Functional models for large-scale gene regulation networks: realism and fiction

High-throughput experiments are shedding light on the topology of large regulatory networks and at the same time their functional states, namely the states of activation of the nodes (for example transcript or protein levels) in different conditions, times, environments. We now possess a certain amount of information about these two levels of description, stored in libraries, databases and ontologies. A current challenge is to bridge the gap between topology and function, i.e. developing quantitative models aimed at characterizing the expression patterns of large sets of genes. However, approaches that work well for small networks become impossible to master at large scales, mainly because parameters proliferate. In this review we discuss the state of the art of large-scale functional network models, addressing the issue of what can be considered as realistic and what the main limitations may be. We also show some directions for future work, trying to set the goals that future models should try to achieve. Finally, we will emphasize the possible benefits in the understanding of biological mechanisms underlying complex multifactorial diseases, and in the development of novel strategies for the description and the treatment of such pathologies.Comment: to appear on Mol. BioSyst. 200

Theory for Phase Transitions in Insulating Vanadium Oxide

We show that the recently proposed S=2 bond model with orbital degrees of freedom for insulating V$_{2}$O$_{3}$ not only explains the anomalous magnetic ordering, but also other mysteries of the magnetic phase transition. The model contains an additional orbital degree of freedom that exhibits a zero temperature quantum phase transtion in the Ising universality class.Comment: 5 pages, 2 figure

Noncommutative geometry and physics: a review of selected recent results

This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry of finite groups, with the explicit example of Z_2, and its application to Kaluza-Klein gauge theories on discrete internal spaces.Comment: Based on lectures given at the TMR School on contemporary string theory and brane physics, Jan 26- Feb 2, 2000, Torino, Italy. To be published in Class. Quant. Grav. 17 (2000). 3 ref.s added, typos corrected, formula on exterior product of n left-invariant one-forms corrected, small changes in the Sect. on integratio

Multifractality: generic property of eigenstates of 2D disordered metals.

The distribution function of local amplitudes of eigenstates of a two-dimensional disordered metal is calculated. Although the distribution of comparatively small amplitudes is governed by laws similar to those known from the random matrix theory, its decay at larger amplitudes is non-universal and much slower. This leads to the multifractal behavior of inverse participation numbers at any disorder. From the formal point of view, the multifractality originates from non-trivial saddle-point solutions of supersymmetric $\sigma$-model used in calculations.Comment: 4 two-column pages, no figures, submitted to PRL

X-Ray Resonant Scattering as a Direct Probe of Orbital Ordering in Transition-Metal Oxides

X-ray resonant scattering at the K-edge of transition metal oxides is shown to measure the orbital order parameter, supposed to accompany magnetic ordering in some cases. Virtual transitions to the 3d-orbitals are quadrupolar in general. In cases with no inversion symmetry, such as V$_2$O$_3$, treated in detail here, a dipole component enhances the resonance. Hence, we argue that the detailed structure of orbital order in V$_2$O$_3$ is experimentally accessible.Comment: LaTex using RevTex, 4 pages and two included postscript figure

Orbitally Degenerate Spin-1 Model for Insulating V2O3

Motivated by recent neutron, X-ray absorption and resonant scattering experiments, we revisit the electronic structure of V2O3. We propose a model in which S=1 V3+ ions are coupled in the vertical V-V pairs forming two-fold orbitally degenerate configurations with S=2. Ferro-orbital ordering of the V-V pairs gives a description which is consistent with all experiments in the antiferromagnetic insulating phase.Comment: 4 pages, including three figure

Crossover from Luttinger- to Fermi-liquid behavior in strongly anisotropic systems in large dimensions

We consider the low-energy region of an array of Luttinger liquids coupled by a weak interchain hopping. The leading logarithmic divergences can be re-summed to all orders within a self-consistent perturbative expansion in the hopping, in the large-dimension limit. The anomalous exponent scales to zero below the one-particle crossover temperature. As a consequence, coherent quasiparticles with finite weight appear along the whole Fermi surface. Extending the expansion self-consistently to all orders turns out to be crucial in order to restore the correct Fermi-liquid behavior.Comment: Shortened version to appear in Physical Review Letter

Non-linear effects and dephasing in disordered electron systems

The calculation of the dephasing time in electron systems is presented. By means of the Keldysh formalism we discuss in a unifying way both weak localization and interaction effects in disordered systems. This allows us to show how dephasing arises both in the particle-particle channel (weak localization) and in the particle-hole channel (interaction effect). First we discuss dephasing by an external field. Besides reviewing previous work on how an external oscillating field suppresses the weak localization correction, we derive a new expression for the effect of a field on the interaction correction. We find that the latter may be suppressed by a static electric field, in contrast to weak localization. We then consider dephasing due to inelastic scattering. The ambiguities involved in the definition of the dephasing time are clarified by directly comparing the diagrammatic approach with the path-integral approach. We show that different dephasing times appear in the particle-particle and particle-hole channels. Finally we comment on recent experiments.Comment: 28 pages, 6 figures (14ps-files

Helioseismology can test the Maxwell-Boltzmann distribution

Nuclear reactions in stars occur between nuclei in the high-energy tail of the energy distribution and are sensitive to possible deviations from the standard equilibrium thermal-energy distribution. We are able to derive strong constraints on such deviations by using the detailed helioseismic information of the solar structure. If a small deviation is parameterized with a factor exp{-delta*(E/kT)^2}, we find that delta should lie between -0.005 and +0.002. However, even values of delta as small as 0.003 would still give important effects on the neutrino fluxes.Comment: 10 pages in ReVTeX + 1 postscript figure. Submitted to Phys. Lett.

Star Counts in the Globular Cluster Omega Centauri. I. Bright Stellar Components

We present an extensive photometry on HB, RGB, and MSTO stars in Omega Cen. The central regions of the cluster were covered with a mosaic of F435W, F625W, and F658N-band data collected with ACS/HST. The outer reaches were covered with a large set of U,B,V,I-band data collected with the [email protected] ESO/MPI telescope. The final catalogue includes ~1.7 million stars. We identified ~3,200 likely HB stars and ~12,500 stars brighter than the subgiant branch and fainter than the RGB bumps. The HB morphology changes with the radial distance. The relative number of extreme HB stars decreases from ~30% to ~21% when moving from the center toward the outer regions of the cluster, while the fraction of less hot HB stars increases from ~62% to ~72%. We performed a detailed comparison between observed ratios of different stellar tracers and predictions based on canonical evolutionary models with a primordial helium (Y=0.23) content and metal abundances (Z=0.0002,0.001) that bracket the observed spread in metallicity of Omega Cen stars. We found that the empirical star counts of HB stars are on average larger (30%-40%) than predicted. Moreover, the rate of HB stars is 43% larger than the MSTO rate. The discrepancy between the rate of HB compared with the rate of RG and MSTO stars supports the evidence that we are facing a true excess of HB stars. The same comparison was performed by assuming a mix of stellar populations made with 70% of canonical stars and 30% of He-enhanced stars. The discrepancy between theory and observations decreases by a factor of two when compared with rates predicted by canonical He content models, but still 15%-25% (Y=0.42) and 15%-20% (Y=0.33) higher than observed. Furthermore, the ratio between HB and MSTO star counts are ~24% (Y=0.42) and 30% (Y=0.33) larger than predicted lifetime ratios.Comment: 54 pages, 17 figures,to be published in ApJ, see link at http://stellari.wiki.zoho.co