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We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry., Comment: Comments and feedback very welcome; 274 pages

We develop techniques for constructing model structures on chain complexes valued in accessible exact categories, and apply this to show that for a closed symmetric monoidal, locally presentable exact category $\mathpzc{E}$ with exact filtered colimits and enough flat objects, the flat cotorsion pair on $\mathpzc{E}$ induces an exact model structure on $\mathrm{Ch}(\mathpzc{E})$. Further we show that when enriched over $\mathbb{Q}$ such categories furnish convenient settings for homotopical algebra - in particular that they are Homotopical Algebra Contexts, and admit powerful Koszul duality theorems. As an example, we consider categories of sheaves valued in monoidal locally presentable exact categories., Comment: Preliminary Version; Comments very welcome! 73 pages

Short-term forecasting of solar photovoltaic energy (PV) production is important for powerplant management. Ideally these forecasts are equipped with error bars, so that downstream decisions can account for uncertainty. To produce predictions with error bars in this setting, we consider Gaussian processes (GPs) for modelling and predicting solar photovoltaic energy production in the UK. A standard application of GP regression on the PV timeseries data is infeasible due to the large data size and non-Gaussianity of PV readings. However, this is made possible by leveraging recent advances in scalable GP inference, in particular, by using the state-space form of GPs, combined with modern variational inference techniques. The resulting model is not only scalable to large datasets but can also handle continuous data streams via Kalman filtering., Comment: Workshop paper submitted to "Tackling Climate Change with Machine Learning: workshop at NeurIPS 2022"

With the increasing availability and size of multi-omics datasets, investigating the casual relationships between molecular phenotypes has become an important aspect of exploring underlying biology and genetics. This paper aims to introduce and review the available methods for building large-scale causal molecular networks that have been developed in the past decade. Existing methods have their own strengths and limitations so there is no one best approach, and it is instead down to the discretion of the researcher. This review also aims to discuss some of the current limitations to biological interpretation of these networks, and important factors to consider for future studies on molecular networks.

Let $R$ be a Banach ring. We prove that the category of chain complexes of complete bornological $R$-modules (and several related categories) is a derived algebraic context in the sense of Raksit. We then use the framework of derived algebra to prove a version of the Hochschild-Kostant-Rosenberg Theorem, which relates the circle action on the Hochschild algebra to the de Rham-differential-enriched-de Rham algebra of a simplicial, commutative, complete bornological algebra. This has a geometric interpretation in the language of derived analytic geometry, namely, the derived loop stack of a derived analytic stack is equivalent to the shifted tangent stack. Using this geometric interpretation we extend our results to derived schemes.

In this short note we show that under very mild conditions on a functor between exact categories $F:\mathcal{D}\rightarrow\mathcal{E}$ it is possible to derive $F$ at the level of unbounded complexes. We also give applications to deriving functors between $Pro$- and $Ind$- categories., Comment: 24 pages, Preliminary version; comments welcome

Advancing probabilistic solar forecasting methods is essential to supporting the integration of solar energy into the electricity grid. In this work, we develop a variety of state-of-the-art probabilistic models for forecasting solar irradiance. We investigate the use of post-hoc calibration techniques for ensuring well-calibrated probabilistic predictions. We train and evaluate the models using public data from seven stations in the SURFRAD network, and demonstrate that the best model, NGBoost, achieves higher performance at an intra-hourly resolution than the best benchmark solar irradiance forecasting model across all stations. Further, we show that NGBoost with CRUDE post-hoc calibration achieves comparable performance to a numerical weather prediction model on hourly-resolution forecasting.

Photovoltaic (PV) power is affected by weather conditions, making the power generated from the PV systems uncertain. Solving this problem would help improve the reliability and cost effectiveness of the grid, and could help reduce reliance on fossil fuel plants. The present paper focuses on evaluating predictions of the energy generated by PV systems in the United Kingdom Gaussian process regression (GPR). Gaussian process regression is a Bayesian non-parametric model that can provide predictions along with the uncertainty in the predicted value, which can be very useful in applications with a high degree of uncertainty. The model is evaluated for short-term forecasts of 48 hours against three main factors -- training period, sky area coverage and kernel model selection -- and for very short-term forecasts of four hours against sky area. We also compare very short-term forecasts in terms of cloud coverage within the prediction period and only initial cloud coverage as a predictor.

