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We propose a new method of determining regional and city boundaries based on the Valeriepieris circle, the smallest circle containing a given fraction of the data. By varying the fraction in the circle we can map complex spatial data to a simple model of concentric rings which we then fit to determine natural density cutoffs. We apply this method to population, occupation, economic and transport data from England and Wales, finding that the regions determined by this method affirm well known social facts such as the disproportionate wealth of London or the relative isolation of the North East and South West of England. We then show how different data sets give us different views of the same cities, providing insight into their development and dynamics., Comment: 13 Figures

Community detection, as well as the identification of other structures like core periphery and disassortative patterns, is an important topic in network analysis. While most methods seek to find the best partition of the network according to some criteria, there is a body of results that suggest that a single network can have many good but distinct partitions. In this paper we introduce the density of states as a tool for studying the space of all possible network partitions. We demonstrate how to use the well known Wang-Landau method to compute a network's density of states. We show that, even using modularity to measure quality, the density of states can still rule out spurious structure in random networks and overcome resolution limits. We demonstrate how these methods can be used to find `building blocks', groups of nodes which are consistently found together in detected communities. This suggests an approach to partitioning based on exploration of the network's structure landscape rather than optimisation.

A key topic in network science is the detection of intermediate or meso-scale structures. Community, core-periphery, disassortative and other partitions allow us to understand the organisation and function of large networks. In this work we study under what conditions certain common meso-scale structures are detectable using the idea of block modularity. We find that the configuration model imposes strong restrictions on core-periphery and related structures in directed networks. We derive inequalities expressing when such structures can be detected under the configuration model. Nestedness is closely related to core-periphery and is similarly restricted to only be detectable under certain conditions. We show that these conditions are a generalisation of the resolution limit to structures other than assortative communities. We show how block modularity is related to the degree corrected Stochastic Block Model and that optimisation of one can be made equivalent to the other in general. Finally, we discuss these issues in inferential versus descriptive approaches to meso-scale structure detection.

This study explores how different weather conditions influence public sentiment on social media, focusing on Twitter data from the UK. By considering climate and linguistic baselines, we improve the accuracy of weather-related sentiment analysis. Our findings show that emotional responses to weather are complex, influenced by combinations of weather variables and regional language differences. The results highlight the importance of context-sensitive methods for better understanding public mood in response to weather, which can enhance impact-based forecasting and risk communication in the context of climate change., Comment: 12 pages, 5 figures

Networks where each node has one or more associated numerical values are common in applications. This work studies how summary statistics used for the analysis of spatial data can be applied to non-spatial networks for the purposes of exploratory data analysis. We focus primarily on Moran-type statistics and discuss measures of global autocorrelation, local autocorrelation and global correlation. We introduce null models based on fixing edges and permuting the data or fixing the data and permuting the edges. We demonstrate the use of these statistics on real and synthetic node-valued networks., Comment: 31 pages, 11 figures, ~5000 words

Life on Earth has experienced numerous upheavals over its approximately 4 billion year history. In previous work we have discussed how interruptions to stability lead, on average, to increases in habitability over time, a tendency we called Entropic Gaia. Here we continue this exploration, working with the Tangled Nature Model of co-evolution, to understand how the evolutionary history of life is shaped by periods of acute environmental stress. We find that while these periods of stress pose a risk of complete extinction, they also create opportunities for evolutionary exploration which would otherwise be impossible, leading to more populous and stable states among the survivors than in alternative histories without a stress period. We also study how the duration, repetition and number of refugia into which life escapes during the perturbation affects the final outcome. The model results are discussed in relation to both Earth history and the search for alien life., Comment: 12 pages, 7 figures

Comparing spatial data sets is a ubiquitous task in data analysis, however the presence of spatial autocorrelation means that standard estimates of variance will be wrong and tend to over-estimate the statistical significance of correlations and other observations. While there are a number of existing approaches to this problem, none are ideal, requiring detailed analytical calculations, which are hard to generalise or detailed knowledge of the data generating process, which may not be available. In this work we propose a resampling approach based on Tobler's Law. By resampling the data with fixed spatial autocorrelation, measured by Moran's I, we generate a more realistic null model. Testing on real and synthetic data, we find that, as long as the spatial autocorrelation is not too strong, this approach works just as well as if we knew the data generating process.

