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We consider the dynamics of small tracer particles in turbulent quantum liquids. The complicated interaction processes of vortex filaments, the quantum constraints on vorticity and the varying influence of both the superfluid and the normal…
These are lecture notes for a mini-course given at the Cornell Probability Summer School in July 2013. Topics include lozenge tilings of polygons and their representation theoretic interpretation, the (q,t)-deformation of those leading to…
The interaction of multiple fluids through a heterogeneous pore space leads to complex pore-scale flow dynamics, such as intermittent pathway flow. The non-local nature of these dynamics, and the size of the 4D datasets acquired to capture…
The fourth international workshop on Computational Models for Cell Processes (CompMod 2013) took place on June 11, 2013 at the {\AA}bo Akademi University, Turku, Finland, in conjunction with iFM 2013. The first edition of the workshop…
The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows. In this paper, we use KMD to study the dynamics of the lid-driven flow in a two-dimensional…
Tensor decomposition is a fundamental framework to analyze data that can be represented by multi-dimensional arrays. In practice, tensor data is often accompanied by temporal information, namely the time points when the entry values were…
This volume contains the proceedings of the Sixth International Workshop on Computing with Terms and Graphs (TERMGRAPH 2011). The workshop took place in Saarbruecken, Germany, on April 2nd, 2011, as part of the fourteenth edition of the…
Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this work, we attempt to provide a consistent framework through Koopman theory and its related…
We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems. For linear signals, we introduce an algorithm with similarities to the Fourier transform but…
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…
Dynamic positron emission tomography imaging (dPET) provides temporally resolved images of a tracer enabling a quantitative measure of physiological processes. Voxel-wise physiologically-based pharmacokinetic (PBPK) modeling of the time…
Image-based tracking of medical instruments is an integral part of surgical data science applications. Previous research has addressed the tasks of detecting, segmenting and tracking medical instruments based on laparoscopic video data.…
Understanding the long-time dynamics of complex physical processes depends on our ability to recognize patterns. To simplify the description of these processes, we often introduce a set of reaction coordinates, customarily referred to as…
Improving the detailed understanding of the underlying properties and functions of biomolecules has recently attracted growing interest, enabled by the possibility of real-space imaging of single, intact macromolecules using Scanning…
The increasing penetration of renewable energy sources, characterised by low inertia and intermittent disturbances, presents substantial challenges to power system stability. As critical indicators of system stability, frequency dynamics…
We present a new approach for representing and reconstructing multidimensional magnetic resonance imaging (MRI) data. Our method builds on a novel, learned feature-based image representation that disentangles different types of features,…
Medical Informatics and the application of modern signal processing in the assistance of the diagnostic process in medical imaging is one of the more recent and active research areas today. This thesis addresses a variety of issues related…
In this paper, we overview, evaluate, and demonstrate the sparse processing particle image velocimetry (SPPIV) as a real-time flow field estimation method using the particle image velocimetry (PIV), whereas SPPIV was previously proposed…
We formulate a low-storage method for performing dynamic mode decomposition that can be updated inexpensively as new data become available; this formulation allows dynamical information to be extracted from large datasets and data streams.…
We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band…