搜索结果：disintegrates

We prove existence and duality on a wide class of metric spaces, and uniqueness results on any connected, complete Riemannian manifold, with or without boundary, for classical Monge--Kantorovich barycenters. In particular, this is the first and only uniqueness result with no restriction on the geometry of the manifold aside from connectedness and completeness. We obtain these via the corresponding results for barycenter problems associated to a new two-parameter family of metrics on probability measures on a general metric fiber bundle, called the $\textit{disintegrated Monge--Kantorovich metrics}$ (previously introduced by the authors).

Conditioning, the central operation in Bayesian statistics, is formalised by the notion of disintegration of measures. However, due to the implicit nature of their definition, constructing disintegrations is often difficult. A folklore result in machine learning conflates the construction of a disintegration with the restriction of probability density functions onto the subset of events that are consistent with a given observation. We provide a comprehensive set of mathematical tools which can be used to construct disintegrations and apply these to find densities of disintegrations on differentiable manifolds. Using our results, we provide a disturbingly simple example in which the restricted density and the disintegration density drastically disagree. Motivated by applications in approximate Bayesian inference and Bayesian inverse problems, we further study the modes of disintegrations. We show that the recently introduced notion of a "conditional mode" does not coincide in general with the modes of the conditional measure obtained through disintegration, but rather the modes of the restricted measure. We also discuss the implications of the discrepancy between the two measures in

We prove a generalisation of the disintegration theorem to the setting of multifunctions between Polish probability spaces. Whereas the classical disintegration theorem guarantees the disintegration of a probability measure along the partition of the underlying space by the fibres of a measurable function, our theorem gives necessary and sufficient conditions for the measure to disintegrate along a cover of the underlying space defined by the fibres of a measurable multifunction. Building on this theorem, we introduce a new statistical notion: We declare a metric Polish probability space to be asymptotically disintegrable if $n$ i.i.d.-centred balls of decreasing radius carry a disintegration of the measure with probability tending to unity as $n\rightarrow\infty$. We give a number of both $1$-dimensional and higher-dimensional examples of asymptotically disintegrable spaces with associated quantitative rates, as well as a strong counterexample. Finally, we give two applications of the notion of asymptotic disintegrability. First, we prove that asymptotically disintegrable spaces admit an easy high-probability quantification of the law of large numbers in Wasserstein space, which i

In this paper, we present a novel approach for analyzing the relationship between the supports of conditional measures and their geometric arrangement in Wasserstein space via the disintegration map. Our method establishes criteria to determine when such conditional measures arise from a metric measure foliation. Additionally, we provide a example demonstrating how this framework can be applied to study perturbations of disintegration-induced foliations.

Given a compact space $K$ and a Banach space $E$ we study the structure of positive measures on the product space $K\times B_{E^*}$ representing functionals on $C(K,E)$, the space of $E$-valued continuous functions on $K$. Using the technique of disintegration we provide an alternative approach to the procedure of transference of measures introduced by Batty (1990). This enables us to substantially strengthen some of his results, to discover a rich order structure on these measures, to identify maximal and minimal elements and to relate them to the classical Choquet order.

The disintegration of near limit flames propagating through the gap of Hele-Shaw cells has recently become a subject of active research. In this paper, the flamelets resulting from the disintegration of the continuous front are interpreted in terms of the Zeldovich flame-balls stabilized by volumetric heat losses. A complicated free-boundary problem for 2D self-drifting near circular flamelets is reduced to a 1D model. The 1D formulation is then utilized to obtain the locus of the flamelet velocity, size, heat losses and Lewis numbers at which the self-drifting flamelets may exist.

We provide a collection of examples involving the concept of a product disintegration, which generalizes exchangeability.

