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• Journal article
Hilton B, Sood AP, Evans TS, 2019,

### Predictive limitations of spatial interaction models: a non-Gaussian analysis

, Scientific Reports, ISSN: 2045-2322

We present a method to compare spatial interaction models against data basedon well known statistical measures which are appropriate for such models anddata. We illustrate our approach using a widely used example: commuting data,specifically from the US Census 2000. We find that the radiation model performssignificantly worse than an appropriately chosen simple gravity model. Variousconclusions are made regarding the development and use of spatial interactionmodels, including: that spatial interaction models fit badly to data in anabsolute sense, that therefore the risk of over-fitting is small and addingadditional fitted parameters improves the predictive power of models, and thatappropriate choices of input data can improve model fit.

• Journal article
Evans TS, Calmon L, Vasiliauskaite V, 2020,

### Longest path in the price model

, Scientific Reports, Vol: 10, Pages: 1-9, ISSN: 2045-2322

The Price model, the directed version of the Barab\'{a}si-Albert model,produces a growing directed acyclic graph. We look at variants of the model inwhich directed edges are added to the new vertex in one of two ways: usingcumulative advantage (preferential attachment) choosing vertices in proportionto their degree, or with random attachment in which vertices are chosenuniformly at random. In such networks, the longest path is well defined and insome cases is known to be a better approximation to geodesics than the shortestpath. We define a reverse greedy path and show both analytically andnumerically that this scales with the logarithm of the size of the network witha coefficient given by the number of edges added using random attachment. Thisis a lower bound on the length of the longest path to any given vertex and weshow numerically that the longest path also scales with the logarithm of thesize of the network but with a larger coefficient that has some weak dependenceon the parameters of the model.

• Journal article
Falkenberg M, Lee J-H, Amano S-I, Ogawa K-I, Yano K, Miyake Y, Evans TS, Christensen Ket al., 2020,

### Identifying time dependence in network growth

, Physical Review & Research International, Vol: 2, Pages: 023352 – 1-023352 – 17, ISSN: 2231-1815

Identifying power-law scaling in real networks—indicative of preferential attachment—has proved controversial. Critics argue that measuring the temporal evolution of a network directly is better than measuring the degree distribution when looking for preferential attachment. However, many of the established methods do not account for any potential time dependence in the attachment kernels of growing networks, or methods assume that node degree is the key observable determining network evolution. In this paper, we argue that these assumptions may lead to misleading conclusions about the evolution of growing networks. We illustrate this by introducing a simple adaptation of the Barabási-Albert model, the “k2 model,” where new nodes attach to nodes in the existing network in proportion to the number of nodes one or two steps from the target node. The k2 model results in time dependent degree distributions and attachment kernels, despite initially appearing to grow as linear preferential attachment, and without the need to include explicit time dependence in key network parameters (such as the average out-degree). We show that similar effects are seen in several real world networks where constant network growth rules do not describe their evolution. This implies that measurements of specific degree distributions in real networks are likely to change over time.

• Journal article
Ciacci A, Falkenberg M, Manani KA, Evans TS, Peters NS, Christensen Ket al., 2020,

### Understanding the transition from paroxysmal to persistent atrial fibrillation

, Physical Review Research, Vol: 2, Pages: 023311-023311

Atrial fibrillation (AF) is the most common cardiac arrhytmia, characterisedby the chaotic motion of electrical wavefronts in the atria. In clinicalpractice, AF is classified under two primary categories: paroxysmal AF, shortintermittent episodes separated by periods of normal electrical activity, andpersistent AF, longer uninterrupted episodes of chaotic electrical activity.However, the precise reasons why AF in a given patient is paroxysmal orpersistent is poorly understood. Recently, we have introduced the percolationbased Christensen-Manani-Peters (CMP) model of AF which naturally exhibits bothparoxysmal and persistent AF, but precisely how these differences emerge in themodel is unclear. In this paper, we dissect the CMP model to identify the causeof these different AF classifications. Starting from a mean-field model wherewe describe AF as a simple birth-death process, we add layers of complexity tothe model and show that persistent AF arises from the formation of temporallystable structural re-entrant circuits that form from the interaction ofwavefront collisions during paroxysmal AF. These results are compatible withrecent findings suggesting that the formation of re-entrant drivers in fibroticborder zones perpetuates persistent AF.

