Shades of Grey: Ethical Dilemmas

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Variations on the Seventh Route to Relativity

As motivated in the full abstract, this paper further investigates Barbour, Foster and O Murchadha (BFO)'s 3-space formulation of GR. This is based on best-matched lapse-eliminated actions and gives rise to several theories including GR and a conformal gravity theory. We study the simplicity postulates assumed in BFO's work and how to weaken them, so as to permit the inclusion of the full set of matter fields known to occur in nature. We study the configuration spaces of gravity-matter systems upon which BFO's formulation leans. In further developments the lapse-eliminated actions used by BFO become impractical and require generalization. We circumvent many of these problems by the equivalent use of lapse-uneliminated actions, which furthermore permit us to interpret BFO's formulation within Kuchar's generally covariant hypersurface framework. This viewpoint provides alternative reasons to BFO's as to why the inclusion of bosonic fields in the 3-space approach gives rise to minimally-coupled scalar fields, electromagnetism and Yang--Mills theory. This viewpoint also permits us to quickly exhibit further GR-matter theories admitted by the 3-space formulation. In particular, we show that the spin-1/2 fermions of the theories of Dirac, Maxwell--Dirac and Yang--Mills--Dirac, all coupled to GR, are admitted by the generalized 3-space formulation we present. Thus all the known fundamental matter fields can be accommodated. This corresponds to being able to pick actions for all these theories which have less kinematics than suggested by the generally covariant hypersurface framework. For all these theories, Wheeler's thin sandwich conjecture may be posed, rendering them timeless in Barbour's sense.Comment: Revtex version; Journal-ref adde

Probabilistic time

The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions that realize a unitary time evolution as described by rotations of the real wave function $q_\tau(t)=\pm \sqrt{p_\tau(t)}$. We establish a map to quantum physics and the Schr\"odinger equation. Suitable classical observables are mapped to quantum operators. The non-commutativity of the operator product is traced back to the incomplete statistics of the local-time subsystem. Our investigation of classical statistics is based on two-level observables that take the values one or zero. Then the wave functions can be mapped to elements of a Grassmann algebra. Quantum field theories for fermions arise naturally from our formulation of probabilistic time.Comment: new references, 30 page

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Categorizing Different Approaches to the Cosmological Constant Problem

We have found that proposals addressing the old cosmological constant problem come in various categories. The aim of this paper is to identify as many different, credible mechanisms as possible and to provide them with a code for future reference. We find that they all can be classified into five different schemes of which we indicate the advantages and drawbacks. Besides, we add a new approach based on a symmetry principle mapping real to imaginary spacetime.Comment: updated version, accepted for publicatio

Search for flavour-changing neutral currents in processes with one top quark and a photon using 81 fb⁻¹ of pp collisions at \sqrts = 13 TeV with the ATLAS experiment

A search for flavour-changing neutral current (FCNC) events via the coupling of a top quark, a photon, and an up or charm quark is presented using 81 fb−1 of proton–proton collision data taken at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. Events with a photon, an electron or muon, a b-tagged jet, and missing transverse momentum are selected. A neural network based on kinematic variables differentiates between events from signal and background processes. The data are consistent with the background-only hypothesis, and limits are set on the strength of the tqγ coupling in an effective field theory. These are also interpreted as 95% CL upper limits on the cross section for FCNC tγ production via a left-handed (right-handed) tuγ coupling of 36 fb (78 fb) and on the branching ratio for t→γu of 2.8×10−5 (6.1×10−5). In addition, they are interpreted as 95% CL upper limits on the cross section for FCNC tγ production via a left-handed (right-handed) tcγ coupling of 40 fb (33 fb) and on the branching ratio for t→γc of 22×10−5 (18×10−5). © 2019 The Author(s

Systematics of the Neotropical Genus Leptodactylus Fitzinger, 1826 (Anura: Leptodactylidae): Phylogeny, the Relevance of Non-molecular Evidence, and Species Accounts

