Browsing by Subject "System modeling"
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Item Open Access Local asymptotic stability conditions for the positive equilibrium of a system modeling cell dynamics in leukemia(Springer, Berlin, Heidelberg, 2012) Özbay, Hitay; Bonnet, C.; Benjelloun H.; Clairambault J.A distributed delay system with static nonlinearity has been considered in the literature to study the cell dynamics in leukemia. In this chapter local asymptotic stability conditions are derived for the positive equilibrium point of this nonlinear system. The stability conditions are expressed in terms of inequalities involving parameters of the system. These inequality conditions give guidelines for development of therapeutic actions. © 2012 Springer-Verlag GmbH Berlin Heidelberg.Item Open Access Modeling of spatio-temporal hawkes processes with randomized kernels(IEEE, 2020) İlhan, Fatih; Kozat, Süleyman SerdarWe investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatio-temporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In particular, we focus on spatio-temporal Hawkes processes that are commonly used due to their capability to capture excitations between event occurrences. We introduce a novel inference framework based on randomized transformations and gradient descent to learn the process. We replace the spatial kernel calculations by randomized Fourier feature-based transformations. The introduced randomization by this representation provides flexibility while modeling the spatial excitation between events. Moreover, the system described by the process is expressed within closed-form in terms of scalable matrix operations. During the optimization, we use maximum likelihood estimation approach and gradient descent while properly handling positivity and orthonormality constraints. The experiment results show the improvements achieved by the introduced method in terms of fitting capability in synthetic and real-life datasets with respect to the conventional inference methods in the spatio-temporal Hawkes process literature. We also analyze the triggering interactions between event types and how their dynamics change in space and time through the interpretation of learned parameters.Item Open Access Stability analysis of cell dynamics in leukemia(E D P Sciences, 2012) Özbay, Hitay; Bonnet, C.; Benjelloun, H.; Clairambault, J.In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations.