130 research outputs found
Triaxial collapse and virialisation of dark-matter haloes
We reconsider the ellipsoidal-collapse model and extend it in two ways: We
modify the treatment of the external gravitational shear field, introducing a
hybrid model in between linear and non-linear evolution, and we introduce a
virialisation criterion derived from the tensor virial theorem to replace the
ad-hoc criterion employed so far. We compute the collapse parameters delta_c
and Delta_v and find that they increase with ellipticity e and decrease with
prolaticity p. We marginalise them over the appropriate distribution of e and p
and show the marginalised results as functions of halo mass and virialisation
redshift. While the hybrid model for the external shear gives results very
similar to those obtained from the non-linear model, ellipsoidal collapse
changes the collapse parameters typically by (20...50)%, in a way increasing
with decreasing halo mass and decreasing virialisation redshift. We
qualitatively confirm the dependence on mass and virialisation redshift of a
fitting formula for delta_c, but find noticeable quantitative differences in
particular at low mass and high redshift. The derived mass function is in good
agreement with mass functions recently proposed in the literature.Comment: 9 pages, 9 figures, published in Astronomy and Astrophysics; slight
modifications to match the published versio
中央銀行行動と東アジア地域の政治経済分析 : 金融政策の主権と独立性
公共政策プログラム / Public Policy Program政策研究大学院大学 / National Graduate Institute for Policy Studies論文審査委員: 吉野 直行(主査), CHEY Hyoung-kyu, LEON-GONZALEZ, Roberto, 園部 哲史, 藤原 一平(慶應義塾大学大学院経済学研究科 教授
Constraints on and from the potential-based cluster temperature function
The abundance of galaxy clusters is in principle a powerful tool to constrain
cosmological parameters, especially and , due to
the exponential dependence in the high-mass regime. While the best observables
are the X-ray temperature and luminosity, the abundance of galaxy clusters,
however, is conventionally predicted as a function of mass. Hence, the
intrinsic scatter and the uncertainties in the scaling relations between mass
and either temperature or luminosity lower the reliability of galaxy clusters
to constrain cosmological parameters. In this article, we further refine the
X-ray temperature function for galaxy clusters by Angrick et al., which is
based on the statistics of perturbations in the cosmic gravitational potential
and proposed to replace the classical mass-based temperature function, by
including a refined analytic merger model and compare the theoretical
prediction to results from a cosmological hydrodynamical simulation. Although
we find already a good agreement if we compare with a cluster temperature
function based on the mass-weighted temperature, including a redshift-dependent
scaling between mass-based and spectroscopic temperature yields even better
agreement between theoretical model and numerical results. As a proof of
concept, incorporating this additional scaling in our model, we constrain the
cosmological parameters and from an X-ray sample
of galaxy clusters and tentatively find agreement with the recent cosmic
microwave background based results from the Planck mission at 1-level.Comment: 10 pages, 5 figures, 2 tables; accepted by MNRAS; some typos
correcte
On the derivation of an X-ray temperature function without reference to mass and the prediction of weak-lensing number counts from the statistics of Gaussian random fields
We present a novel approach for the derivation of the X-ray temperature function for galaxy clusters, which is based on the statistics of Gaussian random fields applied to the cosmic gravitational potential. It invokes only locally defined quantities so that no reference to the cluster's mass is made. To relate linear and non-linear potential and to take into account only structures that have collapsed, we include either spherical- or ellipsoidal-collapse dynamics and compare both resulting models to temperature functions derived from a numerical simulation. Since deviations from the theoretical prediction are found in the simulation for high redshifts, we develop an analytic model to include the effects of mergers in our formalism. We jointly determine the cosmological parameters Omega_m0 and sigma_8 from two different cluster samples for different temperature definitions and find good agreement with constraints from WMAP5. Introducing theoretically a refined detection definition based on the upcrossing criterion, we reformulate our analytic approach for 2D and use it to predict the number density of spurious detections caused by large-scale structure and shot noise in filtered weak-lensing convergence maps. Agreement with a numerical simulation is found at the expected level
Statistics of gravitational potential perturbations: A novel approach to deriving the X-ray temperature function
Context. While the halo mass function is theoretically a very sensitive
measure of cosmological models, masses of dark-matter halos are poorly defined,
global, and unobservable quantities.
