arXiv subjects
Publications and source records attributed to Jack Kelly.
We develop the basic theory of covers and envelopes in proto-exact categories. As an application, we prove the existence of enough injectives for categories of Banach modules over arbitrary Banach rings.
The notion of an LB-space was introduced by Grothendieck in his 1953 th\`{e}se, referring to a countable colimit of Banach spaces taken within the category of locally convex topological vector spaces, and refining prior work done by Dieudonn\'{e}, Schwartz and K\"othe. Recently, two different notions of `bornological LB-spaces' emerged: one, given by Stempfhuber, refers to countable colimits of Banach spaces as well, but now taken in the category of bornological vector spaces. The other one, given by Bambozzi, Ben-Bassat and Kremnizer, refers to bornologifications of regular LB-spaces, i.e., of LB-spaces in the Grothendieck sense having the additional property that every bounded subset of the colimit is contained and bounded in one of its Banach steps. In this note, we show that the two notions are distinct, but nevertheless closely related. This involves, in particular, an intimate study of the idempotent adjunction of the bornologification and topologification functors.
We study several categories of analytic stacks relative to the category of bornological modules over a Banach ring. When the underlying Banach ring is a non-Archimedean valued field, this category contains derived rigid analytic spaces as a full subcategory. When the underlying field is the complex numbers, it contains the category of derived complex analytic spaces. In the second part of the paper, we consider localising invariants of rigid categories associated to bornological algebras. The main results in this part include Nisnevich descent for derived analytic spaces and a version of the Grothendieck-Riemann-Roch Theorem for derived dagger analytic spaces over an arbitrary Banach ring.
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.
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.
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.
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.
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.
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.
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.
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.
In this demonstration, we present an open source toolkit for evaluating non-intrusive load monitoring research; a field which aims to disaggregate a household's total electricity consumption into individual appliances. The toolkit contains: a number of importers for existing public data sets, a set of preprocessing and statistics functions, a benchmark disaggregation algorithm and a set of metrics to evaluate the performance of such algorithms. Specifically, this release of the toolkit has been designed to enable the use of large data sets by only loading individual chunks of the whole data set into memory at once for processing, before combining the results of each chunk.
Non-intrusive load monitoring, or energy disaggregation, aims to separate household energy consumption data collected from a single point of measurement into appliance-level consumption data. In recent years, the field has rapidly expanded due to increased interest as national deployments of smart meters have begun in many countries. However, empirically comparing disaggregation algorithms is currently virtually impossible. This is due to the different data sets used, the lack of reference implementations of these algorithms and the variety of accuracy metrics employed. To address this challenge, we present the Non-intrusive Load Monitoring Toolkit (NILMTK); an open source toolkit designed specifically to enable the comparison of energy disaggregation algorithms in a reproducible manner. This work is the first research to compare multiple disaggregation approaches across multiple publicly available data sets. Our toolkit includes parsers for a range of existing data sets, a collection of preprocessing algorithms, a set of statistics for describing data sets, two reference benchmark disaggregation algorithms and a suite of accuracy metrics. We demonstrate the range of reproducible analyses which are made possible by our toolkit, including the analysis of six publicly available data sets and the evaluation of both benchmark disaggregation algorithms across such data sets.
Many countries are rolling out smart electricity meters. These measure a home's total power demand. However, research into consumer behaviour suggests that consumers are best able to improve their energy efficiency when provided with itemised, appliance-by-appliance consumption information. Energy disaggregation is a computational technique for estimating appliance-by-appliance energy consumption from a whole-house meter signal. To conduct research on disaggregation algorithms, researchers require data describing not just the aggregate demand per building but also the `ground truth' demand of individual appliances. In this context, we present UK-DALE: an open-access dataset from the UK recording Domestic Appliance-Level Electricity at a sample rate of 16 kHz for the whole-house and at 1/6 Hz for individual appliances. This is the first open access UK dataset at this temporal resolution. We recorded from five houses, one of which was recorded for 655 days, the longest duration we are aware of for any energy dataset at this sample rate. We also describe the low-cost, open-source, wireless system we built for collecting our dataset.