Towards a general theory of extremes for observables of chaotic dynamical systems

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the cho- sen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan–Yorke dimension of the attractor. Preliminary numer- ical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.

The economic theory of the firm as a foundation for international business theory

The economic theory of the firm is central to the theory of the multinational enterprise. Recent literature on multinationals, however, makes only limited reference to the economic theory of the firm. Multinationals play an important role in coordinating the international division of labour through internal markets. The paper reviews the economic principles that underlie this view. Optimal internalisation equates marginal benefits and costs. The benefits of internalisation stem mainly from the difficulties of licensing proprietary knowledge, reflecting the view that MNEs possess an ‘ownership’ or ‘firm-specific’ advantage. The costs of internalisation, it is argued, reflect managerial capability, and in particular the capability to manage a large firm. The paper argues that management capability is a complement to ownership advantage. Ownership advantage determines the potential of the firm, and management capability governs the fulfilment of this potential through overcoming barriers to growth. The analysis is applied to a variety of issues, including out-sourcing, geographical dispersion of production, and regional specialisation in marketing.

Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

GM food purchase intentions: linking the theory of planned behaviour with consumer trust and stated choice

After the “European” experience of BSE and further food safety crises consumer trust is playing an increasingly important role in political and marketing decision making. This also relates to the area of consumer acceptance of GM food. This paper integrates consumer trust with the theory of planned behavior and a stated choice model to gain a more complete picture of consumer decision making. Preliminary results indicate that when GM products offer practical benefits to consumers acceptance may increase considerably. Furthermore, both trust and perceived benefits contribute significantly to explaining the level of acceptance.

A unified approach to the recognition of complex actions from sequences of zone-crossings

We present a method for the recognition of complex actions. Our method combines automatic learning of simple actions and manual definition of complex actions in a single grammar. Contrary to the general trend in complex action recognition that consists in dividing recognition into two stages, our method performs recognition of simple and complex actions in a unified way. This is performed by encoding simple action HMMs within the stochastic grammar that models complex actions. This unified approach enables a more effective influence of the higher activity layers into the recognition of simple actions which leads to a substantial improvement in the classification of complex actions. We consider the recognition of complex actions based on person transits between areas in the scene. As input, our method receives crossings of tracks along a set of zones which are derived using unsupervised learning of the movement patterns of the objects in the scene. We evaluate our method on a large dataset showing normal, suspicious and threat behaviour on a parking lot. Experiments show an improvement of ~ 30% in the recognition of both high-level scenarios and their composing simple actions with respect to a two-stage approach. Experiments with synthetic noise simulating the most common tracking failures show that our method only experiences a limited decrease in performance when moderate amounts of noise are added.

The missing pillar: the creativity theory of knowledge spillover entrepreneurship

Knowledge spillover theory of entrepreneurship and the prevailing theory of economic growth treat opportunities as endogenous and generally focus on opportunity recognition by entrepreneurs. New knowledge created endogenously results in knowledge spillovers enabling inventors and entrepreneurs to commercialize it. This article discusses that knowledge spillover entrepreneurship depends not only on ordinary human capital, but more importantly also on creativity embodied in creative individuals and diverse urban environments that attract creative classes. This might result in self-selection of creative individuals into entrepreneurship or enable entrepreneurs to recognize creativity and commercialize it. This creativity theory of knowledge spillover entrepreneurship is tested utilizing data on European cities.

The transaction cost economics theory of the family firm: family-based human asset specificity and the bifurcation bias

We develop a transaction cost economics theory of the family firm, building upon the concepts of family-based asset specificity, bounded rationality, and bounded reliability. We argue that the prosperity and survival of family firms depend on the absence of a dysfunctional bifurcation bias. The bifurcation bias is an expression of bounded reliability, reflected in the de facto asymmetric treatment of family vs. nonfamily assets (especially human assets). We propose that absence of bifurcation bias is critical to fostering reliability in family business functioning. Our study ends the unproductive divide between the agency and stewardship perspectives of the family firm, which offer conflicting accounts of this firm type's functioning. We show that the predictions of the agency and stewardship perspectives can be usefully reconciled when focusing on how family firms address the bifurcation bias or fail to do so.

