Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Intercellular calcium waves in primary cultured rat mesenteric smooth muscle cells are mediated by connexin43.

Intercellular Ca(2+) wave propagation between vascular smooth muscle cells (SMCs) is associated with the propagation of contraction along the vessel. Here, we characterize the involvement of gap junctions (GJs) in Ca(2+) wave propagation between SMCs at the cellular level. Gap junctional communication was assessed by the propagation of intercellular Ca(2+) waves and the transfer of Lucifer Yellow in A7r5 cells, primary rat mesenteric SMCs (pSMCs), and 6B5N cells, a clone of A7r5 cells expressing higher connexin43 (Cx43) to Cx40 ratio. Mechanical stimulation induced an intracellular Ca(2+) wave in pSMC and 6B5N cells that propagated to neighboring cells, whereas Ca(2+) waves in A7r5 cells failed to progress to neighboring cells. We demonstrate that Cx43 forms the functional GJs that are involved in mediating intercellular Ca(2+) waves and that co-expression of Cx40 with Cx43, depending on their expression ratio, may interfere with Cx43 GJ formation, thus altering junctional communication.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Expression of intercellular adhesion molecule-1 in UVA-irradiated human skin cells in vitro and in vivo.

Ultraviolet A (UVA) radiation represents an important oxidative stress to human skin and certain forms of oxidative stress have been shown to modulate intercellular adhesion molecule-1 (ICAM-1) expression. ICAM-1 has been shown to play an important part in many immune reactions and the perturbations of this molecule by ultraviolet radiation could have implications in many inflammatory responses. An enhancement immunohistochemical method with avidin/biotin was used for analysing the early effects of UVA radiation on human cell cultures and human skin (340-400 nm). Both in vitro and in vivo data show that ICAM-1 staining in epidermal keratinocytes, which was expressed constitutively, decreased in a UVA dose-dependent manner. The decrease was most noted at 3-6 h following UVA radiation with some ICAM-1 staining returning by 48 h post-UVA. ICAM-1 positive staining in the dermis was specific for vascular structures and was increased 24 h after UVA radiation. Cultured dermal fibroblasts exhibited ICAM-1 staining which increased slightly within 6-48 h post-UVA radiation. As epidermal ICAM-1 expression is depleted following UVA radiation and dermal expression increases due to an increase in the vascular structures, ICAM-1 provides a valuable marker following UVA radiation in human skin that can be readily measured in situ.

Determinacy and Weakly Ramsey sets in Banach spaces

We give a sufficient condition for a set of block subspaces in an infinite-dimensional Banach space to be weakly Ramsey. Using this condition we prove that in the Levy-collapse of a Mahlo cardinal, every projective set is weakly Ramsey. This, together with a construction of W. H. Woodin, is used to show that the Axiom of Projective Determinacy implies that every projective set is weakly Ramsey. In the case of co we prove similar results for a stronger Ramsey property. And for hereditarily indecomposable spaces we show that the Axiom of Determinacy plus the Axiom of Dependent Choices imply that every set is weakly Ramsey. These results are the generalizations to the class of projective sets of some theorems from W. T. Gowers, and our paper "Weakly Ramsey sets in Banach spaces."

Best approach regions for potential spaces

We characterize the approach regions so that the non-tangential maximal function is of weak-type on potential spaces, for which we use a simple argument involving Carleson measure estimates.

Real interpolation for families of Banach spaces (II)

In this paper, we study the dual space and reiteration theorems for the real method of interpolation for infinite families of Banach spaces introduced in [2]. We also give examples of interpolation spaces constructed with this method.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

Dexamethasone inhibition of leucocyte adhesion to rat mesenteric postcapillary venules: role of intercellular adhesion molecule 1 and KC

BACKGROUND A previous study showed that the glucocorticoid dexamethasone, at doses of 100 ¿g/kg and above, inhibited leucocyte adhesion to rat mesenteric postcapillary venules activated with interleukin 1ß (IL-1ß), as assessed by videomicroscopy. AIMS To identify whether the adhesion molecule, intercellular adhesion molecule 1 (ICAM-1), or the chemokine KC could be targeted by the steroid to mediate its antiadhesive effect. METHODS Rat mesenteries were treated with IL-1ß (20 ng intraperitoneally) and the extent of leucocyte adhesion measured at two and four hours using intravital microscopy. Rats were treated with dexamethasone, and passively immunised against ICAM-1 or KC. Endogenous expression of these two mediators was validated by immunohistochemistry, ELISA, and the injection of specific radiolabelled antibodies. RESULTS Dexamethasone greatly reduced IL-1ß induced leucocyte adhesion, endothelial expression of ICAM-1 in the postcapillary venule, and release of the mast cell derived chemokine KC. Injection of specific antibodies to the latter mediators was also extremely effective in downregulating (>80%) IL-1ß induced leucocyte adhesion. CONCLUSIONS Induction by IL-1ß of endogenous ICAM-1 and KC contributes to leucocyte adhesion to inflamed mesenteric vessels. Without excluding other possible mediators, these data clearly show that dexamethasone interferes with ICAM-1 expression and KC release from mast cells, resulting in suppression of leucocyte accumulation in the bowel wall, which is a prominent feature of several gastrointestinal pathologies.

Chemodiversity and molecular plasticity: recognition processes as explored by property spaces.

In the last few years, a need to account for molecular flexibility in drug-design methodologies has emerged, even if the dynamic behavior of molecular properties is seldom made explicit. For a flexible molecule, it is indeed possible to compute different values for a given conformation-dependent property and the ensemble of such values defines a property space that can be used to describe its molecular variability; a most representative case is the lipophilicity space. In this review, a number of applications of lipophilicity space and other property spaces are presented, showing that this concept can be fruitfully exploited: to investigate the constraints exerted by media of different levels of structural organization, to examine processes of molecular recognition and binding at an atomic level, to derive informative descriptors to be included in quantitative structure--activity relationships and to analyze protein simulations extracting the relevant information. Much molecular information is neglected in the descriptors used by medicinal chemists, while the concept of property space can fill this gap by accounting for the often-disregarded dynamic behavior of both small ligands and biomacromolecules. Property space also introduces some innovative concepts such as molecular sensitivity and plasticity, which appear best suited to explore the ability of a molecule to adapt itself to the environment variously modulating its property and conformational profiles. Globally, such concepts can enhance our understanding of biological phenomena providing fruitful descriptors in drug-design and pharmaceutical sciences.

Traces of functions in Fock spaces on lattices of critical density

Following a scheme of Levin we describe the values that functions in Fock spaces take on lattices of critical density in terms of both the size of the values and a cancelation condition that involves discrete versions of the Cauchy and Beurling-Ahlfors transforms.