Abstract:
In the past decades health care and medicine in most countries got more or less in a state of crisis. This is not surprising because, so far, there is no consensus about the nature of health. This shortcoming inhibits constructive, interdisciplinary dialogues about health values. It renders priority setting controversial and subject to power struggles. A new definition of health, known as the Meikirch Model, could correct this deficiency. It states: “Health is a dynamic state of wellbeing characterized by a physical, mental and social potential, which satisfies the demands of a life commensurate with age, culture, and personal responsibility. If the potential is insufficient to satisfy these de-mands the state is disease.” The potential is composed of a biologically given and a person-ally acquired component. Thus this definition characterizes health with six essential features, which are suitable for an analysis of and priority setting in medical consultations and in health care policy decisions. A wide discussion about this definition of health followed by its imple-mentation is expected to render health care in-dividually and socially more beneficial.

Our main aim is to prove a more general version of the quantum Zeno effect. Then we discuss some examples of the quantum Zeno effect. Furthermore, we discuss a possibility that based on the quantum Zeno effect and certain experiments one could check whether, from the statistical point of view, a concrete system behaves like a quantum system. The more general version of quantum Zeno effect can be helpful to prove that the brain acts like in a quantum system. The proof of our main result is based on certain formulas describing probability distributions of time series related to quantum measurements.

Abstract:
Recent measurements of ultra-high energy cosmic rays and neutrinos are briefly reviewed. With several new large scale observatories nearing completion or becoming fully operational only very recently, a large body of high quality and high statistics data is growing up now. Already these first data have started to open up a new window to the high energy Universe giving us first direct clues about the origin of the most energetic particles with energies of about 10^{20} eV as well as about their interactions from extragalactic sources to Earth. Also, for the first time full sky views of high energy neutrinos have become available with neutrino telescopes operating on either Hemisphere. While a "smoking gun" is still missing on galactic sources of cosmic rays, constraining upper limits to neutrino fluxes from various source candidates are reported. Thus, future neutrino telescopes, such as KM3NeT in the Mediterranean should aim at volumes significantly larger than one cubic kilometer. Besides seeking the sources of galactic and extragalactic cosmic rays, the new generation of cosmic ray and neutrino observatories touches a wide range of scientific issues and they have already provided important results on tests of fundamental physics.

Abstract:
The XVII International Symposium on Very High Energy Cosmic Ray Interactions, held in August of 2012 in Berlin, was the first one in the history of the Symposium, where a plethora of high precision LHC data with relevance for cosmic ray physics was presented. This report aims at giving a brief summary of those measurements and it discusses their relevance for observations of high energy cosmic rays. Enormous progress has been made also in air shower observations and in direct measurements of cosmic rays, exhibiting many more structure in the cosmic ray energy spectrum than just a simple power law with a knee and an ankle. At the highest energy, the flux suppression may not be dominated by the GZK-effect but by the limiting energy of a nearby source or source population. New projects and application of new technologies promise further advances also in the near future. We shall discuss the experimental and theoretical progress in the field and its prospects for coming years.

Abstract:
Observations of cosmic rays have been improved at all energies, both in terms of higher statistics and reduced systematics. As a result, the all particle cosmic ray energy spectrum starts to exhibit more structures than could be seen previously. Most importantly, a second knee in the cosmic ray spectrum -- dominated by heavy primaries -- is reported just below 10^{17} eV. The light component, on the other hand, exhibits an ankle like feature above 10^{17} eV and starts to dominate the flux at the ankle. The key question at the highest energies is about the origin of the flux suppression observed at energies above 5 x 10^{19} eV. Is this the long awaited GZK-effect or the exhaustion of sources? The key to answering this question is again given by the still largely unknown mass composition at the highest energies. Data from different observatories don't quite agree and common efforts have been started to settle that question. The high level of isotropy observed even at the highest energies starts to challenge a proton dominated composition if extragalactic (EG) magnetic fields are on the order of a few nG or more. We shall discuss the experimental and theoretical progress in the field and the prospects for the next decade.

