On Proper Polynomial Maps of C2.\mathbb{C}^2.

Two proper polynomial maps $f_1, f_2 \colon \mathbb{C}^2 \longrightarrow \mathbb{C}^2$ are said to be \emph{equivalent} if there exist $\Phi_1, \Phi_2 \in \textrm{Aut}(\mathbb{C}^2)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$. We investigate proper polynomial maps of arbitrary topological degree $d \geq 2$ up to equivalence. Under the further assumption that the maps are Galois coverings we also provide the complete description of equivalence classes. This widely extends previous results obtained by Lamy in the case $d=2$.Comment: 15 pages. Final version, to appear in Journal of Geometric Analysi

Langevin equation for the extended Rayleigh model with an asymmetric bath

In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The non-linear Langevin equation for the motion of the piston is derived from first principles for the case when the thermodynamic parameters and/or the molecular masses of gas particles on left and right sides of the piston are different. Microscopic expressions involving time correlation functions of the force between bath particles and the piston are obtained for all parameters appearing in the non-linear Langevin equation. It is demonstrated that the equation has stationary solutions corresponding to directional fluctuation-induced drift in the absence of systematic forces. In the case of ideal gases interacting with the piston via a quadratic repulsive potential, the model is exactly solvable and explicit expressions for the kinetic coefficients in the non-linear Langevin equation are derived. The transient solution of the non-linear Langevin equation is analyzed perturbatively and it is demonstrated that previously obtained results for systems with the hard-wall interaction are recovered.Comment: 10 pages. To appear in Phys. Rev.

Evidence of short time dynamical correlations in simple liquids

We report a molecular dynamics (MD) study of the collective dynamics of a simple monatomic liquid -interacting through a two body potential that mimics that of lithium- across the liquid-glass transition. In the glassy phase we find evidences of a fast relaxation process similar to that recently found in Lennard-Jones glasses. The origin of this process is ascribed to the topological disorder, i.e. to the dephasing of the different momentum $Q$ Fourier components of the actual normal modes of vibration of the disordered structure. More important, we find that the fast relaxation persists in the liquid phase with almost no temperature dependence of its characteristic parameters (strength and relaxation time). We conclude, therefore, that in the liquid phase well above the melting point, at variance with the usual assumption of {\it un-correlated} binary collisions, the short time particles motion is strongly {\it correlated} and can be described via a normal mode expansion of the atomic dynamics.Comment: 7 pages, 7 .eps figs. To appear in Phys. Rev.

Inelastic X-ray scattering study of the collective dynamics in liquid sodium

Inelastic X-ray scattering data have been collected for liquid sodium at T=390 K, i.e. slightly above the melting point. Owing to the very high instrumental resolution, pushed up to 1.5 meV, it has been possible to determine accurately the dynamic structure factor, $S(Q,\omega)$, in a wide wavevector range, $1.5 \div 15$ nm$^{-1}$, and to investigate on the dynamical processes underlying the collective dynamics. A detailed analysis of the lineshape of $S(Q,\omega)$, similarly to other liquid metals, reveals the co-existence of two different relaxation processes with slow and fast characteristic timescales respectively. The present data lead to the conclusion that: i) the picture of the relaxation mechanism based on a simple viscoelastic model fails; ii) although the comparison with other liquid metals reveals similar behavior, the data do not exhibit an exact scaling law as the principle of corresponding state would predict.Comment: RevTex, 7 pages, 6 eps figures. Accepted by Phys. Rev.

Dynamical properties of liquid Al near melting. An orbital-free molecular dynamics study

The static and dynamic structure of liquid Al is studied using the orbital free ab-initio molecular dynamics method. Two thermodynamic states along the coexistence line are considered, namely T = 943 K and 1323 K for which X-ray and neutron scattering data are available. A new kinetic energy functional, which fulfills a number of physically relevant conditions is employed, along with a local first principles pseudopotential. In addition to a comparison with experiment, we also compare our ab-initio results with those obtained from conventional molecular dynamics simulations using effective interionic pair potentials derived from second order pseudopotential perturbation theory.Comment: 15 pages, 12 figures, 2 tables, submitted to PR

Nucleus-Electron Model for States Changing from a Liquid Metal to a Plasma and the Saha Equation

