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In this paper we establish the regularity, exponential stability of global (weak) solutions and existence of uniform compact attractors of semiprocesses, which are generated by the global solutions, of a two-parameter family of operators for the nonlinear 1-d non-autonomous viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.
Understanding and reducing complex systems pharmacology models based on a novel input-response index
(2018)
A growing understanding of complex processes in biology has led to large-scale mechanistic models of pharmacologically relevant processes. These models are increasingly used to study the response of the system to a given input or stimulus, e.g., after drug administration. Understanding the input–response relationship, however, is often a challenging task due to the complexity of the interactions between its constituents as well as the size of the models. An approach that quantifies the importance of the different constituents for a given input–output relationship and allows to reduce the dynamics to its essential features is therefore highly desirable. In this article, we present a novel state- and time-dependent quantity called the input–response index that quantifies the importance of state variables for a given input–response relationship at a particular time. It is based on the concept of time-bounded controllability and observability, and defined with respect to a reference dynamics. In application to the brown snake venom–fibrinogen (Fg) network, the input–response indices give insight into the coordinated action of specific coagulation factors and about those factors that contribute only little to the response. We demonstrate how the indices can be used to reduce large-scale models in a two-step procedure: (i) elimination of states whose dynamics have only minor impact on the input–response relationship, and (ii) proper lumping of the remaining (lower order) model. In application to the brown snake venom–fibrinogen network, this resulted in a reduction from 62 to 8 state variables in the first step, and a further reduction to 5 state variables in the second step. We further illustrate that the sequence, in which a recursive algorithm eliminates and/or lumps state variables, has an impact on the final reduced model. The input–response indices are particularly suited to determine an informed sequence, since they are based on the dynamics of the original system. In summary, the novel measure of importance provides a powerful tool for analysing the complex dynamics of large-scale systems and a means for very efficient model order reduction of nonlinear systems.
Ulcerative colitis (UC) is part of the inflammatory bowels diseases, and moderate to severe UC patients can be treated with anti-tumour necrosis alpha monoclonal antibodies, including infliximab (IFX). Even though treatment of UC patients by IFX has been in place for over a decade, many gaps in modelling of IFX PK in this population remain. This is even more true for acute severe UC (ASUC) patients for which early prediction of IFX pharmacokinetic (PK) could highly improve treatment outcome. Thus, this review aims to compile and analyse published population PK models of IFX in UC and ASUC patients, and to assess the current knowledge on disease activity impact on IFX PK. For this, a semi-systematic literature search was conducted, from which 26 publications including a population PK model analysis of UC patients receiving IFX therapy were selected. Amongst those, only four developed a model specifically for UC patients, and only three populations included severe UC patients. Investigations of disease activity impact on PK were reported in only 4 of the 14 models selected. In addition, the lack of reported model codes and assessment of predictive performance make the use of published models in a clinical setting challenging. Thus, more comprehensive investigation of PK in UC and ASUC is needed as well as more adequate reports on developed models and their evaluation in order to apply them in a clinical setting.
We construct eta- and rho-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah-Patodi-Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.
The evolution of the closed Friedmann Universe with a packet of short scalar waves is considered with the help of the Wheeler-DeWitt equation. The packet ensures conservation of homogeneity and isotropy of the metric on average. It is shown that during tunneling the amplitudes of short waves of a scalar field can increase catastrophically promptly if their influence to the metric is not taken into account. This effect is similar to the Rubakov-effect of catastrophic particle creation calculated already in 1984. In our approach to the problem it is possible to consider a self- consistent dynamics of the expansion of the Universe and amplification of short waves. It results in a decrease of the barrier and interruption of amplification of waves, and we get an exit of the wave function from the quantum to the classically available region.
