The block structure spaces of real projective spaces and orthogonal calculus of functors

Given a compact manifold X, the set of simple manifold structures on X x \Delta^k relative to the boundary can be viewed as the k-th homotopy group of a space \S^s (X). This space is called the block structure space of X. We study the block structure spaces of real projective spaces. Generalizing Wall's join construction we show that there is a functor from the category of finite dimensional real vector spaces with inner product to the category of pointed spaces which sends the vector space V to the block structure space of the projective space of V. We study this functor from the point of view of orthogonal calculus of functors; we show that it is polynomial of degree <= 1 in the sense of orthogonal calculus. This result suggests an attractive description of the block structure space of the infinite dimensional real projective space via the Taylor tower of orthogonal calculus. This space is defined as a colimit of block structure spaces of projective spaces of finite-dimensional real vector spaces and is closely related to some automorphisms spaces of real projective spaces.Comment: corrected version, 32 pages, published in Transactions of the AMS at http://www.ams.org/tran/2007-359-01/S0002-9947-06-04180-8

Evaluation of the EU membership of the new member states

When analysing the impacts of EU membership on NMCs, and in particular on the Hungarian economy, we consider integration maturity as a theoretical framework. Integration maturity can be defined as a capability to exploit the benefits of the given form of integration to the maximum, while the costs and drawbacks can be minimised. Integration maturity can be measured by comparing costs and benefits. A country is mature for integration if membership on the whole is advantageous for it

GP-HD: Using Genetic Programming to Generate Dynamical Systems Models for Health Care

The huge wealth of data in the health domain can be exploited to create models that predict development of health states over time. Temporal learning algorithms are well suited to learn relationships between health states and make predictions about their future developments. However, these algorithms: (1) either focus on learning one generic model for all patients, providing general insights but often with limited predictive performance, or (2) learn individualized models from which it is hard to derive generic concepts. In this paper, we present a middle ground, namely parameterized dynamical systems models that are generated from data using a Genetic Programming (GP) framework. A fitness function suitable for the health domain is exploited. An evaluation of the approach in the mental health domain shows that performance of the model generated by the GP is on par with a dynamical systems model developed based on domain knowledge, significantly outperforms a generic Long Term Short Term Memory (LSTM) model and in some cases also outperforms an individualized LSTM model

Increased Bilateral Interactions in Middle-Aged Subjects

A hallmark of the age-related neural reorganization is that old versus young adults execute typical motor tasks by a more diffuse neural activation pattern including stronger ipsilateral activation during unilateral tasks. Whether such changes in neural activation are present already at middle age and affect bimanual interactions is unknown. We compared the amount of associated activity, i.e., muscle activity and force produced by the non-task hand and motor evoked potentials (MEPs) produced by magnetic brain stimulation between young (mean 24 years, n = 10) and middle-aged (mean 50 years, n = 10) subjects during brief unilateral (seven levels of % maximal voluntary contractions, MVCs) and bilateral contractions (4 × 7 levels of % MVC combinations), and during a 120-s-long MVC of sustained unilateral index finger abduction. During the force production, the excitability of the ipsilateral (iM1) or contralateral primary motor cortex (cM1) was assessed. The associated activity in the “resting” hand was ~2-fold higher in middle-aged (28% of MVC) versus young adults (11% of MVC) during brief unilateral MVCs. After controlling for the background muscle activity, MEPs in iM1 were similar in the two groups during brief unilateral contractions. Only at low (bilateral) forces, MEPs evoked in cM1 were 30% higher in the middle-aged versus young adults. At the start of the sustained contraction, the associated activity was higher in the middle-aged versus young subjects and increased progressively in both groups (30 versus 15% MVC at 120 s, respectively). MEPs were greater at the start of the sustained contraction in middle-aged subjects but increased further during the contraction only in young adults. Under these experimental conditions, the data provide evidence for the reorganization of neural control of unilateral force production as early as age 50. Future studies will determine if the altered neural control of such inter-manual interactions are of functional significance