Most of the members of this group are from the Statistics Section and Biomaths research group of the Department of Mathematics. Below you can find a list of research areas that members of this group are currently working on and/or would like to work on by applying their developed mathematical and statistical methods.

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  • Journal article
    Johnson S, Jones NS, 2017,

    Looplessness in networks is linked to trophic coherence

    , Proceedings of the National Academy of Sciences of the United States of America, Vol: 114, Pages: 5618-5623, ISSN: 1091-6490

    Many natural, complex systems are remarkably stable thanks to anabsence of feedback acting on their elements. When described as net-works, these exhibit few or no cycles, and associated matrices have smallleading eigenvalues. It has been suggested that this architecture can con-fer advantages to the system as a whole, such as ‘qualitative stability’,but this observation does not in itself explain how a loopless structuremight arise. We show here that the number of feedback loops in a net-work, as well as the eigenvalues of associated matrices, are determined bya structural property called trophic coherence, a measure of how neatlynodes fall into distinct levels. Our theory correctly classifies a variety ofnetworks – including those derived from genes, metabolites, species, neu-rons, words, computers and trading nations – into two distinct regimesof high and low feedback, and provides a null model to gauge the signifi-cance of related magnitudes. Since trophic coherence suppresses feedback,whereas an absence of feedback alone does not lead to coherence, our worksuggests that the reasons for ‘looplessness’ in nature should be sought incoherence-inducing mechanisms.

  • Journal article
    Battey HS, 2017,

    Eigen structure of a new class of structured covariance and inverse covariance matrices

    , Bernoulli, Vol: 23, Pages: 3166-3177

    There is a one to one mapping between a p dimensional strictly positive definite covariancematrix Σ and its matrix logarithm L. We exploit this relationship to study thestructure induced on Σ through a sparsity constraint on L. Consider L as a randommatrix generated through a basis expansion, with the support of the basis coefficientstaken as a simple random sample of size s = s∗from the index set [p(p + 1)/2] ={1, . . . , p(p + 1)/2}. We find that the expected number of non-unit eigenvalues of Σ, denotedE[|A|], is approximated with near perfect accuracy by the solution of the equation4p + p(p − 1)2(p + 1)hlog pp − d −d2p(p − d)i− s∗ = 0.Furthermore, the corresponding eigenvectors are shown to possess only p − |Ac| nonzeroentries. We use this result to elucidate the precise structure induced on Σ and Σ−1.We demonstrate that a positive definite symmetric matrix whose matrix logarithm issparse is significantly less sparse in the original domain. This finding has importantimplications in high dimensional statistics where it is important to exploit structure inorder to construct consistent estimators in non-trivial norms. An estimator exploitingthe structure of the proposed class is presented.

  • Journal article
    Wills QF, Mellado-Gomez E, Nolan R, Warner D, Sharma E, Broxholme J, Wright B, Lockstone H, James W, Lynch M, Gonzales M, West J, Leyrat A, Padilla-Parra S, Filippi S, Holmes C, Moore MD, Bowden Ret al., 2017,

    The nature and nurture of cell heterogeneity: accounting for macrophage gene-environment interactions with single-cell RNA-Seq.

    , BMC Genomics, Vol: 18, ISSN: 1471-2164

    BACKGROUND: Single-cell RNA-Seq can be a valuable and unbiased tool to dissect cellular heterogeneity, despite the transcriptome's limitations in describing higher functional phenotypes and protein events. Perhaps the most important shortfall with transcriptomic 'snapshots' of cell populations is that they risk being descriptive, only cataloging heterogeneity at one point in time, and without microenvironmental context. Studying the genetic ('nature') and environmental ('nurture') modifiers of heterogeneity, and how cell population dynamics unfold over time in response to these modifiers is key when studying highly plastic cells such as macrophages. RESULTS: We introduce the programmable Polaris™ microfluidic lab-on-chip for single-cell sequencing, which performs live-cell imaging while controlling for the culture microenvironment of each cell. Using gene-edited macrophages we demonstrate how previously unappreciated knockout effects of SAMHD1, such as an altered oxidative stress response, have a large paracrine signaling component. Furthermore, we demonstrate single-cell pathway enrichments for cell cycle arrest and APOBEC3G degradation, both associated with the oxidative stress response and altered proteostasis. Interestingly, SAMHD1 and APOBEC3G are both HIV-1 inhibitors ('restriction factors'), with no known co-regulation. CONCLUSION: As single-cell methods continue to mature, so will the ability to move beyond simple 'snapshots' of cell populations towards studying the determinants of population dynamics. By combining single-cell culture, live-cell imaging, and single-cell sequencing, we have demonstrated the ability to study cell phenotypes and microenvironmental influences. It's these microenvironmental components - ignored by standard single-cell workflows - that likely determine how macrophages, for example, react to inflammation and form treatment resistant HIV reservoirs.

