Steiner's formula in the Heisenberg group

Steiner's tube formula states that the volume of an ∈-neighborhood of a smooth regular domain in ℝn is a polynomial of degree n in the variable ∈ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ∈-neighborhood with respect to the Heisenberg metric is an analytic function of ∈ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms

Molecular mechanisms controlling the phenotype and the EMT/MET dynamics of hepatocyte

The complex spatial and paracrine relationships between the various liver histotypes are essential for proper functioning of the hepatic parenchymal cells. Only within a correct tissue organization, in fact, they stably maintain their identity and differentiated phenotype. The loss of histotype identity, which invariably occurs in the primary hepatocytes in culture, or in vivo in particular pathological conditions (fibrosis and tumors), is mainly due to the phenomenon of epithelial-to-mesenchymal transition (EMT). The EMT process, that occurs in the many epithelial cells, appears to be driven by a number of general, non- tissue-specific, master transcriptional regulators. The reverse process, the mesenchymal-to epithelial transition (MET), as yet much less characterized at a molecular level, restores specific epithelial identities, and thus, must include tissue-specific master elements. In this review, we will summarize the so far unveiled events of EMT/MET occurring in liver cells. In particular, we will focus on hepatocyte and describe the pivotal role in the control of EMT/MET dynamics exerted by a tissue-specific molecular mini-circuitry. Recent evidence, indeed, highlighted as two transcriptional factors, the master gene of EMT Snail, and the master gene of hepatocyte differentiation HNF4α, exhorting a direct reciprocal repression, act as pivotal elements in determining opposite cellular outcomes. The different balances between these two master regulators, further integrated by specific microRNAs, in fact, were found responsible for the EMT/METs dynamics as well as for the preservation of both hepatocyte and stem/precursor cells identity and differentiation. Overall these findings impact the maintenance of stem cells and differentiated cells both in in vivo EMT/MET physio-pathological processes as well as in culture.The complex spatial and paracrine relationships between the various liver histotypes are essential for proper functioning of the hepatic parenchymal cells. Only within a correct tissue organization, in fact, they stably maintain their identity and differentiated phenotype. The loss of histotype identity, which invariably occurs in the primary hepatocytes in culture, or in vivo in particular pathological conditions (fibrosis and tumors), is mainly due to the phenomenon of epithelial-to-mesenchymal transition (EMT). The EMT process, that occurs in the many epithelial cells, appears to be driven by a number of general, non- tissue-specific, master transcriptional regulators. The reverse process, the mesenchymal-to epithelial transition (MET), as yet much less characterized at a molecular level, restores specific epithelial identities, and thus, must include tissue-specific master elements. In this review, we will summarize the so far unveiled events of EMT/MET occurring in liver cells. I

Semiconductor-based geometrical quantum gates

We propose an implementation scheme for holonomic, i.e., geometrical, quantum information processing based on semiconductor nanostructures. Our quantum hardware consists of coupled semiconductor macroatoms addressed/controlled by ultrafast multicolor laser-pulse sequences. More specifically, logical qubits are encoded in excitonic states with different spin polarizations and manipulated by adiabatic time control of the laser amplitudes. The two-qubit gate is realized in a geometric fashion by exploiting dipole-dipole coupling between excitons in neighboring quantum dots

Panel 4: The Next Frontier: Space and Beyond

What does an international law of property portend for future extraterrestrial ambitions, such as moon and near asteroid mining? How does the Outer Space Treaty address the global commons of outer space? The law of outer space is “both unclear and incomplete” – what are the implications of an international law of property for the development of outer space law

BeppoSAX Observations of 2 Jy Lobe-dominated Broad-Line Sources: the Discovery of a Hard X-ray Component

We present new BeppoSAX LECS, MECS, and PDS observations of five lobe-dominated, broad-line active galactic nuclei selected from the 2 Jy sample of southern radio sources. These include three radio quasars and two broad-line radio galaxies. ROSAT PSPC data, available for all the objects, are also used to better constrain the spectral shape in the soft X-ray band. The collected data cover the 0.1 - 10 keV energy range, reaching 40 keV for one source. Detailed spectral fitting shows that all sources have a flat hard X-ray spectrum with energy index alpha_x ~ 0.75 in the 2 - 10 keV energy range. This is a new result, which is at variance with the situation at lower energies where these sources exhibit steeper spectra. Spectral breaks ~0.5 at 1 - 2 keV characterize the overall X-ray spectra of our objects. The flat, high-energy slope is very similar to that displayed by flat-spectrum/core-dominated quasars, which suggests that the same emission mechanism (most likely inverse Compton) produces the hard X-ray spectra in both classes. Contrary to the optical evidence for some of our sources, no absorption above the Galactic value is found in our sample. Finally, a (weak) thermal component is also present at low energies in the two broad-line radio galaxies included in our study.Comment: 4 pages, LateX, 3 figures. Uses espcrc2.sty. To appear in: "The Active X-ray Sky: Results from BeppoSAX and Rossi-XTE", Rome, Italy, 21-24 October, 1997, Eds.: L. Scarsi, H. Bradt, P. Giommi and F. Fior

Multifunctional peri-urban agriculture: Some ecosystem services of a sustainable olive grove

This study reports the influence of a sustainable management model which entails the recycling of urban wastewater and distribution by drip irrigation, recycling of polygenic carbon sources internal to the olive orchard (cover crops, pruning material) on yield, soil water holding capacity, soil biodiversity. Sustainable management practices were applied for a 15-year period in a 2-ha olive orchard located in an hilly peri-urban zone of southern Italy, where olive tree represents the dominant crop and has a key role inside the traditional landscape. A comparison between sustainable and conventional management (soil tillage, burning of the pruning residues, mineral fertilization, empirical irrigation) was carried out. This study suggests some guidelines of a sustainable management of peri-urban olive groves, with benefits to the whole agro-ecosystem stability and to the near town, recognizing the multifunctional role of agriculture that enhances the creation of synergies between urban and rural areas

Strong-field dynamo action in rapidly rotating convection with no inertia

The earth's magnetic field is generated by dynamo action driven by convection in the outer core. For numerical reasons, inertial and viscous forces play an important role in geodynamo models; however, the primary dynamical balance in the earth's core is believed to be between buoyancy, Coriolis, and magnetic forces. The hope has been that by setting the Ekman number to be as small as computationally feasible, an asymptotic regime would be reached in which the correct force balance is achieved. However, recent analyses of geodynamo models suggest that the desired balance has still not yet been attained. Here we adopt a complementary approach consisting of a model of rapidly rotating convection in which inertial forces are neglected from the outset. Within this framework we are able to construct a branch of solutions in which the dynamo generates a strong magnetic field that satisfies the expected force balance. The resulting strongly magnetized convection is dramatically different from the corresponding solutions in which the field is weak