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  • 1. Hansson, Kristin
    et al.
    Jafari-Mamaghani, Mehrdad
    Stockholm University, Faculty of Science, Department of Mathematics. Karolinska Institutet, Sweden.
    Krieger, Patrik
    RipleyGUI: software for analyzing spatial patterns in 3D cell distributions2013In: Frontiers in Neuroinformatics, ISSN 1662-5196, E-ISSN 1662-5196, Vol. 7, article id 5Article in journal (Refereed)
    Abstract [en]

    The true revolution in the age of digital neuroanatomy is the ability to extensively quantify anatomical structures and thus investigate structure-function relationships in great detail. To facilitate the quantification of neuronal cell patterns we have developed RipleyGUI, a MATLAB-based software that can be used to detect patterns in the 3D distribution of cells. RipleyGUI uses Ripley's K-function to analyze spatial distributions. In addition the software contains statistical tools to determine quantitative statistical differences, and tools for spatial transformations that are useful for analyzing non-stationary point patterns. The software has a graphical user interface making it easy to use without programming experience, and an extensive user manual explaining the basic concepts underlying the different statistical tools used to analyze spatial point patterns. The described analysis tool can be used for determining the spatial organization of neurons that is important for a detailed study of structure function relationships. For example, neocortex that can be subdivided into six layers based on cell density and cell types can also be analyzed in terms of organizational principles distinguishing the layers.

  • 2.
    Jafari-Mamaghani, Mehrdad
    Stockholm University, Faculty of Science, Department of Mathematics.
    A Treatise on Measuring Wiener-Granger Causality2014Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Wiener-Granger causality is a well-established concept of causality based on stochasticity and the flow of time, with applications in a broad array of quantitative sciences. The majority of methods used to measure Wiener-Granger causality are based on linear premises and hence insensitive to non-linear signals. Other frameworks based on non-parametric techniques are often computationally expensive and susceptible to overfitting or lack of sensitivity.

    In this thesis, Paper I investigates the application of linear Wiener-Granger causality to migrating cancer cell data obtained using a Systems Microscopy experimental platform. Paper II represents a review of non-parametric measures based on information theory and discusses a number of related bottlenecks and potential routes of circumvention. Paper III studies the properties of a frequently used non-parametric information theoretical measure for a class of non-Gaussian distributions. Paper IV introduces a new efficient scheme for non-parametric analysis of Wiener-Granger causality based on kernel canonical correlations, and studies the connection between this new scheme and the information theoretical approach. Lastly, Paper V draws upon the results in the preceding paper to discuss non-parametric analysis of Wiener-Granger causality in partially observed systems.

    Altogether, the work presented in this thesis constitutes a comprehensive review on measures of Wiener-Granger causality in general, and in particular, features new insights on efficient non-parametric analysis of Wiener-Granger causality in high-dimensional settings.

  • 3.
    Jafari-Mamaghani, Mehrdad
    Stockholm University, Faculty of Science, Department of Mathematics.
    Non-parametric analysis of Granger causality using local measures of divergence2013In: Applied Mathematical Sciences, ISSN 1312-885X, E-ISSN 1314-7552, Vol. 7, no 83, p. 4107-4236Article in journal (Refereed)
    Abstract [en]

    The employment of Granger causality analysis on temporal data is now a standard routine in many scientific disciplines. Since its in- ception, Granger causality has been modeled using a wide variety of analytical frameworks of which, linear models and derivations thereof have been the dominant choice. Nevertheless, a body of research on Granger causality and its applications has focused on non-linear and non-parametric models. One common choice for such models is based on employment of multivariate density estimators and measures of divergence. However, these models are subject to a number of estimations and tuning components that have a great impact on the final outcome. Here we focus on one such general model and improve a number of its tuning bodies. Crucially, we i) investigate the bandwidth selection issue in kernel density estimation, and ii) discuss and propose a solu- tion to the sensitivity of estimated information theoretic measures of divergence to non-linear correspondence. The resulting framework of analysis is evaluated using varied series of simulations.

  • 4.
    Jafari-Mamaghani, Mehrdad
    Stockholm University, Faculty of Science, Department of Mathematics.
    Non-parametric Wiener-Granger Causality in Partially Observed Systems2014In: IEEE 2014 Conference on Norbert Wiener in the 21st Century: Driving Technology's Future, 2014Conference paper (Refereed)
    Abstract [en]

    Wiener’s definition of causality, now known as Wiener-Granger causality, has become a frequently used quantification of temporally resolved causality in numerous fields of science. In many empirical studies, the system of interest cannot be observed in its entirety and the observations may include non-informative data. To this end, partial Wiener-Granger causality has been developed to circumvent this issue. In this paper, we extend partial Wiener-Granger causality to the non-parametric case and discuss two approaches to obtain estimates of this non-parametric, entropy-based measure.

