Propagating Higgs Boundstates from Sfermions

A model of supersymmetric dynamical electroweak breaking with propagating sfermionic Higgs boundstates is constructed. The low energy effective theory is represented by a slight extension of the MSSM, including 2 additional Higgs doublets and neutrino Yukawa couplings. A large tan(beta) is a necessary condition. The model could be relevant in approaches which derive propagating Higgs boundstates from strings.Comment: 12 page

Time series semi-Markov decision process with variable costs for maintenance planning

Deciding when and how to maintain offshore wind turbines is becoming even more complex as the size of wind farms increases, while accessibility is challenging compared to onshore wind farms. Planning future maintenance actions requires the wind farm operator to consider factors such as the current condition of the turbine, the cost of a given maintenance action, revenue generated by the asset, weather factors and vessel availability. Rather than making case-by-case decisions for each turbine, the approach described in this paper allows the wind farm operators to automate the process of short to-medium term maintenance planning through application of a Semi-Markov Decision Process (SMDP). The model proposed here is capable of suggesting the cost-optimal maintenance policy given weather forecast, future vessel costs and availability and the current condition of the turbine. Using the semi-Markov approach, allows the user to implement time varying failure rate. As the model is capable of utilising time-series data, future weather and vessel constraints can be applied depending on the information available to the user at the time, which will be reflected in the optimal policy suggested by the model. The model proposed here facilitates maintenance decision making in wind farms and will lead to cost reduction through more efficient planning. In addition to that, the model can be used to carry out a cost-benefit analysis of using vessels with different properties

Stallings's Fibring Theorem and PD3\mathrm{PD}^3-pairs

We prove that if $G$ fibres algebraically and is part of a $\mathrm{PD}^3$-pair, then $G$ is the fundamental group of a fibred compact aspherical 3-manifold. This yields a new, homological proof of a classical theorem of Stallings: if $G = \pi_1(M^3)$ is the fundamental group of a compact irreducible 3-manifold $M^3$ and $\phi \colon G \to \mathbb{Z}$ is a surjective homomorphism with finitely generated kernel, then $\phi$ is induced by a topological fibration of $M^3$ over the circle.Comment: 7 page

On the Equivalence of Three-Particle Scattering Formalisms

In recent years, different on-shell $\mathbf{3}\to\mathbf{3}$ scattering formalisms have been proposed to be applied to both lattice QCD and infinite volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in Phys.~Rev.~D92, 114509 (2015) and subsequently Brice\~no, Hansen, and Sharpe in Phys.~Rev.~D95, 074510 (2017) can be recovered from the $B$-matrix representation, derived on the basis of $S$-matrix unitarity, presented by Mai {\em et al.} in Eur.~Phys.~J.~A53, 177 (2017) and Jackura {\em et al.} in Eur.~Phys.~J.~C79, 56 (2019). Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the non-relativistic limit of both representations.Comment: 13 pages, 5 figure

Statistical Geometry in Quantum Mechanics

A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the Hilbert space H. By consideration of the square-root density function we can regard M as a submanifold of the unit sphere in H. Therefore, H embodies the `state space' of the probability distributions, and the geometry of M can be described in terms of the embedding of in H. The geometry in question is characterised by a natural Riemannian metric (the Fisher-Rao metric), thus allowing us to formulate the principles of classical statistical inference in a natural geometric setting. In particular, we focus attention on the variance lower bounds for statistical estimation, and establish generalisations of the classical Cramer-Rao and Bhattacharyya inequalities. The statistical model M is then specialised to the case of a submanifold of the state space of a quantum mechanical system. This is pursued by introducing a compatible complex structure on the underlying real Hilbert space, which allows the operations of ordinary quantum mechanics to be reinterpreted in the language of real Hilbert space geometry. The application of generalised variance bounds in the case of quantum statistical estimation leads to a set of higher order corrections to the Heisenberg uncertainty relations for canonically conjugate observables.Comment: 32 pages, LaTex file, Extended version to include quantum measurement theor

Spatial interactions in agent-based modeling

Agent Based Modeling (ABM) has become a widespread approach to model complex interactions. In this chapter after briefly summarizing some features of ABM the different approaches in modeling spatial interactions are discussed. It is stressed that agents can interact either indirectly through a shared environment and/or directly with each other. In such an approach, higher-order variables such as commodity prices, population dynamics or even institutions, are not exogenously specified but instead are seen as the results of interactions. It is highlighted in the chapter that the understanding of patterns emerging from such spatial interaction between agents is a key problem as much as their description through analytical or simulation means. The chapter reviews different approaches for modeling agents' behavior, taking into account either explicit spatial (lattice based) structures or networks. Some emphasis is placed on recent ABM as applied to the description of the dynamics of the geographical distribution of economic activities, - out of equilibrium. The Eurace@Unibi Model, an agent-based macroeconomic model with spatial structure, is used to illustrate the potential of such an approach for spatial policy analysis.Comment: 26 pages, 5 figures, 105 references; a chapter prepared for the book "Complexity and Geographical Economics - Topics and Tools", P. Commendatore, S.S. Kayam and I. Kubin, Eds. (Springer, in press, 2014

Operational Metrics for an Offshore Wind Farm & Their Relation to Turbine Access Restrictions and Position in the Array

Abstract: This study explores operations & maintenance requirements for offshore wind turbines. It does so by calculating performance, reliability and maintenance metrics from an operational database provided by a large offshore wind farm. Distributions of number of repairs and repair times per turbine are shared, as well as number of visits. A focus is placed on the effect of tidal access restrictions and position in the array by comparing clusters of turbines within the wind farm. It was found that tidal access restrictions lead to an increase in mean time to repair of 16%, and 0.22% decrease in technical availability. Turbines in the first few rows with reference to the prominent wind direction experience more minor failures on average, while those constantly operating in the wake of others are characterised by more major failures, and therefore a higher mean time to repair