A phylogeny of the species-rich clade of the Neotropical frog genus Leptodactylus sensu stricto is presented on the basis of a total evidence analysis of molecular (mitochondrial and nuclear markers) and non-molecular (adult and larval morphological and behavioral characters) sampled from > 80% of the 75 currently recognized species. Our results support the monophyly of Leptodactylus sensu stricto, with Hydrolaetare placed as its sister group. The reciprocal monophyly of Hydrolaetare and Leptodactylus sensu stricto does not require that we consider Hydrolaetare as either a subgenus or synonym of Leptodactylus sensu lato. We recognize Leptodactylus sensu stricto, Hydrolaetare, Adenomera, and Lithodytes as valid monophyletic genera. Our results generally support the traditionally recognized Leptodactylus species groups, with exceptions involving only a few species that are easily accommodated without proposing new groups or significantly altering contents. The four groups form a pectinate tree, with the Leptodactylus fuscus group diverging first, followed by the L. pentadactylus group, which is sister to the L. latrans and L. melanonotus groups. To evaluate the impact of non-molecular evidence on our results, we compared our total evidence results with results obtained from analyses using only molecular data. Although non-molecular evidence comprised only 3.5% of the total evidence matrix, it had a strong impact on our total evidence results. Only one species group was monophyletic in the molecular-only analysis, and support differed in 86% of the 54 Leptodactylus clades that are shared by the results of the two analyses. Even though no non-molecular evidence was included for Hydrolaetare, exclusion of that data partition resulted in that genus being nested within Leptodactylus, demonstrating that the inclusion of a small amount of non-molecular evidence for a subset of species can alter not only the placement of those species, but also species that were not scored for those data. The evolution of several natural history and reproductive traits is considered in the light of our phylogenic framework. Invasion of rocky outcrops, larval oophagy, and use of underground reproductive chambers are restricted to species of the Leptodactylus fuscus and L. pentadactylus groups. In contrast, larval schooling, larval attendance, and more complex parental care are restricted to the L. latrans and L. melanonotus groups. Construction of foam nests is plesiomorphic in Leptodactylus but their placement varies extensively (e.g., underground chambers, surface of waterbodies, natural or excavated basins). Information on species synonymy, etymology, adult and larval morphology, advertisement call, and geographic distribution is summarized in species accounts for the 30 species of the Leptodactylus fuscus group, 17 species of the L. pentadactylus group, eight species of the L. latrans group, and 17 species of the L. melanonotus group, as well as the three species that are currently unassigned to any species group.Se presenta una filogenia del género Leptodactylus, un ciado neotropical rico en especies, basada en análises combinados de datos moleculares (marcadores nuclear y mitocondriales) y no moleculares (caracteres de la morfología de adultos y larvas así como de comportamiento) se muestrearon > 80% de las 75 especies reconocidas. Los resultados apoyan la monofília de Leptodactylus sensu stricto, con Hydrolaetare como su grupo hermano. La monofília recíproca de Hydrolaetare y Leptodactylus no requiere considerar a Hydrolaetare como un subgénero o sinónimo de Leptodactylus sensu lato. Se reconocen Leptodactylus sensu stricto, Hydrolaetare, Adenomera y Lithodytes como géneros monofiléticos válidos. Los resultados en general resuelven los grupos tradicionalmente reconocidos de Leptodactylus, con excepciones de algunas especies que son reasignadas sin la necesidad de proponer nuevos grupos o alterar significativamente el contenido de los grupos tradicionales. Los cuatro grupos de especies forman una topología pectinada donde el grupo de L. fuscus tiene una posición basal, seguido por el grupo de L. pentadactylus que es el grupo hermano al clado formado por los grupo de L. latrans y L. melanonotus. Se estimó el impacto de los datos no moleculares en los resultados, comparándose los resultados de evidencia total con los de los análises de datos moleculares solamente. Los datos no moleculares representan un 3.5% de la matriz de evidencia total, pero estos datos tuvieron un impacto significativo en los resultados del análisis de evidencia total. En el análisis estrictamente molecular solamente un grupo de especies resultó monofilético, y el apoyo difirió en 86% de los 54 ciados de Leptodactylus compartidos entre los dos análises. A pesar que datos no moleculares no fueron incluidos para Hydrolaetare, la exclusión de evidencia no molecular resultó en el género estar dentro de Leptodactylus, demostrando que la inclusión de evidencia no molecular pequeña para un subgrupo de especies altera no solamente la posición topológica de esas especies, sino tambien de las especies para las cuales dichos datos no fueron codificados. La evolución de patrones de historia natural y reprodución se evalúan en el contexto filogenético. La invasión de afloramientos rocosos y la construción de cámaras de reprodución subterraneas está limitada a los grupos de Leptodactylus fuscus y L. pentadactylus, mientras que la oofagia larval está restringida al grupo de L. pentadactylus. Por otro lado, los cárdumenes larvales, la proteción del cárdumen, y otros comportamientos parentales complejos carecterizan al clado formado por los grupos de especies de L. latrans y L. melanonotus. Los resúmenes de especies incluyen información de sinonimias, etimología, morfología de adultos y larvas, cantos, y distribución geográfica para las 30 especies del grupo de Leptodactylus fuscus, 17 especies del grupo L. pentadactylus, ocho especies del grupo de L. latrans, 17 especies del grupo de L. melanonotus, así como para las tres especies que actualmente no se encuentran asociadas a ninguno de los grupos de especies.Taran Grant was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico Proc. 307001/2011-3 and Fundação de Amparo à Pesquisa do Estado de São Paulo Proc. 2012/10000-5