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A quantized version of the Sierpinski gasket is proposed, on purely topological grounds, as a $C^*$-algebra $\mathcal{A}_\infty$ with a suitable form of self-similarity. Several properties of $\mathcal{A}_\infty$ are studied, in particular its nuclearity, the structure of ideals as well as the description of irreducible representations and extremal traces. A harmonic structure is introduced, giving rise to a self-similar Dirichlet form $\mathcal{E}$. A spectral triple is also constructed, extending one already known for the classical gasket, from which $\mathcal{E}$ can be reconstructed. Moreover we show that $\mathcal{A}_\infty$ is a compact quantum metric space., 28 pages, accepted for publication on the Journal of Functional Analysis

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.

Experiments in Art and Technology (E.A.T.) is an organi- zation co-founded in 1966 by artists Robert Rauschenberg and Robert Whitman, and engineers Billy Klüver and Fred Waldhauer, in order to support collaboration between artists and engineers. The E.A.T. datascape is a digital instrument for analyzing the digitized traces left by its members via many available resources. Its aim is to study as closely as possible the complexity of collaborative interdisciplinary works. The E.A.T. datascape methodology makes it possible, by means of an anthropological action-centred approach, to go beyond the distinction between art history and art sociology and to renew the social history of art by challeng- ing the notion of authorship and by describing the work as constituted by the intersection between heterogeneous trajectories, rather than an object within a context that would influence it, or constitute its environment. In other words, it allows us to reflect on what digital design does, in turn, to the social history of art, and to put forward hypotheses about what a digital social history of art might be or could offer to the study of complex, interdisciplinary projects that are multiplying in the contemporary art world. Experiments in Art and Technology (E.A.T.) organizacija je koju su 1966. zajedno osnovali umjetnici Robert Rausch- enberg i Robert Whitman te inženjeri Billy Klüver i Fred Waldhauer, kako bi podržali suradnju između umjetnika i in- ženjera. E.A.T. datascape digitalni je instrument za analizu digitaliziranih tragova koje su ostavili članovi organizacije putem brojnih dostupnih resursa. Njegov je cilj što je mo- guće detaljnije analizirati složenost kolaborativnih inter- disciplinarnih radova. Zahvaljujući antropološkom pristupu usmjerenom na djelovanje, metodologija E.A.T datascapea omogućuje nadilaženje razlike između povijesti umjetnosti i sociologije umjetnosti te obnavljanje socijalne povijesti um- jetnosti dovođenjem u pitanje pojma autorstva i opisivanjem djela kao sačinjenoga presijecanjem heterogenih trajektorija, a ne kao objekta u kontekstu koji bi na njega utjecao ili tvo- rio njegovo okruženje. Drugim riječima, ona nam omogućuje razmišljanje o tome što digitalni dizajn čini zauzvrat za so- cijalnu povijest umjetnosti i iznošenje hipoteza o tome što bi digitalna socijalna povijest umjetnosti mogla biti ili što bi mogla ponuditi istraživanju složenih interdisciplinarnih pro- jekata, kojih je sve više u svijetu suvremene umjetnosti.

Arachidonic acid (AA) stimulates endothelial cell (EC) proliferation through an increase in intracellular Ca2 + concentration ([Ca2 +]i), that, in turn, promotes nitric oxide (NO) release. AA-evoked Ca2 + signals are mainly mediated by Transient Receptor Potential Vanilloid 4 (TRPV4) channels. Circulating endothelial colony forming cells (ECFCs) represent the only established precursors of ECs. In the present study, we, therefore, sought to elucidate whether AA promotes human ECFC (hECFC) proliferation through an increase in [Ca2 +]i and the following activation of the endothelial NO synthase (eNOS). AA induced a dose-dependent [Ca2 +]i raise that was mimicked by its non-metabolizable analogue eicosatetraynoic acid. AA-evoked Ca2 + signals required both intracellular Ca2 + release and external Ca2 + inflow. AA-induced Ca2 + release was mediated by inositol-1,4,5-trisphosphate receptors from the endoplasmic reticulum and by two pore channel 1 from the acidic stores of the endolysosomal system. AA-evoked Ca2 + entry was, in turn, mediated by TRPV4, while it did not involve store-operated Ca2 + entry. Moreover, AA caused an increase in NO levels which was blocked by preventing the concomitant increase in [Ca2 +]i and by inhibiting eNOS activity with NG-nitro- l -arginine methyl ester ( l -NAME). Finally, AA per se did not stimulate hECFC growth, but potentiated growth factors-induced hECFC proliferation in a Ca2 +- and NO-dependent manner. Therefore, AA-evoked Ca2 + signals emerge as an additional target to prevent cancer vascularisation, which may be sustained by ECFC recruitment.

