Continuum Random Combs and Scale Dependent Spectral Dimension

Numerical computations have suggested that in causal dynamical triangulation models of quantum gravity the effective dimension of spacetime in the UV is lower than in the IR. In this paper we develop a simple model based on previous work on random combs, which share some of the properties of CDT, in which this effect can be shown to occur analytically. We construct a definition for short and long distance spectral dimensions and show that the random comb models exhibit scale dependent spectral dimension defined in this way. We also observe that a hierarchy of apparent spectral dimensions may be obtained in the cross-over region between UV and IR regimes for suitable choices of the continuum variables. Our main result is valid for a wide class of tooth length distributions thereby extending previous work on random combs by Durhuus et al.Comment: 27 pages, 2 figures. Typos and references corrected, new figure

Laplacians on discrete and quantum geometries

We extend discrete calculus for arbitrary ($p$-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries.Comment: 43 pages, 2 multiple figures. v2: discussion improved, references added, minor typos correcte

Spectral dimension in graph models of causal quantum gravity

The phenomenon of scale dependent spectral dimension has attracted special interest in the quantum gravity community over the last eight years. It was first observed in computer simulations of the causal dynamical triangulation (CDT) approach to quantum gravity and refers to the reduction of the spectral dimension from 4 at classical scales to 2 at short distances. Thereafter several authors confirmed a similar result from different approaches to quantum gravity. Despite the contribution from different approaches, no analytical model was proposed to explain the numerical results as the continuum limit of CDT. In this thesis we introduce graph ensembles as toy models of CDT and show that both the continuum limit and a scale dependent spectral dimension can be defined rigorously. First we focus on a simple graph ensemble, the random comb. It does not have any dynamics from the gravity point of view, but serves as an instructive toy model to introduce the characteristic scale of the graph, study the continuum limit and define the scale dependent spectral dimension. Having defined the continuum limit, we study the reduction of the spectral dimension on more realistic toy models, the multigraph ensembles, which serve as a radial approximation of CDT. We focus on the (recurrent) multigraph approximation of the two-dimensional CDT whose ensemble measure is analytically controlled. The latter comes from the critical Galton-Watson process conditioned on non-extinction. Next we turn our attention to transient multigraph ensembles, corresponding to higher-dimensional CDT. Firstly we study their fractal properties and secondly calculate the scale dependent spectral dimension and compare it to computer simulations. We comment further on the relation between Horava-Lifshitz gravity, asymptotic safety, multifractional spacetimes and CDT-like models.</p

Short term load forecasting and the effect of temperature at the low voltage level

Short term load forecasts will play a key role in the implementation of smart electricity grids. They are required for optimising a wide range of potential network solutions on the low voltage (LV) grid, including the integration of low carbon technologies (such as photovoltaics) and the utilisation of battery storage devices. Despite the need for accurate LV level load forecasts, much of the literature has focused on the individual household or building level using data from smart meters, or on aggregates of such data. This study provides a detailed analysis of several state-of-the-art methods for both point and probabilistic LV load forecasts. We evaluate the out-of-sample forecast accuracies of these methodologies on 100 real LV feeders, for horizons from one to four days ahead. In addition, we also test the effect of the temperature (both actual and forecast) on the accuracy of load forecasts. We present some important results on the drivers of forecasts accuracy as well as on the empirical comparison of point and probabilistic forecast measures

Short term load forecasting and the effect of temperature at the low voltage level

Short term load forecasts will play a key role in the implementation of smart electricity grids. They are required for optimising a wide range of potential network solutions on the low voltage (LV) grid, including the integration of low carbon technologies (such as photovoltaics) and the utilisation of battery storage devices. Despite the need for accurate LV level load forecasts, much of the literature has focused on the individual household or building level using data from smart meters, or on aggregates of such data. This study provides a detailed analysis of several state-of-the-art methods for both point and probabilistic LV load forecasts. We evaluate the out-of-sample forecast accuracies of these methodologies on 100 real LV feeders, for horizons from one to four days ahead. In addition, we also test the effect of the temperature (both actual and forecast) on the accuracy of load forecasts. We present some important results on the drivers of forecasts accuracy as well as on the empirical comparison of point and probabilistic forecast measures

Exploiting context for rumour detection in social media

Tools that are able to detect unverified information posted on social media during a news event can help to avoid the spread of rumours that turn out to be false. In this paper we compare a novel approach using Conditional Random Fields that learns from the sequential dynamics of social media posts with the current state-of-the-art rumour detection system, as well as other baselines. In contrast to existing work, our classifier does not need to observe tweets querying the stance of a post to deem it a rumour but, instead, exploits context learned during the event. Our classifier has improved precision and recall over the state-of-the-art classifier that relies on querying tweets, as well as outperforming our best baseline. Moreover, the results provide evidence for the generalisability of our classifier

Review of low voltage load forecasting: methods, applications, and recommendations

The increased digitalisation and monitoring of the energy system opens up numerous opportunities to decarbonise the energy system. Applications on low voltage, local networks, such as community energy markets and smart storage will facilitate decarbonisation, but they will require advanced control and management. Reliable forecasting will be a necessary component of many of these systems to anticipate key features and uncertainties. Despite this urgent need, there has not yet been an extensive investigation into the current state-of-the-art of low voltage level forecasts, other than at the smart meter level. This paper aims to provide a comprehensive overview of the landscape, current approaches, core applications, challenges and recommendations. Another aim of this paper is to facilitate the continued improvement and advancement in this area. To this end, the paper also surveys some of the most relevant and promising trends. It establishes an open, community-driven list of the known low voltage level open datasets to encourage further research and development