Tensor 22-Product for sl2\mathfrak{sl}_{2}: Extensions to the Negative Half

In a recent paper, the author defined an operation of tensor product for a large class of $2$-representations of $\mathcal{U}^{+}$, the positive half of the $2$-category associated to $\mathfrak{sl}_{2}$. In this paper, we prove that the operation extends to give an operation of tensor product for representations of the full $2$-category $\mathcal{U}$: when the inputs are $2$-representations of the full $\mathcal{U}$, the $2$-product is also a $2$-representation of the full $\mathcal{U}$. As in the previous paper, the $2$-product is given for a simple $2$-representation $\mathcal{L}(1)$ and an abelian $2$-representation $\mathcal{V}$ taken from the $2$-category of algebras. This is the first construction of an operation of tensor product for higher representations of a full Lie algebra in the abelian setting.Comment: 51 pages. Many corrections and improvements throughout. References in this version are compatible with arXiv:2209.06782v

A tensor 2-product of 2-representations of sl2+\mathfrak{sl}_{2}^{+}

We construct an explicit abelian model for the tensor $2$-product of $2$-representations of $\mathfrak{sl}_{2}^{+}$, specifically the product of a simple $2$-representation $\mathcal{L}(1)$ with a given abelian $2$-representation $\mathcal{V}$ taken from the $2$-category of algebras. We study the case $\mathcal{V}=\mathcal{L}(1)$ in detail, and we show that the $2$-product in this case recovers the expected structure. Our construction partially verifies a conjecture of Rouquier from 2008.Comment: 50 pages, 5 diagrams; v2 updates some methods for compatibility with arXiv:2303.17115 and includes some minor improvement

Ethics, Logs and Videotape: Ethics in Large Scale User Trials and User Generated Content. Workshop organized at CHI'11.

Mobile Life CentreMobile 2.

Review of Markov models for maintenance optimization in the context of offshore wind

The offshore environment poses a number of challenges to wind farm operators. Harsher climatic conditions typically result in lower reliability while challenges in accessibility make maintenance difficult. One of the ways to improve availability is to optimize the Operation and Maintenance (O&M) actions such as scheduled, corrective and proactive maintenance. Many authors have attempted to model or optimize O&M through the use of Markov models. Two examples of Markov models, Hidden Markov Models (HMMs) and Partially Observable Markov Decision Processes (POMDPs) are investigated in this paper. In general, Markov models are a powerful statistical tool, which has been successfully applied for component diagnostics, prognostics and maintenance optimization across a range of industries. This paper discusses the suitability of these models to the offshore wind industry. Existing models which have been created for the wind industry are critically reviewed and discussed. As there is little evidence of widespread application of these models, this paper aims to highlight the key factors required for successful application of Markov models to practical problems. From this, the paper identifies the necessary theoretical and practical gaps that must be resolved in order to gain broad acceptance of Markov models to support O&M decision making in the offshore wind industry

Heuristic algorithm for the problem of vessel routing optimisation for offshore wind farms

A new heuristic method is proposed for the problem of vessel routing optimisation for offshore wind farms. Turbines requiring a maintenance action are arranged into clusters, each associated with a vessel and a value for repairing the turbines. The clusters with the highest value are used to produce offspring, which is selected from the remaining high-value clusters, provided the constraints are met. The process is repeated until vessels available or turbines requiring maintenance are exhausted. To test the performance of the proposed approach, the same problem was formulated as integer linear programming problem and benchmarked against the IBM CPLEX commercial solver. The proposed method was shown to consistently produce close-to-optimal policies within seconds, even in problems with 15–20 turbines requiring a maintenance action. Although the proposed method only outperformed the commercial solver in one instance, its benefits include short and consistent computational times and the fact that the users can easily understand, implement and adapt the algorithm to suit their needs

Development of an O&M tool for short term decision making applied to offshore wind farms

Every day, wind farm operators make logistical decisions requiring them to efficiently use resources to maximise wind turbine availability. Deciding which turbines to maintain, the order in which they are visited and vessel routing is challenging due to multiple constraints such as weather, failure type and available vessels and technicians. To automate this decision making process, the authors collaborated with a UK offshore wind farm operator to create a tool, which recommends an on-the-day vessel routing strategy, such that costs are minimised while maximising the number of turbines repaired. To demonstrate the tool's capabilities, a case study is presented and the model's outputs, which include geographical locations of the turbines to be visited, are shown

Efficient Isotropic BRDF Measurement

In this paper we present novel reflectance measurement procedures that require fewer total measurements than standard uniform sampling approaches. First, we acquire densely sampled reflectance data for a large collection of different materials. Using these densely sampled measurements we analyze the general surface reflectance function to determine the local signal variation at each point in the function's domain. We then use wavelet analysis to derive a common basis for all of the acquired reflectance functions as well as a corresponding non-uniform sampling pattern that corresponds to all non-zero wavelet coefficients. Second, we show that the reflectance of an arbitrary material can be represented as a linear combination of the surface reflectance functions. Furthermore, our analysis provides a reduced set of sampling points that permits us to robustly estimate the coefficients of this linear combination. These procedures dramatically shorten the acquisition time for isotropic reflectance measurements. We present a detailed description and analysis of our measurement approaches and sampling strategies.Engineering and Applied Science