@phdthesis{Seelig2021,
  author    = {Seelig, Stefan},
  title     = {Parafoveal processing of lexical information during reading},
  doi       = {10.25932/publishup-50874},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-508743},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xi, 113},
  year      = {2021},
  abstract  = {During sentence reading the eyes quickly jump from word to word to sample visual information with the high acuity of the fovea. Lexical properties of the currently fixated word are known to affect the duration of the fixation, reflecting an interaction of word processing with oculomotor planning. While low level properties of words in the parafovea can likewise affect the current fixation duration, results concerning the influence of lexical properties have been ambiguous (Drieghe, Rayner, \& Pollatsek, 2008; Kliegl, Nuthmann, \& Engbert, 2006). Experimental investigations of such lexical parafoveal-on-foveal effects using the boundary paradigm have instead shown, that lexical properties of parafoveal previews affect fixation durations on the upcoming target words (Risse \& Kliegl, 2014). However, the results were potentially confounded with effects of preview validity. The notion of parafoveal processing of lexical information challenges extant models of eye movements during reading. Models containing serial word processing assumptions have trouble explaining such effects, as they usually couple successful word processing to saccade planning, resulting in skipping of the parafoveal word. Although models with parallel word processing are less restricted, in the SWIFT model (Engbert, Longtin, \& Kliegl, 2002) only processing of the foveal word can directly influence the saccade latency. Here we combine the results of a boundary experiment (Chapter 2) with a predictive modeling approach using the SWIFT model, where we explore mechanisms of parafoveal inhibition in a simulation study (Chapter 4). We construct a likelihood function for the SWIFT model (Chapter 3) and utilize the experimental data in a Bayesian approach to parameter estimation (Chapter 3 \& 4). The experimental results show a substantial effect of parafoveal preview frequency on fixation durations on the target word, which can be clearly distinguished from the effect of preview validity. Using the eye movement data from the participants, we demonstrate the feasibility of the Bayesian approach even for a small set of estimated parameters, by comparing summary statistics of experimental and simulated data. Finally, we can show that the SWIFT model can account for the lexical preview effects, when a mechanism for parafoveal inhibition is added. The effects of preview validity were modeled best, when processing dependent saccade cancellation was added for invalid trials. In the simulation study only the control condition of the experiment was used for parameter estimation, allowing for cross validation. Simultaneously the number of free parameters was increased. High correlations of summary statistics demonstrate the capabilities of the parameter estimation approach. Taken together, the results advocate for a better integration of experimental data into computational modeling via parameter estimation.},
  language  = {en}
}
@misc{NueskenReichRozdeba2019,
  author    = {N{\"u}sken, Nikolas and Reich, Sebastian and Rozdeba, Paul J.},
  title     = {State and parameter estimation from observed signal increments},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {916},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-44260},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-442609},
  pages     = {25},
  year      = {2019},
  abstract  = {The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean-Vlasov equations as the starting point to derive ensemble Kalman-Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.},
  language  = {en}
}
@phdthesis{Angwenyi2019,
  author    = {Angwenyi, David},
  title     = {Time-continuous state and parameter estimation with application to hyperbolic SPDEs},
  doi       = {10.25932/publishup-43654},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436542},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xi, 101},
  year      = {2019},
  abstract  = {Data assimilation has been an active area of research in recent years, owing to its wide utility. At the core of data assimilation are filtering, prediction, and smoothing procedures. Filtering entails incorporation of measurements' information into the model to gain more insight into a given state governed by a noisy state space model. Most natural laws are governed by time-continuous nonlinear models. For the most part, the knowledge available about a model is incomplete; and hence uncertainties are approximated by means of probabilities. Time-continuous filtering, therefore, holds promise for wider usefulness, for it offers a means of combining noisy measurements with imperfect model to provide more insight on a given state. The solution to time-continuous nonlinear Gaussian filtering problem is provided for by the Kushner-Stratonovich equation. Unfortunately, the Kushner-Stratonovich equation lacks a closed-form solution. Moreover, the numerical approximations based on Taylor expansion above third order are fraught with computational complications. For this reason, numerical methods based on Monte Carlo methods have been resorted to. Chief among