Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals

This is a survey article of geometric properties of noncommutative symmetric spaces of measurable operators $E(\mathcal{M},\tau)$, where $\mathcal{M}$ is a semifinite von Neumann algebra with a faithful, normal, semifinite trace $\tau$, and $E$ is a symmetric function space. If $E\subset c_0$ is a symmetric sequence space then the analogous properties in the unitary matrix ideals $C_E$ are also presented. In the preliminaries we provide basic definitions and concepts illustrated by some examples and occasional proofs. In particular we list and discuss the properties of general singular value function, submajorization in the sense of Hardy, Littlewood and P\'olya, K\"othe duality, the spaces $L_p(\mathcal{M},\tau)$, $1\le p<\infty$, the identification between $C_E$ and $G(B(H), \rm{tr})$ for some symmetric function space $G$, the commutative case when $E$ is identified with $E(\mathcal{N}, \tau)$ for $\mathcal{N}$ isometric to $L_\infty$ with the standard integral trace, trace preserving $*$-isomorphisms between $E$ and a $*$-subalgebra of $E(\mathcal{M},\tau)$, and a general method of removing the assumption of non-atomicity of $\mathcal{M}$. The main results on geometric properties are given in separate sections. We present the results on (complex) extreme points, (complex) strict convexity, strong extreme points and midpoint local uniform convexity, $k$-extreme points and $k$-convexity, (complex or local) uniform convexity, smoothness and strong smoothness, (strongly) exposed points, (uniform) Kadec-Klee properties, Banach-Saks properties, Radon-Nikod\'ym property and stability in the sense of Krivine-Maurey. We also state some open problems

Piecewise deterministic Markov processes in biological models

We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene expression, physiologically structured populations, as well as neural activity. General results concerning asymptotic properties of stochastic semigroups induced by such Markov processes are applied to specific examples.Comment: in: Semigroup of Operators - Theory and Applications, J. Banasiak et al. (eds.), Springer Proceedings in Mathematics & Statistics 113, (2015), pp. 235-25

WP 87 - Emigration and labour shortages. An opportunity for trade unions in new member states?

The paper explores whether and how unions in the post-socialist EU member states have responded to the opportunity of improving their situation, offered by the increased emigration after the recent EU enlargements. Migration influences the labour force composition and unemployment rates, which could facilitate union organizing and bargaining position, and in consequence enhance union legitimacy and bargaining institutions. We adopt an actor-oriented framework to examine union strategies and actions, and we test the above hypotheses in the public healthcare sector largely affected by migration in Slovakia, Poland and Hungary. We argue that variation in union strategies depends mainly on the interplay of union capacities and state strategies. Slovak unions used migration-triggered labour shortages to obtain wage increases and to consolidate existing bargaining channels. In contrast, Polish unions responded to migration-induced labour shortages through industrial action, while Hungarian healthcare unions remained the least active in seizing migration-related opportunities to enhance legitimacy or bargaining institutions.

Deterministic Brownian Motion: The Effects of Perturbing a Dynamical System by a Chaotic Semi-Dynamical System

Here we review and extend central limit theorems for highly chaotic but deterministic semi-dynamical discrete time systems. We then apply these results show how Brownian motion-like results are recovered, and how an Ornstein-Uhlenbeck process results within a totally deterministic framework. These results illustrate that the contamination of experimental data by "noise" may, under certain circumstances, be alternately interpreted as the signature of an underlying chaotic process.Comment: 65 pages, 8 figure