9,114 research outputs found
Euler Obstruction and Defects of Functions on Singular Varieties
Several authors have proved Lefschetz type formulae for the local Euler
obstruction. In particular, a result of this type is proved in [BLS].The
formula proved in that paper turns out to be equivalent to saying that the
local Euler obstruction, as a constructible function, satisfies the local Euler
condition (in bivariant theory) with respect to general linear forms.
The purpose of this work is to understand what prevents the local Euler
obstruction of satisfying the local Euler condition with respect to functions
which are singular at the considered point. This is measured by an invariant
(or ``defect'') of such functions that we define below. We give an
interpretation of this defect in terms of vanishing cycles, which allows us to
calculate it algebraically. When the function has an isolated singularity, our
invariant can be defined geometrically, via obstruction theory. We notice that
this invariant unifies the usual concepts of {\it the Milnor number} of a
function and of the {\it local Euler obstruction} of an analytic set.Comment: 18 page
The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
Let be a Hilbert space. Given a bounded positive definite
operator on , and a bounded sequence of non negative real numbers, the pair is
frame admissible, if there exists a frame on
with frame operator , such that , . We relate the existence of such frames with the Schur-Horn
theorem of majorization, and give a reformulation of the extended version of
Schur-Horn theorem, due to A. Neumann. We use it to get necessary conditions
(and to generalize known sufficient conditions) for a pair ,
to be frame admissible.Comment: To appear in Illinois Journal of Mat
Hemiparasitic plant impacts animal and plant communities across four trophic levels
1.Understanding the impact of species on community structure is a fundamental question in ecology. There is a growing body of evidence that suggests that both sub-dominant species and parasites can have a disproportionately large impact.
2.Here we report the impacts of an organism that is both subdominant and parasitic, the hemiparasite Rhinanthus minor. Whilst the impact of parasitic angiosperms on their hosts and, to a lesser degree, co-existing plant species, have been well characterized, much less is known about their impacts on higher trophic levels.
3.We experimentally manipulated field densities of the hemiparasite Rhinanthus minor in a species rich grassland, comparing the plant and invertebrate communities in plots where it was removed, at natural densities or at enhanced densities.
4.Plots with natural and enhanced densities of R. minor had lower plant biomass than plots without the hemiparasite, but enhanced densities almost doubled the abundance of invertebrates within the plots across all trophic levels, with effects evident in herbivores, predators and detritivores.
5.The hemiparasite R. minor, despite being a sub-dominant and transient component within plant communities that it inhabits, has profound effects on four different trophic levels. These effects persist beyond the life of the hemiparasite,
emphasizing its role as a keystone species in grassland communitie
MERLIN radio detection of an interaction zone within a binary Orion proplyd system
Presented here are high angular resolution MERLIN 5 GHz (6 cm) continuum
observations of the binary proplyd system, LV 1 in the Orion nebula, which
consists of proplyd 168--326SE and its binary proplyd companion 168--326NW
(separation 0.4 arcsec). Accurate astrometric alignment allows a detailed
comparison between these data and published HST PC Halpha and [Oiii] images.
Thermal radio sources coincide with the two proplyds and originate in the
ionized photoevaporating flows seen in the optical emission lines. Flow
velocities of approx 50 km/s from the ionized proplyd surfaces and \geq 100
km/s from a possible micro-jet have been detected using the Manchester Echelle
spectrometer.
