The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

The time dimension of neural network models

This review attempts to provide an insightful perspective on the role of time within neural network models and the use of neural networks for problems involving time. The most commonly used neural network models are defined and explained giving mention to important technical issues but avoiding great detail. The relationship between recurrent and feedforward networks is emphasised, along with the distinctions in their practical and theoretical abilities. Some practical examples are discussed to illustrate the major issues concerning the application of neural networks to data with various types of temporal structure, and finally some highlights of current research on the more difficult types of problems are presented.

Innovation and regional absorptive capacity:the labour market dimension

In 2003, Eurostat published an 'experimental' dataset on regional innovation levels derived from the Second Community Innovation Survey. This dataset, part of the European Innovation Scoreboard, also contains a range of regional labour market indicators. In this paper, we report an exploratory analysis of this data, focussing on how the labour market characteristics of regions shape regions' absorptive capacity (RACAP) and their ability to assimilate knowledge from public and externally conducted R&D. In particular, we aim to establish whether labour market aspects of RACAP are more important for innovation in prosperous or lagging regions of the European Union (EU). © Springer-Verlag 2006.

The (n+1)/2 rule for dealiasing in the split-step Fourier methods for n-wave interactions

The aim of this letter is to demonstrate that complete removal of spectral aliasing occurring due to finite numerical bandwidth used in the split-step Fourier simulations of nonlinear interactions of optical waves can be achieved by enlarging each dimension of the spectral domain by a factor (n+1)/2, where n is the number of interacting waves. Alternatively, when using low-pass filtering for dealiasing this amounts to the need for filtering a 2/(n+1) fraction of each spectral dimension.

German-Irish corporate relationships:the cultural dimension

The thesis raises the question of whether or not in an age of internationalisation and globalisation, the cultural differences which exist between Germany and Ireland are still relevant to German-Irish corporate relationships or have internationally accepted best practices removed culture from the equation? The first three chapters establish the theoretical framework of the thesis by outlining the broadly culturalist/institutionalist approach, based on the work of Hofstede and Maurice et al, to be pursued, profiling the business cultures of both countries by analysing the components of their respective national institutional frameworks, and the examining existing approaches to the study of mother company-foreign subsidiary relationships. Chapters four to seven constitute the empirical section of the thesis. Using the interviews carried out with two sample groups (Sample Group A: 15 German mother companies and 14 of their Irish operations and Sample Group B: 7 Irish mother companies and 9 of their German operations), the mother companies in both groups are examined to see whether or not they demonstrate characteristics which are in keeping with their national business cultures. Their foreign operations are then analysed as is the mother company-foreign subsidiary relationship to determine whether or not any mother company influences are visible. The general approaches adopted by the two groups of mother companies to their foreign operations are compared and contrasted. Finally, differences in national attitudes and values are identified and their impact assessed. The analysis reveals that despite existing pressures towards convergence, the cultural differences between both countries are still relevant to the relationship particularly at the level of attitudes and values and although similarities in the mother company approaches to their subsidiaries are present, national specificities may nevertheless be detected.

Sourcing knowledge for innovation:the international dimension

Drawing knowledge from external sources in the UK, or internationally, has become increasingly important to small and medium-sized firms (SMEs). SMEs cannot generate all they need to know to develop new products and processes within their own companies, they need to look elsewhere for new ideas and expertise. This practice is known as knowledge sourcing. This report provides a detailed review of patterns of knowledge sourcing, and the key factors influencing these patterns, particularly from a small business perspective. We present key findings from a survey of 393 UK companies and analyse the results. We also highlight case studies of UK SMEs that work closely with overseas partners and agents to widen their own knowledge.

The external dimension of the EU’s fight against organized crime:the search for coherence between rhetoric and practice

SSince the external dimension of the European Union’s Justice and Home Affairs (JHA) began to be considered, a substantial amount of literature has been dedicated to discussing how the EU is cooperating with non-member states in order to counter problems such as terrorism, organized crime and illegal migration. According to the EU, the degree of security interconnectedness has become so relevant that threats can only be adequately controlled if there is effective concerted regional action. This reasoning has led the EU to develop a number of instruments, which have resulted in the exporting of certain elements of its JHA policies, either through negotiation or socialization. Although the literature has explored how this transfer has been applied to the field of terrorism and immigration, very little has been written on the externalisation of knowledge, practice and norms in the area of organized crime. This article proposes to bridge this gap by looking at EU practice in the development of the external dimension of organized crime policies, through the theoretical lens of the EU governance framework.

The external dimension of EU justice and home affairs after the Lisbon Treaty::analysing the dynamics of expansion and diversification

The article introduces a research framework for analysing the external dimension of EU Justice and Home Affairs after the Lisbon Treaty. The dynamics of expansion and diversification, discernable for both the EU policy-making and the scholarly work dedicated to it, are at the centre of the article and constitute a common reference point for the present Special Issue. These dynamics have been triggered through deliberate decisions of involved policy-makers as well as through unintended spillover effects from other policy areas and/or decisions. The article also engages with the theoretically informed literature on the subject, which struggles with the definition of what this dimension actually constitutes, as well as how to best capture the practices of this field.We take stock of the scholarly debates by comparing the diverse approaches and discussing how much they complement each other and/or present different dimensions of a single ‘policy universe’.