The chebop system for automatic solution of differential equations

In MATLAB, it would be good to be able to solve a linear differential equation by typing u = L\f, where f, u, and L are representations of the right-hand side, the solution, and the differential operator with boundary conditions. Similarly it would be good to be able to exponentiate an operator with expm(L) or determine eigenvalues and eigenfunctions with eigs(L). A system is described in which such calculations are indeed possible, based on the previously developed chebfun system in object-oriented MATLAB. The algorithms involved amount to spectral collocation methods on Chebyshev grids of automatically determined resolution

Differential response at the seafloor during Palaeocene and Eocene ocean warming events at Walvis Ridge, Atlantic Ocean (ODP Site 1262)

The Latest Danian Event (LDE, c. 62.1 Ma) is an early Palaeogene hyperthermal or transient (<200 ka) ocean warming event. We present the first deep-sea benthic foraminiferal faunal record to study deep-sea biotic changes together with new benthic (Nuttallides truempyi) stable isotope data from Walvis Ridge Site 1262 (Atlantic Ocean) to evaluate whether the LDE was controlled by similar processes as the minor early Eocene hyperthermals. The spacing of the double negative δ13C and δ18O excursion and the slope of the δ18O–δ13C regression are comparable, strongly suggesting a similar orbital control and pacing of eccentricity maxima as well as a rather homogeneous carbon pool. However, in contrast to early Eocene hyperthermals, the LDE exhibits a remarkable stability of the benthic foraminiferal fauna. This lack of benthic response could be related to the absence of threshold-related circulation changes or better pre-adaptation to elevated deep-sea temperatures, as the LDE was superimposed on a cooling trend, in contrast to early Eocene warming

Citing retracted papers has a negative domino effect on science, education, and society

Once an academic paper is retracted, it is by no means certain it will not go on being cited. Jaime A. Teixeira da Silva, Judit Dobránszki and Helmar Bornemann-Cimenti use three key examples to demonstrate how the continued citation of retracted papers can lead to the proliferation of erroneous literature, mislead young academics and cause confusion among researchers as to the veracity of scientific claims. Most damagingly, it can undermine the credibility of science and public trust in research. Retracted papers should not be cited and it is the responsibility of researchers, editorial teams and publishers to guard against this happening

Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles

The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painlev\'e II transcendent and its associated isomonodromic system. As a corollary, the density function for the spacing between these two eigenvalues is similarly characterized.The particular solution of Painlev\'e II that arises is a double shifted B\"acklund transformation of the Hasting-McLeod solution, which applies in the case of the distribution of the largest eigenvalue at the soft edge. Our deductions are made by employing the hard-to-soft edge transitions to existing results for the joint distribution of the first and second eigenvalue at the hard edge \cite{FW_2007}. In addition recursions under $a \mapsto a+1$ of quantities specifying the latter are obtained. A Fredholm determinant type characterisation is used to provide accurate numerics for the distribution of the spacing between the two largest eigenvalues.Comment: 26 pages, 1 Figure, 2 Table

Stable isotope paleoecology (d¹³C and d¹⁸O) of early Eocene <i>Zeauvigerina aegyptiaca</i> from the North Atlantic (DSDP Site 401)

Within the expanded and clay-enriched interval following the Paleocene-Eocene Thermal Maximum (PETM; ~55.8 Ma) at Deep Sea Drilling Project (DSDP) Site 401 (eastern North Atlantic), high abundances of well-preserved biserial planktic foraminifera such as Zeauvigerina aegyptiaca and Chiloguembelina spp. occur. The paleoecological preferences of these taxa are only poorly constrained, largely because existing records are patchy in time and space. The thin-walled Z. aegyptiaca is usually rather small (13C and d18O) study of well-preserved specimens of Z. aegyptiaca and several planktic foraminiferal species (Morozovella subbotinae, Subbotina patagonica, Chiloguembelina wilcoxensis) enabled us to determine the preferred depth habitat and mode of life for Z. aegyptiaca. Oxygen isotope values of Z. aegyptiaca range from -1.57‰ to -2.07‰ and overlap with those of M. subbotinae indicating that their habitat is (1) definitely planktic, which has been questioned by some earlier isotopic studies, and (2) probably within the lower surface mixed layer. Carbon isotope ratios range from 0.99‰ to 1.34‰ and are distinctly lower than values for non-biserial planktic species. This may indicate isotopic disequilibrium between ambient seawater and the calcareous tests of Z. aegyptiaca, which we relate to vital effects and to its opportunistic behavior. The observed isotopic signal of Z. aegyptiaca relative to the other planktic foraminiferal species is highly similar to many other microperforate bi- and triserial planktic genera that have appeared through geological time such as Heterohelix, Guembelitria, Chiloguembelina, Streptochilus and Gallitellia and we suggest that Z. aegyptiaca shares a similar ecology and habitat. Thus, in order for the opportunistic Z. aegyptiaca to bloom during the aftermath of the PETM, we assume that at that time, the surface waters at Site 401 were influenced by increased terrestrial run-off and nutrient availability

Under-shelf ice foraging of Weddell seals

The Weddell seal (Leptonychotes weddellii) inhabits the Antarctic coastal ecosystem and aggregates in areas characterized by a stable fast ice layer. Due to their extreme diving capabilities, they are able to exploit both pelagic and benthic prey resources. They mainly feed on fishes but occasionally also take cephalopods and crustaceans. Weddell seals instrumented with still-picture camera loggers in the Drescher Inlet, eastern Weddell Sea, detected an unknown cryo-benthic community underneath the floating ice shelf. Images show dense aggregations of invertebrates that likely represent an attractive food horizon for Weddell seals. In this context, we conducted a retrospective analysis of dive profiles collected in the Drescher Inlet to identify favoured hunting depths of Weddell seals and correlate those to the local physical and biological environment. A total of 34 adult Weddell seals were instrumented with dive loggers in the course of six summer field campaigns between 1990 and 2016. An automated broken stick algorithm was used to separate each dive profile into different segments. Segments with a high sinuosity were considered to indicate hunting. Segments characterized by a straight dive trajectories (low sinuosity), were assumed to be transit phases with no hunting activities. A tri-modal distribution of mean hunting depths suggests that Weddell seals concentrated their foraging activities in three depth strata. A peak in hunting depths below 370 m corresponds to the sea floor of the Drescher Inlet, indicating demersal foraging. A second peak between 110 and 160 m matches with the depth of the underside of the floating ice shelf, which suggests shelf ice associated foraging. The third peak probably represents hunting in the pelagic realm. Our investigation highlights the importance of the shelf ice underside as an attractive food horizon for Weddell seals suggesting a re-evaluation of trophic interactions and bentho-pelagic processes in the coastal Antarctic ecosystem

On the construction of high-order force gradient algorithms for integration of motion in classical and quantum systems

A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the new fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth- and eighth-order-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.Comment: 23 pages, 2 figures; submitted to Phys. Rev.