The growth rate and dimension theory of beta-expansions

In a recent paper of Feng and Sidorov they show that for β∈(1,(1+5√)/2) the set of β-expansions grows exponentially for every x∈(0,1/(β−1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

Toward a theory of semantic representation

We present an account of semantic representation that focuses on distinct types of information from which word meanings can be learned. In particular, we argue that there are at least two major types of information from which we learn word meanings. The first is what we call experiential information. This is data derived both from our sensory-motor interactions with the outside world, as well as from our experience of own inner states, particularly our emotions. The second type of information is language-based. In particular, it is derived from the general linguistic context in which words appear. The paper spells out this proposal, summarizes research supporting this view and presents new predictions emerging from this framework.

Ordinal judgements of depth in monocularly- and binocularly-viewed photographs of complex natural scenes

This study investigated the contribution of stereoscopic depth cues to the reliability of ordinal depth judgments in complex natural scenes. Participants viewed photographs of cluttered natural scenes, either monocularly or stereoscopically. On each trial, they judged which of two indicated points in the scene was closer in depth. We assessed the reliability of these judgments over repeated trials, and how well they correlated with the actual disparities of the points between the left and right eyes' views. The reliability of judgments increased as their depth separation increased, was higher when the points were on separate objects, and deteriorated for point pairs that were more widely separated in the image plane. Stereoscopic viewing improved sensitivity to depth for points on the same surface, but not for points on separate objects. Stereoscopic viewing thus provides depth information that is complementary to that available from monocular occlusion cues.

An example in Beurling's theory of generalised primes

In this paper we prove some connections between the growth of a function and its Mellin transform and apply these to study an explicit example in the theory of Beurling primes.

Genetic and phenotypic characterization of complex hereditary spastic paraplegia

The hereditary spastic paraplegias are a heterogeneous group of degenerative disorders that are clinically classified as either pure with predominant lower limb spasticity, or complex where spastic paraplegia is complicated with additional neurological features, and are inherited in autosomal dominant, autosomal recessive or X-linked patterns. Genetic defects have been identified in over 40 different genes, with more than 70 loci in total. Complex recessive spastic paraplegias have in the past been frequently associated with mutations in SPG11 (spatacsin), ZFYVE26/SPG15, SPG7 (paraplegin) and a handful of other rare genes, but many cases remain genetically undefined. The overlap with other neurodegenerative disorders has been implied in a small number of reports, but not in larger disease series. This deficiency has been largely due to the lack of suitable high throughput techniques to investigate the genetic basis of disease, but the recent availability of next generation sequencing can facilitate the identification of disease- causing mutations even in extremely heterogeneous disorders. We investigated a series of 97 index cases with complex spastic paraplegia referred to a tertiary referral neurology centre in London for diagnosis or management. The mean age of onset was 16 years (range 3 to 39). The SPG11 gene was first analysed, revealing homozygous or compound heterozygous mutations in 30/97 (30.9%) of probands, the largest SPG11 series reported to date, and by far the most common cause of complex spastic paraplegia in the UK, with severe and progressive clinical features and other neurological manifestations, linked with magnetic resonance imaging defects. Given the high frequency of SPG11 mutations, we studied the autophagic response to starvation in eight affected SPG11 cases and control fibroblast cell lines, but in our restricted study we did not observe correlations between disease status and autophagic or lysosomal markers. In the remaining cases, next generation sequencing was carried out revealing variants in a number of other known complex spastic paraplegia genes, including five in SPG7 (5/97), four in FA2H (also known as SPG35) (4/97) and two in ZFYVE26/SPG15. Variants were identified in genes usually associated with pure spastic paraplegia and also in the Parkinson’s disease-associated gene ATP13A2, neuronal ceroid lipofuscinosis gene TPP1 and the hereditary motor and sensory neuropathy DNMT1 gene, highlighting the genetic heterogeneity of spastic paraplegia. No plausible genetic cause was identified in 51% of probands, likely indicating the existence of as yet unidentified genes.