Hierarchy of models: From qualitative to quantitative analysis of circadian rhythms in cyanobacteria

International audienceA hierarchy of models, ranging from high to lower levels of abstraction, is proposed to construct "minimal" but predictive and explanatory models of biological systems. Three hierarchical levels will be considered: Boolean networks, piecewise affine differential (PWA) equations, and a class of continuous, ordinary, differential equations' models derived from the PWA model. This hierarchy provides different levels of approximation of the biological system and, crucially, allows the use of theoretical tools to more exactly analyze and understand the mechanisms of the system. The Kai ABC oscillator, which is at the core of the cyanobacterial circadian rhythm, is analyzed as a case study, showing how several fundamental properties-order of oscillations, synchronization when mixing oscillating samples, structural robustness, and entrainment by external cues-can be obtained from basic mechanisms

Merger of Massive Black Holes using N-Body Simulations with Post-Newtonian Corrections

We present preliminary results from self-consistent, high resolution direct {\it N}-body simulations of massive black hole binaries in mergers of galactic nuclei. The dynamics of the black hole binary includes the full Post-Newtonian corrections (up to 2.5PN) to its equations of motion. We show that massive black holes starting at separations of 100 pc can evolve down to gravitational-wave-induced coalescence in less than a Hubble time. The binaries, in our models, often form with very high eccentricity and, as a result, reach separations of 50 Schwarzschild radius with eccentricities which are clearly distinct from zero -- even though gravitational wave emission damps the eccentricity during the inspiral. These deviations from exact circular orbits, at such small separations, may have important consequences for LISA data analysis.Comment: 8 pages, 6 figures, proceedings to the 7th LISA Symposium, Barcelona, 16-20 June 2008. Submitted to Journal of Physics: Conference Serie

A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems

Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive timestep control is added to a symplectic integrator. We describe an adaptive-timestep symplectic integrator that can be used if the Hamiltonian is the sum of kinetic and potential energy components and the required timestep depends only on the potential energy (e.g. test-particle integrations in fixed potentials). In particular, we describe an explicit, reversible, symplectic, leapfrog integrator for a test particle in a near-Keplerian potential; this integrator has timestep proportional to distance from the attracting mass and has the remarkable property of integrating orbits in an inverse-square force field with only "along-track" errors; i.e. the phase-space shape of a Keplerian orbit is reproduced exactly, but the orbital period is in error by O(1/N^2), where N is the number of steps per period.Comment: 24 pages, 3 figures, submitted to Astronomical Journal; minor errors in equations and one figure correcte

On strong mass segregation around a massive black hole: Implications for lower-frequency gravitational-wave astrophysics

We present, for the first time, a clear $N$-body realization of the {\it strong mass segregation} solution for the stellar distribution around a massive black hole. We compare our $N$-body results with those obtained by solving the orbit-averaged Fokker-Planck (FP) equation in energy space. The $N$-body segregation is slightly stronger than in the FP solution, but both confirm the {\it robustness} of the regime of strong segregation when the number fraction of heavy stars is a (realistically) small fraction of the total population. In view of recent observations revealing a dearth of giant stars in the sub-parsec region of the Milky Way, we show that the time scales associated with cusp re-growth are not longer than $(0.1-0.25) \times T_{rlx}(r_h)$. These time scales are shorter than a Hubble time for black holes masses \mbul \lesssim 4 \times 10^6 M_\odot and we conclude that quasi-steady, mass segregated, stellar cusps may be common around MBHs in this mass range. Since EMRI rates scale as \mbul^{-\alpha}, with \alpha \in [1\4,1], a good fraction of these events should originate from strongly segregated stellar cusps.Comment: 5 pages, 4 figures, 1 table, submitted to ApJ

