On the maximum size of an anti-chain of linearly separable sets and convex pseudo-discs

We show that the maximum cardinality of an anti-chain composed of intersections of a given set of n points in the plane with half-planes is close to quadratic in n. We approach this problem by establishing the equivalence with the problem of the maximum monotone path in an arrangement of n lines. For a related problem on antichains in families of convex pseudo-discs we can establish the precise asymptotic bound: it is quadratic in n. The sets in such a family are characterized as intersections of a given set of n points with convex sets, such that the difference between the convex hulls of any two sets is nonempty and connected.Comment: 10 pages, 3 figures. revised version correctly attributes the idea of Section 3 to Tverberg; and replaced k-sets by "linearly separable sets" in the paper and the title. Accepted for publication in Israel Journal of Mathematic

Hypopituitarism and brain injury: recent advances in screening and management

This review gives an overview of the research on hypothalamopituitary dysfunction as a potential consequence of traumatic brain injury, including the natural history of this complication and its clinical and public health implications

Expression of CD226 is associated to but not required for NK cell education

AbstractDNAX accessory molecule-1 (DNAM-1, also known as CD226) is an activating receptor expressed on subsets of natural killer (NK) and T cells, interacts with its ligands CD155 or CD112, and has co-varied expression with inhibitory receptors. Since inhibitory receptors control NK-cell activation and are necessary for MHC-I-dependent education, we investigated whether DNAM-1 expression is also involved in NK-cell education. Here we show an MHC-I-dependent correlation between DNAM-1 expression and NK-cell education, and an association between DNAM-1 and NKG2A that occurs even in MHC class I deficient mice. DNAM-1 is expressed early during NK-cell development, precedes the expression of MHC-I-specific inhibitory receptors, and is modulated in an education-dependent fashion. Cd226−/− mice have missing self-responses and NK cells with a normal receptor repertoire. We propose a model in which NK-cell education prevents or delays downregulation of DNAM-1. This molecule endows educated NK cells with enhanced effector functions but is dispensable for education.</jats:p

Cosmological Magnetic Fields from Primordial Helical Seeds

Most early Universe scenarios predict negligible magnetic fields on cosmological scales if they are unprocessed during subsequent expansion of the Universe. We present a new numerical treatment of the evolution of primordial fields and apply it to weakly helical seeds as they occur in certain early Universe scenarios. We find that initial helicities not much larger than the baryon to photon number can lead to fields of about 10^{-13} Gauss with coherence scales slightly below a kilo-parsec today.Comment: 4 revtex pages, 2 postscript figures include

Non-Universal Spectra of Ultra-High Energy Cosmic Ray Primaries and Secondaries in a Structured Universe

Analytical calculations of extra-galactic cosmic ray spectra above ~10^17 eV are often performed assuming continuous source distributions, giving rise to spectra that depend little on the propagation mode, be it rectilinear or diffusive. We perform trajectory simulations for proton primaries in the probably more realistic case of discrete sources with a density of ~10^-5/Mpc^3. We find two considerable non-universal effects that depend on source distributions and magnetic fields: First, the primary extra-galactic cosmic ray flux can become strongly suppressed below a few 10^18 eV due to partial confinement in magnetic fields surrounding sources. Second, the secondary photon to primary cosmic ray flux ratio between ~3x10^18 eV and ~10^20 eV decreases with decreasing source density and increasing magnetization. As a consequence, in acceleration scenarios for the origin of highest energy cosmic rays the fraction of secondary photons may be difficult to detect even for experiments such as Pierre Auger. The cosmogenic neutrino flux does not significantly depend on source density and magnetization.Comment: 9 revtex pages, 9 figures, published version, minor change

Classical, semiclassical, and quantum investigations of the 4-sphere scattering system

A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and scaling properties of the computations are discussed by comparisons to the two-dimensional 3-disk system. While in systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods, this situation can be reversed with increasing dimension of the problem. For the 4-sphere system with large separations between the spheres, we demonstrate the superiority of semiclassical versus quantum calculations, i.e., semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques. The 4-sphere system with touching spheres is a challenging problem for both quantum and semiclassical techniques. Here, semiclassical resonances are obtained via harmonic inversion of a cross-correlated periodic orbit signal.Comment: 12 pages, 5 figures, submitted to Phys. Rev.

Comparison between resistive and collisionless double tearing modes for nearby resonant surfaces

The linear instability and nonlinear dynamics of collisional (resistive) and collisionless (due to electron inertia) double tearing modes (DTMs) are compared with the use of a reduced cylindrical model of a tokamak plasma. We focus on cases where two q = 2 resonant surfaces are located a small distance apart. It is found that regardless of the magnetic reconnection mechanism, resistivity or electron inertia, the fastest growing linear eigenmodes may have high poloidal mode numbers m ~ 10. The spectrum of unstable modes tends to be broader in the collisionless case. In the nonlinear regime, it is shown that in both cases fast growing high-m DTMs lead to an annular collapse involving small magnetic island structures. In addition, collisionless DTMs exhibit multiple reconnection cycles due to reversibility of collisionless reconnection and strong ExB flows. Collisionless reconnection leads to a saturated stable state, while in the collisional case resistive decay keeps the system weakly dynamic by driving it back towards the unstable equilibrium maintained by a source term.Comment: 15 pages, 9 figure

Psychotherapy Is Chaotic— (Not Only) in a Computational World

Objective: The aim of this article is to outline the role of chaotic dynamics in psychotherapy. Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client’s functioning can be integrated into a comprehensive nonlinear model of human change processes. Methods: The model combines 5 variables (intensity of emotions, problem intensity, motivation to change, insight and new perspectives, therapeutic success) and 4 parameters into a set of 5 coupled nonlinear difference equations. The results of these simulations are presented as time series, as phase space embedding of these time series (i.e., attractors), and as bifurcation diagrams. Results: The model creates chaotic dynamics, phase transition-like phenomena, bi- or multi-stability, and sensibility of the dynamic patterns on parameter drift. These features are predicted by chaos theory and by Synergetics and correspond to empirical findings. The spectrum of these behaviors illustrates the complexity of psychotherapeutic processes. Conclusion: The model contributes to the development of an integrative conceptualization of psychotherapy. It is consistent with the state of scientific knowledge of common factors, as well as other psychological topics, such as: motivation, emotion regulation, and cognitive processing. The role of chaos theory is underpinned, not only in the world of computer simulations, but also in practice. In practice, chaos demands technologies capable of real-time monitoring and reporting on the nonlinear features of the ongoing process (e.g., its stability or instability). Based on this monitoring, a client-centered, continuous, and cooperative process of feedback and control becomes possible. By contrast, restricted predictability and spontaneous changes challenge the usefulness of prescriptive treatment manuals or other predefined programs of psychotherapy

A synthetic electric force acting on neutral atoms

Electromagnetism is a simple example of a gauge theory where the underlying potentials -- the vector and scalar potentials -- are defined only up to a gauge choice. The vector potential generates magnetic fields through its spatial variation and electric fields through its time-dependence. We experimentally produce a synthetic gauge field that emerges only at low energy in a rubidium Bose-Einstein condensate: the neutral atoms behave as charged particles do in the presence of a homogeneous effective vector potential. We have generated a synthetic electric field through the time dependence of an effective vector potential, a physical consequence even though the vector potential is spatially uniform