Dynamics identification and forecasting of COVID-19 by switching Kalman filters.

The COVID-19 pandemic has captivated scientific activity since its early days. Particular attention has been dedicated to the identification of underlying dynamics and prediction of future trend. In this work, a switching Kalman filter formalism is applied on dynamics learning and forecasting of the daily new cases of COVID-19.

Uncertainty quantification for Markov chain models.

Transition probabilities serve to parameterize Markov chains and control their evolution and associated decisions and controls. Uncertainties in these parameters can be associated with inherent fluctuations in the medium through which a chain evolves, or with insufficient data such that the inferential value of the chain is jeopardized. The behavior of Markov chains associated with such uncertainties is described using a probabilistic model for the transition matrices.

Ultrasound monitoring of tissue ablation via deformation model and shape priors.

A rapid approach to monitor ablative therapy through optimizing shape and elasticity parameters is introduced. Our motivating clinical application is targeting and intraoperative monitoring of hepatic tumor thermal ablation, but the method translates to the generic problem of encapsulated stiff masses (solid organs, tumors, ablated lesions, etc.) in ultrasound imaging.

Equation-free dynamic renormalization: self-similarity in multidimensional particle system dynamics.

We present an equation-free dynamic renormalization approach to the computational study of coarse-grained, self-similar dynamic behavior in multidimensional particle systems. The approach is aimed at problems for which evolution equations for coarse-scale observables (e.g.

A substructure approach for the midfrequency vibration of stochastic systems.

A novel substructure coupling technique based on the proper orthogonal decomposition method is presented for the midfrequency range vibration of linear dynamical systems with parameter uncertainty. For a given frequency band, the methodology permits the derivation of an adaptive basis for each subsystem and the construction of a reduced-order model of the global structure. The formulation is directed toward the efficient probabilistic characterization of model-based predictions in the framework of a stochastic finite element method.

Reduced models for the medium-frequency dynamics of stochastic systems.

In this paper, a frequency domain vibration analysis procedure of a randomly parametered structural system is described for the medium-frequency range. In this frequency range, both traditional modal analysis and statistical energy analysis (SEA) procedures well-suited for low- and high-frequency vibration analysis respectively, lead to computational and conceptual difficulties. The uncertainty in the structural system can be attributed to various reasons such as the coupling of the primary structure with a variety of secondary systems for which conventional modeling is not practical.