Packing dimension of mean porous measures

We prove that the packing dimension of any mean porous Radon measure on $\mathbb R^d$ may be estimated from above by a function which depends on mean porosity. The upper bound tends to $d-1$ as mean porosity tends to its maximum value. This result was stated in \cite{BS}, and in a weaker form in \cite{JJ1}, but the proofs are not correct. Quite surprisingly, it turns out that mean porous measures are not necessarily approximable by mean porous sets. We verify this by constructing an example of a mean porous measure $\mu$ on $\mathbb R$ such that $\mu(A)=0$ for all mean porous sets $A\subset\mathbb R$.Comment: Revised versio

Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below

We prove existence and uniqueness of optimal maps on $RCD^*(K,N)$ spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation. \ua9 2015, Mathematica Josephina, Inc

Marked deterioration in the quality of life of patients with idiopathic pulmonary fibrosis during the last two years of life

BackgroundIdiopathic pulmonary fibrosis (IPF) is a chronic disease with a high symptom burden and poor survival that influences patients' health-related quality of life (HRQOL). We aimed to evaluate IPF patients' symptoms and HRQOL in a well-documented clinical cohort during their last two years of life.MethodsIn April 2015, we sent the Modified Medical Research Council Dyspnea Scale (MMRC), the modified Edmonton Symptom Assessment Scale (ESAS) and a self-rating HRQOL questionnaire (RAND-36) to 300 IPF patients, of which 247 (82%) responded. Thereafter, follow-up questionnaires were sent every six months for two years.ResultsNinety-two patients died by August 2017. Among these patients, HRQOL was found to be considerably low already two years before death. The most prominent declines in HRQOL occurred in physical function, vitality, emotional role and social functioning (pPeer reviewe

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

mMRC dyspnoea scale indicates impaired quality of life and increased pain in patients with idiopathic pulmonary fibrosis

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When do we have the power to detect biological interactions in spatial point patterns

Uncovering the roles of biotic interactions in assembling and maintaining species‐rich communities remains a major challenge in ecology. In plant communities, interactions between individuals of different species are expected to generate positive or negative spatial interspecific associations over short distances. Recent studies using individual‐based point pattern datasets have concluded that (a) detectable interspecific interactions are generally rare, but (b) are most common in communities with fewer species; and (c) the most abundant species tend to have the highest frequency of interactions. However, it is unclear how the detection of spatial interactions may change with the abundances of each species, or the scale and intensity of interactions. We ask if statistical power is sufficient to explain all three key results. We use a simple two‐species model, assuming no habitat associations, and where the abundances, scale and intensity of interactions are controlled to simulate point pattern data. In combination with an approximation to the variance of the spatial summary statistics that we sample, we investigate the power of current spatial point pattern methods to correctly reject the null model of pairwise species independence. We show the power to detect interactions is positively related to both the abundances of the species tested, and the intensity and scale of interactions, but negatively related to imbalance in abundances. Differences in detection power in combination with the abundance distributions found in natural communities are sufficient to explain all the three key empirical results, even if all pairwise interactions are identical. Critically, many hundreds of individuals of both species may be required to detect even intense interactions, implying current abundance thresholds for including species in the analyses are too low. Synthesis. The widespread failure to reject the null model of spatial interspecific independence could be due to low power of the tests rather than any key biological process. Since we do not model habitat associations, our results represent a first step in quantifying sample sizes required to make strong statements about the role of biotic interactions in diverse plant communities. However, power should be factored into analyses and considered when designing empirical studies

Ilmastotoimijuuden edistäminen utopiapedagogiikan avulla

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Perusteita seuraavan sukupolven metsävarajärjestelmälle – Forest Big Data -hanke

Tieteen tori: Yksityiskohtainen metsävaratiet