  • Journal article
    Todd J, Evangelou M, Cutler AJ, Pekalski ML, Walker NM, Stevens HE, Porter L, Smyth DJ, Rainbow DB, Ferreira RC, Esposito L, Hunter KMD, Loudon Ket al., 2016,

    Regulatory T Cell Responses in Participants with Type 1 Diabetes after a Single Dose of Interleukin-2: A Non-Randomised, Open Label, Adaptive Dose-Finding Trial

    , PLOS Medicine, Vol: 13, ISSN: 1549-1277

    BackgroundInterleukin-2 (IL-2) has an essential role in the expansion and function of CD4+ regulatory Tcells (Tregs). Tregs reduce tissue damage by limiting the immune response following infectionand regulate autoreactive CD4+ effector T cells (Teffs) to prevent autoimmune diseases,such as type 1 diabetes (T1D). Genetic susceptibility to T1D causes alterations inthe IL-2 pathway, a finding that supports Tregs as a cellular therapeutic target. Aldesleukin(Proleukin; recombinant human IL-2), which is administered at high doses to activate the immune system in cancer immunotherapy, is now being repositioned to treat inflammatoryand autoimmune disorders at lower doses by targeting Tregs.Methods and FindingsTo define the aldesleukin dose response for Tregs and to find doses that increase Tregsphysiologically for treatment of T1D, a statistical and systematic approach was taken byanalysing the pharmacokinetics and pharmacodynamics of single doses of subcutaneousaldesleukin in the Adaptive Study of IL-2 Dose on Regulatory T Cells in Type 1 Diabetes(DILT1D), a single centre, non-randomised, open label, adaptive dose-finding trial with 40adult participants with recently diagnosed T1D. The primary endpoint was the maximumpercentage increase in Tregs (defined as CD3+CD4+CD25highCD127low) from the baselinefrequency in each participant measured over the 7 d following treatment. There was an initiallearning phase with five pairs of participants, each pair receiving one of five preassignedsingle doses from 0.04 × 106 to 1.5 × 106 IU/m2, in order to model the doseresponsecurve. Results from each participant were then incorporated into interim statisticalmodelling to target the two doses most likely to induce 10% and 20% increases in Treg frequencies.Primary analysis of the evaluable population (n = 39) found that the optimaldoses of aldesleukin to induce 10% and 20% increases in Tregs were 0.101 × 106 IU/m2(standard error [SE] = 0.078, 95% CI = −0.052, 0.254

  • Conference paper
    Larsen E, Truong T, Evangelou M, 2016,

    Exploring GenexEnvironment interactions through pathway analysis

    , Annual Meeting of the International-Genetic-Epidemiology-Society, Publisher: Wiley, Pages: 648-649, ISSN: 1098-2272
  • Journal article
    Nasser S, Lazaridis A, Evangelou M, Jones B, Nixon K, Kyrgiou M, Gabra H, Rockall A, Fotopoulou Cet al., 2016,

    Correlation of pre-operative CT findings with surgical & histological tumor dissemination patterns at cytoreduction for primary advanced and relapsed epithelial ovarian cancer: A retrospective evaluation

    , Gynecologic Oncology, Vol: 143, Pages: 264-269, ISSN: 1095-6859

    ObjectivesComputed tomography (CT) is an essential part of preoperative planning prior to cytoreductive surgery for primary and relapsed epithelial ovarian cancer (EOC). Our aim is to correlate pre-operative CT results with intraoperative surgical and histopathological findings at debulking surgery.MethodsWe performed a systematic comparison of intraoperative tumor dissemination patterns and surgical resections with preoperative CT assessments of infiltrative disease at key resection sites, in women who underwent multivisceral debulking surgery due to EOC between January 2013 and December 2014 at a tertiary referral center. The key sites were defined as follows: diaphragmatic involvement(DI), splenic disease (SI), large (LBI) and small (SBI) bowel involvement, rectal involvement (RI), porta hepatis involvement (PHI), mesenteric disease (MI) and lymph node involvement (LNI).ResultsA total of 155 patients, mostly with FIGO stage IIIC disease (65%) were evaluated (primary = 105, relapsed = 50). Total macroscopic cytoreduction rates were: 89%. Pre-operative CT findings displayed high specificity across all tumor sites apart from the retroperitoneal lymph node status, with a specificity of 65%.The ability however of the CT to accurately identify sites affected by invasive disease was relatively low with the following sensitivities as relating to final histology:32% (DI), 26% (SI), 46% (LBI), 44% (SBI), 39% (RI), 57% (PHI), 31% (MI), 63% (LNI).ConclusionPre-operative CT imaging shows high specificity but low sensitivity in detecting tumor involvement at key sites in ovarian cancer surgery. CT findings alone should not be used for surgical decision making.

  • Journal article
    Battey H, Feng Q, Smith RJ, 2016,

    Improving confidence set estimation when parameters are weakly identified

    , Statistics and Probability Letters, Vol: 118, Pages: 117-123

    © 2016 Elsevier B.V. We consider inference in weakly identified moment condition models when additional partially identifying moment inequality constraints are available. We detail the limiting distribution of the estimation criterion function and consequently propose a confidence set estimator for the true parameter.

  • Journal article
    Nieto-Reyes A, Battey H, 2016,

    A Topologically Valid Definition of Depth for Functional Data

    , Statistical Science, Vol: 31, Pages: 61-79

    The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function.

  • Journal article
    Filippi S, Barnes CP, Kirk PDW, Kudo T, Kunida K, McMahon SS, Tsuchiya T, Wada T, Kuroda S, Stumpf MPHet al., 2016,

    Robustness of MEK-ERK Dynamics and Origins of Cell-to-Cell Variability in MAPK Signaling

    , CellReports
  • Journal article
    Cohen E, Kim D, Ober RJ, 2015,

    The Cramer Rao lower bound for point based image registration with heteroscedastic error model for application in single molecule microscopy

    , IEEE Transactions on Medical Imaging, Vol: 34, Pages: 2632-2644, ISSN: 1558-254X

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