Products of Compartmental Models in Epidemiology.

We show that many structured epidemic models may be described using a straightforward product structure in this paper. Such products, derived from products of directed graphs, may represent useful refinements including geographic and demographic structure, age structure, gender, risk groups, or immunity status. Extension to multistrain dynamics, that is, pathogen heterogeneity, is also shown to be feasible in this framework. Systematic use of such products may aid in model development and exploration, can yield insight, and could form the basis of a systematic approach to numerical structural sensitivity analysis

Free Unstable Modes and Massive Bodies in Saturn's Outer B Ring

Voyager images and Cassini occultation data have previously shown that the behavior of the outer edge of Saturn's massive B ring is determined only in part by a static response to the 2:1 inner Lindblad resonance with Mimas. In Cassini images of this region, we find, in addition to the expected wavenumber-2 forced distortion, evidence for unforced self-excited wavenumber-3, wavenumber-2, and wavenumber-1 normal modes. These are the first observations to suggest substantial wave amplification in Saturn's broad rings. Moreover, the presence of these free modes strongly implicates viscous overstability as their underlying cause and, by inference, the cause for most if not all of the unforced structures throughout the high-mass-density B ring and in other high-mass-density regions in Saturn's rings. Analysis of each of the inferred waves reveals a consistent lower bound on the average surface mass density of ~ 44 g/cm^2 for the outer 250 km of the ring, though the true surface density could be as high as 100 g/cm^2 or higher. Interference between the forced and free wavenumber-2 modes yields a total wavenumber-2 pattern that varies in amplitude and orientation with a characteristic period of ~ 5.5 years. We also find localized disturbances, including 3.5-km-tall vertical structures, that provide circumstantial evidence for embedded massive bodies in the Mimas resonance zone. The presence of such bodies is supported by the presence of a shadow-casting moonlet ~ 0.3 km wide near the ring's edge.Comment: 38 pages, 6 figure

Using Jet Observations to Constrain Enceladus' Rotation State

Observations of Enceladus have revealed active jets of material erupting from cracks on its surface. It has been proposed that diurnal tidal stress may open these cracks daily when they experience tensile stresses across them, allowing eruptions to occur. An analysis of the tidal stress on jet source regions, as identified by the triangulation of jet observations, finds that there is a correlation between observations and tensile stress on the cracks. However, not all regions are predicted to be in tension when jets were observed to be active. Enceladus' rotation state, such as a physical libration or obliquity, will affect the diurnal stresses on these cracks, changing when in its orbit they experience tension and compression. We will use observations of jet activity from 2005-2007 to place constraints on rotation states of Enceladus

Shepherding of the Uranian rings. I. Kinematics

We identify several orbital resonances involving the newly discovered satellites, 1986U7 and 1986U8, and the Uranian rings. The most important resonances in eccentric rings are known as eccentric reson­ances and are generalizations of the more familiar Lindblad resonances. In keeping with the notation established for Lindblad resonances, we distinguish inner and outer eccentric resonances by the symbols IER and OER. We show that by reducing the absolute radius scale of the Uranian ring system by 0.0124% the 24:25 OER of 1986U7 and the 14:13 IER of 1986U8 fall at the inner and outer edges of the Є ring. The same scale change also brings the 23:22 IER of 1986U7 into coincidence with the outer edge of the δ ring and the 6:5 IER of 1986U8 close to the center of the γ ring. Furthermore, adopting the latest Voyager value of GM_u and our reduced radius scale, we find that the pattern speed of the m = 2 distortion in the δ ring corresponds to that expected for a normal mode excited either by an internal viscous overstability or parametrically by shepherd satellites. These kinematic results make a compel­ ling case for our proposed reduction in the ring radius scale and also imply that 1986U7 and 1986U8 are the inner and outer shepherds for the Є ring, that 1986U7 is the outer shepherd for the δ ring, and that 1986U8 is an outer shepherd for the γ ring

Cassini Imaging Science: Initial Results on Saturn's Atmosphere

The Cassini Imaging Science Subsystem (ISS) began observing Saturn in early February 2004. From analysis of cloud motions through early October 2004, we report vertical wind shear in Saturn's equatorial jet and a maximum wind speed of ∼375 meters per second, a value that differs from both Hubble Space Telescope and Voyager values. We also report a particularly active narrow southern mid-latitude region in which dark ovals are observed both to merge with each other and to arise from the eruptions of large, bright storms. Bright storm eruptions are correlated with Saturn's electrostatic discharges, which are thought to originate from lightning

Agreement of Anterior Segment Parameters Obtained From Swept-Source Fourier-Domain and Time-Domain Anterior Segment Optical Coherence Tomography.

PurposeTo assess the interdevice agreement between swept-source Fourier-domain and time-domain anterior segment optical coherence tomography (AS-OCT).MethodsFifty-three eyes from 41 subjects underwent CASIA2 and Visante OCT imaging. One hundred eighty-degree axis images were measured with the built-in two-dimensional analysis software for the swept-source Fourier-domain AS-OCT (CASIA2) and a customized program for the time-domain AS-OCT (Visante OCT). In both devices, we examined the angle opening distance (AOD), trabecular iris space area (TISA), angle recess area (ARA), anterior chamber depth (ACD), anterior chamber width (ACW), and lens vault (LV). Bland-Altman plots and intraclass correlation (ICC) were performed. Orthogonal linear regression assessed any proportional bias.ResultsICC showed strong correlation for LV (0.925) and ACD (0.992) and moderate agreement for ACW (0.801). ICC suggested good agreement for all angle parameters (0.771-0.878) except temporal AOD500 (0.743) and ARA750 (nasal 0.481; temporal 0.481). There was a proportional bias in nasal ARA750 (slope 2.44, 95% confidence interval [CI]: 1.95-3.18), temporal ARA750 (slope 2.57, 95% CI: 2.04-3.40), and nasal TISA500 (slope 1.30, 95% CI: 1.12-1.54). Bland-Altman plots demonstrated in all measured parameters a minimal mean difference between the two devices (-0.089 to 0.063); however, evidence of constant bias was found in nasal AOD250, nasal AOD500, nasal AOD750, nasal ARA750, temporal AOD500, temporal AOD750, temporal ARA750, and ACD. Among the parameters with constant biases, CASIA2 tends to give the larger numbers.ConclusionsBoth devices had generally good agreement. However, there were proportional and constant biases in most angle parameters. Thus, it is not recommended that values be used interchangeably

The effect of treatment on pathogen virulence.

The optimal virulence of a pathogen is determined by a trade-off between maximizing the rate of transmission and maximizing the duration of infectivity. Treatment measures such as curative therapy and case isolation exert selective pressure by reducing the duration of infectivity, reducing the value of duration-increasing strategies to the pathogen and favoring pathogen strategies that maximize the rate of transmission. We extend the trade-off models of previous authors, and represents the reproduction number of the pathogen as a function of the transmissibility, host contact rate, disease-induced mortality, recovery rate, and treatment rate, each of which may be influenced by the virulence. We find that when virulence is subject to a transmissibility-mortality trade-off, treatment can lead to an increase in optimal virulence, but that in other scenarios (such as the activity-recovery trade-off) treatment decreases the optimal virulence. Paradoxically, when levels of treatment rise with pathogen virulence, increasing control efforts may raise predicted levels of optimal virulence. Thus we show that conflict can arise between the epidemiological benefits of treatment and the evolutionary risks of heightened virulence