Bayesian data assimilation in shape registration

In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions\ud for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterisation in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterisation vector field v, informed by regularity results about the forward model. Having done this, we illustrate how Maximum Likelihood Estimators (MLEs) can be used to find regions of high posterior density, but also how we can apply recently developed MCMC methods on function spaces to characterise the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem

The Structure of Debt and Active Equity Investors: The Case of the Buyout Specialist

This paper examines the role buyout specialists play in structuring the debt used to finance the LBO and in monitoring management in the post-LBO firm. We find that when buyout specialists control the majority of the post-LBO equity, the LBO transaction is likely to be financed with less short-term and/or senior debt and less likely to experience financial distress. We also find that buyout specialists have greater board representation on smaller boards, suggesting that they actively monitor managers, and that for these transactions, using debt with tighter terms does not significantly increase the firm\u27s performance. In contrast, in all other transactions using such debt does significantly increase the firm\u27s performance. These findings suggest that active monitoring by a buyout specialist substitutes for tighter debt terms in monitoring and motivating managers of LBOs

Measuring Securities Market Efficiency in the Regulatory Setting

In Nov 1998, the SEC proposed a modification to the federal securities law disclosure requirements to facilitate the process of issuing new securities. Thomas and Cotter discuss how to determine when companies should be able to issue simplified disclosure documents

Unification: An international aerospace information issue

Science and technology projects are becoming more and more international and interdisciplinary. Other parts of the world, notably Europe, are increasingly powerful players in the aerospace business. This change has led to the development of various aerospace information initiatives in other countries. With scarce resources in all areas of government and industry, the NASA STI Program is reviewing its current acquisition and exchange practices and policies to factor in the changing requirements and new opportunities within the international community. Current NASA goals and activities are reviewed with a view toward developing a scenario for establishing an international aerospace data base, maintaining compatibility among national aerospace information systems, eliminating duplication of effort, and sharing resources through international cooperation wherever possible

Fifty Years of Patent Remedies Case Law: Two Steps Forward, One Step Back

Over the past fifty years, courts have developed a body of case law on patent remedies that is, in many respects, solidly grounded in economic reasoning. Among the high points are the courts’ embrace, in various contexts, of the simple principle that patent damages should restore patent owners to the position they would have occupied, but for the infringement—and of an important corollary to that principle, namely the importance to damages calculations of the “noninfringing alternatives” concept. By contrast, certain other developments—including the confusing standards for determining when it is appropriate to use the “entire market value” of a product as the royalty base; the standards for awarding total profits for design patent infringement; and the intricacies of the patent marking statute—cry out for further judicial or legislative reform. Yet other developments, including the standards for granting injunctive relief (and, relatedly, for awarding ongoing royalties in lieu of injunctive relief); for calculating reasonable royalties; and for awarding enhanced damages, have in some respects been positive but could be further improved

The Procompetitive Interest in Intellectual Property Law

When government recognizes intellectual property (IP) rights, it is often viewed as sanctioning the existence of private “monopolies,” in contrast to the general antimonopoly thrust of the antitrust laws. And yet, on occasion IP law itself condemns conduct on the part of IP owners-or excuses otherwise infringing activity on the part of IP defendants-expressly for the purpose of promoting competition. It does so even though antitrust law-if one were to apply it at all under analogous circumstances-would not find anticompetitive harm without conducting a more thorough analysis of whether the antitrust defendant possesses power over a well-defined market. Salient examples include the misuse doctrines in patent and copyright law; some applications of merger and fair use in copyright; and trademark law\u27s functionality doctrine. In this Article, Professor Cotter develops a theoretical explanation for that divergence between antitrust and IP. Specifically, he argues that in some limited contexts the expected social costs, including error costs, of ruling for IP defendants may be low in comparison with the expected anticompetitive harm from ruling for IP plaintiffs. As a result, IP *484 courts sometimes may enhance welfare if they are less concerned than antitrust courts about the expected costs of “false positives,” that is, cases wrongly decided against the party defending the allegedly anticompetitive conduct. Put another way, it sometimes may be appropriate for courts to excuse IP defendants from liability, in order to avert relatively speculative threats of anticompetitive harm. Professor Cotter further contends that such cases probably are more common in the copyright than in the patent law context, and that even in copyright contexts courts should be cautious about casually inferring anticompetitive harm; but that his analysis provides a rationale for a relatively expansive definition of trademark functionality

Comparative Law and Economics of Standard-Essential Patents and FRAND Royalties

Standard setting organizations often require their members to declare which of their patents are essential to the practice of a prospective standard, and to agree to license any such standard-essential patents (SEPs) on fair, reasonable, and nondiscriminatory (FRAND) terms. Among the issues that have arisen in recent disputes involving FRAND-encumbered SEPs are (1) whether a FRAND commitment creates a binding contract for the benefit of third parties, obligating the SEP owner to forgo the right to seek injunctive relief for the infringement of the SEP; (2) whether the law of remedies, or other principles of generally applicable civil law such as the doctrine of abuse of right, can limit the prevailing SEP owner’s ability to obtain injunctive relief; (3) the circustances under which competition law (antitrust) may play a role in resolving these matters; (4) whether the patentee is entitled to relief in the form of ongoing damages, if one or more of these bodies of law eliminates the possibility of an injunction; and (5) if so, how should courts calculate those damages. This article provides both an overview of how courts and other entities have begun to address these questions in the United States and elsewhere, and my analysis of the advantages and disadvantages of different possible approaches. I argue, among other things, first that courts generally should not allow SEP owners to obtain injunctions, but rather only ongoing damages; second, that in principle though perhaps not always in practice, it is preferable to use contract and patent law to achieve this result, as opposed to antitrust; and third, that in awarding monetary relief for the infringement of SEPs courts should apply the same methodology the use to calculate reasonable royalties generally, subject to a few modifications