Experiments in Art and Technology (E.A.T.) organizacija je koju su 1966. zajedno osnovali umjetnici Robert Rauschenberg i Robert Whitman te inženjeri Billy Klüver i Fred Waldhauer, kako bi podržali suradnju između umjetnika i inženjera. E.A.T. datascape digitalni je instrument za analizu digitaliziranih tragova koje su ostavili članovi organizacije putem brojnih dostupnih resursa. Njegov je cilj što je moguće detaljnije analizirati složenost kolaborativnih interdisciplinarnih radova. Zahvaljujući antropološkom pristupu usmjerenom na djelovanje, metodologija E.A.T datascapea omogućuje nadilaženje razlike između povijesti umjetnosti i sociologije umjetnosti te obnavljanje socijalne povijesti umjetnosti dovođenjem u pitanje pojma autorstva i opisivanjem djela kao sačinjenoga presijecanjem heterogenih trajektorija, a ne kao objekta u kontekstu koji bi na njega utjecao ili tvorio njegovo okruženje. Drugim riječima, ona nam omogućuje razmišljanje o tome što digitalni dizajn čini zauzvrat za socijalnu povijest umjetnosti i iznošenje hipoteza o tome što bi digitalna socijalna povijest umjetnosti mogla biti ili što bi mogla ponuditi istraživanju složenih interdisciplinarnih projekata, kojih je sve više u svijetu suvremene umjetnosti., Experiments in Art and Technology (E.A.T.) is an organization co-founded in 1966 by artists Robert Rauschenberg and Robert Whitman, and engineers Billy Klüver and Fred Waldhauer, in order to support collaboration between artists and engineers. The E.A.T. datascape is a digital instrument for analyzing the digitized traces left by its members via many available resources. Its aim is to study as closely as possible the complexity of collaborative interdisciplinary works. The E.A.T. datascape methodology makes it possible, by means of an anthropological action-centred approach, to go beyond the distinction between art history and art sociology and to renew the social history of art by challenging the notion of authorship and by describing the work as constituted by the intersection between heterogeneous trajectories, rather than an object within a context that would influence it, or constitute its environment. In other words, it allows us to reflect on what digital design does, in turn, to the social history of art, and to put forward hypotheses about what a digital social history of art might be or could offer to the study of complex, interdisciplinary projects that are multiplying in the contemporary art world.

Area and volume values of buildings and building parts have been used in many applications including taxation, valuation and land use planning. Many countries maintain a national standard for representing the measurements of floor areas in buildings. The national standards generally use similar basis for measuring building floor areas, in fact, areas specified in national standards often have semantic differences. An abundance of geographic information is hidden within texts and multimedia objects that has the potential to enrich our knowledge about the relationship between people and places. One such example is the geographic information embedded within user-generated content collected and curated by the social media giants. Such geographic data can be encoded either explicitly as geotags or implicitly as geographical references expressed as texts that comprise part of a title or image caption. To use such data for knowledge building there is a need for new mapping interfaces. These interfaces should support both data integration and visualization, and geographical exploration with open-ended discovery. Based on a user scenario on the Via Francigena (a significant European cultural route), we set out to adapt an existing humanities interface to support social and spatial exploration of how the route is perceived. Our dataset was derived from Instagram. We adopted a thinking by doing approach to co-design an interdisciplinary prototype and discuss the six stages of activity, beginning with the definition of the use case and ending in experimentation with a working technology prototype. Through reflection on the process of tool modification and an in-depth exploration of the data encoding, we were better able to understand the strengths and limitations of the data, the tool, and the underlying workflows. This in-depth knowledge helped us to define a set of requirements for tools and data that will serve as a valuable contribution for those engaged in the design of deep mapping interfaces for place-based research.