• Journal article
Vasiliauskaite V, Evans TS, 2020,

### Making communities show respect for order

, Applied Network Science, Vol: 5, Pages: 1-24, ISSN: 2364-8228

In this work we give a community detection algorithm in which the communities both respects the intrinsic order of a directed acyclic graph and also finds similar nodes. We take inspiration from classic similarity measures of bibliometrics, used to assess how similar two publications are, based on their relative citation patterns. We study the algorithm’s performance and antichain properties in artificial models and in real networks, such as citation graphs and food webs. We show how well this partitioning algorithm distinguishes and groups together nodes of the same origin (in a citation network, the origin is a topic or a research field). We make the comparison between our partitioning algorithm and standard hierarchical layering tools as well as community detection methods. We show that our algorithm produces different communities from standard layering algorithms.

• Journal article
Yao Q, Evans TS, Christensen K, 2019,

### How the network properties of shareholders vary with investor type and country

, PLoS One, Vol: 14, Pages: 1-19, ISSN: 1932-6203

We construct two examples of shareholder networks in which shareholders are connected if they have shares in the same company. We do this for the shareholders in Turkish companies and we compare this against the network formed from the shareholdings in Dutch companies. We analyse the properties of these two networks in terms of the different types of shareholder. We create a suitable randomised version of these networks to enable us to find significant features in our networks. For that we find the roles played by different types of shareholder in these networks, and also show how these roles differ in the two countries we study.

• Journal article
Vasiliauskaite V, Evans TS, 2019,

### Social success of perfumes

, PLoS ONE, Vol: 14, ISSN: 1932-6203

We study data on perfumes and their odour descriptors-notes-to understand how note compositions, called accords, influence successful fragrance formulas. We obtain accords which tend to be present in perfumes that receive significantly more customer ratings. Our findings show that the most popular notes and the most over-represented accords are different to those that have the strongest effect to the perfume ratings. We also used network centrality to understand which notes have the highest potential to enhance note compositions. We find that large degree notes, such as musk and vanilla as well as generically-named notes, e.g. floral notes, are amongst the notes that enhance accords the most. This work presents a framework which would be a timely tool for perfumers to explore a multidimensional space of scent compositions.

• Journal article
Patel VM, Panzarasa P, Ashrafian H, Evans TS, Kirresh A, Sevdalis N, Darzi A, Athanasiou Tet al., 2019,

### Collaborative patterns, authorship practices and scientific success in biomedical research: a network analysis.

, Journal of the Royal Society of Medicine, Vol: 112, Pages: 245-257, ISSN: 1758-1095

OBJECTIVE: To investigate the relationship between biomedical researchers' collaborative and authorship practices and scientific success. DESIGN: Longitudinal quantitative analysis of individual researchers' careers over a nine-year period. SETTING: A leading biomedical research institution in the United Kingdom. PARTICIPANTS: Five hundred and twenty-five biomedical researchers who were in employment on 31 December 2009. MAIN OUTCOME MEASURES: We constructed the co-authorship network in which nodes are the researchers, and links are established between any two researchers if they co-authored one or more articles. For each researcher, we recorded the position held in the co-authorship network and in the bylines of all articles published in each three-year interval and calculated the number of citations these articles accrued until January 2013. We estimated maximum likelihood negative binomial panel regression models. RESULTS: Our analysis suggests that collaboration sustained success, yet excessive co-authorship did not. Last positions in non-alphabetised bylines were beneficial for higher academic ranks but not for junior ones. A professor could witness a 20.57% increase in the expected citation count if last-listed non-alphabetically in one additional publication; yet, a lecturer suffered from a 13.04% reduction. First positions in alphabetised bylines were positively associated with performance for junior academics only. A lecturer could experience a 8.78% increase in the expected citation count if first-listed alphabetically in one additional publication. While junior researchers amplified success when brokering among otherwise disconnected collaborators, senior researchers prospered from socially cohesive networks, rich in third-party relationships. CONCLUSIONS: These results help biomedical scientists shape successful careers and research institutions develop effective assessment and recruitment policies that will ultimately sustain the quality of biomedical r

• Journal article
Renzini AI, Contaldi CR, 2019,

### Gravitational wave background sky maps from advanced LIGO O1 data

, PHYSICAL REVIEW LETTERS

We integrate the publicly available O1 LIGO time-domain data to obtain maximum-likelihood constraints on the Gravitational Wave Background (GWB) arising from stochastic, persistent signals. Our method produces sky-maps of the strain intensity I as a function of direction on the sky at a reference frequency f0. The data is integrated assuming a set of fixed power-law spectra for the signal. The maps provide upper limits on the amplitude of the GWB density ΩGW(f0) and any anisotropy around the background. We find 95\% confidence upper limits of ΩGW<4.8×10−7 at f0=50 Hz with similar constraints on a dipole modulation for the inspiral-dominated stochastic background case.

