Towards a Definition of Locality in a Manifoldlike Causal Set

It is a common misconception that spacetime discreteness necessarily implies a violation of local Lorentz invariance. In fact, in the causal set approach to quantum gravity, Lorentz invariance follows from the specific implementation of the discreteness hypothesis. However, this comes at the cost of locality. In particular, it is difficult to define a "local" region in a manifoldlike causal set, i.e., one that corresponds to an approximately flat spacetime region. Following up on suggestions from previous work, we bridge this lacuna by proposing a definition of locality based on the abundance of m-element order-intervals as a function of m in a causal set. We obtain analytic expressions for the expectation value of this function for an ensemble of causal set that faithfully embeds into an Alexandrov interval in d-dimensional Minkowski spacetime and use it to define local regions in a manifoldlike causal set. We use this to argue that evidence of local regions is a necessary condition for manifoldlikeness in a causal set. This in addition provides a new continuum dimension estimator. We perform extensive simulations which support our claims.Comment: 35 pages, 17 figure

Graptolites from Silurian (Llandovery Series) sedimentary deposits attributed to a forearc setting, Co To Formation, Co To archipelago, northeast Vietnam

Newly collected graptolites from the Co To Formation, Co To archipelago, NE Vietnam, comprise assemblages indicative of two biostratigraphical levels within the lower Silurian, Llandovery Series, Telychian Stage: the co-occurrence of Spirograptus turriculatus and Torquigraptus proteus? suggests an interval most likely within the upper part of the Spirograptus turriculatus Biozone or 'Monograptus' crispus Biozone, whilst Oktavites spirally and Monoclimacis cf. suhgeinitzi identify the Oktavites spiralis Biozone. The graptolites provide important biostratigraphical evidence for the age of the upper part of the lower Co To Formation, biostratigraphical ties between the NE Vietnamese succession of the Bac Bo Region and graptolite assemblages of the Long Dai Formation in the Viet-Lao Region of central Vietnam, and include the new species Monograptus hanutlus sp. nov. co-occurring with S. turriculatus, which is perhaps an ancestral form to the later Telychian species Monograptus drepanoformis. We also report the lirst chitinozoans, including Belonechitina, from the Co To Formation

A taxonomic review of the subtribe Pericalina (Coleoptera: Carabidae: Lebiini) in the Western hemisphere : with descriptions of new species and notes about classification and zoogeography

A taxonomic review of the lebiine sub tribe Pericalina in the Western Hemisphere, this paper includes a treatment of the genus-groups, a key to the genera, keys to subgenera, species groups, and species of each polybasic genus, descriptions of new species and new subgenera, new locality records for previously described species, re-rankings, and new synonymy. In total, 111 species and subspecies are treated, 26 of which are described as new