Cumulants and convolutions via Abel polynomials

We provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show that in the free cumulant theory the volume polynomial of Pitman and Stanley plays the role of the complete Bell exponential polynomial in the classical theory. Moreover via generalized Abel polynomials we construct a new class of cumulants, including the classical, boolean and free ones, and the convolutions linearized by them. Finally, via an umbral Fourier transform, we state a explicit connection between boolean and free convolution

Natural statistics for spectral samples

Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric functions, k-statistics and polykays. We construct spectral k-statistics as unbiased estimators of cumulants of trace powers of a suitable random matrix. Moreover we define normalized spectral polykays in such a way that when the sampling is from an infinite population they return products of free cumulants.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1107 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Competition between Visual Events Modulates the Influence of Salience during Free-Viewing of Naturalistic Videos

In daily life the brain is exposed to a large amount of external signals that compete for processing resources. The attentional system can select relevant information based on many possible combinations of goal-directed and stimulus-driven control signals. Here, we investigate the behavioral and physiological effects of competition between distinctive visual events during free-viewing of naturalistic videos. Nineteen healthy subjects underwent functional magnetic resonance imaging (fMRI) while viewing short video-clips of everyday life situations, without any explicit goal-directed task. Each video contained either a single semantically-relevant event on the left or right side (Lat-trials), or multiple distinctive events in both hemifields (Multi-trials). For each video, we computed a salience index to quantify the lateralization bias due to stimulus-driven signals, and a gaze index (based on eye-tracking data) to quantify the efficacy of the stimuli in capturing attention to either side. Behaviorally, our results showed that stimulus-driven salience influenced spatial orienting only in presence of multiple competing events (Multi-trials). fMRI results showed that the processing of competing events engaged the ventral attention network, including the right temporoparietal junction (R TPJ) and the right inferior frontal cortex. Salience was found to modulate activity in the visual cortex, but only in the presence of competing events; while the orienting efficacy of Multi-trials affected activity in both the visual cortex and posterior parietal cortex (PPC). We conclude that in presence of multiple competing events, the ventral attention system detects semantically-relevant events, while regions of the dorsal system make use of saliency signals to select relevant locations and guide spatial orienting

Finite Temperature Effective Potential for Gauge Models in de Sitter Space

The one-loop effective potential for gauge models in static de Sitter space at finite temperatures is computed by means of the $\zeta$--function method. We found a simple relation which links the effective potentials of gauge and scalar fields at all temperatures. In the de Sitter invariant and zero-temperature states the potential for the scalar electrodynamics is explicitly obtained, and its properties in these two vacua are compared. In this theory the two states are shown to behave similarly in the regimes of very large and very small radii a of the background space. For the gauge symmetry broken in the flat limit ($a \to \infty$) there is a critical value of a for which the symmetry is restored in both quantum states. Moreover, the phase transitions which occur at large or at small a are of the first or of the second order, respectively, regardless the vacuum considered. The analytical and numerical analysis of the critical parameters of the above theory is performed. We also established a class of models for which the kind of phase transition occurring depends on the choice of the vacuum.Comment: 23 pages, LaTeX, 5 figure.ep

Atrial natriuretic peptide effects on intracellular pH changes and ROS production in HEPG2 cells: Role of p38 MAPK and phospholipase D

Aims: The present study was performed to evaluate Atrial Natriuretic Peptide ( ANP) effects on intracellular pH, phospholipase D and ROS production and the possible relationship among them in HepG2 cells. Cancer extracellular microenvironment is more acidic than normal tissues and the activation of NHE- 1, the only system able to regulate pHi homeostasis in this condition, can represent an important event in cell proliferation and malignant transformation. Methods: The ANP effects on pHi were evaluated by fluorescence spectrometry. The effects on p38 MAPK and ROS production were evaluated by immunoblots and analysis of DCF- DA fluorescence, respectively. RT- PCR analysis and Western blotting were used to determine the ANP effect on mRNA NHE- 1 expression and protein levels. PLD- catalyzed conversion of phosphatidylcholine to phosphatydilethanol ( PetOH), in the presence of ethanol, was monitored by thin layer chromatography. Results: A significant pHi decrease was observed in ANP- treated HepG2 cells and this effect was paralleled by the enhancement of PLD activity and ROS production. The ANP effect on pHi was coupled to an increased p38 MAPK phosphorylation and a down- regulation of mRNA NHE- 1 expression and protein levels. Moreover, the relationship between PLD and ROS production was demonstrated by calphostin- c, a potent inhibitor of PLD. At the same time, all assessed ANP- effects were mediated by NPR- C receptors. Conclusion: Our results indicate that ANP recruits a signal pathway associated with p38 MAPK, NHE- 1 and PLD responsible for ROS production, suggesting a possible role for ANP as novel modulator of ROS generation in HepG2 cells. Copyright (C) 2005 S. Karger AG, Basel

Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities

The spherical domains $S^d_\beta$ with conical singularities are a convenient arena for studying the properties of tensor Laplacians on arbitrary manifolds with such a kind of singular points. In this paper the vector Laplacian on $S^d_\beta$ is considered and its spectrum is calculated exactly for any dimension $d$. This enables one to find the Schwinger-DeWitt coefficients of this operator by using the residues of the $\zeta$-function. In particular, the second coefficient, defining the conformal anomaly, is explicitly calculated on $S^d_\beta$ and its generalization to arbitrary manifolds is found. As an application of this result, the standard renormalization of the one-loop effective action of gauge fields is demonstrated to be sufficient to remove the ultraviolet divergences up to the first order in the conical deficit angle.Comment: plain LaTeX, 23 pp., revised version, a misprint in expressions (1.8) and (4.38) of the second heat coefficient for the vector Laplacian is corrected. No other change

Thermal Fields, Entropy, and Black Holes

In this review we describe statistical mechanics of quantum systems in the presence of a Killing horizon and compare statistical-mechanical and one-loop contributions to black hole entropy. Studying these questions was motivated by attempts to explain the entropy of black holes as a statistical-mechanical entropy of quantum fields propagating near the black hole horizon. We provide an introduction to this field of research and review its results. In particular, we discuss the relation between the statistical-mechanical entropy of quantum fields and the Bekenstein-Hawking entropy in the standard scheme with renormalization of gravitational coupling constants and in the theories of induced gravity.Comment: 44 pages, LaTeX fil

Smart ECM-based electrospun biomaterials for skeletal muscle regeneration

The development of smart and intelligent regenerative biomaterials for skeletal muscle tissue engineering is an ongoing challenge, owing to the requirement of achieving biomimetic systems able to communicate biological signals and thus promote optimal tissue regeneration. Electrospinning is a well-known technique to produce fibers that mimic the three dimensional microstructural arrangements, down to nanoscale and the properties of the extracellular matrix fibers. Natural and synthetic polymers are used in the electrospinning process; moreover, a blend of them provides composite materials that have demonstrated the potential advantage of supporting cell function and adhesion. Recently, the decellularized extracellular matrix (dECM), which is the noncellular component of tissue that retains relevant biological cues for cells, has been evaluated as a starting biomaterial to realize composite electrospun constructs. The properties of the electrospun systems can be further improved with innovative procedures of functionalization with biomolecules. Among the various approaches, great attention is devoted to the “click” concept in constructing a bioactive system, due to the modularity, orthogonality, and simplicity features of the “click” reactions. In this paper, we first provide an overview of current approaches that can be used to obtain biofunctional composite electrospun biomaterials. Finally, we propose a design of composite electrospun biomaterials suitable for skeletal muscle tissue regeneration