The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic
⊢
. We prove that the description of the algebraic counterpart of the left ...variable inclusion companion of a given logic
⊢
is related to the construction of Płonka sums of the matrix models of
⊢
. This observation allows to obtain a Hilbert-style axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, and to locate them in the Leibniz hierarchy.
ABSTRACT
Cosmic voids occupy most of the volume of the Universe, and their statistical properties can be exploited for constraining dark energy, as well as for testing theories of gravity. ...Nevertheless, in spite of their growing popularity as cosmological probes, a gap of knowledge between cosmic void observations and theory still persists. In particular, the void size function models proposed in literature have been proven unsuccessful in reproducing the results obtained from cosmological simulations in which cosmic voids are detected from biased tracers of the density field. The goal of this work is to cover this gap. In particular, we make use of the findings of a previous work in which we have improved the void selection procedure, presenting an algorithm that redefines the void ridges and, consequently, their radii. By applying this algorithm, we validate the volume conserving model of the void size function on a set of unbiased simulated density field tracers. We highlight the difference in the internal structure between voids selected in this way and those identified by the popular vide void finder. We also extend the validation of the model to the case of biased tracers. We find that a relation exists between the tracer used to sample the underlying dark matter density field and its unbiased counterpart. Moreover, we demonstrate that, as long as this relation is accounted for, the size function is a viable approach for studying cosmology with cosmic voids.
Flood estimation and flood management have traditionally been the domain of hydrologists, water resources engineers and statisticians, and disciplinary approaches abound. Dominant views have been ...shaped; one example is the catchment perspective: floods are formed and influenced by the interaction of local, catchment-specific characteristics, such as meteorology, topography and geology. These traditional views have been beneficial, but they have a narrow framing. In this paper we contrast traditional views with broader perspectives that are emerging from an improved understanding of the climatic context of floods. We come to the following conclusions: (1) extending the traditional system boundaries (local catchment, recent decades, hydrological/hydraulic processes) opens up exciting possibilities for better understanding and improved tools for flood risk assessment and management. (2) Statistical approaches in flood estimation need to be complemented by the search for the causal mechanisms and dominant processes in the atmosphere, catchment and river system that leave their fingerprints on flood characteristics. (3) Natural climate variability leads to time-varying flood characteristics, and this variation may be partially quantifiable and predictable, with the perspective of dynamic, climate-informed flood risk management. (4) Efforts are needed to fully account for factors that contribute to changes in all three risk components (hazard, exposure, vulnerability) and to better understand the interactions between society and floods. (5) Given the global scale and societal importance, we call for the organization of an international multidisciplinary collaboration and data-sharing initiative to further understand the links between climate and flooding and to advance flood research.
We investigate the non-linear evolution of the matter power spectrum by using a large set of high-resolution N-body/hydrodynamic simulations. The linear matter power in the initial conditions is ...consistently modified to mimic the presence of warm dark matter (WDM) particles which induce a small-scale cut-off in the power as compared to standard cold dark matter scenarios. The impact of such thermal relics is examined at small scales k > 1 h Mpc−1, at redshifts of z < 5, which are particularly important for the next generation of Lyman α forest, weak lensing and galaxy clustering surveys. We measure the mass and redshift dependence of the WDM non-linear matter power and provide a fitting formula which is accurate at the ∼2 per cent level below z= 3 and for particle masses of m
WDM≥ 0.5 keV. The role of baryonic physics on the WDM-induced suppression is also quantified. In particular, we examine the effects of cooling, star formation and feedback from strong galactic winds. Finally, we find that a modified version of the halo model describes the shape of the WDM suppressed power spectra better than halofit. In the case of weak lensing however, the latter works better than the former, since it is more accurate on the relevant, mid-range scales, albeit very inaccurate on the smallest scales (k > 10 h Mpc−1) of the matter power spectrum.
