The Controversy of Myopia as a Risk Factor for Glaucoma: a Mathematical Approach

poster abstractPurpose: to quantify how individual variations in anatomical parameters often associated with myopia (e.g. longer ocular axial length (OAL), reduced scleral thickness (ST), lamina cribrosa diameter (LCD) and thickness (LCT)) affect retinal blood flow (RBF) and its sensitivity to ocular perfusion pressure (OPP). Methods: A mathematical model is used to calculate RBF through central retinal artery (CRA), arterioles, capillaries, venules, and central retinal vein (CRV). The flow is time-dependent, driven by systemic pressure and regulated by variable resistances to account for nonlinear effects due to (1) autoregulation (AR), and (2) lamina cribrosa effect on CRA and CRV. The latter is a nonlinear function of intraocular pressure (IOP), cerebrospinal fluid pressure (CSF) and OAL, ST, LCD, and LCT. RBF is computed as the solution of a system of five non-linear ordinary differential equations. The system is solved for different OPP values, obtained by varying independently IOP and mean arterial pressure (MAP), with and without AR. Results: Four representative eyes are compared: Eye 1 (OAL=24mm, ST=1mm, LCD=3mm, LCT=0.4mm), Eye 2 (OAL=28mm, ST=1mm, LCD=3mm, LCT=0.4mm), Eye 3 (OAL=24mm, ST=0.7mm, LCD=2mm, LCT=0.2mm), Eye 4 (OAL=28mm, ST=0.7mm, LCD=2mm, LCT=0.2mm). The model predicts that the cardiac cycle RBF average (RBFav) for eyes with smaller LCD and LCT is notably less than in normal eyes when IOP is elevated and without AR (c). Without AR and reduced MAP, the four eyes show similar RBFav reductions (d). With AR, anatomical changes do not induce notable changes in RBFav, (a) and (b). Conclusions: Reduced LCD and LCT, often associated with myopia, seem to affect RBFav more than elevated OAL. RBFav reductions magnify when AR is impaired, and this might reduce IOP safe levels for eyes with reduced LCD and LCT. These findings suggest that a combination of anatomical and vascular factors might cause certain myopic eyes to be at higher risk for glaucomatous damage than others

Encoding argument graphs in logic

International audienceArgument graphs are a common way to model argumentative reasoning. For reasoning or computational purposes, such graphs may have to be encoded in a given logic. This paper aims at providing a systematic approach for this encoding. This approach relies upon a general, principle-based characterization of argumentation semantics

Computing Consensus: A Logic for Reasoning About Deliberative Processes Based on Argumentation

Argumentation theory can encode an agent’s assessment of the state of an exchange of points of view. We present a conservative model of multiple agents potentially disagreeing on the views presented during a process of deliberation. We model this process as iteratively adding points of view (arguments), or aspects of points of view. This gives rise to a modal logic, deliberative dynamic logic, which permits us to reason about the possible developments of the deliberative state. The logic we propose applies to all natural semantics of argumentation theory. Furthermore, under a very weak assumption that the consensus considered by a group of agents is faithful to their individual views, we show that model checking these models is feasible, as long as the argumentation frameworks, which may be infinite, does not have infinite branching.acceptedVersio

Feedback from Central Black Holes in Elliptical Galaxies: Two-dimensional Models Compared to One-dimensional Models

We extend the black hole (BH) feedback models of Ciotti, Ostriker, and Proga to two dimensions. In this paper, we focus on identifying the differences between the one-dimensional and two-dimensional hydrodynamical simulations. We examine a normal, isolated $L_*$ galaxy subject to the cooling flow instability of gas in the inner regions. Allowance is made for subsequent star formation, Type Ia and Type II supernovae, radiation pressure, and inflow to the central BH from mildly rotating galactic gas which is being replenished as a normal consequence of stellar evolution. The central BH accretes some of the infalling gas and expels a conical wind with mass, momentum, and energy flux derived from both observational and theoretical studies. The galaxy is assumed to have low specific angular momentum in analogy with the existing one-dimensional case in order to isolate the effect of dimensionality. The code then tracks the interaction of the outflowing radiation and winds with the galactic gas and their effects on regulating the accretion. After matching physical modeling to the extent possible between the one-dimensional and two-dimensional treatments, we find essentially similar results in terms of BH growth and duty cycle (fraction of the time above a given fraction of the Eddington luminosity). In the two-dimensional calculations, the cool shells forming at 0.1--1 kpc from the center are Rayleigh--Taylor unstable to fragmentation, leading to a somewhat higher accretion rate, less effective feedback, and a more irregular pattern of bursting compared to the one-dimensional case.Comment: 15 pages, 10 figures, ApJ 237:26. Updated to match published versio

Using penetration depth for phase matching in photonic crystal waveguides

A new method of design for the phase-matching in waveguides is suggested. The approach is based on utilizing the concept of the penetration depth of light into the waveguide walls. The lateral components of wavevectors are employed to adjust the phase-matching condition in the propagation direction. The method is demonstrated in two systems: one using single and the other using double photonic-crystal mirrors

Weak pairwise correlations imply strongly correlated network states in a neural population

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher order interactions among large groups of elements play an important role. In the vertebrate retina, we show that weak correlations between pairs of neurons coexist with strongly collective behavior in the responses of ten or more neurons. Surprisingly, we find that this collective behavior is described quantitatively by models that capture the observed pairwise correlations but assume no higher order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behavior. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.Comment: Full account of work presented at the conference on Computational and Systems Neuroscience (COSYNE), 17-20 March 2005, in Salt Lake City, Utah (http://cosyne.org

The polytropic approximation and X-ray scaling relations: constraints on gas and dark matter profiles for galaxy groups and clusters

We constrain gas and dark matter (DM) parameters of galaxy groups and clusters, by comparing X-ray scaling relations to theoretical expectations, obtained assuming that the gas is in hydrostatic equilibrium with the DM and follows a polytropic relation. We vary four parameters: the gas polytropic index Gamma, its temperature at large radii T_xi, the DM logarithmic slope at large radii zeta and its concentration c_vir. When comparing the model to the observed mass-temperature (M-T) relation of local clusters, our results are independent of both T_xi and c_vir. We thus obtain constraints on Gamma, by fixing the DM profile, and on zeta, by fixing the gas profile. For an NFW DM profile, we find that 6/5<Gamma<13/10, which is consistent with numerical simulations and observations of individual clusters. Taking 6/5<Gamma<13/10 allows the DM profile to be slightly steeper than the NFW profile at large radii. Upon including local groups, we constrain the mass-dependence of Gamma and the value of T_xi. Interestingly, with Gamma=6/5 and zeta=-3, we reproduce the observed steepening/breaking of the M-T relation at low M, if 10^6 K<T_xi<10^7 K, consistent with simulations and observations of the warm-hot intergalactic medium. When extrapolated to high redshift z, the model with a constant Gamma reproduces the expected self-similar behaviour. We also account for the observed, non-self-similar relations provided by some high-z clusters, as they provide constraints on the evolution of Gamma. Comparing our model to the observed luminosity-temperature relation, we discriminate between different M-c_vir relations: a weak dependence of c_vir on M is currently preferred by data. This simple theoretical model accounts for much of the complexity of recent, improved X-ray scaling relations, provided that we allow for a mild dependence of Gamma on M or for T_xi consistent with intercluster values. [abridged]Comment: 20 pages, 18 figures, 2 tables. Accepted for publication in MNRAS, with minor changes. Accepted version plus two typos corrected. Abstract abridged for astro-ph submissio