The mathematics of cancer: integrating quantitative models (Q38644551)

5 September 2017

The mathematics of cancer: integrating quantitative models (English)

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5 September 2017

3

Franziska Michor

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5 September 2017

Philipp M Altrock

1

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5 September 2017

Lin L Liu

series ordinal

2

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5 September 2017

language of work or name

English

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publication date

1 November 2015

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5 September 2017

Nature Reviews Cancer

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5 September 2017

15

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5 September 2017

12

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5 September 2017

730-745

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maintained by WikiProject

5 September 2017

WikiProject Mathematics

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https://scigraph.springernature.com/pub.10.1038/nrc4029

inferred from title

exact match

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Mathematical modeling of PDGF-driven glioblastoma reveals optimized radiation dosing schedules

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An Evolutionary Approach for Identifying Driver Mutations in Colorectal Cancer

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A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues

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Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications.

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A progenitor cell origin of myeloid malignancies

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Mathematical model for the cancer stem cell hypothesis

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The probable cell of origin of NF1- and PDGF-driven glioblastomas

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A genetic model for colorectal tumorigenesis

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Distance-based reconstruction of tree models for oncogenesis.

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Statistical behavior of complex cancer karyotypes

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Learning multiple evolutionary pathways from cross-sectional data

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Construction of tree models for pathogenesis of nasopharyngeal carcinoma.

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Construction of oncogenetic tree models reveals multiple pathways of oral cancer progression

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New probabilistic network models and algorithms for oncogenesis.

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Quantifying cancer progression with conjunctive Bayesian networks

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The temporal order of genetic and pathway alterations in tumorigenesis

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A mathematical framework to determine the temporal sequence of somatic genetic events in cancer

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A mathematical methodology for determining the temporal order of pathway alterations arising during gliomagenesis

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Fixation of strategies for an evolutionary game in finite populations.

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Temporal and spatial evolution of somatic chromosomal alterations: a case-cohort study of Barrett's esophagus

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Accurate reconstruction of the temporal order of mutations in neoplastic progression

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Clonal evolution in breast cancer revealed by single nucleus genome sequencing.

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Evolutionary pathways in BRCA1-associated breast tumors

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Temporal dissection of tumorigenesis in primary cancers

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Estimation of rearrangement phylogeny for cancer genomes

31 March 2020

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Methods and challenges in timing chromosomal abnormalities within cancer samples

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A Big Bang model of human colorectal tumor growth

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The pathogenesis of cancer metastasis: the 'seed and soil' hypothesis revisited

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The microenvironment of the tumour-host interface

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Friends or foes - bipolar effects of the tumour stroma in cancer

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Growth of necrotic tumors in the presence and absence of inhibitors.

31 March 2020

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A new mathematical model for avascular tumour growth

31 March 2020

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Reaction-diffusion model for the growth of avascular tumor

31 March 2020

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Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis

31 March 2020

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Multiscale modelling and nonlinear simulation of vascular tumour growth.

31 March 2020

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Hybrid models of tumor growth.

31 March 2020

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'Go or grow': the key to the emergence of invasion in tumour progression?

31 March 2020

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Continuous and discrete mathematical models of tumor-induced angiogenesis.

31 March 2020

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Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies.

31 March 2020

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A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion

31 March 2020

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An integrated computational model of the bone microenvironment in bone-metastatic prostate cancer

31 March 2020

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31 March 2020

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31 March 2020

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Prediction of drug response in breast cancer using integrative experimental/computational modeling

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A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity

31 March 2020

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THE METABOLISM OF TUMORS IN THE BODY

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A cellular automaton model of early tumor growth and invasion

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Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion

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31 March 2020

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Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology

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31 March 2020

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Complexity and stability in growing cancer cell populations

31 March 2020

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Non-cell-autonomous driving of tumour growth supports sub-clonal heterogeneity

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Migration rules: tumours are conglomerates of self-metastases.