We present imaging observations of the disintegrating long-period comet C/2021 A1 (Leonard). High resolution observations with Hubble Space Telescope show no evidence for surviving fragments, and place a 3 sigma upper limit to their possible radius about 60 m (albedo 0.1 assumed). In contrast, wide field observations from the Swan Hill Observatory, Australia, show an extensive debris cloud, the cross-section and estimated mass of which are consistent with complete disintegration of the nucleus near mid- December 2021 (at about 0.8 au). Two methods give the pre-disruption nucleus radius, r = 0.6+/-0.2 km. Tidal, collisional, sublimation and pressure-confined explosion models provide implausible explanations of the disintegration. However, rotational instability driven by outgassing torques has a very short timescale (of order 0.1 year) given the orbit and size of the C/2021 A1 nucleus, and offers the most plausible mechanism for the disruption. Initial rotational breakup is accelerated by the exposure and strong sublimation of previously buried volatiles, leading to catastrophic destruction of the nucleus.

Disintegrating multiple systems have been previously discovered from kinematic studies of the $\it Hipparcos$ catalogue. They are presumably the result of dynamical encounters taking place in the Galactic disk between single/multiple systems. In this paper, we aim to expand the search for such systems, to study their properties, as well as to characterize possible low-mass ejecta (i.e. brown dwarfs and planets). We have assembled a list of 15 candidate systems using astrometry from the Tycho-Gaia astrometric solution (later upgraded with $\it Gaia$ DR3), and here we present the discovery and follow-up of 5 of them. We have obtained DECam imaging for all 5 systems and by combining near-infrared photometry and proper motion, we searched for ultra-cool ejected components. We find that the system consisting of TYC 7731-1951-1, TYC 7731-2128 AB, and TYC 7731-1995-1ABC?, contains one very promising ultra-cool dwarf candidate. Using additional data from the literature, we have found that 3 out of 5 disintegrating system candidates are likely to be true disintegrating systems.

In this paper, we study a connection between disintegration of measures and geometric properties of probability spaces. We prove a disintegration theorem, addressing disintegration from the perspective of an optimal transport problem. We look at the disintegration of transport plans, which are used to define and study disintegration maps. Using these objects, we study the regularity and absolute continuity of disintegration of measures. In particular, we exhibit conditions for which the disintegration map is weakly continuous and one can obtain a path of measures given by this map. We show a rigidity condition for the disintegration of measures to be given into absolutely continuous measures.

In this paper we discuss the possibility of $J/ψ$ disintegration due the $Z(3)$ domain walls that are expected to form in QGP medium. These domain walls give rise to localised color electric field which disintegrates $J/ψ$, on interaction, by changing the color composition and simultaneously exciting it to higher states of $c\bar{c}$ system.

In recent years discrepancies have emerged in measurements of the present-day rate of expansion of the universe $H_0$ and in estimates of the clustering of matter $S_8$. Using the most recent cosmological observations we reexamine a novel model proposed to address these tensions, in which cold dark matter disintegrates into dark radiation. The disintegration process is controlled by its rate $Q = α\mathcal{H} ρ_{\rm ddm}$, where $α$ is a (constant) dimensionless parameter quantifying the strength of the disintegration mechanism and $\mathcal{H}$ is the conformal Hubble rate in the spatially flat Friedmann-Lemaître-Robertson-Walker universe and $ρ_{\rm ddm}$ is the energy density of the disintegrating cold dark matter. We constrain this model with the latest 2018 Planck temperature and polarization data, showing that there is no evidence for $α eq 0$ and that it cannot solve the $H_0$ tension below $3σ$, clashing with the result obtained by analyzing the Planck 2015 temperature data. We also investigate two possible extensions of the model in which the dark energy equation-of-state parameter $w eq -1$. In this case it is possible to combine Planck data with the SH0ES measurement, a

In a quasi two-dimensional electron system with non-zero layer thickness, a parallel magnetic field (B||) can couple to the out-of-plane electron motion and lead to a severe distortion and eventual disintegration of the Fermi contour. Here we directly and quantitatively probe this evolution through commensurability and Shubnikov-de Haas measurements on electrons confined to a 40-nm-wide GaAs (001) quantum well. We are able to observe the Fermi contour disintegration phenomenon, in good agreement with the results of semi-classical calculations. Experimentally we also observe intriguing features, suggesting magnetic-breakdown-type behavior when the Fermi contour disintegrates.

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