Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model. Here, we present an approach for reduced model construction, that preserves the symplectic symmetry of dissipative Hamiltonian systems. The method constructs a closed reduced Hamiltonian system by coupling the full model with a canonical heat bath. This allows the reduced system to be integrated with a symplectic integrator, resulting in a correct dissipation of energy, preservation of the total energy and, ultimately, in the stability of the solution. Accuracy and stability of the method are illustrated through the numerical simulation of the dissipative wave equation and a port-Hamiltonian model of an electric circuit

Structure Preserving Model Reduction of Parametric Hamiltonian Systems

While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM generation of parametric Hamiltonian systems that captures the symplectic structure of Hamiltonian systems to ensure stability of the reduced model. Through the greedy selection of basis vectors, two new vectors are added at each iteration to the linear vector space to increase the accuracy of the reduced basis. We use the error in the Hamiltonian due to model reduction as an error indicator to search the parameter space and identify the next best basis vectors. Under natural assumptions on the set of all solutions of the Hamiltonian system under variation of the parameters, we show that the greedy algorithm converges with exponential rate. Moreover, we demonstrate that combining the greedy basis with the discrete empirical interpolation method also preserves the symplectic structure. This enables the reduction of the computational cost for nonlinear Hamiltonian systems. The efficiency, accuracy, and stability of this model reduction technique is illustrated through simulations of the parametric wave equation and the parametric Schrodinger equation

Evaluation of service quality by using fuzzy MCDM: A case study in Iranian health-care centers

Service quality plays an important role in health care systems since hospitals are responsible for people's lives. This study presents an effective approach for evaluating and comparing service qualities of four hospitals. Service quality consists of different attributes and many of them are intangible and difficult to measure. Therefore, we propose a fuzzy method to resolve the ambiguity of the concepts, which are associated with human judgments. SERVQUAL model is used to evaluate the respondents' judgments of service quality and multi attribute decision making approach is implemented for the comparison among hospitals. The paper use analytical hierarchy process (AHP) for obtaining criteria weight and TOPSIS for ranking the cases

Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks

In this work, we describe a new approach that uses variational encoder-decoder (VED) networks for efficient goal-oriented uncertainty quantification for inverse problems. Contrary to standard inverse problems, these approaches are \emph{goal-oriented} in that the goal is to estimate some quantities of interest (QoI) that are functions of the solution of an inverse problem, rather than the solution itself. Moreover, we are interested in computing uncertainty metrics associated with the QoI, thus utilizing a Bayesian approach for inverse problems that incorporates the prediction operator and techniques for exploring the posterior. This may be particularly challenging, especially for nonlinear, possibly unknown, operators and nonstandard prior assumptions. We harness recent advances in machine learning, i.e., VED networks, to describe a data-driven approach to large-scale inverse problems. This enables a real-time goal-oriented uncertainty quantification for the QoI. One of the advantages of our approach is that we avoid the need to solve challenging inversion problems by training a network to approximate the mapping from observations to QoI. Another main benefit is that we enable uncertainty quantification for the QoI by leveraging probability distributions in the latent space. This allows us to efficiently generate QoI samples and circumvent complicated or even unknown forward models and prediction operators. Numerical results from medical tomography reconstruction and nonlinear hydraulic tomography demonstrate the potential and broad applicability of the approach.Comment: 28 pages, 13 figure

Geometric Model Order Reduction

During the past decade, model order reduction (MOR) has been successfully applied to reduce the computational complexity of elliptic and parabolic systems of partial differential equations (PDEs). However, MOR of hyperbolic equations remains a challenge. Symmetries and conservation laws, which are a distinctive feature of such systems, are often destroyed by conventional MOR techniques, resulting in a perturbed and often unstable reduced system. The goal of this thesis is to study and develop model order reduction techniques that can preserve nonlinear invariants, symmetries, and conservation laws and to understand the stability properties of these methods compared to conventional techniques. Hamiltonian systems, as systems that are driven by symmetries, are studied intensively from the point of view of MOR. Furthermore, a conservative model reduction of fluid flow is presented. It is illustrated that conserving invariants, conservation laws, and symmetries not only result in a physically meaningful reduced system but also result in an accurate and robust reduced system with enhanced stability

A rapid and green synthesis of 1,1-diacetates from aldehydes catalyzed by triethylamine-bonded sulfonic acid [Et3NâSO3H]Cl