We analyze a general class of difference operators Hε=Tε+Vε on ℓ2((εZ)d), where Vε is a multi-well potential and ε is a small parameter. We derive full asymptotic expansions of the prefactor of the exponentially small eigenvalue splitting due to interactions between two “wells” (minima) of the potential energy, i.e., for the discrete tunneling effect. We treat both the case where there is a single minimal geodesic (with respect to the natural Finsler metric induced by the leading symbol h0(x,ξ) of Hε) connecting the two minima and the case where the minimal geodesics form an ℓ+1 dimensional manifold, ℓ≥1. These results on the tunneling problem are as sharp as the classical results for the Schrödinger operator in Helffer and Sjöstrand (Commun PDE 9:337–408, 1984). Technically, our approach is pseudo-differential and we adapt techniques from Helffer and Sjöstrand [Analyse semi-classique pour l’équation de Harper (avec application à l’équation de Schrödinger avec champ magnétique), Mémoires de la S.M.F., 2 series, tome 34, pp 1–113, 1988)] and Helffer and Parisse (Ann Inst Henri Poincaré 60(2):147–187, 1994) to our discrete setting.
We analyze a general class of difference operators on where is a multi-well potential and is a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we shall treat the eigenvalue problem for as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix, similar to the analysis for the Schrodinger operator [see Helffer and Sjostrand in Commun Partial Differ Equ 9:337-408, 1984], and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schrödinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
Trees and Valuation Rings
(2000)
This article assesses the distance between the laws of stochastic differential equations with multiplicative Lévy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Lévy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.
This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.
Broad-spectrum antibiotic combination therapy is frequently applied due to increasing resistance development of infective pathogens. The objective of the present study was to evaluate two common empiric broad-spectrum combination therapies consisting of either linezolid (LZD) or vancomycin (VAN) combined with meropenem (MER) against Staphylococcus aureus (S. aureus) as the most frequent causative pathogen of severe infections. A semimechanistic pharmacokinetic-pharmacodynamic (PK-PD) model mimicking a simplified bacterial life-cycle of S. aureus was developed upon time-kill curve data to describe the effects of LZD, VAN, and MER alone and in dual combinations. The PK-PD model was successfully (i) evaluated with external data from two clinical S. aureus isolates and further drug combinations and (ii) challenged to predict common clinical PK-PD indices and breakpoints. Finally, clinical trial simulations were performed that revealed that the combination of VAN-MER might be favorable over LZD-MER due to an unfavorable antagonistic interaction between LZD and MER.
As a potentially toxic agent on nervous system and bone, the safety of aluminium exposure from adjuvants in vaccines and subcutaneous immune therapy (SCIT) products has to be continuously reevaluated, especially regarding concomitant administrations. For this purpose, knowledge on absorption and disposition of aluminium in plasma and tissues is essential. Pharmacokinetic data after vaccination in humans, however, are not available, and for methodological and ethical reasons difficult to obtain. To overcome these limitations, we discuss the possibility of an in vitro-in silico approach combining a toxicokinetic model for aluminium disposition with biorelevant kinetic absorption parameters from adjuvants. We critically review available kinetic aluminium-26 data for model building and, on the basis of a reparameterized toxicokinetic model (Nolte et al., 2001), we identify main modelling gaps. The potential of in vitro dissolution experiments for the prediction of intramuscular absorption kinetics of aluminium after vaccination is explored. It becomes apparent that there is need for detailed in vitro dissolution and in vivo absorption data to establish an in vitro-in vivo correlation (IVIVC) for aluminium adjuvants. We conclude that a combination of new experimental data and further refinement of the Nolte model has the potential to fill a gap in aluminium risk assessment. (C) 2017 Elsevier Inc. All rights reserved.
Towards the right Hamiltonians for singular perturbations via regularization and extension theory
(1996)
Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques
(2016)
This paper investigates the applicability of the Vaganov–Shashkin–Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) “switching recording” of 2 variables and (3) bounded response windows leading to “thresholded response”. We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL’s nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL’s formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL’s performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes.
