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We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control. The structure is ideal for automated network-based modelling since it is invariant under power-conserving interconnection, congruence transformations and Galerkin projection. Moreover, stability and passivity properties are easily shown. Condensed forms under orthogonal transformations present easy analysis tools for existence, uniqueness, regularity and numerical methods to check these properties. After recalling the concepts for general linear and nonlinear descriptor systems, we demonstrate that many difficulties that arise in general descriptor systems can be easily overcome within the port-Hamiltonian framework. The properties of port-Hamiltonian descriptor systems are analysed, and time discretization and numerical linear algebra techniques are discussed. Structure-preserving regularization procedures for descriptor systems are presented to make them suitable for simulation and control. Model reduction techniques that preserve the structure and stabilization and optimal control techniques are discussed. The properties of port-Hamiltonian descriptor systems and their use in modelling simulation and control methods are illustrated with several examples from different physical domains. The survey concludes with open problems and research topics that deserve further attention.

Background Decreased activity of forkhead transcription factor class O (FoxO)3A, a negative regulator of NF-κB-mediated chemokine expression, is implicated in the pathogenesis of chronic obstructive pulmonary disease (COPD). Previously, we showed that quercetin reduces lung inflammation in a murine model of COPD. Here, we examined the mechanisms underlying decreased FoxO3A activation and its modulation by quercetin in COPD human airway epithelial cells and in a COPD mouse model. Methods Primary COPD and normal human airway epithelial cells were treated with quercetin, LY294002 or erlotinib for 2 weeks. IL-8 was measured by ELISA. FoxO3A, Akt, and epidermal growth factor (EGF) receptor (EGFR) phosphorylation and nuclear FoxO3A levels were determined by Western blot analysis. Effects of quercetin on lung chemokine expression, nuclear FoxO3A levels and phosphorylation of EGFR and Akt were determined in COPD mouse model. Results Compared with normal, COPD cells showed significantly increased IL-8, which negatively correlated with nuclear FoxO3A levels. COPD bronchial biopsies also showed reduced nuclear FoxO3A. Decreased FoxO3A in COPD cells was associated with increased phosphorylation of EGFR, Akt and FoxO3A and treatment with quercetin, LY294002 or erlotinib increased nuclear FoxO3A and decreased IL-8 and phosphorylation of Akt, EGFR and FoxO3A, Compared with control, elastase/LPS-exposed mice showed decreased nuclear FoxO3A, increased chemokines and phosphorylation of EGFR and Akt. Treatment with quercetin partially reversed these changes. Conclusions In COPD airways, aberrant EGFR activity increases PI 3-kinase/Akt-mediated phosphorylation of FoxO3A, thereby decreasing nuclear FoxO3A and increasing chemokine expression. Quercetin restores nuclear FoxO3A and reduces chemokine expression partly by modulating EGFR/PI 3-kinase/Akt activity.

Bacterial infections following rhinovirus (RV), a common cold virus, are well documented, but pathogenic mechanisms are poorly understood. We developed animal and cell culture models to examine the effects of RV on subsequent infection with non-typeable Hemophilus influenzae (NTHi). We focused on NTHI-induced neutrophil chemoattractants expression that is essential for bacterial clearance. Mice infected with RV1B were superinfected with NTHi and lung bacterial density, chemokines and neutrophil counts determined. Human bronchial epithelial cells (BEAS-2B) or mouse alveolar macrophages (MH-S) were infected with RV and challenged with NHTi, TLR2 or TLR5 agonists. Chemokine levels were measured by ELISA and expression of IRAK-1, a component of MyD88-dependent TLR signaling, assessed by immunoblotting. While sham-infected mice cleared all NTHi from the lungs, RV-infected mice showed bacteria up to 72 h post-infection. However, animals in RV/NTHi cleared bacteria by day 7. Delayed bacterial clearance in RV/NTHi animals was associated with suppressed chemokine levels and neutrophil recruitment. RV-infected BEAS-2B and MH-S cells showed attenuated chemokine production after challenge with either NTHi or TLR agonists. Attenuated chemokine responses were associated with IRAK-1 protein degradation. Inhibition of RV-induced IRAK-1 degradation restored NTHi-stimulated IL-8 expression. Knockdown of TLR2, but not other MyD88-dependent TLRs, also restored IRAK-1, suggesting that TLR2 is required for RV-induced IRAK-1 degradation.In conclusion, we demonstrate for the first time that RV infection delays bacterial clearance in vivo and suppresses NTHi-stimulated chemokine responses via degradation of IRAK-1. Based on these observations, we speculate that modulation of TLR-dependent innate immune responses by RV may predispose the host to secondary bacterial infection, particularly in patients with underlying chronic respiratory disorders.

Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge–Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge–Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings.

