The spectral shift function and spectral flow

This paper extends Krein's spectral shift function theory to the setting of semifinite spectral triples. We define the spectral shift function under these hypotheses via Birman-Solomyak spectral averaging formula and show that it computes spectral flow.Comment: 47 page

Spinor Parallel Propagator and Green's Function in Maximally Symmetric Spaces

We introduce the spinor parallel propagator for maximally symmetric spaces in any dimension. Then, the Dirac spinor Green's functions in the maximally symmetric spaces R^n, S^n and H^n are calculated in terms of intrinsic geometric objects. The results are covariant and coordinate-independent.Comment: 7 page

Tracing the energetics and evolution of dust with Spitzer : a chapter in the history of the Eagle Nebula

Context. The Spitzer GLIMPSE and MIPSGAL surveys have revealed a wealth of details about the Galactic plane in the infrared (IR)with orders of magnitude higher sensitivity, higher resolution, and wider coverage than previous IR observations. The structure of the interstellar medium (ISM) is tightly connected to the countless star-forming regions. We use these surveys to study the energetics and dust properties of the Eagle Nebula (M16), one of the best known star-forming regions. Aims. We present MIPSGAL observations of M16 at 24 and 70 μm and combine them with previous IR data. The mid-IR image shows a shell inside the well-known molecular borders of the nebula, as in the ISO and MSX observations from 15 to 21 μm. The morphologies at 24 and 70 μm are quite different, and its color ratio is unusually warm. The far-IR image resembles the one at 8 μm that enhances the structure of the molecular cloud and the "pillars of creation". We use this set of IR data to analyze the dust energetics and properties within this template for Galactic star-forming regions. Methods. We measure IR spectral energy distributions (SEDs) across the entire nebula, both within the inner shell and the photodissociation regions (PDRs).We use the DUSTEM model to fit these SEDs and constrain the dust temperature, the dust-size distribution, and the radiation field intensity relative to that provided by the star cluster NGC 6611 (χ/χ0). Results. Within the PDRs, the inferred dust temperature (~35 K), the dust-size distribution, and the radiation field intensity (χ/χ0 < 1) are consistent with expectations. Within the inner shell, the dust is hotter (~70 K). Moreover, the radiation field required to fit the SED is larger than that provided by NGC 6611 (χ/χ0 > 1). We quantify two solutions to this problem: (1) The size distribution of the dust in the shell is not that of interstellar dust. There is a significant enhancement of the carbon dust-mass in stochastically heated very small grains. (2) The dust emission arises from a hot (~10^6 K) plasma where both UV and collisions with electrons contribute to the heating. Within this hypothesis, the shell SED may be fit for a plasma pressure p/k ~ 5 × 10^7 K cm^(−3). Conclusions. We suggest two interpretations for the M16 inner shell: (1) The shell matter is supplied by photo-evaporative flows arising from dense gas exposed to ionized radiation. The flows renew the shell matter as it is pushed out by the pressure from stellar winds. Within this scenario, we conclude that massive-star forming regions such as M16 have a major impact on the carbon dustsize distribution. The grinding of the carbon dust could result from shattering in grain-grain collisions within shocks driven by the dynamical interaction between the stellar winds and the shell. (2) We also consider a more speculative scenario where the shell is a supernova remnant. In this case, we would be witnessing a specific time in the evolution of the remnant where the plasma pressure and temperature would enable the remnant to cool through dust emission

Age, sex, adult and larval diet shape starvation resistance in the Mediterranean fruit fly: an ecological and gerontological perspective.

The ability of an animal to withstand periods of food deprivation is a key driver of invasion success (biodiversity), adaptation to new conditions, and a crucial determinant of senescence in populations. Starvation resistance (SR) is a highly plastic trait and varies in relation to environmental and genetic variables. However, beyond Drosophila, SR has been studied poorly. Exploiting an interesting model species in invasion and ageing studies-the Mediterranean fruit fly (Ceratitis capitata)- we investigated how age, food and gender, shape SR in this species. We measured SR in adults feeding in rich and poor dietary conditions, which had been reared either on natural hosts or artificial larval diet, for every single day across their lifespan. We defined which factor is the most significant determinant of SR and we explored potential links between SR and ageing. We found that SR declines with age, and that age-specific patterns are shaped in relation to adult and larval diet. Females exhibited higher SR than males. Age and adult diet were the most significant determinants of SR, followed by gender and the larval diet. Starvation resistance proved to be a weak predictor of functional ageing. Possible underlying mechanisms, ecological and gerontological significance and potential applied benefits are discussed

Gravity vs radiation model: on the importance of scale and heterogeneity in commuting flows

We test the recently introduced radiation model against the gravity model for the system composed of England and Wales, both for commuting patterns and for public transportation flows. The analysis is performed both at macroscopic scales, i.e. at the national scale, and at microscopic scales, i.e. at the city level. It is shown that the thermodynamic limit assumption for the original radiation model significantly underestimates the commuting flows for large cities. We then generalize the radiation model, introducing the correct normalisation factor for finite systems. We show that even if the gravity model has a better overall performance the parameter-free radiation model gives competitive results, especially for large scales.Comment: in press Phys. Rev. E, 201