ABSTRACT
The key to understand the nature of dark energy lies in our ability to probe the distant Universe. In this framework, the recent detection of the kinematic Sunyaev–Zel’dovich (kSZ) effect ...signature in the cosmic microwave background obtained with the South Pole Telescope (SPT) is extremely useful since this observable is sensitive to the high-redshift diffuse plasma. We analyse a set of cosmological hydrodynamical simulation with four different realizations of a Hu & Sawicki f(R) gravity model, parametrized by the values of $\overline{f}_{\rm R,0}$= (0, −10−6, −10−5, −10−4), to compute the properties of the kSZ effect due to the ionized Universe and how they depend on $\overline{f}_{\rm R,0}$ and on the redshift of reionization, zre. In the standard General Relativity limit ($\overline{f}_{\rm R,0}$= 0) we obtain an amplitude of the kSZ power spectrum of $\mathcal {D}^{\rm kSZ}_{3000}$$= 4.1\,$$\mu$K2 (zre= 8.8), close to the +1σ limit of the $\mathcal {D}^{\rm kSZ}_{3000}$$= (2.9\pm 1.3)\,$$\mu$K2 measurement by SPT. This corresponds to an upper limit on the kSZ contribute from patchy reionization of $\mathcal {D}^{\rm kSZ,patchy}_{3000}$$\lt 0.9\,$$\mu$K2 (95 per cent confidence level). Modified gravity boosts the kSZ signal by about 3, 12, and 50 per cent for $\overline{f}_{\rm R,0}$=(− 10−6, −10−5, −10−4), respectively, with almost no dependence on the angular scale. This means that with modified gravity the limits on patchy reionization shrink significantly: for $\overline{f}_{\rm R,0}$=−10−5 we obtain $\mathcal {D}^{\rm kSZ,patchy}_{3000}$$\lt 0.4\,$$\mu$K2. Finally, we provide an analytical formula for the scaling of the kSZ power spectrum with zre and $\overline{f}_{\rm R,0}$ at different multipoles: at ℓ = 3000 we obtain $\mathcal {D}^{\rm kSZ}_{3000}$ ∝ zre$^{0.24}\left(1+\sqrt{\left|\overline{f}_{\rm R,0}\right|}\right)^{41}$.
A Logical Modeling of Severe Ignorance Bonzio, S.; Fano, V.; Graziani, P. ...
Journal of philosophical logic,
08/2023, Letnik:
52, Številka:
4
Journal Article
Recenzirano
Odprti dostop
In the logical context, ignorance is traditionally defined recurring to epistemic logic. In particular, ignorance is essentially interpreted as “lack of knowledge”. This received view has - as we ...point out - some problems, in particular we will highlight how it does not allow to express a type of content-theoretic ignorance, i.e. an ignorance of
φ
that stems from an unfamiliarity with its meaning. Contrarily to this trend, in this paper, we introduce and investigate a modal logic having a primitive epistemic operator
I
, modeling ignorance. Our modal logic is essentially constructed on the modal logics based on weak Kleene three-valued logic introduced by Segerberg (
Theoria, 33
(1):53–71,
1997
). Such non-classical propositional basis allows to define a Kripke-style semantics with the following, very intuitive, interpretation: a formula
φ
is ignored by an agent if
φ
is neither true nor false in every world accessible to the agent. As a consequence of this choice, we obtain a type of content-theoretic notion of ignorance, which is essentially different from the traditional approach. We dub it
severe ignorance
. We axiomatize, prove completeness and decidability for the logic of reflexive (three-valued) Kripke frames, which we find the most suitable candidate for our novel proposal and, finally, compare our approach with the most traditional one.
ABSTRACT We explore the possibility of measuring the mass accretion rate (MAR) of galaxy clusters from their mass profiles beyond the virial radius R200. We derive the accretion rate from the mass of ...a spherical shell whose inner radius is 2R200, whose thickness changes with redshift, and whose infall velocity is assumed to be equal to the mean infall velocity of the spherical shells of dark matter halos extracted from N-body simulations. This approximation is rather crude in hierarchical clustering scenarios where both smooth accretion and aggregation of smaller dark matter halos contribute to the mass accretion of clusters. Nevertheless, in the redshift range z = 0, 2, our prescription returns an average MAR within 20%-40% of the average rate derived from the merger trees of dark matter halos extracted from N-body simulations. The MAR of galaxy clusters has been the topic of numerous detailed numerical and theoretical investigations, but so far it has remained inaccessible to measurements in the real universe. Since the measurement of the mass profile of clusters beyond their virial radius can be performed with the caustic technique applied to dense redshift surveys of the cluster outer regions, our result suggests that measuring the mean MAR of a sample of galaxy clusters is actually feasible. We thus provide a new potential observational test of the cosmological and structure formation models.
