Integrable Discretizations of Chiral Models

A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is achieved via a deformation of the ordinary differential calculus. In particular, the nonlinear Toda lattice results in this way from the linear (continuum) wave equation. The method is applied to several further examples. We also construct Lax pairs and B\"acklund transformations for the class of models considered in this work.Comment: 14 pages, Late

Oceanic Rossby waves drive inter-annual predictability of net primary production in the central tropical Pacific

In the Pacific Ocean, off-equatorial Rossby waves (RWs), initiated by atmosphere-ocean interaction, modulate the inter-annual variability of the thermocline. In this study, we explore the resulting potential gain in predictability of central tropical Pacific primary production, which in this region strongly depends on the supply of macronutrients from below the thermocline. We use a decadal prediction system based on the Max Planck Institute Earth system model to demonstrate that for the time period 1998-2014 properly initialized RWs explain an increase in predictability of net primary productivity (NPP) in the off-equatorial central tropical Pacific. We show that, for up to 5 years in advance, predictability of NPP derived from the decadal prediction system is significantly larger than that derived from persistence alone, or an uninitialized historical simulation. The predicted signal can be explained by the following mechanism: off-equatorial RWs are initiated in the eastern Pacific and travel towards the central tropical Pacific on a time scale of 2-6 years. On their arrival the RWs modify the depths of both thermocline and nutricline, which is fundamental to the availability of nutrients in the euphotic layer. Local upwelling transports nutrients from below the nutricline into the euphotic zone, effectively transferring the RW signal to the near-surface ocean. While we show that skillful prediction of central off-equatorial tropical Pacific NPP is possible, we open the door for establishing predictive systems for food web and ecosystem services in that region

Differential Calculi on Commutative Algebras

A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in very much the same way we are used to from the geometrical arena underlying classical physical theories and models. In previous work, certain differential calculi on a commutative algebra exhibited relations with lattice structures, stochastics, and parametrized quantum theories. This motivated the present systematic investigation of differential calculi on commutative and associative algebras. Various results about their structure are obtained. In particular, it is shown that there is a correspondence between first order differential calculi on such an algebra and commutative and associative products in the space of 1-forms. An example of such a product is provided by the Ito calculus of stochastic differentials. For the case where the algebra A is freely generated by `coordinates' x^i, i=1,...,n, we study calculi for which the differentials dx^i constitute a basis of the space of 1-forms (as a left A-module). These may be regarded as `deformations' of the ordinary differential calculus on R^n. For n < 4 a classification of all (orbits under the general linear group of) such calculi with `constant structure functions' is presented. We analyse whether these calculi are reducible (i.e., a skew tensor product of lower-dimensional calculi) or whether they are the extension (as defined in this article) of a one dimension lower calculus. Furthermore, generalizations to arbitrary n are obtained for all these calculi.Comment: 33 pages, LaTeX. Revision: A remark about a quasilattice and Penrose tiling was incorrect in the first version of the paper (p. 14

Flow Phase Diagram for the Helium Superfluids

The flow phase diagram for He II and $^3$He-B is established and discussed based on available experimental data and the theory of Volovik [JETP Letters {\bf{78}} (2003) 553]. The effective temperature - dependent but scale - independent Reynolds number $Re_{eff}=1/q=(1+\alpha')/\alpha$, where $\alpha$ and $\alpha'$ are the mutual friction parameters and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram allows identification of experimentally observed turbulent states I and II in counterflowing He II with the turbulent regimes suggested by Volovik.Comment: 2 figure

Forecast skill of multi-year seasonal means in the decadal prediction system of the Max Planck Institute for Meteorology

We examine the latest decadal predictions performed with the coupled model MPI-ESM as part of the Coupled Model Intercomparison Project Phase 5 (CMIP5). We use ensembles of uninitialized and yearly initialized experiments to estimate the forecast skill for surface air temperature. Like for its precursor, the initialisation of MPI-ESM improves forecast skill for yearly and multi-yearly means, predominately over the North Atlantic for all lead times. Over the tropical Pacific, negative skill scores reflect a systematic error in the initialisation. We also examine the forecast skill of multi-year seasonal means. Skill scores of winter means are predominantly positive over northern Europe. In contrast, summer to autumn means reveal positive skill scores over central and south-eastern Europe. The skill scores of summer means are attributable to an observed pressure-gradient response to the North Atlantic surface temperatures

Genuine Counterfactual Communication with a Nanophotonic Processor

In standard communication information is carried by particles or waves. Counterintuitively, in counterfactual communication particles and information can travel in opposite directions. The quantum Zeno effect allows Bob to transmit a message to Alice by encoding information in particles he never interacts with. The first suggested protocol not only required thousands of ideal optical components, but also resulted in a so-called "weak trace" of the particles having travelled from Bob to Alice, calling the scalability and counterfactuality of previous proposals and experiments into question. Here we overcome these challenges, implementing a new protocol in a programmable nanophotonic processor, based on reconfigurable silicon-on-insulator waveguides that operate at telecom wavelengths. This, together with our telecom single-photon source and highly-efficient superconducting nanowire single-photon detectors, provides a versatile and stable platform for a high-fidelity implementation of genuinely trace-free counterfactual communication, allowing us to actively tune the number of steps in the Zeno measurement, and achieve a bit error probability below 1%, with neither post-selection nor a weak trace. Our demonstration shows how our programmable nanophotonic processor could be applied to more complex counterfactual tasks and quantum information protocols.Comment: 6 pages, 4 figure

Soliton equations and the zero curvature condition in noncommutative geometry

Familiar nonlinear and in particular soliton equations arise as zero curvature conditions for GL(1,R) connections with noncommutative differential calculi. The Burgers equation is formulated in this way and the Cole-Hopf transformation for it attains the interpretation of a transformation of the connection to a pure gauge in this mathematical framework. The KdV, modified KdV equation and the Miura transformation are obtained jointly in a similar setting and a rather straightforward generalization leads to the KP and a modified KP equation. Furthermore, a differential calculus associated with the Boussinesq equation is derived from the KP calculus.Comment: Latex, 10 page

Cáncer pulmonar: prevención y pesquisa precoz

ResumenEl cáncer pulmonar es el más mortal de todos los cánceres. Debido a que la gran mayoría de los cánceres pulmonares son causados por el hábito de fumar, su erradicación es la mejor estrategia de prevención primaria. El diagnóstico del cáncer pulmonar en etapas tempranas mejora significativamente su pronóstico, por lo que ésta es la mejor estrategia de prevención secundaria. Recientemente se ha reportado que un programa de pesquisa de cáncer pulmonar con escáner de tórax (TAC) reduce la mortalidad por cáncer. El objetivo de esta revisión es, en primer lugar, apelar a la evidencia en cuanto al rendimiento de los programas de pesquisa de cáncer pulmonar en poblaciones de alto riesgo, y en segundo lugar, analizar las distintas estrategias que tiene un médico cuando se enfrenta a un paciente a quien se le ha encontrado incidentalmente un nódulo pulmonar.SummaryLung cancer is a deadly disease. Since this cancer is closely related to tobacco smoke, the best way to avoid this disease is smoking prevention. Unfortunately smoking is a worldwide epidemic and in Chile its prevalence is not decreasing. The second best strategy is an early detection. For the first time there is a report showing that screening with the use of low-dose CT reduces mortality from lung cancer. The prognosis is much better in early stages. The purpose of this publication is to review the evidence about screening of lung cancer, and to analyze the different strategies to deal, in the general practice, with a finding of a lung nodule