Volumes of Restricted Minkowski Sums and the Free Analogue of the Entropy Power Inequality

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality has a counterpart for the free analogue of entropy . The free entropy (introduced recently by the second named author), consistently with Boltzmann's formula $S=k\log W$, was defined via volumes of matricial microstates. Proving the free entropy power inequality naturally becomes a geometric question. Restricting the Minkowski sum of two sets means to specify the set of pairs of points which will be added. The relevant inequality, which holds when the set of "addable" points is sufficiently large, differs from the Brunn-Minkowski inequality by having the exponent $1/n$ replaced by $2/n$. Its proof uses the rearrangement inequality of Brascamp-Lieb-L\"uttinger

Fas ligand elicits a caspase-independent proinflammatory response in human keratinocytes: implications for dermatitis.

Fas ligand (FasL) causes apoptosis of epidermal keratinocytes and triggers the appearance of spongiosis in eczematous dermatitis. We demonstrate here that FasL also aggravates inflammation by triggering the expression of proinflammatory cytokines, chemokines, and adhesion molecules in keratinocytes. In HaCaT cells and in reconstructed human epidermis (RHE), FasL triggered a NF-kappaB-dependent mRNA accumulation of inflammatory cytokines (tumor necrosis factor-alpha, IL-6, and IL-1beta), chemokines (CCL2/MCP-1, CXCL1/GROalpha, CXCL3/GROgamma, and CXCL8/IL-8), and the adhesion molecule ICAM-1. Oligomerization of Fas was required both for apoptosis and for gene expression. Inhibition of caspase activity abolished FasL-dependent apoptosis; however, it failed to suppress the expression of FasL-induced genes. Additionally, in the presence of caspase inhibitors, but not in their absence, FasL triggered the accumulation of CCL5/RANTES (regulated on activation normal T cell expressed and secreted) mRNA. Our findings identify a novel proinflammatory role of FasL in keratinocytes that is independent of caspase activity and is separable from apoptosis. Thus, in addition to causing spongiosis, FasL may play a direct role in triggering and/or sustaining inflammation in eczemas

The spatial distribution of cold gas in hierarchical galaxy formation models

The distribution of cold gas in dark matter haloes is driven by key processes in galaxy formation: gas cooling, galaxy mergers, star formation and reheating of gas by supernovae. We compare the predictions of four different galaxy formation models for the spatial distribution of cold gas. We find that satellite galaxies make little contribution to the abundance or clustering strength of cold gas selected samples, and are far less important than they are in optically selected samples. The halo occupation distribution function of present-day central galaxies with cold gas mass >109 h−1 M⊙ is peaked around a halo mass of ≈1011 h−1 M⊙, a scale that is set by the AGN suppression of gas cooling. The model predictions for the projected correlation function are in good agreement with measurements from the H i Parkes All-Sky Survey. We compare the effective volume of possible surveys with the Square Kilometre Array with those expected for a redshift survey in the near-infrared. Future redshift surveys using neutral hydrogen emission will make possible measurements of the baryonic acoustic oscillations that are competitive with the most ambitious spectroscopic surveys planned in the near-infrared

Ground state non-universality in the random field Ising model

Two attractive and often used ideas, namely universality and the concept of a zero temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are non-universal. However, we also show that at finite temperature the thermal order parameter exponent one half is restored so that temperature is a relevant variable. The broader implications of these results are discussed.Comment: 4 pages 2 figures, corrected prefactors caused by a missing factor of two in Eq. 2., added a paragraph in conclusions for clarit

Mesoscopic mean-field theory for spin-boson chains in quantum optical systems

We present a theoretical description of a system of many spins strongly coupled to a bosonic chain. We rely on the use of a spin-wave theory describing the Gaussian fluctuations around the mean-field solution, and focus on spin-boson chains arising as a generalization of the Dicke Hamiltonian. Our model is motivated by experimental setups such as trapped ions, or atoms/qubits coupled to cavity arrays. This situation corresponds to the cooperative (E⊗β) Jahn-Teller distortion studied in solid-state physics. However, the ability to tune the parameters of the model in quantum optical setups opens up a variety of novel intriguing situations. The main focus of this paper is to review the spin-wave theoretical description of this problem as well as to test the validity of mean-field theory. Our main result is that deviations from mean-field effects are determined by the interplay between magnetic order and mesoscopic cooperativity effects, being the latter strongly size-dependent

Quantum teardrops

Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops are described in detail. In particular the presentation of the coordinate algebra of the quantum teardrop in terms of generators and relations and classification of irreducible *-representations are derived. The algebras are then analysed from the point of view of Hopf-Galois theory or the theory of quantum principal bundles. Fredholm modules and associated traces are constructed. C*-algebras of continuous functions on quantum weighted projective lines are described and their K-groups computed.Comment: 18 page

Probing the Environment with Galaxy Dynamics

I present various projects to study the halo dynamics of elliptical galaxies. This allows one to study the outer mass and orbital distributions of ellipticals in different environments, and the inner distributions of groups and clusters themselves.Comment: 5 pages, 2 figs, to appear in Proc. ESO Workshop, Groups of Galaxies in the Nearby Universe (5-9 Dec 2005), eds. I. Saviane, V. Ivanov & J. Borissova (Springer-Verlag

Interplay among critical temperature, hole content, and pressure in the cuprate superconductors

Within a BCS-type mean-field approach to the extended Hubbard model, a nontrivial dependence of T_c on the hole content per unit CuO_2 is recovered, in good agreement with the celebrated non-monotonic universal behaviour at normal pressure. Evaluation of T_c at higher pressures is then made possible by the introduction of an explicit dependence of the tight-binding band and of the carrier concentration on pressure P. Comparison with the known experimental data for underdoped Bi2212 allows to single out an `intrinsic' contribution to d T_c / d P from that due to the carrier concentration, and provides a remarkable estimate of the dependence of the inter-site coupling strength on the lattice scale.Comment: REVTeX 8 pages, including 5 embedded PostScript figures; other required macros included; to be published in Phys. Rev. B (vol. 54

Gap Formation in the Dust Layer of 3D Protoplanetary Disks

We numerically model the evolution of dust in a protoplanetary disk using a two-phase (gas+dust) Smoothed Particle Hydrodynamics (SPH) code, which is non-self-gravitating and locally isothermal. The code follows the three dimensional distribution of dust in a protoplanetary disk as it interacts with the gas via aerodynamic drag. In this work, we present the evolution of a disk comprising 1% dust by mass in the presence of an embedded planet for two different disk configurations: a small, minimum mass solar nebular (MMSN) disk and a larger, more massive Classical T Tauri star (CTTS) disk. We then vary the grain size and planetary mass to see how they effect the resulting disk structure. We find that gap formation is much more rapid and striking in the dust layer than in the gaseous disk and that a system with a given stellar, disk and planetary mass will have a different appearance depending on the grain size and that such differences will be detectable in the millimetre domain with ALMA. For low mass planets in our MMSN models, a gap can open in the dust disk while not in the gas disk. We also note that dust accumulates at the external edge of the planetary gap and speculate that the presence of a planet in the disk may facilitate the growth of planetesimals in this high density region.Comment: 5 page, 4 figures. Accepted for publication in Astrophysics & Space Scienc