We investigate the main tensions within the current standard model of cosmology from the perspective of the main statistics of cosmic voids, using the final BOSS DR12 data set. For this purpose, we ...present the first estimate of the
S
8
≡
σ
8
Ω
m
/0.3 and
H
0
parameters obtained from void number counts and shape distortions. To analyze void counts we relied on an extension of the popular volume-conserving model for the void size function, tailored to the application on data, including geometric and dynamic distortions. We calibrated the two nuisance parameters of this model with the official BOSS Collaboration mock catalogs and propagated their uncertainty through the statistical analysis of the BOSS void number counts. The constraints from void shapes come from the study of the geometric distortions of the stacked void-galaxy cross-correlation function. In this work we focus our analysis on the Ω
m
−
σ
8
and Ω
m
−
H
0
parameter planes and derive the marginalized constraints
S
8
= 0.813
−0.068
+0.093
and
H
0
= 67.3
−9.1
+10.0
km s
−1
Mpc
−1
, which are fully compatible with constraints from the literature. These results are expected to notably improve in precision when analyzed jointly with independent probes and will open a new viewing angle on the rising cosmological tensions in the near future.
A wide range of astrophysical and cosmological observations support the evidence that the energy density of the Universe is presently largely dominated by particles and fields that do not belong to ...the standard model of particle physics. Such cosmic dark sector appears to be made of two distinct entities capable to account for the growth of large‐scale structures and for the observed acceleration of the expansion rate of the Universe, respectively dubbed dark matter and dark energy. Nevertheless, the fundamental nature of these two dark components has so far remained mysterious. In the currently accepted scenario dark matter is associated to a single new massive and weakly interacting particle beyond the standard model, while dark energy is assumed to be a simple cosmological constant. However, present cosmological constraints and the absence of a direct detection and identification of any dark matter particle candidate leave room to the possibility that the dark sector of the Universe be actually more complex than it is normally assumed. In particular, more than one new fundamental particle could be responsible for the observed dark matter density in the Universe, and possible new interactions between dark energy and dark matter might characterize the dark sector. In the present work, the possibility that two dark matter particles may exist in nature is investigated. These different species are assumed to have identical physical properties except for the sign of their coupling constant to dark energy. Extending previous works on similar scenarios, the evolution of the background cosmology as well as the growth of linear density perturbations for a wide range of parameters of such multiple dark matter model is studied. Interestingly, the results show how the simple assumption that dark matter particles carry a “charge” with respect to their interaction with the dark energy field allows for new long‐range scalar forces of gravitational strength in the dark sector without conflicting with present observations both at the background and linear levels. The presented scenario does not introduce new parameters with respect to the case of a single dark matter species for which such strong dark interactions have been already ruled out. Therefore, the present investigation suggests that only a detailed study of nonlinear structure formation processes might possibly provide effective constraints on new scalar interactions of gravitational strength in the dark sector.
The present cosmological constraints and the absence of a direct detection and identification of any dark matter particle candidate leave room to the possibility that the dark sector of the Universe be actually more complex than it is normally assumed. In particular, more than one new fundamental particle could be responsible for the observed dark matter density in the Universe.
In this paper we investigate AGM belief contraction operators by using the tools of algebraic logic. We generalize the notion of contraction to arbitrary finitary propositional logics, and we show ...how to switch from a syntactic-based approach to a semantic one. This allows to build a solid bridge between the validity of AGM postulates in a propositional logic and specific algebraic properties of its intended algebraic counterpart. Such a connection deserves particular attention when we deal with maxichoice contractions, as studied in the final part of the paper.
PDF