Antigen cross-presentation by dendritic cells (DC) stimulates cytotoxic T cell activation to promote immunity to intracellular pathogens, viruses and cancer. Phagocytosed antigens generate potent T cell responses, but the signalling and trafficking pathways regulating their cross-presentation are unclear. Here, we show that ablation of the store-operated-Ca2+-entry regulator STIM1 in mouse myeloid cells impairs cross-presentation and DC migration in vivo and in vitro. Stim1 ablation reduces Ca2+ signals, cross-presentation, and chemotaxis in mouse bone-marrow-derived DCs without altering cell differentiation, maturation or phagocytic capacity. Phagosomal pH homoeostasis and ROS production are unaffected by STIM1 deficiency, but phagosomal proteolysis and leucyl aminopeptidase activity, IRAP recruitment, as well as fusion of phagosomes with endosomes and lysosomes are all impaired. These data suggest that STIM1-dependent Ca2+ signalling promotes the delivery of endolysosomal enzymes to phagosomes to enable efficient cross-presentation., STIM proteins sense Ca2+ depletion in the ER and activate store-operated Ca2+-entry (SOCE) in response, a process associated with dendritic cell functions. Here the authors show STIM1 is the major isoform controlling SOCE in mouse dendritic cells and provide a mechanism for its requirement in antigen cross-presentation.

Store-operated Ca

A distance between von Neumann algebras is introduced, depending on a further norm inducing the $w^*$-topology on bounded sets. Such notion is related both with the Gromov-Hausdorff distance for quantum metric spaces of Rieffel and with the Effros-Marechal topology on the von Neumann algebras acting on a Hilbert space. This construction is tested on the local algebras of free quantum fields endowed with norms related with the Buchholz-Wichmann nuclearity condition, showing the continuity of such algebras w.r.t. the mass parameter., Comment: 22 pages, no figures. To apper in the Journal of Functional Analysis

Hydrogen sulphide (H 2 S) is a newly discovered gasotransmitter that regulates multiple steps in VEGF-induced angiogenesis. An increase in intracellular Ca 2+ concentration ([Ca 2+ ] i ) is central to endothelial proliferation and may be triggered by both VEGF and H 2 S. Albeit VEGFR-2 might serve as H 2 S receptor, the mechanistic relationship between VEGF- and H 2 S-induced Ca 2+ signals in endothelial cells is unclear. The present study aimed at assessing whether and how NaHS, a widely employed H 2 S donor, stimulates pro-angiogenic Ca 2+ signals in Ea.hy926 cells, a suitable surrogate for mature endothelial cells, and human endothelial progenitor cells (EPCs). We found that NaHS induced a dose-dependent increase in [Ca 2+ ] i in Ea.hy926 cells. NaHS-induced Ca 2+ signals in Ea.hy926 cells did not require extracellular Ca 2+ entry, while they were inhibited upon pharmacological blockade of the phospholipase C/inositol-1,4,5-trisphosphate (InsP 3 ) signalling pathway. Moreover, the Ca 2+ response to NaHS was prevented by genistein, but not by SU5416, which selectively inhibits VEGFR-2. However, VEGF-induced Ca 2+ signals were suppressed by dl -propargylglycine (PAG), which blocks the H 2 S-producing enzyme, cystathionine γ-lyase. Consistent with these data, VEGF-induced proliferation and migration were inhibited by PAG in Ea.hy926 cells, albeit NaHS alone did not influence these processes. Conversely, NaHS elevated [Ca 2+ ] i only in a modest fraction of circulating EPCs, whereas neither VEGF-induced Ca 2+ oscillations nor VEGF-dependent proliferation were affected by PAG. Therefore, H 2 S-evoked elevation in [Ca 2+ ] i is essential to trigger the pro-angiogenic Ca 2+ response to VEGF in mature endothelial cells, but not in their immature progenitors.