• Journal article
Bergman AS, Ade PAR, Akers S, Amiri M, Austermann JA, Beall JA, Becker DT, Benton SJ, Bock JJ, Bond JR, Bryan SA, Chiang HC, Contaldi CR, Domagalski RS, Dore O, Duff SM, Duivenvoorden AJ, Eriksen HK, Farhang M, Filippini JP, Fissel LM, Fraisse AA, Freese K, Galloway M, Gambrel AE, Gandilo NN, Ganga K, Grigorian A, Gualtieri R, Gudmundsson JE, Halpern M, Hartley J, Hasselfield M, Hilton G, Holmes W, Hristov VV, Huang Z, Hubmayr J, Irwin KD, Jones WC, Khan A, Kuo CL, Kermish ZD, Li S, Mason PV, Megerian K, Moncelsi L, Morford TA, Nagy JM, Netterfield CB, Nolta M, Osherson B, Padilla IL, Racine B, Rahlin AS, Redmond S, Reintsema C, Romualdez LJ, Ruhl JE, Runyan MC, Ruud TM, Shariff JA, Shaw EC, Shiu C, Soler JD, Song X, Trangsrud A, Tucker C, Tucker RS, Turner AD, Ullom J, van der List JF, Van Lanen J, Vissers MR, Weber AC, Wehus IK, Wen S, Wiebe DV, Young EYet al., 2018,

### 280 GHz Focal Plane Unit Design and Characterization for the SPIDER-2 Suborbital Polarimeter

, JOURNAL OF LOW TEMPERATURE PHYSICS, Vol: 193, Pages: 1075-1084, ISSN: 0022-2291
• Journal article
Gualtieri R, Filippini JP, Ade PAR, Amiri M, Benton SJ, Bergman AS, Bihary R, Bock JJ, Bond JR, Bryan SA, Chiang HC, Contaldi CR, Doré O, Duivenvoorden AJ, Eriksen HK, Farhang M, Fissel LM, Fraisse AA, Freese K, Galloway M, Gambrel AE, Gandilo NN, Ganga K, Gramillano RV, Gudmundsson JE, Halpern M, Hartley J, Hasselfield M, Hilton G, Holmes W, Hristov VV, Huang Z, Irwin KD, Jones WC, Kuo CL, Kermish ZD, Li S, Mason PV, Megerian K, Moncelsi L, Morford TA, Nagy JM, Netterfield CB, Nolta M, Osherson B, Padilla IL, Racine B, Rahlin AS, Reintsema C, Ruhl JE, Runyan MC, Ruud TM, Shariff JA, Soler JD, Song X, Trangsrud A, Tucker C, Tucker RS, Turner AD, List JFVD, Weber AC, Wehus IK, Wiebe DV, Young EYet al., 2018,

### SPIDER: CMB polarimetry from the edge of space

, Journal of Low Temperature Physics, Vol: 193, Pages: 1112-1121, ISSN: 0022-2291

Spider is a balloon-borne instrument designed to map the polarization of the millimeter-wave sky at large angular scales. Spider targets the B-mode signature of primordial gravitational waves in the cosmic microwave background (CMB), with a focus on mapping a large sky area with high fidelity at multiple frequencies. Spider ’s first long-duration balloon (LDB) flight in January 2015 deployed a total of 2400 antenna-coupled transition-edge sensors (TESs) at 90 GHz and 150 GHz. In this work we review the design and in-flight performance of the Spider instrument, with a particular focus on the measured performance of the detectors and instrument in a space-like loading and radiation environment. Spider ’s second flight in December 2018 will incorporate payload upgrades and new receivers to map the sky at 285 GHz, providing valuable information for cleaning polarized dust emission from CMB maps.