We extend the quantal hypernetted-chain (QHNC) method, which has been proved to yield accurate results for liquid metals, to treat a partially ionized plasma. In a plasma, the electrons change from a quantum to a classical fluid gradually with increasing temperature; the QHNC method applied to the electron gas is in fact able to provide the electron-electron correlation at arbitrary temperature. As an illustrating example of this approach, we investigate how liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV at a fixed normal ion-density $1.03 \times 10^{22}/cm^3$. The electron-ion radial distribution function (RDF) in liquid Rb has distinct inner-core and outer-core parts. Even at a temperature of 1 eV, this clear distinction remains as a characteristic of a liquid metal. At a temperature of 3 eV, this distinction disappears, and rubidium becomes a plasma with the ionization 1.21. The temperature variations of bound levels in each ion and the average ionization are calculated in Rb plasmas at the same time. Using the density-functional theory, we also derive the Saha equation applicable even to a high-density plasma at low temperatures. The QHNC method provides a procedure to solve this Saha equation with ease by using a recursive formula; the charge population of differently ionized species are obtained in Rb plasmas at several temperatures. In this way, it is shown that, with the atomic number as the only input, the QHNC method produces the average ionization, the electron-ion and ion-ion RDF's, and the charge population which are consistent with the atomic structure of each ion for a partially ionized plasma.Comment: 28 pages(TeX) and 11 figures (PS

Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an expicit description for all projective compactifications. We also construct explicitly (in elementary geometrical terms) a universal object for all projective compactifications of GL_n.Comment: 24 pages, corrected varian

Geography-dependent horizontal gene transfer from vertebrate predators to their prey

Horizontal transfer (HT) of genes between multicellular animals, once thought to be extremely rare, is being more commonly detected, but its global geographic trend and transfer mechanism have not been investigated. We discovered a unique HT pattern of Bovine-B (BovB) LINE retrotransposons in vertebrates, with a bizarre transfer direction from predators (snakes) to their prey (frogs). At least 54 instances of BovB HT were detected, which we estimate to have occurred across time between 85 and 1.3 Ma. Using comprehensive transcontinental sampling, our study demonstrates that BovB HT is highly prevalent in one geographical region, Madagascar, suggesting important regional differences in the occurrence of HTs. We discovered parasite vectors that may plausibly transmit BovB and found that the proportion of BovB-positive parasites is also high in Madagascar where BovB thus might be physically transported by parasites to diverse vertebrates, potentially including humans. Remarkably, in two frog lineages, BovB HT occurred after migration from a non-HT area (Africa) to the HT hotspot (Madagascar). These results provide a novel perspective on how the prevalence of parasites influences the occurrence of HT in a region, similar to pathogens and their vectors in some endemic diseases

Renal cell carcinoma induces interleukin 10 and prostaglandin E2 production by monocytes

Immunotherapy with interleukin 2 (IL-2) is not an effective anti-cancer treatment in the majority of patients with renal cell carcinoma (RCC), suggesting that the activation of cytotoxic T cells or NK cells may be impaired in vivo in these patients. The production of immunosuppressive factors by RCC was investigated. Using immunohistochemistry, IL-10 was detectable in 10 of 21 tumour samples tested. IL-10 was undetectable in the supernatant of cell lines derived from these RCCs. However, these cell lines or their conditioned medium (RCC CM), but not normal renal epithelial cells adjacent to the RCC or breastcarcinoma cell lines, were found to induce IL-10, as well as prostaglandin E2 (PGE2) and tumour necrosis factor (TNF)α production by autologous or allogeneic peripheral blood mononuclear cells (PBMCs) and monocytes. IL-10 production induced by RCC CM was found to be dependent on TNF-α and PGE2 since an anti-TNF-α antibody (Ab) inhibited 40–70% of IL-10 production by monocytes, and the combination of anti-TNF-α Ab and indomethacin, an inhibitor of PGE2 production, inhibited 80–94% of RCC CM-induced IL-10 production by monocytes. The RCC CM of the five cell lines tested were found to induce a down-regulation of the expression of HLA-DR and CD86, as well as a strong inhibition of mannose receptor-dependent endocytosis by monocytes. The blockade of HLA-DR and CD86 expression was partially abrogated by indomethacin and anti-IL-10 Ab respectively, and completely abrogated by an anti-TNF-α Ab. The inhibition of mannose receptor-dependent endocytosis was partially abrogated by an anti-IL-10 Ab and completely abrogated by an anti-TNF-α Ab. These esults indicate that RCCs induce IL-10, PGE2 and TNF-α production by monocytes, which down-regulate the expression of cell-surface molecules involved in antigen presentation as well as their endocytic capacity. © 1999 Cancer Research Campaig