Store-operated Ca2+ entry (SOCE) is a cell signaling pathway essential for immune and muscle function controlled by dynamic interactions between Ca2+-sensing STIM proteins on the endoplasmic reticulum (ER) and Ca2+-permeable ORAI channels on the plasma membrane (PM). STIM-ORAI interactions occur at membrane contact sites (MCS), evolutionarily conserved cellular structures characterized by the close apposition (10-20 nm) between the ER and target membranes that facilitate the exchange of lipids by non-vesicular transport mechanisms. STIM-ORAI interactions were considered to be restricted to ER-PM MCS, but recent evidence indicates that productive interactions take place between ER-bound STIM1 and Ca2+ channels located in intracellular organelles. Interactions between the ER and endosomes or lysosomes regulate the lipid homeostasis of these organelles and the propagation of Ca2+ signals initiated by the release of Ca2+ from acidic stores. Intracellular MCS also regulate the efficiency of phagocytosis, a fundamental cellular process essential for immunity and tissue homeostasis, by ensuring the coordinated opening of Ca2+ channels on phagocytic vacuoles and of Ca2+ release channels on juxtaposed ER stores. In this chapter, we review the current knowledge on the molecular composition and architecture of membrane contact sites that sustain Ca2+ signals at the plasma membrane and in intracellular organelles.

In this case study we describe the iterative process of paper prototyping, using a board game, to co-design a location-based mobile application. The end goal of the application is to motivate reflection on historical topics about migration. The board game serves to capture the core concerns of this application by simulating movement through the city. Three play tests highlighted the users' interest and issues with the historical content, the way this content is represented, and the players' responses to the interactions and motivating mechanisms of the application. Results show that the board game helped capture important design preferences and problems, ensuring the improvement of our scenario. This feedback can help reduce development effort and implement a future technology prototype closer to the needs of our end users.

The definitions and main properties of the Ihara and Bartholdi zeta functions for infinite graphs are reviewed. The general question of the validity of a functional equation is discussed, and various possible solutions are proposed., 23 pages, 3 figures. Accepted for publication in "Fractals in Applied Mathematics", Contemporary Mathematics, Editors Carfi, Lapidus, Pearse, van Frankenhuijsen

A class of CW-complexes, called self-similar complexes, is introduced, together with C ∗ -algebras A j of operators, endowed with a finite trace, acting on square-summable cellular j -chains. Since the Laplacian Δ j belongs to A j , L 2 -Betti numbers and Novikov–Shubin numbers are defined for such complexes in terms of the trace. In particular a relation involving the Euler–Poincare characteristic is proved. L 2 -Betti and Novikov–Shubin numbers are computed for some self-similar complexes arising from self-similar fractals.

In this paper, we give a more direct proof of the results by Clair and Mokhtari-Sharghi on the zeta functions of periodic graphs. In particular, using appropriate operator-algebraic techniques, we establish a determinant formula in this context and examine its consequences for the Ihara zeta function. Moreover, we answer in the affirmative one of the questions raised by Grigorchuk and Zuk. Accordingly, we show that the zeta function of a periodic graph with an amenable group action is the limit of the zeta functions of a suitable sequence of finite subgraphs., 21 pages, 4 figures

Arachidonic acid (AA) stimulates endothelial cell (EC) proliferation through an increase in intracellular Ca

It is shown that, for nested fractals [T.Lindstrom, Mem. Amer. Math. Soc. 420, 1990], the main structural data, such as the Hausdorff dimension and measure, the geodesic distance (when it exists) induced by the immersion in $R^n$, and the self-similar energy can all be recovered by the description of the fractals in terms of the spectral triples considered in [D.Guido, T.Isola, in "Advances in Operator Algebras and Mathematical Physics", Theta Series in Advanced Mathematics, Bucharest 2005]., 19 pages, 1 figure. Some points have been clarified, the introduction has been expanded in order to better explain the purpose of the paper. This version will appear in JNCG

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek

It is shown that many important features of nested fractals, such as the Hausdorff dimension and measure, the geodesic distance induced by the immersion in \(\mathbb{R}^n\) (when it exists), and the self-similar energy can be recovered by the description of the fractal in terms of spectral triples. We describe in particular the case of the Vicsek square, showing that all self-similar energies can be described through a deformation of the square to a rhombus.