A third radio source is found to coincide with a region of extended, high
excitation, optical line emission that lies between the binary proplyds
168--326SE/326NW . This is modelled as a bowshock due to the collision of the
photoevaporating flows from the two proplyds. Both a thermal and a non-thermal
origin for the radio emission in this collision zone are considered.Comment: 23 pages, 9 figures, accepted by Ap
Massive runaway stars in the Small Magellanic Cloud
Using archival Spitzer Space Telescope data, we identified for the first time
a dozen runaway OB stars in the Small Magellanic Cloud (SMC) through the
detection of their bow shocks. The geometry of detected bow shocks allows us to
infer the direction of motion of the associated stars and to determine their
possible parent clusters and associations. One of the identified runaway stars,
AzV 471, was already known as a high-velocity star on the basis of its high
peculiar radial velocity, which is offset by ~40 km/s from the local systemic
velocity. We discuss implications of our findings for the problem of the origin
of field OB stars. Several of the bow shock-producing stars are found in the
confines of associations, suggesting that these may be "alien" stars
contributing to the age spread observed for some young stellar systems. We also
report the discovery of a kidney-shaped nebula attached to the early WN-type
star SMC-WR3 (AzV 60a). We interpreted this nebula as an interstellar structure
created owing to the interaction between the stellar wind and the ambient
interstellar medium.Comment: Accepted by A&
The impact of mass-loss on the evolution and pre-supernova properties of red supergiants
The post main-sequence evolution of massive stars is very sensitive to many
parameters of the stellar models. Key parameters are the mixing processes, the
metallicity, the mass-loss rate and the effect of a close companion. We study
how the red supergiant lifetimes, the tracks in the Hertzsprung-Russel diagram
(HRD), the positions in this diagram of the pre-supernova progenitor as well as
the structure of the stars at that time change for various mass-loss rates
during the red supergiant phase (RSG), and for two different initial rotation
velocities. The surface abundances of RSGs are much more sensitive to rotation
than to the mass-loss rates during that phase. A change of the RSG mass-loss
rate has a strong impact on the RSG lifetimes and therefore on the luminosity
function of RSGs. At solar metallicity, the enhanced mass-loss rate models do
produce significant changes on the populations of blue, yellow and red
supergiants. When extended blue loops or blue ward excursions are produced by
enhanced mass-loss, the models predict that a majority of blue (yellow)
supergiants are post RSG objects. These post RSG stars are predicted to show
much smaller surface rotational velocities than similar blue supergiants on
their first crossing of the HR gap. The position in the HRD of the end point of
the evolution depends on the mass of the hydrogen envelope. More precisely,
whenever, at the pre-supernova stage, the H-rich envelope contains more than
about 5\% of the initial mass, the star is a red supergiant, and whenever the
H-rich envelope contains less than 1\% of the total mass the star is a blue
supergiant. For intermediate situations, intermediate colors/effective
temperatures are obtained. Yellow progenitors for core collapse supernovae can
be explained by the enhanced mass-loss rate models, while the red progenitors
are better fitted by the standard mass-loss rate models.Comment: 19 pages, 11 figures, 6 tables, accepted for publication in Astronomy
and Astrophysic
Overcoming Algorithm Aversion: People will Use Imperfect Algorithms If They Can (Even Slightly) Modify Them
Although evidence-based algorithms consistently outperform human forecasters, people often fail to use them after learning that they are imperfect, a phenomenon known as algorithm aversion. In this paper, we present three studies investigating how to reduce algorithm aversion. In incentivized forecasting tasks, participants chose between using their own forecasts or those of an algorithm that was built by experts. Participants were considerably more likely to choose to use an imperfect algorithm when they could modify its forecasts, and they performed better as a result. Notably, the preference for modifiable algorithms held even when participants were severely restricted in the modifications they could make (Stuides 1-3). In fact, our results suggest that participants\u27 preference for modifiable algorithms was indicative of a desire for some control over the forecasting outcome, and not for a desire for greater control over the forecasting outcome, as participants\u27 preference for modifiable was relatively insensitive to the magnitude of the modifications they were able to make (Study 2). Additionally, we found that giving participants the freedom to modify an imperfect algorithm made them feel more satisfied with the forecasting process, more likely to believe that the algorithm was superior, and more likely to choose to use an algorithm to make subsequent forecasts (Study 3). This research suggests that one can reduce algorithm aversion by giving people some control—even a slight amount—over an imperfect algorithm\u27s forecast
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