31 March 2020

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Angiogenesis in cancer and other diseases

31 March 2020

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Multiscale modeling of fluid transport in tumors.

31 March 2020

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Mathematical modeling of tumor-induced angiogenesis

31 March 2020

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Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach.

31 March 2020

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The application of the linear-quadratic dose-effect equation to fractionated and protracted radiotherapy.

31 March 2020

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Cancer immunotherapy: moving beyond current vaccines

31 March 2020

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T cells with chimeric antigen receptors have potent antitumor effects and can establish memory in patients with advanced leukemia

31 March 2020

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Cancer immunotherapy: a treatment for the masses

31 March 2020

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The blockade of immune checkpoints in cancer immunotherapy

31 March 2020

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A validated mathematical model of cell-mediated immune response to tumor growth.

31 March 2020

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A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences

31 March 2020

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Interleukin-21 is a T-helper cytokine that regulates humoral immunity and cell-mediated anti-tumour responses

31 March 2020

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Cancer immunotherapy by interleukin-21: potential treatment strategies evaluated in a mathematical model

31 March 2020

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SimB16: modeling induced immune system response against B16-melanoma

31 March 2020

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The cancer diaspora: Metastasis beyond the seed and soil hypothesis

31 March 2020

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31 March 2020

Self-seeding in cancer

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System dynamics of metastatic process from an implanted tumor

31 March 2020

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Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics

31 March 2020

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Genetic and phenotypic diversity in breast tumor metastases

31 March 2020

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Unifying metastasis--integrating intravasation, circulation and end-organ colonization

31 March 2020

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Comments on hematogenous metastatic patterns in humans as revealed by autopsy

31 March 2020

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A mathematical model of tumour self-seeding reveals secondary metastatic deposits as drivers of primary tumour growth.

31 March 2020

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A filter-flow perspective of haematogenous metastasis offers a non-genetic paradigm for personalised cancer therapy.

31 March 2020

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Spatial heterogeneity in drug concentrations can facilitate the emergence of resistance to cancer therapy

31 March 2020

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Computational modeling of pancreatic cancer reveals kinetics of metastasis suggesting optimum treatment strategies

31 March 2020

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The evolution of tumor metastases during clonal expansion

31 March 2020

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A stochastic Markov chain model to describe lung cancer growth and metastasis

31 March 2020

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Spreaders and sponges define metastasis in lung cancer: a Markov chain Monte Carlo mathematical model.

31 March 2020

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Surgical treatment of lung cancer with adrenal metastasis

31 March 2020

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Adrenal metastases in lung cancer: clinical implications of a mathematical model.

31 March 2020

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Independent regulation of tumor cell migration by matrix stiffness and confinement.

31 March 2020

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What does physics have to do with cancer?

31 March 2020

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Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical model

31 March 2020

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Normalizing tumor microenvironment to treat cancer: bench to bedside to biomarkers

31 March 2020

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A stochastic model for the origin and treatment of tumors containing drug-resistant cells.

31 March 2020

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Growth Curve of an Experimental Solid Tumor Following Radiotherapy

31 March 2020

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Randomized Trial of Dose-Dense Versus Conventionally Scheduled and Sequential Versus Concurrent Combination Chemotherapy as Postoperative Adjuvant Treatment of Node-Positive Primary Breast Cancer: First Report of Intergroup Trial C9741/Cancer and Leu

31 March 2020

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Clinical relevance of different sequencing of doxorubicin and cyclophosphamide, methotrexate, and Fluorouracil in operable breast cancer

31 March 2020

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Evolution of acquired resistance to anti-cancer therapy

31 March 2020

1 reference

Evolution of resistance to targeted anti-cancer therapies during continuous and pulsed administration strategies

31 March 2020

1 reference

Optimization of dosing for EGFR-mutant non-small cell lung cancer with evolutionary cancer modeling

31 March 2020

1 reference

Effects of pharmacokinetic processes and varied dosing schedules on the dynamics of acquired resistance to erlotinib in EGFR-mutant lung cancer

31 March 2020

1 reference

Dynamics of chronic myeloid leukaemia.