Phagocytosis is a fundamental process through which innate immune cells engulf bacteria, apoptotic cells or other foreign particles in order to kill or neutralize the ingested material, or to present it as antigens and initiate adaptive immune responses. The pH of phagosomes is a critical parameter regulating fission or fusion with endomembranes and activation of proteolytic enzymes, events that allow the phagocytic vacuole to mature into a degradative organelle. In addition, translocation of H(+) is required for the production of high levels of reactive oxygen species (ROS), which are essential for efficient killing and signaling to other host tissues. Many intracellular pathogens subvert phagocytic killing by limiting phagosomal acidification, highlighting the importance of pH in phagosome biology. Here we describe a ratiometric method for measuring phagosomal pH in neutrophils using fluorescein isothiocyanate (FITC)-labeled zymosan as phagocytic targets, and live-cell imaging. The assay is based on the fluorescence properties of FITC, which is quenched by acidic pH when excited at 490 nm but not when excited at 440 nm, allowing quantification of a pH-dependent ratio, rather than absolute fluorescence, of a single dye. A detailed protocol for performing in situ dye calibration and conversion of ratio to real pH values is also provided. Single-dye ratiometric methods are generally considered superior to single wavelength or dual-dye pseudo-ratiometric protocols, as they are less sensitive to perturbations such as bleaching, focus changes, laser variations, and uneven labeling, which distort the measured signal. This method can be easily modified to measure pH in other phagocytic cell types, and zymosan can be replaced by any other amine-containing particle, from inert beads to living microorganisms. Finally, this method can be adapted to make use of other fluorescent probes sensitive to different pH ranges or other phagosomal activities, making it a generalized protocol for the functional imaging of phagosomes.

Given a spectral triple (A,D,H), the functionals on A of the form a -> tau_omega(a|D|^(-t)) are studied, where tau_omega is a singular trace, and omega is a generalised limit. When tau_omega is the Dixmier trace, the unique exponent d giving rise possibly to a non-trivial functional is called Hausdorff dimension, and the corresponding functional the (d-dimensional) Hausdorff functional. It is shown that the Hausdorff dimension d coincides with the abscissa of convergence of the zeta function of |D|^(-1), and that the set of t's for which there exists a singular trace tau_omega giving rise to a non-trivial functional is an interval containing d. Moreover, the endpoints of such traceability interval have a dimensional interpretation. The corresponding functionals are called Hausdorff-Besicovitch functionals. These definitions are tested on fractals in R, by computing the mentioned quantities and showing in many cases their correspondence with classical objects. In particular, for self-similar fractals the traceability interval consists only of the Hausdorff dimension, and the corresponding Hausdorff-Besicovitch functional gives rise to the Hausdorff measure. More generally, for any limit fractal, the described functionals do not depend on the generalized limit omega., latex, 36 pages, no figures, to appear on Journ. Funct. Analysis

Local intracellular Ca(2+) elevations increase the efficiency of phagocytosis, a process that is essential for innate and adaptive immunity. These local Ca(2+) elevations are generated in part by the store-operated Ca(2+) entry (SOCE) sensor STIM1, which recruits endoplasmic reticulum (ER) cisternae to phagosomes and opens phagosomal Ca(2+) channels at ER-phagosome junctions. However, residual ER-phagosome contacts and periphagosomal Ca(2+) hotspots remain in Stim1(-/-) cells. Here, we tested whether junctate (also called ASPH isoform 8), a molecule that targets STIM1 to ER-plasma-membrane contacts upon Ca(2+)-store depletion, cooperates with STIM1 at phagosome junctions. Junctate expression in Stim1(-/-) and Stim1(-/-); Stim2(-/-) phagocytic fibroblasts increased phagocytosis and periphagosomal Ca(2+) elevations, yet with only a minimal impact on global SOCE. These Ca(2+) hotspots were only marginally reduced by the SOCE channel blocker lanthanum chloride (La(3+)) but were abrogated by inositol trisphosphate receptor inhibitors 2-APB and xestospongin-C, revealing that unlike STIM1-mediated hotspots, junctate-mediated Ca(2+) originates predominantly from periphagosomal Ca(2+) stores. Accordingly, junctate accumulates near phagosomes and elongates ER-phagosome junctions in Stim1(-/-) cells. Thus, junctate mediates an alternative mechanism for generating localized Ca(2+) elevations within cells, promoting Ca(2+) release from internal stores recruited to phagosomes, thereby boosting phagocytosis.

The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of some singular trace. We show that the answers are positive in general, namely for any (compact, infinite rank) positive operator A we exhibit two singular traces, the first being zero and the second being infinite on A. However, if we assume that the singular traces are generated by a "regular" operator, the answers change, namely such traces always vanish on trace-class, non singularly traceable operators and are always infinite on non trace-class, non singularly traceable operators. These results are achieved on a general semifinite factor, and make use of a new characterization of singular traceability (cf. math.OA/0202108)., 7 pages, LaTeX. Minor corrections, to appear on the International Journal of Mathematics

A nonnegative number d1, called asymptotic dimension, is associated with any metric space. Such number detects the asymptotic properties of the space (being zero on bounded metric spaces), fulfills the properties of a dimension, and is invariant under rough isometries. It is then shown that for a class of open manifolds with bounded geometry the asymptotic dimension coincides with the 0-th Novikov-Shubin number 0 defined in a previous paper [D. Guido, T. Isola, J. Funct. Analysis, 176 (2000)]. Thus the dimensional interpretation of 0 given in the mentioned paper in the framework of noncommutative geometry is established on metrics grounds. Since the asymptotic dimension of a covering manifold coincides with the polynomial growth of its covering group, the stated equality generalises to open manifolds a result by Varopoulos.

Hydrogen sulphide (H2S) is a newly discovered gasotransmitter that regulates multiple steps in VEGF-induced angiogenesis. An increase in intracellular Ca(2+) concentration ([Ca(2+)]i) is central to endothelial proliferation and may be triggered by both VEGF and H2S. Albeit VEGFR-2 might serve as H2S receptor, the mechanistic relationship between VEGF- and H2S-induced Ca(2+) signals in endothelial cells is unclear. The present study aimed at assessing whether and how NaHS, a widely employed H2S donor, stimulates pro-angiogenic Ca(2+) signals in Ea.hy926 cells, a suitable surrogate for mature endothelial cells, and human endothelial progenitor cells (EPCs). We found that NaHS induced a dose-dependent increase in [Ca(2+)]i in Ea.hy926 cells. NaHS-induced Ca(2+) signals in Ea.hy926 cells did not require extracellular Ca(2+) entry, while they were inhibited upon pharmacological blockade of the phospholipase C/inositol-1,4,5-trisphosphate (InsP3) signalling pathway. Moreover, the Ca(2+) response to NaHS was prevented by genistein, but not by SU5416, which selectively inhibits VEGFR-2. However, VEGF-induced Ca(2+) signals were suppressed by dl-propargylglycine (PAG), which blocks the H2S-producing enzyme, cystathionine γ-lyase. Consistent with these data, VEGF-induced proliferation and migration were inhibited by PAG in Ea.hy926 cells, albeit NaHS alone did not influence these processes. Conversely, NaHS elevated [Ca(2+)]i only in a modest fraction of circulating EPCs, whereas neither VEGF-induced Ca(2+) oscillations nor VEGF-dependent proliferation were affected by PAG. Therefore, H2S-evoked elevation in [Ca(2+)]i is essential to trigger the pro-angiogenic Ca(2+) response to VEGF in mature endothelial cells, but not in their immature progenitors.