Tomographic Reservoir Imaging with DNA-Labeled Silica Nanotracers: The First Field Validation
(2018)
This study presents the first field validation of using DNA-labeled silica nanoparticles as tracers to image subsurface reservoirs by travel time based tomography. During a field campaign in Switzerland, we performed short-pulse tracer tests under a forced hydraulic head gradient to conduct a multisource-multireceiver tracer test and tomographic inversion, determining the two-dimensional hydraulic conductivity field between two vertical wells. Together with three traditional solute dye tracers, we injected spherical silica nanotracers, encoded with synthetic DNA molecules, which are protected by a silica layer against damage due to chemicals, microorganisms, and enzymes. Temporal moment analyses of the recorded tracer concentration breakthrough curves (BTCs) indicate higher mass recovery, less mean residence time, and smaller dispersion of the DNA-labeled nanotracers, compared to solute dye tracers. Importantly, travel time based tomography, using nanotracer BTCs, yields a satisfactory hydraulic conductivity tomogram, validated by the dye tracer results and previous field investigations. These advantages of DNA-labeled nanotracers, in comparison to traditional solute dye tracers, make them well-suited for tomographic reservoir characterizations in fields such as hydrogeology, petroleum engineering, and geothermal energy, particularly with respect to resolving preferential flow paths or the heterogeneity of contact surfaces or by enabling source zone characterizations of dense nonaqueous phase liquids.
Toeplitz operators, and ellipticity of boundary value problems with global projection conditions
(2003)
Toeplitz operators, and ellipticity of boundary value problems with global projection conditions
(2003)
Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.
This work is an introduction to anisotropic spaces, which have an ω-weight of analytic functions and are generalizations of Lipshitz classes in the polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. These operators are bounded in these (Lipshitz and Djrbashian) spaces. As an application, we show a theorem about the division by good-inner functions in the mentioned classes is proved.
Toda chains with type A(m) Lie algebra for multidimensional m-component perfect fluid cosmology
(1999)
Toda chains with type A m Lie algebra for multidimensional m-component perfect fluid cosmology
(1998)
Rapid population and economic growth in Southeast Asia has been accompanied by extensive land use change with consequent impacts on catchment hydrology. Modeling methodologies capable of handling changing land use conditions are therefore becoming ever more important and are receiving increasing attention from hydrologists. A recently developed data-assimilation-based framework that allows model parameters to vary through time in response to signals of change in observations is considered for a medium-sized catchment (2880 km(2)) in northern Vietnam experiencing substantial but gradual land cover change. We investigate the efficacy of the method as well as the importance of the chosen model structure in ensuring the success of a time-varying parameter method. The method was used with two lumped daily conceptual models (HBV and HyMOD) that gave good-quality streamflow predictions during pre-change conditions. Although both time-varying parameter models gave improved streamflow predictions under changed conditions compared to the time-invariant parameter model, persistent biases for low flows were apparent in the HyMOD case. It was found that HyMOD was not suited to representing the modified baseflow conditions, resulting in extreme and unrealistic time-varying parameter estimates. This work shows that the chosen model can be critical for ensuring the time-varying parameter framework successfully models streamflow under changing land cover conditions. It can also be used to determine whether land cover changes (and not just meteorological factors) contribute to the observed hydrologic changes in retrospective studies where the lack of a paired control catchment precludes such an assessment.
Studying the influence of the updating scheme for MCMC algorithm on spatially extended models is a well known problem. For discrete-time interacting particle systems we study through simulations the effectiveness of a synchronous updating scheme versus the usual sequential one. We compare the speed of convergence of the associated Markov chains from the point of view of the time-to-coalescence arising in the coupling-from-the-past algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the time-to-coalescence for these spatially extended models is studied too.
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 Itô 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.
In quantum mechanics the temporal decay of certain resonance states is associated with an effective time evolution e(-ith(kappa)), where h(.) is an analytic family of non-self-adjoint matrices. In general the corresponding resonance states do not decay exponentially in time. Using analytic perturbation theory, we derive asymptotic expansions for e(-ith(kappa)), simultaneously in the limits kappa -> 0 and t -> infinity, where the corrections with respect to pure exponential decay have uniform bounds in one complex variable kappa(2)t.
In the Appendix we briefly review analytic perturbation theory, replacing the classical reference to the 1920 book of Knopp [Funktionentheorie II, Anwendungen und Weiterfuhrung der allgemeinen Theorie, Sammlung Goschen, Vereinigung wissenschaftlicher Verleger Walter de Gruyter, 1920] and its terminology by standard modern references. This might be of independent interest.
Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems
(2020)
In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces.
Satellite-measured tidal magnetic signals are of growing importance. These fields are mainly used to infer Earth's mantle conductivity, but also to derive changes in the oceanic heat content. We present a new Kalman filter-based method to derive tidal magnetic fields from satellite magnetometers: KALMAG. The method's advantage is that it allows to study a precisely estimated posterior error covariance matrix. We present the results of a simultaneous estimation of the magnetic signals of 8 major tides from 17 years of Swarm and CHAMP data. For the first time, robustly derived posterior error distributions are reported along with the reported tidal magnetic fields. The results are compared to other estimates that are either based on numerical forward models or on satellite inversions of the same data. For all comparisons, maximal differences and the corresponding globally averaged RMSE are reported. We found that the inter-product differences are comparable with the KALMAG-based errors only in a global mean sense. Here, all approaches give values of the same order, e.g., 0.09 nT-0.14 nT for M2. Locally, the KALMAG posterior errors are up to one order smaller than the inter-product differences, e.g., 0.12 nT vs. 0.96 nT for M2.
Thermophysical modelling and parameter estimation of small solar system bodies via data assimilation
(2020)
Deriving thermophysical properties such as thermal inertia from thermal infrared observations provides useful insights into the structure of the surface material on planetary bodies. The estimation of these properties is usually done by fitting temperature variations calculated by thermophysical models to infrared observations. For multiple free model parameters, traditional methods such as least-squares fitting or Markov chain Monte Carlo methods become computationally too expensive. Consequently, the simultaneous estimation of several thermophysical parameters, together with their corresponding uncertainties and correlations, is often not computationally feasible and the analysis is usually reduced to fitting one or two parameters. Data assimilation (DA) methods have been shown to be robust while sufficiently accurate and computationally affordable even for a large number of parameters. This paper will introduce a standard sequential DA method, the ensemble square root filter, for thermophysical modelling of asteroid surfaces. This method is used to re-analyse infrared observations of the MARA instrument, which measured the diurnal temperature variation of a single boulder on the surface of near-Earth asteroid (162173) Ryugu. The thermal inertia is estimated to be 295 +/- 18 Jm(-2) K-1 s(-1/2), while all five free parameters of the initial analysis are varied and estimated simultaneously. Based on this thermal inertia estimate the thermal conductivity of the boulder is estimated to be between 0.07 and 0.12,Wm(-1) K-1 and the porosity to be between 0.30 and 0.52. For the first time in thermophysical parameter derivation, correlations and uncertainties of all free model parameters are incorporated in the estimation procedure that is more than 5000 times more efficient than a comparable parameter sweep.
In June 2018, after 4 years of cruise, the Japanese space probe Hayabusa2 [1-Watanabe S. et al.: Hayabusa2 Mission Overview. (2017)] reached the Near-Earth Asteroid (162173) Ryugu. Hayabusa2 carried a small Lander named MASCOT (Mobile Asteroid Surface Scout) [2-Ho T. M. et al.: MASCOT-The Mobile Asteroid Surface Scout onboard the Hayabusa2 mission. (2017)], jointly developed by the German Aerospace Center (DLR) and the French Space Agency (CNES), to investigate Ryugu's surface structure, composition and physical properties including its thermal behaviour and magnetization in-situ. The Microgravity User Support Centre (DLR-MUSC) in Cologne was in charge of providing all thermal conditions and constraints necessary for the selection of the final landing site and for the final operations of the Lander MASCOT on the surface of the asteroid Ryugu. This article provides a comprehensive assessment of these thermal conditions and constraints, based on predictions performed with the Thermal Mathematical Model (TMM) of MASCOT using different asteroid surface thermal models, ephemeris data for approach as well as descent and hopping trajectories, the related operation sequences and scenarios and the possible environmental conditions driven by the Hayabusa2 spacecraft. A comparison with the real telemetry data confirms the analysis and provides further information about the asteroid characteristics.
Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window.