Volatile opinions and optimal control of vaccine awareness campaigns: chaotic behaviour of the Forward-Backward Sweep algorithm vs heuristic direct optimization

In modern societies the main sources of information are Internet-based social networks. Thus, the opinion of citizens on key topics, such as vaccines, is very volatile. Here, we explore the impact of volatility on the modelling of public response to vaccine awareness campaigns for favouring vaccine uptake. We apply a quasi-steady-state approximation to the model of spread and control of Susceptible-Infected-Removed diseases proposed in (d’Onofrio et al., PLoS One, 2012). This allows us to infer and analyze a new behavioural epidemiology model that is nonlinear in the control. Then, we investigate the efficient design of vaccine awareness campaigns by adopting optimal control theory. The resulting problem has important issues: (i) the integrand of its objective functional is non-convex; (ii) the application of forward-backward sweep (FBS) and gradient descent algorithms in some key cases does not work; (iii) analytical approaches provide continuous solutions that cannot rigorously be implemented since Public Health interventions cannot be fully flexible. Thus, on the one hand, we resort to direct optimization of the objective functional via heuristic stochastic optimization, in particular via particle swarm optimization and differential evolution algorithms. On the other hand, we investigate the non-convergence of the FBS algorithm with tools of the statistical theory of nonlinear chaotic time-series. Finally, since the direct optimization algorithms are stochastic, we provide a statistical assessment of the obtained solutions

The evolution of the number density of compact galaxies

We compare the number density of compact (small size) massive galaxies at low and high redshift using our Padova Millennium Galaxy and Group Catalogue (PM2GC) at z=0.03-0.11 and the CANDELS results from Barro et al. (2013) at z=1-2. The number density of local compact galaxies with luminosity weighted (LW) ages compatible with being already passive at high redshift is compared with the density of compact passive galaxies observed at high-z. Our results place an upper limit of a factor ~2 to the evolution of the number density and are inconsistent with a significant size evolution for most of the compact galaxies observed at high-z. The evolution may be instead significant (up to a factor 5) for the most extreme, ultracompact galaxies. Considering all compact galaxies, regardless of LW age and star formation activity, a minority of local compact galaxies (<=1/3) might have formed at z<1. Finally, we show that the secular decrease of the galaxy stellar mass due to simple stellar evolution may in some cases be a non-negligible factor in the context of the evolution of the mass-size relation, and we caution that passive evolution in mass should be taken into account when comparing samples at different redshifts.Comment: ApJ in pres

Duality and o-O structure in non reflexive banach spaces

Let E be a Banach space with a supremum type norm induced by a collection of functionals L ⊂ X∗where X is a reflexive Banach space. Familiar spaces of this type are BMO, BV, C0,α(0 &lt; α &lt; 1), Lq,∞, for q &gt; 1. For most of these spaces E, the predual E∗ exists and can be defined by atomic decomposition of its elements. Another typical result, when it is possible to define a rich vanishing subspace E0⊂ E is the "two star theorem ", namely (E0)∗ = E∗. This fails for E = BV and E =C0,1= Lip

Optimal Public Health intervention in a behavioural vaccination model: the interplay between seasonality, behaviour and latency period

Hesitancy and refusal of vaccines preventing childhood diseases are spreading due to ‘pseudo-rational’ behaviours: parents overweigh real and imaginary side effects of vaccines. Nonetheless, the ‘Public Health System’ (PHS) may enact public campaigns to favour vaccine uptake. To determine the optimal time profiles for such campaigns, we apply the optimal control theory to an extension of the susceptible-infectious-removed (SIR)-based behavioural vaccination model by d’Onofrio et al. (2012, PLoS ONE, 7, e45653). The new model is of susceptible-exposed-infectious-removed (SEIR) type under seasonal fluctuations of the transmission rate. Our objective is to minimize the total costs of the disease: the disease burden, the vaccination costs and a less usual cost: the economic burden to enact the PHS campaigns. We apply the Pontryagin minimum principle and numerically explore the impact of seasonality, human behaviour and latency rate on the control and spread of the target disease. We focus on two noteworthy case studies: the low (resp. intermediate) relative perceived risk of vaccine side effects and relatively low (resp. very low) speed of imitation. One general result is that seasonality may produce a remarkable impact on PHS campaigns aimed at controlling, via an increase of the vaccination uptake, the spread of a target infectious disease. In particular, a higher amplitude of the seasonal variation produces a higher effort and this, in turn, beneficially impacts the induced vaccine uptake since the larger is the strength of seasonality, the longer the vaccine propensity remains large. However, such increased effort is not able to fully compensate the action of seasonality on the prevalence

Planktic foraminiferal response to early Eocene carbon cycle perturbations in the southeast Atlantic Ocean (ODP Site 1263)

At low latitude locations in the northern hemisphere, striking changes in the relative abundances and diversity of the two dominant planktic foraminifera genera, Morozovella and Acarinina, are known to have occurred close to the Early Eocene Climatic Optimum (EECO; ~ 49–53 Ma). Lower Eocene carbonate-rich sediments at Ocean Drilling Program (ODP) Site 1263 were deposited on a bathymetric high (Walvis Ridge) at ~ 40° S, and afford an opportunity to examine such planktic foraminiferal assemblage changes in a temperate southern hemisphere setting. We present here quantified counts of early Eocene planktic foraminiferal assemblages from Hole 1263B, along with bulk sediment stable isotope analyses and proxy measurements for carbonate dissolution. The bulk sediment δ13C record at Site 1263 resembles similar records generated elsewhere, such that known and inferred hyperthermal events can be readily identified. Although some carbonate dissolution has occurred, the well-preserved planktic foraminiferal assemblages mostly represent primary changes in environmental conditions. Our results document the permanent decrease in Morozovella abundance and increase in Acarinina abundance at the beginning of the EECO, although this switch occurred ~ 165 kyr after that at low-latitude northern hemisphere locations. This suggests that unfavourable environmental conditions for morozovellids at the start of the EECO, such as sustained passage of a temperature threshold or other changes in surface waters, occurred at lower latitudes first. The remarkable turnover from Morozovella to Acarinina was widely geographically widespread, although the causal mechanism remains elusive. In addition, at Site 1263, we document the virtual disappearance within the EECO of the biserial chiloguembelinids, commonly considered as inhabiting intermediate water depths, and a reduction in abundance of the thermocline-dwelling subbotinids. We interpret these changes as signals of subsurface water properties, perhaps warming, and the associated contraction of ecological niches

Dextral to sinistral coiling switch in planktic foraminifer Morozovella during the Early Eocene Climatic Optimum

Coiling direction is a basic characteristic of trochospiral planktic foraminifera. Modifications in the coiling direction within ancient planktic foraminiferal populations may reflect important changes in evolution or environment, yet they remain scarcely discussed. Here we investigate fluctuations in the coiling direction within Morozovella assemblages from sections that span the interval of peak Cenozoic warmth, the Early Eocene Climatic Optimum (EECO; ~53-49 million years ago, Ma), at Atlantic Ocean Drilling Program (ODP) sites 1051, 1258 and 1263. The surface-dwelling genus Morozovella is of particular interest because it dominated tropical-subtropical early Paleogene assemblages then suffered an abrupt and permanent decline in abundance and taxonomic diversity at the start of the EECO. At all ODP sites, morozovellids display a dominant dextral coiling preference during the interval preceding the EECO. However, all the Morozovella species at all sites modify their coiling from preferentially dextral to sinistral coiling within the EECO < 200 kyr after the K/X event (~52.8 Ma), providing a new biostratigraphic tool for correlation. We also document that before the major shift in morozovellid coiling, transient excursions to higher abundances of sinistral tests occurred in conjunction with negative carbon isotope excursions. Significantly, carbon isotope data reveal that sinistral morphotypes belonging to the same morphospecies typically have lower 13C values. The dominance of sinistral morphotypes, at the expense of dextral forms within the EECO, coupled with the lower 13C signatures of the former, suggests that the sinistral forms were less dependent on their photosymbiotic partnerships and thus able to adapt more readily to paleoceanographic change at the EECO. The observed sinistral and dextral coiling of morozovellids can be a genetically heritable characteristic that lies within cryptic speciation across multiple morphologically defined species. Alternatively the coiling changes were exclusively ecophenotypic responses whereby different species were able to preferentially adopt sinistral coiling in reaction to the changed conditions in the mixed-layer during the EECO. Previous interpretations of coiling flips in planktic foraminifera in the early Eocene, especially including morozovellids, have favoured a genetic explanation rather than an ecological response. Our present data cannot validate or disprove this idea, but should stimulate renewed thought on the matter

