Growing interest in understanding ecological patterns from phylogenetic and functional perspectives has driven the development of metrics that capture variation in evolutionary histories or ecological functions of species. Recently, an integrated framework based on Hill numbers was developed that measures three dimensions of biodiversity based on abundance, phylogeny and function of species. Th...

Vittorio Giovannetti, Seth Lloyd, Lorenzo Maccone, and Jeffrey H. Shapiro NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, piazza dei Cavalieri 7, I-56126 Pisa, Italy Dept. of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Dip. Fisica “A. Volta”, Univ. of Pavia, via Bassi 6, I-27100 Pavia, Italy 4 Research Laboratory of Electronics, Massachus...

Alessandro Cresti , Giuseppe Grosso (2) and Giuseppe Pastori Parravicini (3) (1) NEST-INFM, Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy, and Dipartimento di Fisica E. Fermi, Largo B. Pontecorvo 3, I-56127 Pisa, Italy [email protected] (2) NEST-INFM and Dipartimento di Fisica E. Fermi, Largo B. Pontecorvo 3, I-56127 Pisa, Italy (3) NEST-INFM and Dipartimento di Fisica ...

Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In 2014 Asadi and {it et al.} [New Extension of $p$-Metric Spaces with Some fixed point Results on $M$-metric paces, J. Ineq. Appl. 2014 (2014): 18] extend the Partial metric spaces to $M$-metric spaces. In this work, we introduce the class of $F(psi,varphi)$-contrac...

We study the behavior of metric perturbations in a recently proposed model of phantom dark energy with tachyonic instability at long wavelengths. We find that metric perturbations exponentially grow in time, starting from very small values determined by vacuum fluctuations, and may become sizeable at late times. This property may be of interest for phenomenology.

We consider the heat semigroup generated by the Laplace operator on metric trees. Among our results we show how the behavior of the associated heat kernel depends on the geometry of the tree. As applications we establish new eigenvalue estimates for Schrödinger operators on metric trees.

in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.

When a new metric is introduced, often there is a "hidden variable" in the similarity relation (frequently depends on the specific area of research), so that we should always speak of similarity with respect to some property, and there is a plethora of measures in part because researchers are often inexplicit on this point. On the other hand, one should have some knowledge about the nature of t...