We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel’dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gra...
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We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel’dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample is constructed from the combined SPT-SZ, SPTpol ECS, and SPTpol 500d surveys, and comprises 1,005 confirmed clusters in the redshift range 0.25–1.78 over a total sky area of 5200 deg2. We use DES Year 3 weak-lensing data for 688 clusters with redshifts z<0.95 and HST weak-lensing data for 39 clusters with 0.6logical constant. We use the cluster abundance to measure σ8 in five redshift bins between 0.25 and 1.8, and we find the results to be consistent with structure growth as predicted by the ΛCDM model fit to Planck primary CMB data.
Properties valid on classical theory (Boolean laws) have been extended to fuzzy set theory. Such generalizations of Boolean laws (Boolean-like laws) are not always valid in any standard fuzzy set theory and this fact ...
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ISBN:
(纸本)9781467315074
Properties valid on classical theory (Boolean laws) have been extended to fuzzy set theory. Such generalizations of Boolean laws (Boolean-like laws) are not always valid in any standard fuzzy set theory and this fact induced a wide investigation. In this paper we show the conditions that the Boolean-like law x ≤ I(y,x) holds in fuzzy logic. We focus the investigation on three main classes of fuzzy implications, namely: (S,N)-, R- and QL-implications. Further, we show that the operator I satisfies this Boolean-like law if, and only if, Φ-conjugate of I also satisfies it.
There are various formalizations of soft constraints in the literature; so far, we have analyzed the semiring-based approach of [BMR97], the fuzzy ones in [Rut94] and the Max-CSP’s from [FW92]. If we abstrac...
ISBN:
(纸本)3540428631
There are various formalizations of soft constraints in the literature; so far, we have analyzed the semiring-based approach of [BMR97], the fuzzy ones in [Rut94] and the Max-CSP’s from [FW92]. If we abstract the common features from those frameworks, we can define soft constraints and frameworks via a restricted collection: a finite set of variables, a finite variable domain, a universal algebra. The latest is composed by a set, called universe, and functions to combine universe elements. A universe collects the values (for instance, only 0 and 1 in the hard constraint case) that a constraint can assign to variable domain elements. An algebra function combines universe elements; hence an algebra function can be used to derive constraints from input ones, as it can be applied to the universe values in the input constraints’ range. We can generalize all the soft constraint operations of [BMR97],[Rut94],[FW92] via universal algebra functions; and we can construct all solution sets of [BMR97],Rut94] by means of such operations. So, bingo!, all aformentioned soft frameworks are instances of ours: i.e., constraints, constraint operations and solution sets of those frameworks are instances of ours.
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