In this paper we establish Koszul duality type results in the setting of chain complexes in exact categories. In particular we prove generalisations of Vallette's cooperadic Koszul duality theorem, and operadic Koszul duality along the lines of Lurie. We also prove a connective version. We conclude with some applications, including our main example, the category of complete bornological spaces over a Banach field., Comment: 67 Pages; Some minor errors corrected; some other minor changes based on referee comments

We examine 12 studies on the efficacy of disaggregated energy feedback. The average electricity reduction across these studies is 4.5%. However, 4.5% may be a positively-biased estimate of the savings achievable across the entire population because all 12 studies are likely to be prone to opt-in bias hence none test the effect of disaggregated feedback on the general population. Disaggregation may not be required to achieve these savings: Aggregate feedback alone drives 3% reductions; and the 4 studies which directly compared aggregate feedback against disaggregated feedback found that aggregate feedback is at least as effective as disaggregated feedback, possibly because web apps are viewed less often than in-home-displays (in the short-term, at least) and because some users do not trust fine-grained disaggregation (although this may be an issue with the specific user interface studied). Disaggregated electricity feedback may help a motivated sub-group of the population to save more energy but fine-grained disaggregation may not be necessary to achieve these energy savings. Disaggregation has many uses beyond those discussed in this paper but, on the specific question of promoting energy reduction in the general population, there is no robust evidence that current forms of disaggregated energy feedback are more effective than aggregate energy feedback. The effectiveness of disaggregated feedback may increase if the general population become more energy-conscious (e.g. if energy prices rise or concern about climate change deepens); or if users' trust in fine-grained disaggregation improves; or if innovative new approaches or alternative disaggregation strategies (e.g. disaggregating by behaviour rather than by appliance) out-perform existing feedback. We also discuss opportunities for new research into the effectiveness of disaggregated feedback., Comment: Accepted for oral presentation at the 3rd International NILM Workshop, Vancouver, 14-15 May 2016

In this monograph we develop various aspects of the homotopy theory of exact categories. We introduce different notions of compactness and generation in exact categories $E$, and use these to study model structures on categories of chain complexes $Ch_{*}(E)$ which are induced by cotorsion pairs on $E$. As a special case we show that under very general conditions the categories $Ch_{+}(E)$, $Ch_{\ge0}(E)$, and $Ch(E)$ are equipped with the projective model structure, and that a generalisation of the Dold-Kan correspondence holds. We also establish conditions under which categories of filtered objects in exact categories are equipped with natural model structures. When $E$ is monoidal we also examine when these model structures are monoidal and conclude by studying some homotopical algebra in such categories. In particular we provide conditions under which $Ch(E)$ and $Ch_{\ge0}(E)$ are homotopical algebra contexts, thus making them suitable settings for derived geometry., Comment: 131 pages; major revision based on referee comments: new material on complete and homotopically complete filtered objects, model structures on algebras over operads, and both Dold-Kan and cosimplicial Dold-Kan equivalences for algebras

Energy disaggregation estimates appliance-by-appliance electricity consumption from a single meter that measures the whole home's electricity demand. Recently, deep neural networks have driven remarkable improvements in classification performance in neighbouring machine learning fields such as image classification and automatic speech recognition. In this paper, we adapt three deep neural network architectures to energy disaggregation: 1) a form of recurrent neural network called `long short-term memory' (LSTM); 2) denoising autoencoders; and 3) a network which regresses the start time, end time and average power demand of each appliance activation. We use seven metrics to test the performance of these algorithms on real aggregate power data from five appliances. Tests are performed against a house not seen during training and against houses seen during training. We find that all three neural nets achieve better F1 scores (averaged over all five appliances) than either combinatorial optimisation or factorial hidden Markov models and that our neural net algorithms generalise well to an unseen house., Comment: To appear in ACM BuildSys'15, November 4--5, 2015, Seoul