Given a linear self-adjoint differential operator
L
along with a discretization scheme (like Finite Differences, Finite Elements, Galerkin Isogeometric Analysis, etc.), in many numerical applications ...it is crucial to understand how good the (relative) approximation of the whole spectrum of the discretized operator
L
(
n
)
is, compared to the spectrum of the continuous operator
L
. The theory of Generalized Locally Toeplitz sequences allows to compute the spectral symbol function
ω
associated to the discrete matrix
L
(
n
)
. Inspired by a recent work by T. J. R. Hughes and coauthors, we prove that the symbol
ω
can measure, asymptotically, the maximum spectral relative error
E
≥
0
. It measures how the scheme is far from a good relative approximation of the whole spectrum of
L
, and it suggests a suitable (possibly non-uniform) grid such that, if coupled to an increasing refinement of the order of accuracy of the scheme, guarantees
E
=
0
.
Abstract
In order to be efficient, spectroscopic galaxy redshift surveys do not obtain redshifts for all galaxies in the population targeted. The missing galaxies are often clustered, commonly ...leading to a lower proportion of successful observations in dense regions. One example is the close-pair issue for SDSS spectroscopic galaxy surveys, which have a deficit of pairs of observed galaxies with angular separation closer than the hardware limit on placing neighbouring fibres. Spatially clustered missing observations will exist in the next generations of surveys. Various schemes have previously been suggested to mitigate these effects, but none works for all situations. We argue that the solution is to link the missing galaxies to those observed with statistically equivalent clustering properties, and that the best way to do this is to rerun the targeting algorithm, varying the angular position of the observations. Provided that every pair has a non-zero probability of being observed in one realization of the algorithm, then a pair-upweighting scheme linking targets to successful observations, can correct these issues. We present such a scheme, and demonstrate its validity using realizations of an idealized simple survey strategy.
Observed galaxy clustering exhibits local transverse statistical isotropy around the line of sight (LOS). The variation of the LOS across a galaxy survey complicates the measurement of the observed ...clustering as a function of the angle to the LOS, as fast Fourier transforms (FFTs) based on Cartesian grids, cannot individually allow for this. Recent advances in methodology for calculating LOS-dependent clustering in Fourier space include the realization that power spectrum LOS-dependent moments can be constructed from sums over galaxies, based on approximating the LOS to each pair of galaxies by the LOS to one of them. We show that we can implement this method using multiple FFTs, each measuring the LOS-weighted clustering along different axes. The Nlog N nature of FFTs means that the computational speed-up is a factor of >1000 compared with summing over galaxies. This development should be beneficial for future projects such as DESI and Euclid which will provide an order of magnitude more galaxies than current surveys.
Since the World Health Organization (WHO) declared the coronavirus infectious disease 2019 (COVID-19) outbreak a pandemic on 11 March, severe lockdown measures have been adopted by the Italian ...Government. For over two months of stay-at-home orders, houses became the only place where people slept, ate, worked, practiced sports, and socialized. As consolidated evidence exists on housing as a determinant of health, it is of great interest to explore the impact that COVID-19 response-related lockdown measures have had on mental health and well-being. We conducted a large web-based survey on 8177 students from a university institute in Milan, Northern Italy, one of the regions most heavily hit by the pandemic in Europe. As emerged from our analysis, poor housing is associated with increased risk of depressive symptoms during lockdown. In particular, living in apartments <60 m
with poor views and scarce indoor quality is associated with, respectively, 1.31 (95% CI: 1046-1637), 1.368 (95% CI: 1166-1605), and 2.253 (95% CI: 1918-2647) times the risk of moderate-severe and severe depressive symptoms. Subjects reporting worsened working performance from home were over four times more likely to also report depression (OR = 4.28, 95% CI: 3713-4924). Housing design strategies should focus on larger and more livable living spaces facing green areas. We argue that a strengthened multi-interdisciplinary approach, involving urban planning, public mental health, environmental health, epidemiology, and sociology, is needed to investigate the effects of the built environment on mental health, so as to inform welfare and housing policies centered on population well-being.
We construct exhaustion and cut-off functions with controlled gradient and Laplacian on manifolds with Ricci curvature bounded from below by a (possibly unbounded) nonpositive function of the ...distance from a fixed reference point, without any assumptions on the topology or the injectivity radius. Along the way we prove a generalization of the Li-Yau gradient estimate which is of independent interest. We then apply our cut-offs to the study of the fast and porous media diffusion, of
L
q
-properties of the gradient and of the self-adjointness of Schrödinger-type operators.
Plants respond to drought stress through different physiological mechanisms. To highlight a specific adaptation strategy related to stem photosynthetic activity, woody tissue pigmentation was ...studied. In this work, 25
Vitis
hybrids were studied in two experimental vineyards: one of them with sufficient water availability and the other showing drought stress. 1500 reflectance spectra of woody tissues were collected. Beside the spectral elaboration and interpretation, indexes for the pigment quantification were calculated. The content and the proportion in chlorophylls (
a
and
b
) in stems were significantly modified in response to water stress. Genotypes were classified based on their plasticity/elasticity and adaptive/susceptible behavior. The cluster analysis produced 4 main groups based on their average spectra and on the spectral variations between watered and stress conditions. The most interesting genotypes concerning this trait were pointed out. Nevertheless, this adaptation mechanism could also be due to an increased detoxification necessity related to other physiological disfunctions caused by water stress. A multi-parameter approach is encouraged for phenotyping of abiotic stress tolerant plant selection. In the next future, this work will support the release of new drought tolerant rootstocks for viticulture.
Modifications of the equations of general relativity at large distances offer one possibility to explain the observed properties of our Universe without invoking a cosmological constant. Numerous ...proposals for such modified gravity cosmologies exist, but often their consequences for structure formation in the non-linear sector are not yet accurately known. In this work, we employ high-resolution numerical simulations of f (R)-gravity models coupled with a semi-analytic model (SAM) for galaxy formation to obtain detailed predictions for the evolution of galaxy properties. The f (R)-gravity models imply the existence of a 'fifth-force', which is however locally suppressed, preserving the successes of general relativity on Solar system scales. We show that dark matter haloes in f (R)-gravity models are characterized by a modified virial scaling with respect to the Λ cold dark matter (ΛCDM ) scenario, reflecting a higher dark matter velocity dispersion at a given mass. This effect is taken into account in the SAM by an appropriate modification of the mass-temperature relation. We find that the statistical properties predicted for galaxies (such as the stellar mass function and the cosmic star formation rate) in f (R)-gravity show generally only very small differences relative to ΛCDM, smaller than the dispersion between the results of different SAM models, which can be viewed as a measure of their systematic uncertainty. We also demonstrate that galaxy bias is not able to disentangle between f (R)-gravity and the standard cosmological scenario. However, f (R)-gravity imprints modifications in the linear growth rate of cosmic structures at large scale, which can be recovered from the statistical properties of large galaxy samples.
The production and quality of grapes are determined by the hydric and nutritional status of the vine. In modern viticulture, the interface between grapevine and soil is represented by the rootstock, ...which modulates the uptake of water and nutrients. Thus, selection of new rootstocks for abiotic stress tolerance represents an adaptation strategy for viticulture to the new environmental conditions imposed by climate change. The aim of this work is to evaluate the water-use efficiency (WUE) and the nutritional status of a selection of 30 new rootstock genotypes, originating from several breeding programs. WUE and gas exchange were measured for each genotype in two environments characterized by different water availability, and the levels of N, P, K, Mg, Ca, Na, Fe, Mn, and Zn in the leaf blades were determined during the phenological stages of flowering and ripening. Water availability was different in the two environments, affecting gas exchange, with mean values of carbon assimilation of 10.43 ± 0.32 and 3.84 ± 0.34 µmol CO2 m−2 s−1, respectively. Genotypes were classified according to their water stress tolerance, vigor, and affinity for macronutrients and micronutrients. A total of 14 genotypes showed tolerance to water stress, and 10 of them reported high vigor and carbon assimilation. Furthermore, the majority of water-stress-tolerant genotypes had greater affinity for Mg than for K. In further studies, the most promising rootstocks will be evaluated in grafting combination with Vitis vinifera.
We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solutions on any graph. ...For changing sign integrable data, we show existence and uniqueness under extra assumptions such as local finiteness or a uniform lower bound on the node measure.
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