31 March 2020

1 reference

Response classification based on a minimal model of glioblastoma growth is prognostic for clinical outcomes and distinguishes progression from pseudoprogression

31 March 2020

1 reference

Toward patient-specific, biologically optimized radiation therapy plans for the treatment of glioblastoma.

31 March 2020

1 reference

Mathematical modeling of prostate cancer progression in response to androgen ablation therapy

31 March 2020

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31 March 2020

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Inducing catastrophe in malignant growth

31 March 2020

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Somatic mosaicism and cancer: inference based on a conditional Luria-Delbrück distribution

31 March 2020

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The evolution of two mutations during clonal expansion

31 March 2020

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Evolution of resistance and progression to disease during clonal expansion of cancer.

31 March 2020

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Evolutionary dynamics of escape from biomedical intervention.

31 March 2020

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Stochastic modeling of cellular colonies with quiescence: an application to drug resistance in cancer

31 March 2020

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Timing and heterogeneity of mutations associated with drug resistance in metastatic cancers

31 March 2020

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Evolutionary modeling of combination treatment strategies to overcome resistance to tyrosine kinase inhibitors in non-small cell lung cancer

31 March 2020

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Stochastic modeling of drug resistance in cancer.

31 March 2020

1 reference

Evolution of ibrutinib resistance in chronic lymphocytic leukemia (CLL)

31 March 2020

1 reference

Deterministic evolutionary game dynamics in finite populations.

31 March 2020

1 reference

Dynamics of resistance development to imatinib under increasing selection pressure: a combination of mathematical models and in vitro data

31 March 2020

1 reference

Evolution of intratumoral phenotypic heterogeneity: the role of trait inheritance.

31 March 2020

1 reference

Emergence of stable polymorphisms driven by evolutionary games between mutants

31 March 2020

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Stochastic game dynamics under demographic fluctuations

31 March 2020

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Reply to Gerlee and Altrock: Diffusion and population size in game theory models of cancer

31 March 2020

1 reference

Tumorigenesis: it takes a village

31 March 2020

1 reference

The ecology of cancer from an evolutionary game theory perspective

31 March 2020

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Evolution of cooperation among tumor cells

31 March 2020

1 reference

Evolutionary game theory of growth factor production: implications for tumour heterogeneity and resistance to therapies

31 March 2020

1 reference

Investigating prostate cancer tumour-stroma interactions: clinical and biological insights from an evolutionary game

31 March 2020

1 reference

Critical transitions in a game theoretic model of tumour metabolism

31 March 2020

1 reference

Evolutionary game theory elucidates the role of glycolysis in glioma progression and invasion

31 March 2020

1 reference

The Impact of Microenvironmental Heterogeneity on the Evolution of Drug Resistance in Cancer Cells

31 March 2020

1 reference

12 December 2020

Blood flow, oxygen and nutrient supply, and metabolic microenvironment of human tumors: a review.

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12 December 2020

Quantitative model for multiple levels of drug resistance in clinical tumors.

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12 December 2020

Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies.

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12 December 2020

Cancer immunology: the search for specificity--G. H. A. Clowes Memorial lecture

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12 December 2020

A mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate

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12 December 2020

A reaction-diffusion model of cancer invasion.

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12 December 2020

Patterns of Cell Division and the Risk of Cancer

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12 December 2020

A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competitive environment.

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12 December 2020

The distribution of secondary growths in cancer of the breast. 1889

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12 December 2020

Mutations of Bacteria from Virus Sensitivity to Virus Resistance

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12 December 2020

Chromosome abnormalities in ovarian adenocarcinoma: III. Using breakpoint data to infer and test mathematical models for oncogenesis

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12 December 2020

The genetic origin of drug resistance in neoplasms: implications for systemic therapy.

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12 December 2020

Identifiers

DOI

10.1038/NRC4029

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Dimensions Publication ID

5 September 2017

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