Aims. We argue that local, observable quantities such as the X-ray
temperatures of galaxy clusters can be directly compared to theoretical
predictions without invoking masses. We derive the X-ray temperature function
directly from the statistics of Gaussian random fluctuations in the
gravitational potential.
Methods. We derive the abundance of potential minima constrained by the
requirement that they belong to linearly collapsed structures. We then use the
spherical-collapse model to relate linear to non-linear perturbations, and the
virial theorem to convert potential depths to temperatures. No reference is
made to mass or other global quantities in the derivation.
Results. Applying a proper high-pass filter that removes large enough modes
from the gravitational potential, we derive an X-ray temperature function that
agrees very well with the classical Press-Schechter approach on relevant
temperature scales, but avoids the necessity of measuring masses.
Conclusions. TThis first study shows that and how an X-ray temperature
function of galaxy clusters can be analytically derived, avoiding the
introduction of poorly defined global quantities such as halo masses. This
approach will be useful for reducing scatter in observed cluster distributions
and thus in cosmological conclusions drawn from them.Comment: 10 pages, 5 figures, accepted for publication in A&A. Revision to
match the published version. Equation 8 corrected. Notable changes in section
4 including new figure
An analytic approach to number counts of weak-lensing peak detections
We develop and apply an analytic method to predict peak counts in
weak-lensing surveys. It is based on the theory of Gaussian random fields and
suitable to quantify the level of spurious detections caused by chance
projections of large-scale structures as well as the shape and shot noise
contributed by the background galaxies. We compare our method to peak counts
obtained from numerical ray-tracing simulations and find good agreement at the
expected level. The number of peak detections depends substantially on the
shape and size of the filter applied to the gravitational shear field. Our main
results are that weak-lensing peak counts are dominated by spurious detections
up to signal-to-noise ratios of 3--5 and that most filters yield only a few
detections per square degree above this level, while a filter optimised for
suppressing large-scale structure noise returns up to an order of magnitude
more.Comment: 9 pages, 5 figures, submitted to A&
Towards explainable real estate valuation via evolutionary algorithms
Human lives are increasingly influenced by algorithms, which therefore need to meet higher standards not only in accuracy but also with respect to explainability. This is especially true for high-stakes areas such as real estate valuation. Unfortunately, the methods applied there often exhibit a trade-off between accuracy and explainability.
One explainable approach is case-based reasoning (CBR), where each decision is supported by specific previous cases. However, such methods can be wanting in accuracy. The unexplainable machine learning approaches are often observed to provide higher accuracy but are not scrutable in their decision-making.
In this paper, we apply evolutionary algorithms (EAs) to CBR predictors in order to improve their performance. In particular, we deploy EAs to the similarity functions (used in CBR to find comparable cases), which are fitted to the data set at hand. As a consequence, we achieve higher accuracy than state-of-the-art deep neural networks (DNNs), while keeping interpretability and explainability.
These results stem from our empirical evaluation on a large data set of real estate offers where we compare known similarity functions, their EA-improved counterparts, and DNNs. Surprisingly, DNNs are only on par with standard CBR techniques. However, using EA-learned similarity functions does yield an improved performance
Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover
In the Directed Feedback Vertex Set (DFVS) problem, one is given a directed graph G = (V,E) and wants to find a minimum cardinality set S ? V such that G-S is acyclic. DFVS is a fundamental problem in computer science and finds applications in areas such as deadlock detection. The problem was the subject of the 2022 PACE coding challenge. We develop a novel exact algorithm for the problem that is tailored to perform well on instances that are mostly bi-directed. For such instances, we adapt techniques from the well-researched vertex cover problem. Our core idea is an iterative reduction to vertex cover. To this end, we also develop a new reduction rule that reduces the number of not bi-directed edges. With the resulting algorithm, we were able to win third place in the exact track of the PACE challenge. We perform computational experiments and compare the running time to other exact algorithms, in particular to the winning algorithm in PACE. Our experiments show that we outpace the other algorithms on instances that have a low density of uni-directed edges
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