  • 5.
    Jafari-Mamaghani, Mehrdad
    Stockholm University, Faculty of Science, Department of Mathematics.
    Robust Non-linear Wiener-Granger Causality For Large High-dimensional DataManuscript (preprint) (Other academic)
    Abstract [en]

    Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analysis with specific advantages in the context of large high-dimensional data. The introduced measure is able to detect non-linear and non-monotonous signals, is designed to be immune to noise, and offers tunability in terms of computational complexity in its estimations. Furthermore, we show that, under specified conditions, the intro- duced measure can be regarded as an estimate of conditional mutual information (tranfer entropy). The functionality of this measure is assessed using comparative simulations where it outperforms other existing methods. The paper is concluded with an application to climatological data.

  • 6.
    Jafari-Mamaghani, Mehrdad
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Tyrcha, Joanna
    Stockholm University, Faculty of Science, Department of Mathematics.
    Transfer entropy expressions for a class of non-Gaussian distributionsManuscript (preprint) (Other academic)
    Abstract [en]

    Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I − IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.

  • 7.
    Jafari-Mamaghani, Mehrdad
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Karolinska Institutet, Sweden.
    Tyrcha, Joanna
    Stockholm University, Faculty of Science, Department of Mathematics.
    Transfer Entropy Expressions for a Class of Non-Gaussian Distributions2014In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 16, no 3, p. 1743-1755Article in journal (Refereed)
    Abstract [en]

    Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I - IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.

  • 8. Kowalewski, Jacob M.
    et al.
    Shafqat-Abbasi, Hamdah
    Jafari-Mamaghani, Mehrdad
    Stockholm University, Faculty of Science, Department of Mathematics. Karolinska Institutet, Sweden.
    Ganebo, Bereket Endrias
    Gong, Xiaowei
    Strömblad, Staffan
    Lock, John G.
    Disentangling Membrane Dynamics and Cell Migration; Differential Influences of F-actin and Cell-Matrix Adhesions2015In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 10, no 8, article id e0135204Article in journal (Refereed)
    Abstract [en]

    Cell migration is heavily interconnected with plasma membrane protrusion and retraction (collectively termed membrane dynamics). This makes it difficult to distinguish regulatory mechanisms that differentially influence migration and membrane dynamics. Yet such distinctions may be valuable given evidence that cancer cell invasion in 3D may be better predicted by 2D membrane dynamics than by 2D cell migration, implying a degree of functional independence between these processes. Here, we applied multi-scale single cell imaging and a systematic statistical approach to disentangle regulatory associations underlying either migration or membrane dynamics. This revealed preferential correlations between membrane dynamics and F-actin features, contrasting with an enrichment of links between cell migration and adhesion complex properties. These correlative linkages were often nonlinear and therefore context-dependent, strengthening or weakening with spontaneous heterogeneity in cell behavior. More broadly, we observed that slow moving cells tend to increase in area, while fast moving cells tend to shrink, and that the size of dynamic membrane domains is independent of cell area. Overall, we define macromolecular features preferentially associated with either cell migration or membrane dynamics, enabling more specific interrogation and targeting of these processes in future.

  • 9. Lock, John G.
    et al.
    Jafari-Mamaghani, Mehrdad
    Stockholm University, Faculty of Science, Department of Mathematics. Karolinska Institute, Sweden.
    Shafqat-Abbasi, Hamdah
    Gong, Xiaowei
    Tyrcha, Joanna
    Stockholm University, Faculty of Science, Department of Mathematics.
    Strömblad, Staffan
    Plasticity in the Macromolecular-Scale Causal Networks of Cell Migration2014In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 9, no 2, p. e90593-Article in journal (Refereed)
    Abstract [en]

    Heterogeneous and dynamic single cell migration behaviours arise from a complex multi-scale signalling network comprising both molecular components and macromolecular modules, among which cell-matrix adhesions and F-actin directly mediate migration. To date, the global wiring architecture characterizing this network remains poorly defined. It is also unclear whether such a wiring pattern may be stable and generalizable to different conditions, or plastic and context dependent. Here, synchronous imaging-based quantification of migration systemorganization, represented by 87 morphological and dynamic macromolecular module features, and migration system behaviour, i.e., migration speed, facilitated Granger causality analysis. We thereby leveraged natural cellular heterogeneity to begin mapping the directionally specific causal wiring between organizational and behavioural features of the cell migration system. This represents an important advance on commonly used correlative analyses that do not resolve causal directionality. We identified organizational features such as adhesion stability and adhesion F-actin content that, as anticipated, causally influenced cell migration speed. Strikingly, we also found that cell speed can exert causal influence over organizationalfeatures, including cell shape and adhesion complex location, thus revealing causality in directions contradictory to previous expectations. Importantly, by comparing unperturbed and signalling-modulated cells, we provide proof-of-principle that causal interaction patterns are in fact plastic and context dependent, rather than stable and generalizable.

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