What3Words is a geocoding application that uses triples of words instead of alphanumeric coordinates to identify locations. What3Words has grown rapidly in popularity over the past few years and is used in logistical applications worldwide, including by emergency services. What3Words has also attracted criticism for being less reliable than claimed, in particular that the chance of confusing one address with another is high. This paper investigates these claims and shows that the What3Words algorithm for assigning addresses to grid boxes creates many pairs of confusable addresses, some of which are quite close together. The implications of this for the use of What3Words in critical or emergency situations is discussed.

The Valeriepieris circle is the smallest circle that can be draw on the globe containing half of the world's population. The Valeriepieris (VP) circle acts as a spatial median, effectively splitting spatial data into two halves in a unique way. In this paper the idea of the VP circle is generalised and a fast algorithm and corresponding software package to compute it are described. The VP circle is compared to other measures of centre and dispersion for population distributions and is shown to reflect expected differences between countries and changes over time. By studying the VP circle as a function of the included population fraction a new way of representing population distributions is constructed, as well as a mathematical model of its expected behaviour. Finally a measure of population `centralisation' is constructed which measures the tendency of a territory to be dominated by a single population centre or to have a more even distribution of population.

Researchers commonly perform sentiment analysis on large collections of short texts like tweets, Reddit posts or newspaper headlines that are all focused on a specific topic, theme or event. Usually, general-purpose sentiment analysis methods are used. These perform well on average but miss the variation in meaning that happens across different contexts, for example, the word "active" has a very different intention and valence in the phrase "active lifestyle" versus "active volcano". This work presents a new approach, CIDER (Context Informed Dictionary and sEmantic Reasoner), which performs context-sensitive linguistic analysis, where the valence of sentiment-laden terms is inferred from the whole corpus before being used to score the individual texts. In this paper, we detail the CIDER algorithm and demonstrate that it outperforms state-of-the-art generalist unsupervised sentiment analysis techniques on a large collection of tweets about the weather. CIDER is also applicable to alternative (non-sentiment) linguistic scales. A case study on gender in the UK is presented, with the identification of highly gendered and sentiment-laden days. We have made our implementation of CIDER available as a Python package: https://pypi.org/project/ciderpolarity/., Comment: 20 pages, 6 figures, 3 tables

In this paper we introduce some simple models, based on rolling dice, to explore mechanisms proposed to explain planetary habitability. The idea is to study these selection mechanisms in an analytically tractable setting, isolating their consequences from other details which can confound or obscure their effect in more realistic models. We find that while the observable of interest, the face value shown on the die, `improves' over time in all models, for two of the more popular ideas, Selection by Survival and Sequential Selection, this is down to sampling effects. A modified version of Sequential Selection, Sequential Selection with Memory, implies a statistical tendency for systems to improve over time. We discuss the implications of this and its relationship to the ideas of the `Inhabitance Paradox' and the `Gaian bottleneck'.

When searching for inhabited exoplanets, understanding the boundaries of the habitable zone around the parent star is key. If life can strongly influence its global environment, then we would expect the boundaries of the habitable zone to be influenced by the presence of life. Here using a simple abstract model of `tangled-ecology' where life can influence a global parameter, labelled as temperature, we investigate the boundaries of the habitable zone of our model system. As with other models of life-climate interactions, the species act to regulate the temperature. However, the system can also experience `punctuations', where the system's state jumps between different equilibria. Despite this, an ensemble of systems still tends to sustain or even improve conditions for life on average, a feature we call Entropic Gaia. The mechanism behind this is sequential selection with memory which is discussed in detail. With this modelling framework we investigate questions about how Gaia can affect and ultimately extend the habitable zone to what we call the Gaian habitable zone. This generates concrete predictions for the size of the habitable zone around stars, suggests directions for future work on the simulation of exoplanets and provides insight into the Gaian bottleneck hypothesis and the habitability/inhabitance paradox.

A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network structures can be compared and an optimal block matrix can be determined. Some simple algorithms for optimising block modularity are described and applied on networks with planted structure. In many cases the planted structure is recovered. Cases where it is not are analysed and it is found that strong degree-correlations explain the planted structure so that the discovered pattern is more `surprising' than the planted one under the configuration model. Some well studied networks are analysed with this new method, which is found to automatically deconstruct the network in a very useful way for creating a summary of its key features.