We propose a new hyper-reduction method for a recently introduced nonlinear model reduction framework based on dynamically transformed basis functions and especially well-suited for transport-dominated systems. Furthermore, we discuss applying this new method to a wildland fire model whose dynamics feature traveling combustion waves and local ignition and is thus challenging for classical model reduction schemes based on linear subspaces. The new hyper-reduction framework allows us to construct parameter-dependent reduced-order models (ROMs) with efficient offline/online decomposition. The numerical experiments demonstrate that the ROMs obtained by the novel method outperform those obtained by a classical approach using the proper orthogonal decomposition and the discrete empirical interpolation method in terms of run time and accuracy.

Rhinovirus (RV), which causes exacerbation in patients with chronic airway diseases, readily infects injured airway epithelium and has been reported to delay wound closure. In this study, we examined the effects of RV on cell repolarization and differentiation in a model of injured/regenerating airway epithelium (polarized, undifferentiated cells). RV causes only a transient barrier disruption in a model of normal (mucociliary-differentiated) airway epithelium. However, in the injury/regeneration model, RV prolongs barrier dysfunction and alters the differentiation of cells. The prolonged barrier dysfunction caused by RV was not a result of excessive cell death but was instead associated with epithelial-to-mesenchymal transition (EMT)-like features, such as reduced expression of the apicolateral junction and polarity complex proteins, E-cadherin, occludin, ZO-1, claudins 1 and 4, and Crumbs3 and increased expression of vimentin, a mesenchymal cell marker. The expression of Snail, a transcriptional repressor of tight and adherence junctions, was also up-regulated in RV-infected injured/regenerating airway epithelium, and inhibition of Snail reversed RV-induced EMT-like features. In addition, compared with sham-infected cells, the RV-infected injured/regenerating airway epithelium showed more goblet cells and fewer ciliated cells. Inhibition of epithelial growth factor receptor promoted repolarization of cells by inhibiting Snail and enhancing expression of E-cadherin, occludin, and Crumbs3 proteins, reduced the number of goblet cells, and increased the number of ciliated cells. Together, these results suggest that RV not only disrupts barrier function, but also interferes with normal renewal of injured/regenerating airway epithelium by inducing EMT-like features and subsequent goblet cell hyperplasia.

For the iterative decoupling of elliptic–parabolic problems such as poroelasticity, we introduce time discretization schemes up to order five based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the temporal discretization. As the main result, we show that the convergence depends on the interplay between the time step size and the parameters for the contraction of the iterative scheme. Moreover, this connection is quantified explicitly, which allows for balancing the single error components. Several numerical experiments illustrate and validate the theoretical results, including a three-dimensional example from biomechanics.

A variety of cytokines have been detected in inflamed intestinal mucosal tissues, including the pro-inflammatory cytokine, interleukin-1 (IL-1), along with growth factors involved in wound healing processes such as proliferation and cell migration. However, little is known about how IL-1 and growth factors interact with intestinal epithelial cells to regulate the production of inflammatory cytokines such as interleukin-8 (IL-8). Previously, we have shown that hepatocyte growth factor (HGF) could significantly enhance IL-1-stimulated IL-8 secretion by the Caco-2 colonic epithelial cell line, yet HGF, by itself, did not stimulate IL-8 secretion. In this report, a second growth factor, keratinocyte growth factor (KGF), was also found to significantly enhance IL-1-induced IL-8 secretion by Caco-2 cells, yet KGF, by itself, also had no effect. Simultaneous addition of both IL-1 and KGF was also required for the enhancing effect. Treatment of the Caco-2 cells with wortmannin or triciribine suppressed the enhancing effect of HGF, suggesting that the effect was mediated by signaling through phosphatidylinositol-3-kinase (PI3K) and the kinase AKT. The enhancing effect of KGF was not affected by wortmannin, but was suppressed by triciribine, suggesting that the effect of KGF was through a PI3K-independent activation of AKT. These results suggest that the growth factors HGF and KGF may play a role in enhancing IL-1-stimulated production of IL-8 by epithelial cells during mucosal inflammations. However, the mechanism by which the growth factors enhance the IL-1 response may be through different initial signaling pathways.

