Automated parameters for troubled-cell indicators using outlier detection

In Vuik and Ryan (2014) we studied the use of troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problem-dependent parameter is chosen. This parameter is used in a threshold which decides whether or not to detect an element as a troubled cell. Until now, these parameters could not be chosen automatically. The choice of the parameter has impact on the approximation: it determines the strictness of the troubled-cell indicator. An inappropriate choice of the parameter will result in detection (and limiting) of too few or too many elements. The optimal parameter is chosen such that the minimal number of troubled cells is detected and the resulting approximation is free of spurious oscillations. In this paper we will see that for each troubled-cell indicator the sudden increase or decrease of the indicator value with respect to the neighboring values is important for detection. Indication basically reduces to detecting the outliers of a vector (one dimension) or matrix (two dimensions). This is done using Tukey's boxplot approach to detect which coefficients in a vector are straying far beyond others (Tukey, 1977). We provide an algorithm that can be applied to various troubled-cell indication variables. Using this technique the problem-dependent parameter that the original indicator requires is no longer necessary as the parameter will be chosen automatically

University Research, Industrial R&D, and the Anchor Tenant Hypothesis

We examine geographic concentration, agglomeration, and co-location of university research and industrial R&D in three technological areas: medical imaging, neural networks, and signal processing. Using data on scientific publications and patents as indicators of university research and industrial R&D, we find strong evidence of geographic concentration in both activities at the level of MSAs. While evidence for agglomeration (in the sense of excess' concentration relative to the size of MSAs and the size distribution of research labs) of research in these fields is mixed, we do find strong evidence of co-location of upstream and downstream activity. We view such co-located vertically connected activities as constituents of a local innovation system,' and these appear to vary markedly in their ability to convert local academic research into local commercial innovation. We develop and test the hypothesis that the presence of a large, local, R&D-intensive firm an anchor tenant' enhances the productivity of local innovation systems by making local university research more likely to be absorbed by and to stimulate local industrial R&D. Presence of anchor tenant firms may be an important factor in stimulating both the demand and supply sides of local markets for innovation and may be an important channel for transmission of spillovers. While our empirical results are preliminary, they indicate that anchor tenant technology firms may be an economically important aspect of the institutional structure of local economies.

Patents, Thickets, and the Financing of Early-Stage Firms: Evidence from the Software Industry

The impact of stronger intellectual property rights in the software industry is controversial. One means by which patents can affect technical change, industry dynamics, and ultimately welfare, is through their role in stimulating or stifling entry by new ventures. Patents can block entry, or raise entrants' costs in variety of ways, while at the same time they may stimulate entry by improving the bargaining position of entrants vis-à-vis incumbents, and supporting a "market for technology" which enables new ventures to license their way into the market, or realize value through trade in their intangible assets. One important impact of patents may be their influence on capital markets, and here we find evidence that the extraordinary growth in patenting of software during the 1990s is associated with significant effects on the financing of software companies. Start-up software companies operating in markets characterized by denser patent thickets see their initial acquisition of VC funding delayed relative to firms in markets less affected by patents. The relationship between patents and the probability of IPO or acquisition is more complex, but there is some evidence that firms without patents are less likely to go public if they operate in a market characterized by patent thickets.

Patents and the Survival of Internet-related IPOs

We examine the effect of patenting on the survival prospects of 356 internet-related firms that IPO'd at the height of the stock market bubble of the late 1990s. By March 2005, nearly 2/3 of these firms had delisted from the NASDAQ exchange. Although changes in the legal environment in the US in the 1990s made it much easier to obtain patents on software and, ultimately, on business methods, less than half of the firms in this sample obtained, or attempted to obtain, patents. For those that did, we hypothesize that patents conferred competitive advantages that translate into higher probability of survival, though they may also simply be a signal of firm quality. Controlling for age, venture-capital backing, financial characteristics, and stock market conditions, patenting is positively associated with survival. Quite different processes appear to govern exit via acquisition compared to exit via delisting from the exchange due to business failure. Firms that applied for more patents were less likely to be acquired, though obtaining unusually highly cited patents may make them more attractive acquisition target. These findings do not hold for business method patents, which do not appear to confer a survival advantage.

Faster, Smaller, Cheaper: An Hedonic Price Analysis of PDAs

We compute quality-adjusted price indexes for Personal Digital Assistants (PDAs) for the period 1999-2004, using data on prices and characteristics of 203 models sold by 12 manufacturers. The PDA market is growing in size, it is technologically dynamic with very substantial changes in measured characteristics over time, and it has experienced rapid rates of product introduction. Hedonic regressions consistently show prices to be positively related to processor performance, RAM memory, permanent storage capacity, and battery life, as well as several measures of screen size and quality. Features such as networking, biometric identification, camera, and cellphone capability are also positively associated with price. Hedonic price indexes implied by these regressions decline at an AAGR of 21.1% to 25.6% per year during this period. A matched model price index computed from a subset of observations declines at 18.75% per year. Though these PDA rates of price decline are lower than have been estimated for desktop and laptop PCs, consumers in this "ultra-portable" segment of the computer market appear to have enjoyed substantial welfare gains over the past five years.

Entry and Patenting in the Software Industry

To what extent are firms kept out of a market by patents covering related technologies? Do patents held by potential entrants make it easier to enter markets? We estimate the empirical relationship between market entry and patents for 27 narrowly defined categories of software products during the period 1990-2004. Controlling for demand, market structure, average patent quality, and other factors, we find that a 10% increase in the number of patents relevant to market reduces the rate of entry by 3-8%, and this relationship intensified following expansions in the patentability of software in the mid-1990s. However, potential entrants with patent applications relevant to a market are more likely to enter it. Finally, patents appear to substitute for complementary assets in the entry process, as patents have both greater entry-deterring and entry-promoting effects for firms without prior experience in other markets.