The COVID-19 global pandemic and the lockdown policies enacted to mitigate it have had profound effects on the labour market. Understanding these effects requires us to obtain and analyse data in as close to real time as possible, especially as rules change rapidly and local lockdowns are enacted. In this work we study the UK labour market by analysing data from the online job board Reed.co.uk. Using topic modelling and geo-inference methods we are able to break down the data by sector and geography. We also study how the salary, contract type and mode of work have changed since the COVID-19 crisis hit the UK in March. Overall, vacancies were down by 60 to 70\% in the first weeks of lockdown. By the end of the year numbers had recovered somewhat, but the total job ad deficit is measured to be over 40\%. Broken down by sector, vacancies for hospitality and graduate jobs are greatly reduced, while there were more care work and nursing vacancies during lockdown. Differences by geography are less significant than between sectors, though there is some indication that local lockdowns stall recovery and less badly hit areas may have experienced a smaller reduction in vacancies. There are also small but significant changes in the salary distribution and number of full time and permanent jobs. In addition to these results, this work presents an open methodology that enables a rapid and detailed survey of the job market in these unsettled conditions and we describe a web application \url{jobtrender.com} that allows others to query this data set., Comment: 33 pages, 20 figures

This paper investigates community detection by modularity maximisation on bipartite networks. In particular we are interested in how the operation of projection, using one node set of the bipartite network to infer connections between nodes in the other set, interacts with community detection. We first define a notion of modularity appropriate for a projected bipartite network and outline an algorithm for maximising it in order to partition the network. Using both real and synthetic networks we compare the communities found by five different algorithms, where each algorithm maximises a different modularity function and sees different aspects of the bipartite structure. Based on these results we suggest a simple heuristic for finding communities in bipartite networks.

Given the centrality of regions in social movements, politics and public administration we aim to quantitatively study inter- and intra-regional communication for the first time. This work uses social media posts to first identify contiguous geographical regions with a shared social identity and then investigate patterns of communication within and between them. Our case study uses over 150 days of located Twitter data from England and Wales. In contrast to other approaches, (e.g. phone call data records or online friendship networks) we have the message contents as well as the social connection. This allows us to investigate not only the volume of communication but also the sentiment and vocabulary. We find that the South-East and North-West regions are the most talked about; regions tend to be more positive about themselves than about others; people talk politics much more between regions than within. This methodology gives researchers a powerful tool to study identity and interaction within and between social-geographic regions., Comment: 11 pages, 5 figures, 4 tables, 6 pages of Supporting Information

We observe and report on a systematic relationship between population density and Twitter use. Number of tweets, number of users and population per unit area are related by power laws, with exponents greater than one, that are consistent with each other and across a range of spatial scales. This implies that population density can accurately predict Twitter activity. Furthermore this trend can be used to identify `anomalous' areas that deviate from the trend. Analysis of geo-tagged and place-tagged tweets show that geo-tagged tweets are different with respect to user type and content. Our findings have implications for the spatial analysis of Twitter data and for understanding demographic biases in the Twitter user base., Comment: 21 pages, 11 figures

"Social sensing" is a form of crowd-sourcing that involves systematic analysis of digital communications to detect real-world events. Here we consider the use of social sensing for observing natural hazards. In particular, we present a case study that uses data from a popular social media platform (Twitter) to detect and locate flood events in the UK. In order to improve data quality we apply a number of filters (timezone, simple text filters and a naive Bayes `relevance' filter) to the data. We then use place names in the user profile and message text to infer the location of the tweets. These two steps remove most of the irrelevant tweets and yield orders of magnitude more located tweets than we have by relying on geo-tagged data. We demonstrate that high resolution social sensing of floods is feasible and we can produce high-quality historical and real-time maps of floods using Twitter., Comment: 24 pages, 6 figures

We modify the Tangled Nature Model of Christensen et. al. so that the agents affect the carrying capacity. This leads to a model of species-environment co-evolution where the system tends to have a larger carrying capacity with life than without. We discuss the model as an example of an entropic hierarchy and some implications for Gaia theory., Comment: 13 pages, 4 figures

