The bounds of heavy-tailed return distributions in evolving complex networks

We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an agent model, presented in the context of economic networks of trades, which shows the emergence of critical behavior. Starting from a brief discussion about the main features of the evolving network of trades, we show that the logarithmic return distributions have bounded heavy-tails, and the corresponding bounding exponent values can be derived. Finally, we discuss these findings in the context of model risk

On the normalization of Killing vectors and energy conservation in two-dimensional gravity

We explicitly show that, in the context of a recently proposed 2D dilaton gravity theory, energy conservation requires the ``natural'' Killing vector to have, asymptotically, an unusual normalization. The Hawking temperature $T_H$ is then calculated according to this prescription.Comment: 7 pages, Latex, no figure

Electron and Phonon Thermal Waves in Semiconductors: an Application to Photothermal Effects

The electron and phonon temperature distribution function are calculated in semiconductors. We solved the coupled one-dimensional heat-diffussion equations in the linear approximation in which the physical parameters on the sample are independent of the temperature. We also consider the heat flux at the surface of the semiconductor as a boundary condition for each electron and phonon systems instead of using a fixed temperature. From this, we obtain an expression for electron and phonon temperature respectively. The characterization of the thermal waves properties is duscussed and some practical procedures for this purpose provide us information about the electron and phonon thermal parameters.Comment: 12 pages, amstex and amssymb macro package (LaTeX2e edition

Epidemic model on a network: analysis and applications to COVID-19

We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic criterion and examine different vaccination/containment strategies: we prove that it is most effective to vaccinate a node of highest degree. The model is also useful to evaluate deconfinement scenarios and prevent a so-called second wave. The model has few parameters enabling fitting to the data and the essential ingredient of importation of infected; these features are particularly important for the current COVID-19 epidemic

Vacuum-UV spectroscopy of interstellar ice analogs. II. Absorption cross-sections of nonpolar ice molecules

Dust grains in cold circumstellar regions and dark-cloud interiors at 10-20 K are covered by ice mantles. A nonthermal desorption mechanism is invoked to explain the presence of gas-phase molecules in these environments, such as the photodesorption induced by irradiation of ice due to secondary ultraviolet photons. To quantify the effects of ice photoprocessing, an estimate of the photon absorption in ice mantles is required. In a recent work, we reported the vacuum-ultraviolet (VUV) absorption cross sections of nonpolar molecules in the solid phase. The aim was to estimate the VUV-absorption cross sections of nonpolar molecular ice components, including CH4, CO2, N2, and O2. The column densities of the ice samples deposited at 8 K were measured in situ by infrared spectroscopy in transmittance. VUV spectra of the ice samples were collected in the 120-160 nm (10.33-7.74 eV) range using a commercial microwave-discharged hydrogen flow lamp. We found that, as expected, solid N2 has the lowest VUV-absorption cross section, which about three orders of magnitude lower than that of other species such as O2, which is also homonuclear. Methane (CH4) ice presents a high absorption near Ly-alpha (121.6 nm) and does not absorb below 148 nm. Estimating the ice absorption cross sections is essential for models of ice photoprocessing and allows estimating the ice photodesorption rates as the number of photodesorbed molecules per absorbed photon in the ice.Comment: 9 pages, 6 figures, 7 table