Bronsted acidic ionic liquid, [Et3N–SO3H]Cl, catalyzed the reaction of acetic anhydride with aryl aldehydes under solvent-free condition. Various 1,1-diacetates are obtained using 15 mol% of  triethylamine-bonded sulfonic acid in satisfactory to excellent yields in very short reaction times at ambient temperature. Different groups including electron donating or electron withdrawing groups linked to benzene ring such as methyl, chloro, nitro and methoxy were tolerated under the optimized reaction conditions. This ionic liquid was air stable and easily prepared from accessible amine and chlorosulfonic acid. The present report is a green protocol as it eliminates the need of an organic solvent. Very short reaction times, high yields, simple operational procedure and green conditions are merits of this methodology

General Dental Practitioners’ Concept towards Using Radiography and Apex-Locators in Endodontics

Introduction:Despite being the gold standard as well as a routine technique in endodontics, radiographic working length (WL) determination owns many drawbacks. Electronic apex-locators (EALs) are recommended to complement radiographies. The aim of this study was to evaluate the perceptions of Iranian general dental practitioners (GDPs) towards using radiography and EAL. Methods and Materials: Three hundred and ninety one GDPs attending the 53th Iranian Dental Association Congress completed a questionnaire focusing on the use of radiography and EALs during the various stages of root canal treatment. The data was analyzed with the chi-square test with the level of significance set at 0.05. The results were then calculated as frequencies and percentages. Results: More than half of the GDPs reported using radiographs as the sole method for WL determination. A total of 30.4% of the practitioners were using the combined approach during root canal therapy of a single-rooted tooth, while 38.9% used this method in multi-rooted teeth. Approximately half of the respondents would not order follow-up radiographies after root canal treatment. Conclusion: Radiography continues to be the most common method for WL determination in Iran

Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods

A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the number of modes. The two essential elements to non-linear stability are: (1) first discretise the full order model, and then project the discretised equations, and (2) use spatial and temporal discretisation schemes for the full order model that are globally energy-conserving (in the limit of vanishing viscosity). For this purpose, as full order model a staggered-grid finite volume method in conjunction with an implicit Runge-Kutta method is employed. In addition, a constrained singular value decomposition is employed which enforces global momentum conservation. The resulting `velocity-only' ROM is thus globally conserving mass, momentum and kinetic energy. For non-homogeneous boundary conditions, a (one-time) Poisson equation is solved that accounts for the boundary contribution. The stability of the proposed ROM is demonstrated in several test cases. Furthermore, it is shown that explicit Runge-Kutta methods can be used as a practical alternative to implicit time integration at a slight loss in energy conservation

The association between serum 25-hydroxyvitamin D level and recurrent falls in the elderly population: a cohort study

Introduction: Serum vitamin D concentration is a major contributing factor for increasing the risk of fall and fall-related injuries in older adults. However, when prescribed and supplemented for these populations, the outcomes are controversial, and in several cases no improvement has been reported in reducing the risk of recurrent falls. This study aimed to examine the association between serum vitamin D concentration and recurrent falls in Iranian older adults. Methods: This cohort study was conducted in the emergency departments of two university hospitals. A cohort of 82 elderly participants aged over 60 and suffered from an unintentional episode of falling was evaluated six months after their first ED visit. A structured, self-administered checklist was developed to obtain the participants’ demographic and clinical information. Participants also were asked about any recurrent fall experience during follow-up. Results: The mean (SD) age of the study population was 75 (8). Over half of the participants were male (57.3%). The mean (median) serum 25-hydroxyvitamin D (25 (OH)D) concentration was 38 (34) ng/ml. Mean serum 25(OH)D levels varied slightly between gender groups (p=0.450). An inverse but insignificant association was found between the age of participants and their serum 25(OH)D levels (r=-0.03, p=0.7). A small but insignificant association also was found between the mean serum 25(OH)D level and the number of recurrent falls in elderly patients irrespective of their age, gender, or physical activity groups (OR=1.008, p=0.992). Conclusion: In contrast to previous studies, no significant association of serum 25(OH)D concentration was found with recurrent falls in Iranian older adults. Keywords: 25-hydroxyvitamin D,falls, Vitamin D insufficiency, Iran, Elderl