We discuss fitness landscapes and how they can be modified to account for co-evolution. We are interested in using the landscape as a way to model rational decision making in a toy economic system. We develop a model very similar to the Tangled Nature Model of Christensen et. al. that we call the Tangled Decision Model. This is a natural setting for our discussion of co-evolutionary fitness landscapes. We use a Monte Carlo step to simulate decision making and investigate two different decision making procedures., Comment: 10 pages, 4 figures

We investigate the scalar and pseudoscalar spectrum of the $SU(2)$ gauge theory with $N_f=2$ flavours of fermions in the fundamental representation using non perturbative lattice simulations. We provide first benchmark estimates of the mass of the lightest $0(0^{+})$ ($\sigma$), $0(0^{-})$ ($\eta'$) and $1(0^+)$ ($a_0$) states, including estimates of the relevant disconnected contributions. We find $m_{a_0}/F_{\rm{PS}}= 16.7(4.9)$, $m_\sigma/F_{\rm{PS}}=19.2(10.8)$ and $m_{\eta'}/F_{\rm{PS}} = 12.8(4.7)$. These values for the masses of light scalar states provide crucial information for composite extensions of the Standard Model from the unified Fundamental Composi te Higgs-Technicolor theory \cite{Cacciapaglia:2014uja} to models of composite dark matter., Comment: 18 pages, 9 figures

We investigate the continuum spectrum of the SU(2) gauge theory with $N_f=2$ flavours of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the SIMPs. We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the $w_0$ parameter, and by measuring the relevant renormalisation constants non-perturbatively in the RI'-MOM scheme. Our results for the lightest isovector states in the vector and axial channels, in units of the pseudoscalar decay constant, are $m_V/F_{\rm{PS}}\sim 13.1(2.2)$ and $m_A/F_{\rm{PS}}\sim 14.5(3.6)$ (combining statistical and systematic errors). In the context of the composite (Goldstone) Higgs models, our result for the spin-one resonances are $m_V > 3.2(5)$ TeV and $m_A > 3.6(9)$ TeV, which are above the current LHC constraints. In the context of dark matter models, for the SIMP case our results indicate the occurrence of a compressed spectrum at the required large dark pion mass, which implies the need to include the effects of spin-one resonances in phenomenological estimates., Comment: 35 pages, 18 figures

We study the meson spectrum of the SU(2) gauge theory with two Wilson fermions in the fundamental representation. The theory unifies both Technicolor and composite Goldstone Boson Higgs models of electroweak symmetry breaking. We have calculated the masses of the lightest spin one vector and axial vector mesons. In addition, we have also obtained preliminary results for the mass of the lightest scalar (singlet) meson state. The simulations have been done with multiple masses and two different lattice spacings for chiral and continuum extrapolations. The spin one meson masses set lower limits for accelerator experiments, whereas the scalar meson will mix with a pGB of the theory and produce two scalar states. The lighter of the states is the 125 GeV Higgs boson, and the heavier would be a new yet unobserved scalar state., Comment: 7 pages, 5 figures, talk presented at The 32nd International Symposium on Lattice Field Theory, June 23-28, 2014, Columbia University, New York

We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost., Comment: 47 pages, 17 figures, reference added and minor revision, v2: added figure, published version

This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration domain into a set of bins specified by some parameters. We then consider two adaptations; the first is to subtract the histogram approximation, whose integral we may easily evaluate explicitly, from the function and integrate the difference using Monte Carlo; the second is to modify the bin parameters in order to make the variance of the Monte Carlo estimate of the integral the same for all bins. This allows us to use Student's t-test as a trigger for rebinning, which we claim is more stable than the \chi-squared test that is commonly used for this purpose. We provide a program that we have used to study the algorithm for the case where the histogram is represented as a product of one-dimensional histograms. We discuss the assumptions and approximations made, as well as giving a pedagogical discussion of the myriad ways in which the results of any such Monte Carlo integration program can be misleading., Comment: Code PANIC included as a set of ancillary files

A method for computing renormalization constants in the Rome Southampton scheme with volume sources and arbitrary momenta is described. This new method is found to enable controlled and precise continuum extrapolations and opens the way to compute the running of operators nonperturbatively in the Rome Southampton scheme. We describe this in detail and exhibit several examples of lattice step scaling functions., Comment: 7 pages, 3 figures. Talk given by Rudy Arthur at the XXVIII International Symposium on Lattice Field Theory (Lattice 2010), Villasimius, Italy, June 2010