Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.Comment: 21 pages, 5 figures, Final revision to appear in Bulletin of Mathematical Biolog

Dust Emissivity in the Far-Infrared

We have derived the dust emissivity in the Far-Infrared (FIR) using data available in the literature. We use two wavelength dependences derived from spectra of Galactic FIR emission (Reach et al. 1995). A value for the emissivity, normalised to the extinction efficiency in the V band, has been retrieved from maps of Galactic FIR emission, dust temperature and extinction (Schlegel et al. 1998). Our results are similar to other measurements in the Galaxy but only marginally consistent with the widely quoted values of Hildebrand (1983) derived on one reflection nebula. The discrepancy with measurements on other reflection nebulae (Casey 1991) is higher and suggests a different grain composition in these environments with respect to the diffuse interstellar medium. We measure dust masses for a sample of six spiral galaxies with FIR observations and obtain gas-to-dust ratios close to the Galactic value.Comment: 5 pages, 1 ps file, A&A letter accepte

ISO observations of spirals: modelling the FIR emission

ISO observations at 200 micron have modified our view of the dust component in spiral galaxies. For a sample of seven resolved spirals we have retrieved a mean temperature of 20K, about 10K lower than previous estimates based on IRAS data at shorter wavelengths. Because of the steep dependence of far-infrared emission on the dust temperature, the dust masses inferred from ISO fluxes are a factor of 10 higher than those derived from IRAS data only, leading to gas-to-dust ratios close to the value observed in the Galaxy. The scale-length of the 200 micron emission is larger than for the IRAS 100 micron emission, with colder dust at larger distances from the galactic centre, as expected if the interstellar radiation field is the main source of dust heating. The 200 micron scale-length is also larger than the optical, for all the galaxies in the sample. This suggests that the dust distribution is more extended than that of the stars.A model of the dust heating is needed to derive the parameters of the dust distribution from the FIR emission. Therefore, we have adapted an existing radiative transfer code to deal with dust emission. Simulated maps of the temperature distribution within the dust disk and of the dust emission at any wavelength can be produced. The stellar spectral energy distribution is derived from observations in the ultraviolet, optical and near infrared. The parameters of the dust distribution (scale-lengths and optical depth) are chosen to reproduce the observed characteristics of the FIR emission, i.e. the shape of the spectrum, the flux and the spatial distribution. We describe the application of the model to one of the galaxies in the sample, NGC 6946.Comment: 6 pages, 5 figures. Contribution to the proceedings of the workshop "ISO Beyond Point Sources" held at VILSPA 14-17 September 199

Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections

This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective in this context; nevertheless, their computation may be very expensive for large-scale problems, and resorting to approximations of them may be convenient. Here we propose a procedure for building inexact constraint preconditioners by updating a "seed" constraint preconditioner computed for a KKT matrix at a previous interior point iteration. These updates are obtained through low-rank corrections of the Schur complement of the (1,1) block of the seed preconditioner. The updated preconditioners are analyzed both theoretically and computationally. The results obtained show that our updating procedure, coupled with an adaptive strategy for determining whether to reinitialize or update the preconditioner, can enhance the performance of interior point methods on large problems.Comment: 22 page

Competing Glauber and Kawasaki Dynamics

Using a quantum formulation of the master equation we study a kinetic Ising model with competing stochastic processes: the Glauber dynamics with probability $p$ and the Kawasaki dynamics with probability $1 - p$. Introducing explicitely the coupling to a heat bath and the mutual static interaction of the spins the model can be traced back exactly to a Ginzburg Landau functional when the interaction is of long range order. The dependence of the correlation length on the temperature and on the probability $p$ is calculated. In case that the spins are subject to flip processes the correlation length disappears for each finite temperature. In the exchange dominated case the system is strongly correlated for each temperature.Comment: 9 pages, Revte

Dualism between Physical Frames and Time in Quantum Gravity

In this work we present a discussion of the existing links between the procedures of endowing the quantum gravity with a real time and of including in the theory a physical reference frame. More precisely, as first step, we develop the canonical quantum dynamics, starting from the Einstein equations in presence of a dust fluid and arrive to a Schroedinger evolution. Then, by fixing the lapse function in the path integral of gravity, we get a Schroedinger quantum dynamics, of which eigenvalues problem provides the appearance of a dust fluid in the classical limit. The main issue of our analysis is to claim that a theory, in which the time displacement invariance, on a quantum level, is broken, is indistinguishable from a theory for which this symmetry holds, but a real reference fluid is included.Comment: 9 pages, submitted to Mod. Phys. Lett. A, major replacements in section 3 and

Latest evidence for a late time vacuum -- geodesic CDM interaction

We perform a reconstruction of the coupling function between vacuum energy and geodesic cold dark matter using the latest observational data. We bin the interaction in seventeen redshift bins but use a correlation prior to prevent rapid, unphysical oscillations in the coupling function. This prior also serves to eliminate any dependence of the reconstruction on the binning method. We use two different forms of the correlation prior, finding that both give similar results for the reconstruction of the dark matter -- dark energy interaction. Calculating the Bayes factor for each case, we find no meaningful evidence for deviation from the null interacting case, i.e. $\Lambda$CDM, in our reconstruction.Comment: 14 pages, 7 figures. Version 2 matches published version in Physics of the Dark Universe (Figure 2 updated to better show H0 and sigma 8 tensions, additional discussion of results added in section 4.1

Disorder-Induced Stabilization of the Pseudogap in Strongly Correlated Systems

The interplay of strong interaction and strong disorder, as contained in the Anderson-Hubbard model, is addressed using two non-perturbative numerical methods: the Lanczos algorithm in the grand canonical ensemble at zero temperature and Quantum Monte Carlo. We find distinctive evidence for a zero-energy anomaly which is robust upon variation of doping, disorder and interaction strength. Its similarities to, and differences from, pseudogap formation in other contexts, including perturbative treatments of interactions and disorder, classical theories of localized charges, and in the clean Hubbard model, are discussed.Comment: 4.2 pages, 4 figure