Dimensionality reduction with subgaussian matrices: a unified theory

We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we recover and, in several cases, improve results for sets of sparse and structured sparse vectors, low-rank matrices and tensors, and smooth manifolds. In addition, we establish a new Johnson-Lindenstrauss embedding for data sets taking the form of an infinite union of subspaces of a Hilbert space

Tail bounds via generic chaining

We modify Talagrand's generic chaining method to obtain upper bounds for all p-th moments of the supremum of a stochastic process. These bounds lead to an estimate for the upper tail of the supremum with optimal deviation parameters. We apply our procedure to improve and extend some known deviation inequalities for suprema of unbounded empirical processes and chaos processes. As an application we give a significantly simplified proof of the restricted isometry property of the subsampled discrete Fourier transform.Comment: Added detailed proof of Theorem 3.5; Application to dimensionality reduction expanded and moved to separate note arXiv:1402.397

It\^{o} isomorphisms for LpL^{p}-valued Poisson stochastic integrals

Motivated by the study of existence, uniqueness and regularity of solutions to stochastic partial differential equations driven by jump noise, we prove It\^{o} isomorphisms for $L^p$-valued stochastic integrals with respect to a compensated Poisson random measure. The principal ingredients for the proof are novel Rosenthal type inequalities for independent random variables taking values in a (noncommutative) $L^p$-space, which may be of independent interest. As a by-product of our proof, we observe some moment estimates for the operator norm of a sum of independent random matrices.Comment: Published in at http://dx.doi.org/10.1214/13-AOP906 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Applying persuasive design in a diabetes mellitus application

This paper describes persuasive design methods and compares this to an application currently under development for diabetes mellitus patients. Various elements of persuasion and a categorization of persuasion types are mentioned. Also discussed are principles of how successful persuasion should be designed, as well as the practical applications and ethics of persuasive design. This paper is not striving for completeness of theories on the topic, but uses the theories to compare it to an application intended for diabetes mellitus patients. The results of this comparison can be used for improvements of the application

The Emergence of a Dominant Design – a study on hydrogen prototypes

The notion of dominant designs deals with dominance in the market and the dominant design is thought to be dominant because of market selection forces. The notion thus ignores the possible selection that takes place in pre-market R&D stages of technological trajectories. In this paper we ask the question whether pre-market selection takes place and if this can lead to an early dominant design. Furthermore we study what selection criteria apply during this phase, in the absence of actual market criteria. We do so through an analysis of prototyping trajectories for hydrogen vehicles. Prototypes are used by firms in their internal search process towards new designs and at the same time they are means of communicating technological expectations to outsiders. In both senses, prototypes can be taken as indicators of technological trajectories in the ongoing search process of an industry for the dominant prototype design of the future. Using prototypes as representation of intermediate outcomes of the search process, a dominant design can possibly be recognized also in a pre-market phase of development. We analyzed the designs of prototypes of hydrogen passenger cars from the 1970s till 2008. In our analysis we try to show to what extent the designs configurations of the technological components, converge or diverge over time. For this we compiled a database of 224 prototypes of hydrogen passenger cars. The database describes: the car’s manufacturer, year of construction, type of drivetrain, fuel cell type, and capacity of its hydrogen storage system. We draw conclusions with regard to the convergence/divergence of the prototypes’ designs and the role of diverse performance criteria therein. We conclude that there is convergence towards a dominant design in the prototyping phase; the PEM fuel cell combined with high pressure storage. Performance played a role as selection criterion, but so did regulation and strategic behaviour of the firms. Especially imitation dynamics, with industry leaders and followers, seems to be the major explanatory factor.Dominant design, expectations, prototypes, hydrogen, fuel cell

Entrepreneurial Culture, Regional Innovativeness and Economic Growth

This paper presents the results of an empirical study on the relationship between entrepreneurial culture, regional rates of innovation and regional economic growth. Recent literature mainly in regional science and economic geography has emphasized the role of an entrepreneurial culture in explaining the economic success of regions. Most of these contributions are however conceptual or case-based. Building on Leibenstein’s view of the entrepreneur as the ‘input completer’ and the Austrian school in which entrepreneurial activity is attributed a central role I hypothesize that regions which can be characterized as having an entrepreneurial culture are more innovative and grow faster. I use a standard economic growth model and test this hypothesis on a sample of 54 European regions. The results confirm the importance of an entrepreneurial culture. Keywords: entrepreneurship, culture, innovation, regional economic growth JEL code: Z1, R11