• Journal article
Renzini AI, Contaldi CR, 2018,

### Mapping incoherent gravitational wave backgrounds

, Monthly Notices of the Royal Astronomical Society, Vol: 481, Pages: 4650-4661, ISSN: 0035-8711

Given the recent detection of gravitational waves from individual sources, it is almost a certainty that some form of background of gravitational waves will be detected in future. The most promising candidate for such a detection is backgrounds made up of incoherent superposition of the signal of unresolved astrophysical, or backgrounds sourced by earlier cosmological events. Such backgrounds will also contain anisotropies about an average value. The information contained in the background level and any anisotropies will be extremely valuable as an astrophysical and cosmological probe. As such, the ability to reconstruct sky maps of the signal will become important as the sensitivity increases. We build and test a pixel-based, maximum-likelihood gravitational wave background (GWB) map-maker that uses the cross-correlation of sets of generalized baselines as input. The resulting maps are a representation of the GWB power, or strain ‘intensity’ on the sky. We test the algorithm by reconstructing known input maps with different baseline configurations. We also apply the map-maker to a subset of the Advanced Laser Interferometer Gravitational Wave observatory data.

• Journal article
Contaldi CR, Magueijo J, 2018,

### Unsqueezing of standing waves due to inflationary domain structure

, Physical Review D, Vol: 98, ISSN: 2470-0010

The so-called trans-Planckian problem of inflation may be evaded by positing that modes come into existence only when they became “cis-Planckian” by virtue of expansion. However, this would imply that for any mode a new random realization would have to be drawn every N wavelengths, with N typically of order 1000 (but it could be larger or smaller). Such a redrawing of realizations leads to a heteroskodastic distribution if the region under observation contains several such independent domains. This has no effect on the sampled power spectrum for a scale-invariant raw spectrum, but at very small scales, it leads to a spectral index bias toward scale invariance and smooths oscillations in the spectrum. The domain structure would also “unsqueeze” some of the propagating waves, i.e., dismantle their standing wave character. By describing standing waves as traveling waves of the same amplitude moving in opposite directions, we determine the observational effects of unsqueezing. We find that it would erase the Doppler peaks in the cosmic microwave background, but only on very small angular scales, in which the primordial signal may not be readily accessible. The standing waves in a primordial gravitational wave background would also be turned into traveling waves. This unsqueezing of the gravitational wave background may constitute a detectable phenomenon.

• Journal article
Clough JR, Evans TS, 2017,

### Embedding graphs in Lorentzian spacetime

, PLOS ONE, Vol: 12, ISSN: 1932-6203

Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs (DAG) into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Riemannian signature, to manifolds of any metric signature. We then use this general method to develop an algorithm which exploits the causal structure of a DAG to assign space and time coordinates in a Minkowski spacetime to each vertex. As in the causal set approach to quantum gravity, causal connections in the discrete graph correspond to timelike separation in the continuous spacetime. The method is demonstrated by calculating embeddings for simple models of causal sets and random DAGs, as well as real citation networks. We find that the citation networks we test yield significantly more accurate embeddings that random DAGs of the same size. Finally we suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.

• Journal article
Nagy JM, Ade PAR, Amiri M, Benton SJ, Bergman AS, Bihary R, Bock JJ, Bond JR, Bryan SA, Chiang HC, Contaldi CR, Dore O, Duivenvoorden AJ, Eriksen HK, Farhang M, Filippini JP, Fissel LM, Fraisse AA, Freese K, Galloway M, Gambrel AE, Gandilo NN, Ganga K, Gudmundsson JE, Halpern M, Hartley J, Hasselfield M, Hilton G, Holmes W, Hristov VV, Huang Z, Irwin KD, Jones WC, Kuo CL, Kermish ZD, Li S, Mason PV, Megerian K, Moncelsi L, Morford TA, Netterfield CB, Nolta M, Padilla IL, Racine B, Rahlin AS, Reintsema C, Ruhl JE, Runyan MC, Ruud TM, Shariff JA, Soler JD, Song X, Trangsrud A, Tucker C, Tucker RS, Turner AD, Van Der List JF, Weber AC, Wehus IK, Wiebe DV, Young EYet al., 2017,

### A New Limit on CMB Circular Polarization from SPIDER

, Astrophysical Journal, Vol: 844, ISSN: 0004-637X

We present a new upper limit on cosmic microwave background (CMB) circular polarization from the 2015 flight of Spider, a balloon-borne telescope designed to search for B-mode linear polarization from cosmic inflation. Although the level of circular polarization in the CMB is predicted to be very small, experimental limits provide a valuable test of the underlying models. By exploiting the nonzero circular-to-linear polarization coupling of the half-wave plate polarization modulators, data from Spider's 2015 Antarctic flight provide a constraint on Stokes V at 95 and 150 GHz in the range $33\lt {\ell }\lt 307$. No other limits exist over this full range of angular scales, and Spider improves on the previous limit by several orders of magnitude, providing 95% C.L. constraints on ${\ell }({\ell }+1){C}_{{\ell }}^{{VV}}/(2\pi )$ ranging from 141 to 255 μK2 at 150 GHz for a thermal CMB spectrum. As linear CMB polarization experiments become increasingly sensitive, the techniques described in this paper can be applied to obtain even stronger constraints on circular polarization.

