Extended Object Tracking: Introduction, Overview and Applications

This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.Comment: 30 pages, 19 figure

Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis

Genotoxic mixtures and dissimilar action: Concepts for prediction and assessment

This article has been made available through the Brunel Open Access Publishing Fund. This article is distributed under the terms of the creative commons Attribution license which permits any use, distribution, and reproduction in any medium, provided the original author(s)and the source are credited.Combinations of genotoxic agents have frequently been assessed without clear assumptions regarding their expected (additive) mixture effects, often leading to claims of synergisms that might in fact be compatible with additivity. We have shown earlier that the combined effects of chemicals, which induce micronuclei (MN) in the cytokinesis-block micronucleus assay in Chinese hamster ovary-K1 cells by a similar mechanism, were additive according to the concept of concentration addition (CA). Here, we extended these studies and investigated for the first time whether valid additivity expectations can be formulated for MN-inducing chemicals that operate through a variety of mechanisms, including aneugens and clastogens (DNA cross-linkers, topoisomerase II inhibitors, minor groove binders). We expected that their effects should follow the additivity principles of independent action (IA). With two mixtures, one composed of various aneugens (colchicine, flubendazole, vinblastine sulphate, griseofulvin, paclitaxel), and another composed of aneugens and clastogens (flubendazole, doxorubicin, etoposide, melphalan and mitomycin C), we observed mixture effects that fell between the additivity predictions derived from CA and IA. We achieved better agreement between observation and prediction by grouping the chemicals into common assessment groups and using hybrid CA/IA prediction models. The combined effects of four dissimilarly acting compounds (flubendazole, paclitaxel, doxorubicin and melphalan) also fell within CA and IA. Two binary mixtures (flubendazole/paclitaxel and flubendazole/doxorubicin) showed effects in reasonable agreement with IA additivity. Our studies provide a systematic basis for the investigation of mixtures that affect endpoints of relevance to genotoxicity and show that their effects are largely additive.UK Food Standards Agenc

On the foundations of cancer modelling: selected topics, speculations, & perspectives

This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution

Validation of Soft Classification Models using Partial Class Memberships: An Extended Concept of Sensitivity & Co. applied to the Grading of Astrocytoma Tissues

We use partial class memberships in soft classification to model uncertain labelling and mixtures of classes. Partial class memberships are not restricted to predictions, but may also occur in reference labels (ground truth, gold standard diagnosis) for training and validation data. Classifier performance is usually expressed as fractions of the confusion matrix, such as sensitivity, specificity, negative and positive predictive values. We extend this concept to soft classification and discuss the bias and variance properties of the extended performance measures. Ambiguity in reference labels translates to differences between best-case, expected and worst-case performance. We show a second set of measures comparing expected and ideal performance which is closely related to regression performance, namely the root mean squared error RMSE and the mean absolute error MAE. All calculations apply to classical crisp classification as well as to soft classification (partial class memberships and/or one-class classifiers). The proposed performance measures allow to test classifiers with actual borderline cases. In addition, hardening of e.g. posterior probabilities into class labels is not necessary, avoiding the corresponding information loss and increase in variance. We implement the proposed performance measures in the R package "softclassval", which is available from CRAN and at http://softclassval.r-forge.r-project.org. Our reasoning as well as the importance of partial memberships for chemometric classification is illustrated by a real-word application: astrocytoma brain tumor tissue grading (80 patients, 37000 spectra) for finding surgical excision borders. As borderline cases are the actual target of the analytical technique, samples which are diagnosed to be borderline cases must be included in the validation.Comment: The manuscript is accepted for publication in Chemometrics and Intelligent Laboratory Systems. Supplementary figures and tables are at the end of the pd

Combined population dynamics and entropy modelling supports patient stratification in chronic myeloid leukemia

Modelling the parameters of multistep carcinogenesis is key for a better understanding of cancer progression, biomarker identification and the design of individualized therapies. Using chronic myeloid leukemia (CML) as a paradigm for hierarchical disease evolution we show that combined population dynamic modelling and CML patient biopsy genomic analysis enables patient stratification at unprecedented resolution. Linking CD34+ similarity as a disease progression marker to patientderived gene expression entropy separated established CML progression stages and uncovered additional heterogeneity within disease stages. Importantly, our patient data informed model enables quantitative approximation of individual patients’ disease history within chronic phase (CP) and significantly separates “early” from “late” CP. Our findings provide a novel rationale for personalized and genome-informed disease progression risk assessment that is independent and complementary to conventional measures of CML disease burden and prognosis