Introdução

A importância conferida ao papel desempenhado pelo empreendedorismo na sociedade mudou radicalmente ao longo do último meio século. Após a Segunda Guerra Mundial, imperava na teoria económica a noção de que as grandes empresas seriam as únicas que reuniam condições para explorar plenamente as oportunidades de inovação (Schumpeter, 1942). Porém, desde os anos noventa, o empreendedorismo (entendido como criação de novas empresas, por natureza de pequena/média dimensão) tem sido identificado como uma das principais tendências socioeconómicas e um motor da inovação, da competitividade e do desenvolvimento económico. De facto, há resultados empíricos que comprovam a ideia de que as novas empresas estão mais associadas à introdução de inovações tecnológicas nos mercados e à promoção do crescimento económico e do emprego (Audretsch, 2003).(...

N-body studies of galactic nuclei with massive black holes

Massive black holes (MBHs) are ubiquituous in galactic nuclei. The collisional dynamics of these $systems is studied with high resolution, direct$N$-body simulations and its results are thorough$those obtained from the Fokker-Planck equation, written in energy space. The predictions from the$equation are validated by the$N$-body results and it is concluded that the formation of a Bahcal$a MBH is a robust prediction for the old stellar populations of spheroidal systems older than the$as measured at the hole's influence radius. The mass segregation and the scaling relations predic$different mass ranges are also confirmed. $N$-Body simulations of galaxy mergers show that binary MBHs can form with very high eccentriciti$galaxies settle into a newly merged nucleus. These high eccentricities should lead to a coalescen$time scale, as the MBHs should emmit strong bursts of gravitational waves at each pericenter pass$harmonics of the gravitational wave strain amplitude$h$are estimated as the massive binary with mass$\sim 1$enters the Laser Interferometer Space Antenna (LISA) frequency band. We conclude that large-scale$N$-body modelling of galactic nuclei with one (several) MBH(s) is p$currently available software (Sverre Aarseth's NBODY codes and developments therefrom) and hardwa$cluster)

Mergers of Unequal Mass Galaxies: Supermassive Black Hole Binary Evolution and Structure of Merger Remnants

Galaxy centers are residing places for Super Massive Black Holes (SMBHs). Galaxy mergers bring SMBHs close together to form gravitationally bound binary systems which, if able to coalesce in less than a Hubble time, would be one of the most promising sources of gravitational waves for the Laser Interferometer Space Antenna (LISA). In spherical galaxy models, SMBH binaries stall at a separation of approximately one parsec, leading to the "final parsec problem" (FPP). On the other hand, it has been shown that merger-induced triaxiality of the remnant in equal-mass mergers is capable of supporting a constant supply of stars on so-called centrophilic orbits that interact with the binary and thus avoid the FPP. In this paper, using a set of direct N-body simulations of mergers of initially spherically symmetric galaxies with different mass ratios, we show that the merger-induced triaxiality is able to drive unequal-mass SMBH binaries to coalescence. The binary hardening rates are high and depend only weakly on the mass ratios of SMBHs for a wide range of mass ratios q. The hardening rates are significantly higher for galaxies having steep cusps in comparison with those having shallow cups at centers. The evolution of the binary SMBH leads to relatively shallower inner slopes at the centers of the merger remnants. The stellar mass displaced by the SMBH binary on its way to coalescence is ~ 1-5 times the combined mass of binary SMBHs. The coalescence times for SMBH binary with mass ~ million solar masses are less than 1 Gyr and for those at the upper end of SMBH masses (~ billion solar masses) are 1-2 Gyr for less eccentric binaries whereas less than 1 Gyr for highly eccentric binaries. SMBH binaries are thus expected to be promising sources of gravitational waves at low and high redshifts.Comment: Accepted for publication in the Astrophysical Journal (ApJ). 14 pages, 8 figure

Foreign divestment: What stays when multinationals leave?

When an MNE closes its doors, workers may find themselves in demand or struggling, depending on the nature of their employment and the characteristics of the foreign affiliate itself. The authors recommend a targeted policy approach that focuses on transition assistance for the most vulnerable employees