform and its associated ‘software’ or ‘services’ can generate indirect network effects (that is positive feedback between the number of consumers using that platform and the utility of an individual consumer). In this paper we introduce a model of ‘porting’ in such markets where porting denotes the conversion of ‘software’ or ‘services’ developed for one platform to run on another. Focusing on the case where a dominant platform exists we investigate the impact on equilibrium and the consequences for welfare of the ability to control porting. Specifically, we show that the welfare costs associated with the ‘control of porting’ may be more significant than those arising from pricing alone. This model and its associated results are of particular relevance because of the light they shed on debates about the motivations and effects of actions by a dominant platform owner. Recent examples of such debates include those about Microsoft’s behaviour both in relation to its operating system and its media player, Apple’s behaviour in relation to its DRM and iTunes platform, and Ebay’s use of the cyber-trespass doctrine to prevent access to its site

Is Google the next Microsoft? Competition, Welfare and Regulation in Internet Search

Internet search (or perhaps more accurately `web-search') has grown exponentially over the last decade at an even more rapid rate than the Internet itself. Starting from nothing in the 1990s, today search is a multi-billion dollar business. Search engine providers such as Google and Yahoo! have become household names, and the use of a search engine, like use of the Web, is now a part of everyday life. The rapid growth of online search and its growing centrality to the ecology of the Internet raise a variety of questions for economists to answer. Why is the search engine market so concentrated and will it evolve towards monopoly? What are the implications of this concentration for different `participants' (consumers, search engines, advertisers)? Does the fact that search engines act as `information gatekeepers', determining, in effect, what can be found on the web, mean that search deserves particularly close attention from policy-makers? This paper supplies empirical and theoretical material with which to examine many of these questions. In particular, we (a) show that the already large levels of concentration are likely to continue (b) identify the consequences, negative and positive, of this outcome (c) discuss the possible regulatory interventions that policy-makers could utilize to address these

On the Exact Simulation of (Jump) Diffusion Bridges

In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of recent work developing a mathematical framework for simulating finite dimensional sample path skeletons (which flexibly characterise the entirety of sample paths).Comment: 12 pages, 3 figure

Changing the Numbers: UK Directory Enquiries Deregulation and the Failure of Choice

Abstract. In 2003, the UK ‘liberalised ’ its telephone directory enquiries service with the aim of introducing competition so as to improve quality and lower costs. Unfortu-nately the results did not match expectations. Proliferation of numbers led to consumer confusion and high price firms with no discernible quality advantages but which employed heavy advertising came to dominate the market. Consumer and total welfare appear to have declined. This example raises important questions for regulators. In particular, with limits on information and rationality, it may sometimes be better to limit choice but increase competition to supply that choice

IDEOLOG: A Program for Filtering Econometric Data - A Synopsis of Alternative Methods

An account is given of various filtering procedures that have been implemented in a computer program, which can be used in analysing econometric time series. The program provides some new filtering procedures that operate primarily in the frequency domain. Their advantage is that they are able to achieve clear separations of components of the data that reside in adjacent frequency bands in a way that the conventional time-domain methods cannot. Several procedures that operate exclusively within the time domain have also been implemented in the program. Amongst these are the bandpass filters of Baxter and King and of Christiano and Fitzgerald, which have been used in estimating business cycles. The Henderson filter, the Butterworth filter and the Leser or Hodrick–Prescott filter are also implemented. These are also described in this paper. Econometric filtering procedures must be able to cope with the trends that are typical of economic time series. If a trended data sequence has been reduced to stationarity by differencing prior to its filtering, then the filtered sequence will need to be re-inflated. This can be achieved within the time domain via the summation operator, which is the inverse of the difference operator. The effects of the differencing can also be reversed within the frequency domain by recourse to the frequency-response function of the summation operator.