Algebraic properties of Gardner's deformations for integrable systems

An algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. An exactly solvable two-component extension of the Liouville equation is found.Comment: Proc. conf. "Nonlinear Physics: Theory and Experiment IV" (Gallipoli, 2006); Theor. Math. Phys. (2007) 151:3/152:1-2, 16p. (to appear

Relations among neutrino observables in the light of a large theta_13 angle

The recent T2K and MINOS indications for a "large" theta_13 neutrino mixing angle can be accommodated in principle by an infinite number of Yukawa flavour structures in the seesaw model. Without considering any explicit flavour symmetry, there is an instructive exercise one can do: to determine the simplest flavour structures which can account for the data with a minimum number of parameters, simply assuming these parameters to be uncorrelated. This approach points towards a limited number of simple structures which show the minimum complexity a neutrino mass model must generally involve to account for the data. These basic structures essentially lead to only 4 relations between the neutrino observables. We emphasize that 2 of these relations, |sin theta_13|=(tan theta_23/cos delta)*(1-tan theta_12)/(1+tan theta_12) and |sin theta_13| = sin theta_12 R^1/4, with R= Delta m^2_21/Delta m^2_32, have several distinctive properties. First, they hold not only with a minimum number of parameters, but also for complete classes of more general models. Second, any value of theta_13 within the T2K and MINOS ranges can be obtained from these relations by taking into account small perturbations. Third, they turn out to be the pivot relations of models with approximate conservation of lepton number, which allow the seesaw interactions to induce observable flavour violating processes, such as mu -> e gamma and tau -> mu gamma. Finally, in specific cases of this kind, these structures have the rather unique property to allow a full reconstruction of the seesaw Lagrangian from low energy data.Comment: 13 pages, 3 figure

Ableitung kumulativer Dosismodelle zur Auswertung physischer Belastungen

Zusammenfassung Hintergrund Als vertiefende Reanalyse der Deutschen Wirbelsäulenstudie (DWS1) versucht die DWS-Richtwertestudie die Ableitung von kumulativen Dosismodellen, mit denen der Dosis-Wirkung-Zusammenhang zwischen bandscheibenbedingten Erkrankungen an der Lendenwirbelsäule und physischen Belastungen im Sinne der Berufskrankheit Nr. 2108 der Berufskrankheiten-Verordnung (BKV) für Männer und Frauen beschrieben werden kann. Drei besondere Herausforderungen ergeben sich für die statistische Analyse: 1. Dosimetrie: Das optimale Dosismodell ist unbekannt. Kandidatenmodelle variieren weit mit angesetzten „Schwellen“ für die Rumpfvorneigung, die Lendenwirbelsäulen-Bandscheiben-Druckkraft und die Tagesdosis. (Erst ab der jeweiligen Schwelle werden die Belastungsanteile bei der Dosisbestimmung mit quadratischer Kraftwichtung relativ zur Vorgangsdauer und „Vollwertberücksichtigung“ der Bandscheibendruckkraft einbezogen.) 2. Epidemiologie: Die Form des optimalen Risikomodells [stetige „Odds-ratio“(OR)-Kurve] über der Lebensdosis ist unbekannt und kann komplex sein (z. B. „W-Form“); dies führt zu einer großen Zahl an Kandidatenmodellen. 3. Richtwertermittlung: Auf Basis der Risikoanalyse soll geprüft werden, ob eine Verdopplungsdosis mit 95 %-Konfidenzintervall abgeleitet werden kann, also die Lebensdosis, die mit einer Verdopplung des Erkrankungsrisikos einhergeht. Material und Methoden Es wurde eine 2-schrittige Multi-Modell-Analyse (MMA) mit informationsgestützter Modellmittelung durchgeführt. Zu allen sinnvollen Kombinationen der Dosismodelleigenschaften werden als Risikomodelle multivariable fraktionale Polynome (FP) 2. und 4. Grades berechnet. Deren Anpassungsgüte wird mit dem Akaike-Informations-Kriterium (AIC) gemessen. Im 1. Schritt der MMA werden für jede Eigenschaft separat optimale Schwellenwerte durch gewichtete Mittelung bestimmt; hierbei wird als Gewicht der relative Informationsgehalt des jeweiligen FP verwendet (Akaike-Gewicht). Diese optimalen Schwellenwerte werden dann eingesetzt, um ein Kombinationsdosismodell zu ermitteln, dessen Werte als Referenzdosis (Bezugsabszisse) für alle weiteren Analysen dienen. Über dieser Referenzdosis werden in einem 2. Schritt der MMA alle kontinuierlichen Regressionskurven und deren Konfidenzbänder Akaike-gewichtet gemittelt (Mittelung der Modellprädiktoren für jedes Individuum) und auf ein OR = 1 bei einer Dosis = 0 bezogen. Die so ermittelten OR-Schätzer werden mit FP 4. Grades geglättet, um finale stetige OR-Kurven über der Referenzdosis mit 95 %-Konfidenzintervallen zu erhalten. Aus diesen Kurven werden durch Umkehrung die Verdopplungsdosis und ein zugehöriges Konfidenzintervall geschätzt. Ergebnisse Die MMA wird auf alle 4 Fallgruppen (FG; 2 Geschlechter, 2 Endpunkte: Prolaps und Chondrose) erfolgreich angewendet. Die Methodik wird an FG 1 (Männer/Prolaps) demonstriert. Schlussfolgerung Bei fehlenden oder strittigen biologischen A-priori-Kriterien zur Spezifizierung des optimalen dosimetrischen oder epidemiologischen Modells stellt die MMA einen Lösungsweg dar. </jats:sec