Given a stationary state for a noncommutative flow, we study a boundedness condition, depending on a positive parameter beta, which is weaker than the KMS equilibrium condition at inverse temperature beta. This condition is equivalent to a holomorphic property closely related to the one recently considered by Ruelle and D'Antoni-Zsido and shared by a natural class of non-equilibrium steady states. Our holomorphic property is stronger than the Ruelle's one and thus selects a restricted class of non-equilibrium steady states. We also introduce the complete boundedness condition and show this notion to be equivalent to the Pusz-Woronowicz complete passivity property, hence to the KMS condition. In Quantum Field Theory, the beta-boundedness condition can be interpreted as the property that localized state vectors have energy density levels increasing beta-subexponentially, a property which is similar in the form and weaker in the spirit than the modular compactness-nuclearity condition. In particular, for a Poincare' covariant net of C*-algebras on the Minkowski spacetime, the beta-boundedness property, for beta greater equal than 2 pi, for the boosts is shown to be equivalent to the Bisognano-Wichmann property. The Hawking temperature is thus minimal for a thermodynamical system in the background of a Rindler black hole within the class of beta-holomorphic states. More generally, concerning the Killing evolution associated with a class of stationary quantum black holes, we characterize KMS thermal equilibrium states at Hawking temperature in terms of the boundedness property and the existence of a translation symmetry on the horizon., Comment: 28 pages, LaTeX. Minor modifications in the abstract, to appear in Commun. Math. Phys

The first part of this paper extends the Doplicher-Haag-Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a superselection sector may be defined as in flat spacetime and each charge has a conjugate charge when the spacetime possesses non-compact Cauchy surfaces. In this case, the field net and the gauge group can be constructed as in Minkowski spacetime. The second part of this paper derives spin-statistics theorems on spacetimes with appropriate symmetries. Two situations are considered: First, if the spacetime has a bifurcate Killing horizon, as is the case in the presence of black holes, then restricting the observables to the Killing horizon together with "modular covariance" for the Killing flow yields a conformally covariant quantum field theory on the circle and a conformal spin-statistics theorem for charged sectors localizable on the Killing horizon. Secondly, if the spacetime has a rotation and PT symmetry like the Schwarzschild-Kruskal black holes, "geometric modular action" of the rotational symmetry leads to a spin-statistics theorem for charged covariant sectors where the spin is defined via the SU(2)-covering of the spatial rotation group SO(3)., latex2e, 73 pages

Suppose B is a unital algebra which is an algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the sigma -complete ultrafilters on X (Theorem 2.6). Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducible representations of B are labeled by points of X, and all representations of B are described (Theorem 3.3).

Given a C*-algebra A with a semicontinuous semifinite trace tau acting on the Hilbert space H, we define the family R of bounded Riemann measurable elements w.r.t. tau as a suitable closure, a la Dedekind, of A, in analogy with one of the classical characterizations of Riemann measurable functions, and show that R is a C*-algebra, and tau extends to a semicontinuous semifinite trace on R. Then, unbounded Riemann measurable operators are defined as the closed operators on H which are affiliated to A'' and can be approximated in measure by operators in R, in analogy with unbounded Riemann integration. Unbounded Riemann measurable operators form a tau-a.e. bimodule on R, denoted by R^, and such bimodule contains the functional calculi of selfadjoint elements of R under unbounded Riemann measurable functions. Besides, tau extends to a bimodule trace on R^. Type II_1 singular traces for C*-algebras can be defined on the bimodule of unbounded Riemann-measurable operators. Noncommutative Riemann integration, and singular traces for C*-algebras, are then used to define Novikov-Shubin numbers for amenable open manifolds, show their invariance under quasi-isometries, and prove that they are (noncommutative) asymptotic dimensions., Comment: 34 pages, LaTeX, a new section has been added, concerning an application to Novikov-Shubin invariants, the title changed accordingly