these methods are sequential Monte-Carlo methods (or particle filters), for they allow for online assimilation of data. Particle filters are not without challenges: they suffer from particle degeneracy, sample impoverishment, and computational costs arising from resampling. The goal of this thesis is to:— i) Review the derivation of Kushner-Stratonovich equation from first principles and its extant numerical approximation methods, ii) Study the feedback particle filters as a way of avoiding resampling in particle filters, iii) Study joint state and parameter estimation in time-continuous settings, iv) Apply the notions studied to linear hyperbolic stochastic differential equations. The interconnection between It{\^o} integrals and stochastic partial differential equations and those of Stratonovich is introduced in anticipation of feedback particle filters. With these ideas and motivated by the variants of ensemble Kalman-Bucy filters founded on the structure of the innovation process, a feedback particle filter with randomly perturbed innovation is proposed. Moreover, feedback particle filters based on coupling of prediction and analysis measures are proposed. They register a better performance than the bootstrap particle filter at lower ensemble sizes. We study joint state and parameter estimation, both by means of extended state spaces and by use of dual filters. Feedback particle filters seem to perform well in both cases. Finally, we apply joint state and parameter estimation in the advection and wave equation, whose velocity is spatially varying. Two methods are employed: Metropolis Hastings with filter likelihood and a dual filter comprising of Kalman-Bucy filter and ensemble Kalman-Bucy filter. The former performs better than the latter.},
  language  = {en}
}
@phdthesis{Gopalakrishnan2016,
  author    = {Gopalakrishnan, Sathej},
  title     = {Mathematical modelling of host-disease-drug interactions in HIV disease},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100100},
  school      = {Universit{\"a}t Potsdam},
  pages     = {121},
  year      = {2016},
  abstract  = {The human immunodeficiency virus (HIV) has resisted nearly three decades of efforts targeting a cure. Sustained suppression of the virus has remained a challenge, mainly due to the remarkable evolutionary adaptation that the virus exhibits by the accumulation of drug-resistant mutations in its genome. Current therapeutic strategies aim at achieving and maintaining a low viral burden and typically involve multiple drugs. The choice of optimal combinations of these drugs is crucial, particularly in the background of treatment failure having occurred previously with certain other drugs. An understanding of the dynamics of viral mutant genotypes aids in the assessment of treatment failure with a certain drug combination, and exploring potential salvage treatment regimens. Mathematical models of viral dynamics have proved invaluable in understanding the viral life cycle and the impact of antiretroviral drugs. However, such models typically use simplified and coarse-grained mutation schemes, that curbs the extent of their application to drug-specific clinical mutation data, in order to assess potential next-line therapies. Statistical models of mutation accumulation have served well in dissecting mechanisms of resistance evolution by reconstructing mutation pathways under different drug-environments. While these models perform well in predicting treatment outcomes by statistical learning, they do not incorporate drug effect mechanistically. Additionally, due to an inherent lack of temporal features in such models, they are less informative on aspects such as predicting mutational abundance at treatment failure. This limits their application in analyzing the pharmacology of antiretroviral drugs, in particular, time-dependent characteristics of HIV therapy such as pharmacokinetics and pharmacodynamics, and also in understanding the impact of drug efficacy on mutation dynamics. In this thesis, we develop an integrated model of in vivo viral dynamics incorporating drug-specific mutation schemes learned from clinical data. Our combined modelling approach enables us to study the dynamics of different mutant genotypes and assess mutational abundance at virological failure. As an application of our model, we estimate in vivo fitness characteristics of viral mutants under different drug environments. Our approach also extends naturally to multiple-drug therapies. Further, we demonstrate the versatility of our model by showing how it can be modified to incorporate recently elucidated mechanisms of drug action including molecules that target host factors. Additionally, we address another important aspect in the clinical management of HIV disease, namely drug pharmacokinetics. It is clear that time-dependent changes in in vivo drug concentration could have an impact on the antiviral effect, and also influence decisions on dosing intervals. We present a framework that provides an integrated understanding of key characteristics of multiple-dosing regimens including drug accumulation ratios and half-lifes, and then explore the impact of drug pharmacokinetics on viral suppression. Finally, parameter identifiability in such nonlinear models of viral dynamics is always a concern, and we investigate techniques that alleviate this issue in our setting.},
  language  = {en}
}