Creating a FACETS digital toolkit to promote quality of life of people with multiple sclerosis through Participatory Design

In this paper, we report on the first stages of creating a stand-alone digital toolkit focusing on the homework elements of FACETS (Fatigue: Applying Cognitive behavioural and Energy effectiveness Techniques to lifeStyle). FACETS is an evidence-based face-to-face fatigue management group programme for people with multiple sclerosis. This paper details the participatory design process from requirements elicitation to initial prototyping and how offline activities linked to each session have been mapped in the digitised solution (mobile app)

The Minimal Scale Invariant Extension of the Standard Model

We perform a systematic analysis of an extension of the Standard Model that includes a complex singlet scalar field and is scale invariant at the tree level. We call such a model the Minimal Scale Invariant extension of the Standard Model (MSISM). The tree-level scale invariance of the model is explicitly broken by quantum corrections, which can trigger electroweak symmetry breaking and potentially provide a mechanism for solving the gauge hierarchy problem. Even though the scale invariant Standard Model is not a realistic scenario, the addition of a complex singlet scalar field may result in a perturbative and phenomenologically viable theory. We present a complete classification of the flat directions which may occur in the classical scalar potential of the MSISM. After calculating the one-loop effective potential of the MSISM, we investigate a number of representative scenarios and determine their scalar boson mass spectra, as well as their perturbatively allowed parameter space compatible with electroweak precision data. We discuss the phenomenological implications of these scenarios, in particular, whether they realize explicit or spontaneous CP violation, neutrino masses or provide dark matter candidates. In particular, we find a new minimal scale-invariant model of maximal spontaneous CP violation which can stay perturbative up to Planck-mass energy scales, without introducing an unnaturally large hierarchy in the scalar-potential couplings.Comment: 71 pages, 34 eps figures, numerical error corrected, clarifying comments adde

Physics at a Fermilab Proton Driver

This report documents the physics case for building a 2 MW, 8 GeV superconducting linac proton driver at Fermilab.Comment: 52 pages, 15 figure

The Gravitino-Stau Scenario after Catalyzed BBN

We consider the impact of Catalyzed Big Bang Nucleosynthesis on theories with a gravitino LSP and a charged slepton NLSP. In models where the gravitino to gaugino mass ratio is bounded from below, such as gaugino-mediated SUSY breaking, we derive a lower bound on the gaugino mass parameter m_1/2. As a concrete example, we determine the parameter space of gaugino mediation that is compatible with all cosmological constraints.Comment: 1+14 pages, 6 figures; v2: minor clarifications, 1 reference added, matches version to appear in JCA

Reinforcement learning or active inference?

This paper questions the need for reinforcement learning or control theory when optimising behaviour. We show that it is fairly simple to teach an agent complicated and adaptive behaviours using a free-energy formulation of perception. In this formulation, agents adjust their internal states and sampling of the environment to minimize their free-energy. Such agents learn causal structure in the environment and sample it in an adaptive and self-supervised fashion. This results in behavioural policies that reproduce those optimised by reinforcement learning and dynamic programming. Critically, we do not need to invoke the notion of reward, value or utility. We illustrate these points by solving a benchmark problem in dynamic programming; namely the mountain-car problem, using active perception or inference under the free-energy principle. The ensuing proof-of-concept may be important because the free-energy formulation furnishes a unified account of both action and perception and may speak to a reappraisal of the role of dopamine in the brain

Fitting Neutrino Physics with a U(1)_R Lepton Number

We study neutrino physics in the context of a supersymmetric model where a continuous R-symmetry is identified with the total Lepton Number and one sneutrino can thus play the role of the down type Higgs. We show that R-breaking effects communicated to the visible sector by Anomaly Mediation can reproduce neutrino masses and mixing solely via radiative contributions, without requiring any additional degree of freedom. In particular, a relatively large reactor angle (as recently observed by the Daya Bay collaboration) can be accommodated in ample regions of the parameter space. On the contrary, if the R-breaking is communicated to the visible sector by gravitational effects at the Planck scale, additional particles are necessary to accommodate neutrino data.Comment: 19 pages, 3 figures; v2: references added, constraints updated, overall conclusions unchange