Intensified systemic chemotherapy has the highest primary cure rate for advanced-stage, classical Hodgkin lymphoma but this comes with a cost of severe and potentially life long, persisting toxicities. With the new regimen of brentuximab vedotin, etoposide, cyclophosphamide, doxorubicin, dacarbazine, and dexamethasone (BrECADD), we aimed to improve the risk-to-benefit ratio of treatment of advanced-stage, classical Hodgkin lymphoma guided by PET after two cycles. This randomised, multicentre, parallel, open-label, phase 3 trial was done in 233 trial sites across nine countries. Eligible patients were adults (aged ≤60 years) with newly diagnosed, advanced-stage, classical Hodgkin lymphoma (ie, Ann Arbor stage III/IV, stage II with B symptoms, and either one or both risk factors of large mediastinal mass and extranodal lesions). Patients were randomly assigned (1:1) to four or six cycles (21-day intervals) of escalated doses of etoposide (200 mg/m2 intravenously on days 1–3), doxorubicin (35 mg/m2 intravenously on day 1), and cyclophosphamide (1250 mg/m2 intravenously on day 1), and standard doses of bleomycin (10 mg/m2 intravenously on day 8), vincristine (1·4 mg/m2 intravenously on day 8), procarbazine (100 mg/m2 orally on days 1–7), and prednisone (40 mg/m2 orally on days 1–14; eBEACOPP) or BrECADD, guided by PET after two cycles. Patients and investigators were not masked to treatment assignment. Hierarchical coprimary objectives were to show (1) improved tolerability defined by treatment-related morbidity and (2) non-inferior efficacy defined by progression-free survival with an absolute non-inferiority margin of 6 percentage points of BrECADD compared with eBEACOPP. An additional test of superiority of progression-free survival was to be done if non-inferiority had been established. Analyses were done by intention to treat; the treatment-related morbidity assessment required documentation of at least one chemotherapy cycle. This trial was registered at ClinicalTrials.gov (NCT02661503). Between July 22, 2016, and Aug 27, 2020, 1500 patients were enrolled, of whom 749 were randomly assigned to BrECADD and 751 to eBEACOPP. 1482 patients were included in the intention-to-treat analysis. The median age of patients was 31 years (IQR 24–42). 838 (56%) of 1482 patients were male and 644 (44%) were female. Most patients were White (1352 [91%] of 1482). Treatment-related morbidity was significantly lower with BrECADD (312 [42%] of 738 patients) than with eBEACOPP (430 [59%] of 732 patients; relative risk 0·72 [95% CI 0·65–0·80]; p<0·0001). At a median follow-up of 48 months, BrECADD improved progression-free survival with a hazard ratio of 0·66 (0·45–0·97; p=0·035); 4-year progression-free survival estimates were 94·3% (95% CI 92·6–96·1) for BrECADD and 90·9% (88·7–93·1) for eBEACOPP. 4-year overall survival rates were 98·6% (97·7–99·5) and 98·2% (97·2–99·3), respectively. BrECADD guided by PET after two cycles is better tolerated and more effective than eBEACOPP in first-line treatment of adult patients with advanced-stage, classical Hodgkin lymphoma. Takeda Oncology.

This thesis is dedicated to delay differential-algebraic equations (DDAEs), i.e., constraint dynamical systems where the rate of change depends on the current state and its past. Typical applications include(i) feedback control, where the delay is a direct consequence of the time required to measure the current state, compute the feedback, and implement the control action,(ii) hybrid numerical-experimental testing environments, used for instance in earthquake engineering, (iii) transmission and propagation delays, encountered for example in chemical reactions connected in series and wide-area power-networks, and(iv) as a mathematical tool to analyze hyperbolic equations and time-integration schemes.The fact that algebraic equations can be included in the implicit system description fosters a rapid model development since complex models can be assembled from a library of existing models with well-defined interaction variables.From a mathematical point of view, DDAEs do not only feature difficulties already known from the theory of differential-algebraic equations (DAEs) and delay differential equations (DDEs) but pose additional challenges. For instance, initial trajectory problems for DDAEs may not be causal. Thus, even in a distributional solution space, they may not have a solution for all initial trajectories. This fact, combined with the infinite-dimensional character of delay equations and the high sensitivity to perturbation known from the theory of DAEs, renders DDAEs a challenging mathematical object. Consequently, the analysis of DDAEs is far from complete. The aim of this thesis is to address some of the many open problems.In the first part of the thesis, initial trajectory problems for linear time-invariant (LTI) and nonlinear DDAEs are discussed. We start our analysis with a distributional solution concept and establish the existence and uniqueness of solutions, whenever the DDAE is delay-regular. Jumps and Dirac-impulses in the solution can be avoided if the coefficient matrices of the LTI DDAE satisfy some algebraic conditions, which are obtained by tracking so-called primary discontinuities. We extend some of the results to the nonlinear setting resulting in existence and uniqueness results for a large class of nonlinear DDAEs.The second part of the thesis is dedicated to constructing a DDAE solely from a prescribed set of data points. Having a time-delay in the realization allows us to build an infinite-dimensional system from finitely many points capable of reproducing the transcendental character of the transfer function of a distributed parameter subsystem that models convection or transport. We construct a realization so that it interpolates the data set in the frequency domain and demonstrate its applicability with several numerical examples.