Orlicz regularity of the gradient of solutions to quasilinear elliptic equations in the plane

Given a planar domain Omega, we study the Dirichlet problem {-divA(x, del v) = f in Omega, v = 0 on partial derivative Omega, where the higher-order term is a quasilinear elliptic operator, and f belongs to the Zygmund space L(log L)delta(log log log L)(beta/2) (Omega) with beta >= 0 and delta >= 1/2. We prove that the gradient of the variational solution v is an element of W-0(1,2) (Omega) belongs to the space L-2(log L)(2 delta-1)(log log log L)(beta)(Omega)

Physiological changes induced by either pre- or post-veraison deficit irrigation in 'Merlot' vines grafted on two different rootstocks

Reduced summer precipitations and higher evapotranspiration due to elevated temperatures are expected to enhance the impact of water deficit in modern viticulture. We investigated the effect of the timing of deficit irrigation on vine growth, water relations, yield and grape composition in 'Merlot' vines grafted on 1103P or SO4. In both years we did not measure any differences between rootstocks in stem water potential (SWP). Vegetative growth was decreased by the restriction of irrigation between fruit set and veraison. Stomatal conductance (gs) was affected by irrigation, but not by the rootstock. During the pre-veraison period there was a clear inverse relationship between gs and SWP. The leaf non photochemical quenching readily responded to the stress imposed on 1103P rootstock. Vines subjected to water deficit between fruit set and veraison produced smaller berries than well irrigated ones, whereas deficit applied after veraison determined about 10 % differences in berry weight. The highest and lowest values of pH and TA were measured in berries from pre-veraison deficit irrigated vines grafted on both 1103P and SO4, respectively

A New Approach to the Study of Stellar Populations in Early-Type Galaxies: K-band Spectral Indices and an Application to the Fornax Cluster

New measurements of K-band spectral features are presented for eleven early-type galaxies in the nearby Fornax galaxy cluster. Based on these measurements, the following conclusions have been reached: (1) in galaxies with no signatures of a young stellar component, the K-band Na I index is highly correlated with both the optical metallicity indicator [MgFe]' and central velocity dispersion; (2) in the same galaxies, the K-band Fe features saturate in galaxies with sigma > 150 km/s while Na I (and [MgFe]') continues to increase; (3) [Si/Fe] (and possibly [Na/Fe]) is larger in all observed Fornax galaxies than in Galactic open clusters with near-solar metallicity; (4) in various near-IR diagnostic diagrams, galaxies with signatures of a young stellar component (strong Hbeta, weak [MgFe]') are clearly separated from galaxies with purely old stellar populations; furthermore, this separation is consistent with the presence of an increased number of M-giant stars (most likely to be thermally pulsating AGB stars); (5) the near-IR diagrams discussed here seem as efficient for detecting putatively young stellar components in early-type galaxies as the more commonly used age/metallicity diagnostic plots using optical indices (e.g Hbeta vs. [MgFe]').Comment: 47 pages, 16 figures, ApJ accepte