Mesozoic fossils (>145 Mya) suggest the antiquity of the subgenera of Daphnia and their coevolution with chaoborid predators

<p>Abstract</p> <p>Background</p> <p>The timescale of the origins of <it>Daphnia </it>O. F. Mueller (Crustacea: Cladocera) remains controversial. The origin of the two main subgenera has been associated with the breakup of the supercontinent Pangaea. This vicariance hypothesis is supported by reciprocal monophyly, present day associations with the former Gondwanaland and Laurasia regions, and mitochondrial DNA divergence estimates. However, previous multilocus nuclear DNA sequence divergence estimates at < 10 Million years are inconsistent with the breakup of Pangaea. We examined new and existing cladoceran fossils from a Mesozoic Mongolian site, in hopes of gaining insights into the timescale of the evolution of <it>Daphnia</it>.</p> <p>Results</p> <p>We describe new fossils of ephippia from the Khotont site in Mongolia associated with the Jurassic-Cretaceous boundary (about 145 MYA) that are morphologically similar to several modern genera of the family Daphniidae, including the two major subgenera of <it>Daphnia</it>, i.e., <it>Daphnia </it>s. str. and <it>Ctenodaphnia</it>. The daphniid fossils co-occurred with fossils of the predaceous phantom midge (Chaoboridae).</p> <p>Conclusions</p> <p>Our findings indicate that the main subgenera of <it>Daphnia </it>are likely much older than previously known from fossils (at least 100 MY older) or from nuclear DNA estimates of divergence. The results showing co-occurrence of the main subgenera far from the presumed Laurasia/Gondwanaland dispersal barrier shortly after formation suggests that vicariance from the breakup of Pangaea is an unlikely explanation for the origin of the main subgenera. The fossil impressions also reveal that the coevolution of a dipteran predator (Chaoboridae) with the subgenus <it>Daphnia </it>is much older than previously known -- since the Mesozoic.</p

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

The R*-operation for Feynman graphs with generic numerators

Abstract The R *-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R *-operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all top-level propagator graphs at five loops in four dimensional ϕ 3 theory

The laminar-turbulent transition in a fibre laser

Studying the transition from a linearly stable coherent laminar state to a highly disordered state of turbulence is conceptually and technically challenging, and of great interest because all pipe and channel flows are of that type. In optics, understanding how a system loses coherence, as spatial size or the strength of excitation increases, is a fundamental problem of practical importance. Here, we report our studies of a fibre laser that operates in both laminar and turbulent regimes. We show that the laminar phase is analogous to a one-dimensional coherent condensate and the onset of turbulence is due to the loss of spatial coherence. Our investigations suggest that the laminar-turbulent transition in the laser is due to condensate destruction by clustering dark and grey solitons. This finding could prove valuable for the design of coherent optical devices as well as systems operating far from thermodynamic equilibrium

Classical Morphology of Plants as an Elementary Instance of Classical Invariant Theory

It has long been known that structural chemistry shows an intriguing correspondence with Classical Invariant Theory (CIT). Under this view, an algebraic binary form of the degree n corresponds to a chemical atom with valence n and each physical molecule or ion has an invariant-theoretic counterpart. This theory was developed using the Aronhold symbolical approach and the symbolical processes of convolution/transvection in CIT was characterized as a potential “accurate morphological method”. However, CIT has not been applied to the formal morphology of living organisms. Based on the morphological interpretation of binary form, as well as the process of convolution/transvection, the First and Second Fundamental Theorems of CIT and the Nullforms of CIT, we show how CIT can be applied to the structure of plants, especially when conceptualized as a series of plant metamers (phytomers). We also show that the weight of the covariant/invariant that describes a morphological structure is a criterion of simplicity and, therefore, we argue that this allows us to formulate a parsimonious method of formal morphology. We demonstrate that the “theory of axilar bud” is the simplest treatment of the grass seedling/embryo. Our interpretations also represent Troll's bauplan of the angiosperms, the principle of variable proportions, morphological misfits, the basic types of stem segmentation, and Goethe's principle of metamorphosis in terms of CIT. Binary forms of different degrees might describe any repeated module of plant organisms. As bacteria, invertebrates, and higher vertebrates are all generally shared a metameric morphology, wider implications of the proposed symmetry between CIT and formal morphology of plants are apparent

Measurement of Trilinear Gauge Couplings in e+e−e^+ e^- Collisions at 161 GeV and 172 GeV

Trilinear gauge boson couplings are measured using data taken by DELPHI at 161~GeV and 172~GeV. Values for $WWV$ couplings ($V=Z, \gamma$) are determined from a study of the reactions \eeWW\ and \eeWev, using differential distributions from the $WW$ final state in which one $W$ decays hadronically and the other leptonically, and total cross-section data from other channels. Limits are also derived on neutral $ZV\gamma$ couplings from an analysis of the reaction \eegi

Search for neutral heavy leptons produced in ZZ decays

Weak isosinglet Neutral Heavy Leptons (νm) have been searched for using data collected by the DELPHI detector corresponding to 3.3 × 106 hadronic Z0 decays at LEP1. Four separate searches have been performed, for short-lived νm production giving monojet or acollinear jet topologies, and for long-lived νm giving detectable secondary vertices or calorimeter clusters. No indication of the existence of these particles has been found, leading to an upper limit for the branching ratio BR(Z0 → νmν̄) of about 1.3 × 10-6 at 95% confidence level for νm masses between 3.5 and 50 GeV/c2. Outside this range the limit weakens rapidly with the νm mass. The results are also interpreted in terms of limits for the single production of excited neutrinos. © Springer-Verlag 1997