BackgroundAn increase in the frequency of circulating endothelial colony forming cells (ECFCs), the only subset of endothelial progenitor cells (EPCs) truly belonging to the endothelial phenotype, occurs in patients affected by primary myelofibrosis (PMF). Herein, they might contribute to the enhanced neovascularisation of fibrotic bone marrow and spleen. Store-operated Ca2+ entry (SOCE) activated by the depletion of the inositol-1,4,5-trisphosphate (InsP3)-sensitive Ca2+ store drives proliferation in ECFCs isolated from both healthy donors (N-ECFCs) and subjects suffering from renal cellular carcinoma (RCC-ECFCs). SOCE is up-regulated in RCC-ECFCs due to the over-expression of its underlying molecular components, namely Stim1, Orai1, and TRPC1.Methodology/principal findingsWe utilized Ca2+ imaging, real-time polymerase chain reaction, western blot analysis and functional assays to evaluate molecular structure and the functional role of SOCE in ECFCs derived from PMF patients (PMF-ECFCs). SOCE, induced by either pharmacological (i.e. cyclopiazonic acid or CPA) or physiological (i.e. ATP) stimulation, was significantly higher in PMF-ECFCs. ATP-induced SOCE was inhibited upon blockade of the phospholipase C/InsP3 signalling pathway with U73111 and 2-APB. The higher amplitude of SOCE was associated to the over-expression of the transcripts encoding for Stim2, Orai2-3, and TRPC1. Conversely, immunoblotting revealed that Stim2 levels remained constant as compared to N-ECFCs, while Stim1, Orai1, Orai3, TRPC1 and TRPC4 proteins were over-expressed in PMF-ECFCs. ATP-induced SOCE was inhibited by BTP-2 and low micromolar La3+ and Gd3+, while CPA-elicited SOCE was insensitive to Gd3+. Finally, BTP-2 and La3+ weakly blocked PMF-ECFC proliferation, while Gd3+ was ineffective.ConclusionsTwo distinct signalling pathways mediate SOCE in PMF-ECFCs; one is activated by passive store depletion and is Gd3+-resistant, while the other one is regulated by the InsP3-sensitive Ca2+ pool and is inhibited by Gd3+. Unlike N- and RCC-ECFCs, the InsP3-dependent SOCE does not drive PMF-ECFC proliferation.

We construct a family of spectral triples for the Sierpinski Gasket $K$. For suitable values of the parameters, we determine the dimensional spectrum and recover the Hausdorff measure of $K$ in terms of the residue of the volume functional $a\to$ tr$(a\,|D|^{-s})$ at its abscissa of convergence $d_D$, which coincides with the Hausdorff dimension $d_H$ of the fractal. We determine the associated Connes' distance showing that it is bi-Lipschitz equivalent to the distance on $K$ induced by the Euclidean metric of the plane, and show that the pairing of the associated Fredholm module with (odd) $K$-theory is non-trivial. When the parameters belong to a suitable range, the abscissa of convergence $\delta_D$ of the energy functional $a\to$ tr$(|D|^{-s/2}|[D,a]|^2\,|D|^{-s/2})$ takes the value $d_E=\frac{\log(12/5)}{\log 2}$, which we call energy dimension, and the corresponding residue gives the standard Dirichlet form on $K$., Comment: 48 pages, 9 figures. Final version, to appear in J.Funct.Anal

We give a necessary and sufficient condition on a positive compact operator $T$ for the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value on $T$. This generalizes previous results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states on $\ell^\infty(\Bbb N)$ using tools of non standard analysis in an essential way., Comment: 20 pages, AMS TeX, SFB 237-Preprint Nr.180-May 93

The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Examples of non symmetric Dirichlet forms given by derivations on Hilbert algebras are studied., Comment: 32 pages, plain TeX, Preprint Roma TOR VERGATA Nr.9-93-May 93

We provide a definition of integral, along paths in the Sierpinski gasket K, for differential smooth 1-forms associated to the standard Dirichlet form K. We show how this tool can be used to study the potential theory on K. In particular, we prove: i) a de Rham reconstruction of a 1-form from its periods around lacunas in K; ii) a Hodge decomposition of 1-forms with respect to the Hilbertian energy norm; iii) the existence of potentials of smooth 1-forms on a suitable covering space of K. We finally show that this framework provides versions of the de Rham duality theorem for the fractal K., Some proofs have been clarified, reference to previous literature is now more accurate, 33 pages, 6 figures