Abstract:
Measurements of cosmic ray particles at energies above E = 5 x 10^{14} eV are performed by large area ground based air shower experiments. Only they provide the collection power required for obtaining sufficient statistics at the low flux levels involved. In this review we briefly outline the physics and astrophysics interests of such measurements and discuss in more detail various experimental techniques applied for reconstructing the energy and mass of the primary particles. These include surface arrays of particle detectors as well as observations of Cherenkov- and of fluorescence light. A large variety of air shower observables is then reconstructed from such data and used to infer the properties of the primary particles via comparisons to air shower simulations. Advantages, limitations, and systematic uncertainties of different approaches will be critically discussed.

Abstract:
The study of high energy cosmic rays is a diversified field of observational and phenomenological physics addressing questions ranging from shock acceleration of charged particles in various astrophysical objects, via transport properties through galactic and extragalactic space, to questions of dark matter, and even to those of particle physics beyond the Standard Model including processes taking place in the earliest moments of our Universe. After decades of mostly independent evolution of nuclear-, particle- and high energy cosmic ray physics we find ourselves entering a symbiotic era of these fields of research. Some examples of interrelations will be given from the perspective of modern Particle-Astrophysics and new major experiments will briefly be sketched.

Abstract:
Recent advances in measuring and interpreting cosmic rays from the spectral ankle to the highest energies are briefly reviewed. A knee of heavy primaries and an ankle of light primaries have been observed at about 10^{17} eV. The light component starts to dominate the flux at the ankle in the all particle spectrum at about 4x10^{18} eV and sheds light on the transition from galactic to extragalactic cosmic rays. The prime question at the highest energies is about the origin of the flux suppression observed at E > 4x10^{19} eV. Is this the long awaited GZK-effect or the exhaustion of sources? The key to answering this question is again the still largely unknown mass composition at the highest energies. Data from different observatories don't quite agree and common efforts have been started to settle that question. The high level of isotropy observed even at the highest energies challenges models of a proton dominated composition if extragalactic magnetic fields are on the order of a few nG or less. We will discuss the experimental and theoretical progress in the field and the prospects for the next decade.

Abstract:
The real intersection cohomology of a toric variety is described in a purely combinatorial way using methods of elementary commutative algebra only. We define, for arbitrary fans, the notion of a ``minimal extension sheaf'' on the fan as an axiomatic characterization of the equivariant intersection cohomology sheaf. This provides a purely algebraic interpretation of Stanley's generalized f- and g-vector of an arbitrary polytope or complete fan under a natural vanishing condition. -- The results presented in this note originate from joint work with G.Barthel, J.-P.Brasselet and L.Kaup, continuing earlier research (see math.AG/9904159). A detailed exposition will appear elsewhere (see math.AG/0002181).

Abstract:
In two articles by Barthel, Brasselet, Fieseler and Kaup, and, Bressler and Lunts, a combinatorial theory of intersection cohomology and perverse sheaves has been developed on fans. In the first one, one tried to present everything on an elementary level,using only some commutative algebra and no derived categories. There remained two major gaps: First of all the Hard Lefschetz Theorem was only conjectured and secondly the intersection product seemed to depend on some non-canonical choices. Meanwhile the Hard Lefschetz theorem has been proved by Karu. The proof relies heavily on the intersection product, since what finally has to be shown are the Hodge-Riemann relations. In fact here again choices enter: The intersection product is induced from the intersection product on some simplicial subdivision via a direct embedding of the corresponding intersection cohomology sheaves, a fact, which makes the argumentation quite involved. In a recent paper by Bressler and Lunts, one shows by a detailed analysis that eventually all possible choices do not affect the definition of the pairing. Our goal here is the same, but we shall try to follow the spirit of the first cited paper avoiding the formalism of derived categories. For perverse sheaves we define their dual sheaf and check that the intersection cohomology sheaf is self- dual in a natural way.