• Journal article
Renzini AI, Contaldi CR, Heavens A, 2017,

### Mapping weak lensing distortions in the Kerr metric

, Physical Review D, Vol: 95, ISSN: 2470-0010

Einstein’s theory of General Relativity implies that energy, i.e., matter, curves space-time and thusdeforms lightlike geodesics, giving rise to gravitational lensing. This phenomenon is well understood in thecase of the Schwarzschild metric and has been accurately described in the past; however, lensing in the Kerrspace-time has received less attention in the literature despite potential practical observational applications.In particular, lensing in such space is not expressible as the gradient of a scalar potential and as such is asource of curl-like signatures and an asymmetric shear pattern. In this paper, we develop a differentiablelensing map in the Kerr metric, reworking and extending previous approaches. By using standard tools ofweak gravitational lensing, we isolate and quantify the distortion that is uniquely induced by the presenceof angular momentum in the metric. We apply this framework to the distortion induced by a Kerr-likeforeground object on a distribution of background of sources. We verify that the new unique lensingsignature is orders of magnitude below current observational bounds for a range of lens configurations.

• Journal article
Contaldi CR, 2017,

### Anisotropies of gravitational wave backgrounds: a line of sight approach

, Physics Letters B, Vol: 771, Pages: 9-12, ISSN: 0370-2693

In the weak field regime, gravitational waves can be considered as being made up of collisionless, relativistic tensor modes that travel along null geodesics of the perturbed background metric. We work in this geometric optics picture to calculate the anisotropies in gravitational wave backgrounds resulting from astrophysical and cosmological sources. Our formalism yields expressions for the angular power spectrum of the anisotropies. We show how the anisotropies are sourced by intrinsic, Doppler, Sachs–Wolfe, and Integrated Sachs–Wolfe terms in analogy with Cosmic Microwave Background photons.

• Journal article
Contaldi CR, 2017,

### Imaging parity-violating modes in the CMB

, Astronomical Journal, Vol: 153, ISSN: 0004-6256

Correlations of polarization components in the coordinate frame are a natural basis for searches of parity-violating modes in the cosmic microwave background. This fact can be exploited to build estimators of parity-violating modes that are local and robust with respect to partial-sky coverage or inhomogeneous weighting. As an example application of a method based on these ideas, we develop a peak stacking tool that isolates the signature of parity-violating modes. We apply the tool to Planck maps and obtain a constraint on the monopole of the polarization rotation angle $\alpha \lt 0\buildrel{\circ}\over{.} 72$ at 95% We also demonstrate how the tool can be used as a local method for reconstructing maps of direction dependent rotation $\alpha (\hat{{\boldsymbol{n}}})$.

• Journal article
Contaldi CR, 2016,

### Imaging cosmic polarization rotation

, International Journal of Modern Physics D, Vol: 25, ISSN: 0218-2718

We introduce a method to isolate the contribution of parity-violating modes to the peak constrained correlation function. This method can be used as a local estimate of polarization rotation. We test this method using simulations and by applying it to Planck maps [P. A. R. Ade et al., arXiv:1502.01589 astro.ph.co]. We obtain a constraint on the monopole of the polarization rotation angle α=0.31±0.23α=0.31±0.23.

• Journal article
Clough JR, Evans TS, 2016,

### What is the dimension of citation space?

, Physica A, 448 (2016) 235-247

Citation networks represent the flow of information between agents. They areconstrained in time and so form directed acyclic graphs which have a causalstructure. Here we provide novel quantitative methods to characterise thatstructure by adapting methods used in the causal set approach to quantumgravity by considering the networks to be embedded in a Minkowski spacetime andmeasuring its dimension using Myrheim-Meyer and Midpoint-scaling estimates. Weillustrate these methods on citation networks from the arXiv, supreme courtjudgements from the USA, and patents and find that otherwise similar citationnetworks have measurably different dimensions. We suggest that thesedifferences can be interpreted in terms of the level of diversity or narrownessin citation behaviour.

• Journal article
Goldberg SR, Anthony H, Evans TS,

### Modelling citation networks

, Scientometrics, ISSN: 1588-2861

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