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Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion
No full textEnsemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov strategies for EKI. This work builds upon Tikhonov EKI (TEKI) which was proposed for a fixed regularization constant. By adaptively learning the regularization parameter, this procedure is known to improve the recovery of the underlying unknown. For the analysis, we consider a continuous-time setting where we extend known results such as well-posdeness and convergence of various loss functions, but with the addition of noisy observations. Furthermore, we allow a time-varying noise and regularization covariance in our presented convergence result which mimic adaptive regularization schemes. In turn we present three adaptive regularization schemes, which are highlighted from both the deterministic and Bayesian approaches for inverse problems, which include bilevel optimization, the MAP formulation and covariance learning. We numerically test these schemes and the theory on linear and nonlinear partial differential equations, where they outperform the non-adaptive TEKI and EKI
The soundproof model of an acoustic-internal waves system with low stratification
No full textThis work is devoted to investigating a compressible fluid system with low stratification, which is driven by fast acoustic waves and internal waves. The approximation using a soundproof model is justified. More precisely, the soundproof model captures the dynamics of both the non-oscillating mean flows and the oscillating internal waves, while filters out the fast acoustic waves, of the compressible system with or without initial acoustic waves. Moreover, the fast-slow oscillation structure is investigated
Linking digital surveillance and in-depth virology to study clinical patterns of viral respiratory infections in vulnerable patient populations
No full textTo improve the identification and management of viral respiratory infections, we established a clinical and virologic surveillance program for pediatric patients fulfilling pre-defined case criteria of influenza-like illness and viral respiratory infections. The program resulted in a cohort comprising 6,073 patients (56% male, median age 1.6 years, range 0–18.8 years), where every patient was assessed with a validated disease severity score at the point-of-care using the ViVI ScoreApp. We used machine learning and agnostic feature selection to identify characteristic clinical patterns. We tested all patients for human adenoviruses, 571 (9%) were positive. Adenovirus infections were particularly common and mild in children ≥1 month of age but rare and potentially severe in neonates: with lower airway involvement, disseminated disease, and a 50% mortality rate (n = 2/4). In one fatal case, we discovered a novel virus: HAdV-80. Standardized surveillance leveraging digital technology helps to identify characteristic clinical patterns, risk factors, and emerging pathogens
Parallel Exchange of Randomized SubGraphs for Optimization of Network Alignment: PERSONA
No full textThe aim of Network Alignment in Protein-Protein Interaction Networks is discovering functionally similar regions between compared organisms. One major compromise for solving a network alignment problem is the trade-off among multiple similarity objectives while applying an alignment strategy. An alignment may lose its biological relevance while favoring certain objectives upon others due to the actual relevance of unfavored objectives. One possible solution for solving this issue may be blending the stronger aspects of various alignment strategies until achieving mature solutions. This study proposes a parallel approach called PERSONA that allows aligners to share their partial solutions continuously while they progress. All these aligners pursue their particular heuristics as part of a particle swarm that searches for multi-objective solutions of the same alignment problem in a reactive actor environment. The actors use the stronger portion of a solution as a subgraph that they receive from leading or other actors and send their own stronger subgraphs back upon evaluation of those partial solutions. Moreover, the individual heuristics of each actor takes randomized parameter values at each cycle of parallel execution so that the problem search space can thoroughly be investigated. The results achieved with PERSONA are remarkably optimized and balanced for both topological and node similarity objectives
Investigating the entropic nature of membrane-mediated interactions driving the aggregation of peripheral proteins
No full textPeripheral membrane-associated proteins are known to accumulate on the surface of biomembranes as a result of membrane-mediated interactions. For a pair of rotationally-symmetric curvature-inducing proteins, membrane mechanics at the low-temperature limit predicts pure repulsion. On the other hand, temperature-dependent entropic forces arise between pairs of stiff-binding proteins suppressing membrane fluctuations. These Casimir-like interactions have thus been suggested as candidates for attractive forces leading to aggregation. With dense assemblies of peripheral proteins on the membrane, both these abstractions encounter short-range and multi-body complications. Here, we make use of a particle-based membrane model augmented with flexible peripheral proteins to quantify purely membrane-mediated interactions and investigate their underlying nature. We introduce a continuous reaction coordinate corresponding to the progression of protein aggregation. We obtain free energy and entropy landscapes for different surface concentrations along this reaction coordinate. In parallel, we investigate time-dependent estimates of membrane entropy corresponding to membrane undulations and coarse-grained director field and how they change dynamically with protein aggregation. Congruent outcomes of the two approaches point to the conclusion that for low surface concentrations, interactions with an entropic nature may drive the aggregation. But at high concentrations, enthalpic contributions due to concerted membrane deformation by protein clusters are dominant
Consistency analysis of bilevel data-driven learning in inverse problems
No full textOne fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization parameter from data by means of optimization. This approach can be interpreted as solving an empirical risk minimization problem, and we analyze its performance in the large data sample size limit for general nonlinear problems. We demonstrate how to implement our framework on linear inverse problems, where we can further show the inverse accuracy does not depend on the ambient space dimension. To reduce the associated computational cost, online numerical schemes are derived using the stochastic gradient descent method. We prove convergence of these numerical schemes under suitable assumptions on the forward problem. Numerical experiments are presented illustrating the theoretical results and demonstrating the applicability and efficiency of the proposed approaches for various linear and nonlinear inverse problems, including Darcy flow, the eikonal equation, and an image denoising example
The closer the better? Theoretical assessment of the impact of catalytic site separation for bifunctional core–shell catalyst particles
No full textOne-pot heterogeneous catalysis with different active centers offers great potential for increasing yield and selectivity. In this field, the distance between the different catalytically active centers starts playing a role and its influence as well as its control is an open question. Here, porous core–shell particles provide the opportunity to control the distance on a mesoscopic scale, where the centers are placed on different shells and are separated by an inert porous matrix. We present a continuum-mechanical model of such particles and exploit symmetry to arrive at a computationally efficient reduced model. Using methanol synthesis from CO on the first kind of center followed by a dimethylether synthesis on a second kind of center as an example, we investigate the influence of the distance between these two centers. In particular, we consider three simple backcoupling mechanisms and address the question whether it is best to place the centers as close as possible or at a non-zero optimal distance. We find that this question cannot a priori be answered but the answer depends largely on the employed backcoupling mechanism
Foamquake: a novel analog model mimicking megathrust seismic cycles
No full textIn the last decades, seismotectonic analog models have been developed to better understand many aspects of the seismic cycle. Differently from other lab-quake experiments, seismotectonic models mimic the first order characteristics of the seismic cycle in a scaled fashion. Here we introduce Foamquake: a novel seismotectonic model with a granular frictional interface that as a whole behaves elastoplastically. The model experiences cycles of elastic loading and release via spontaneous nucleation of frictional instabilities at the base of an elastic foam wedge, hereafter called foamquakes. These analog earthquakes show source parameters (i.e., moment-duration and moment-rupture area) scaling as great interplate earthquakes and a coseismic displacement of few tens of meters when scaled to nature. Models with two asperities separated by a barrier can be performed with Foamquake given the 3D nature of the setup. Such model configuration generates sequences of full and partial ruptures with different recurrence intervals as well as rupture cascades. By tuning the normal load acting on individual asperities, Foamquake reproduces superimposed cycles rupture patterns such as those observed along natural megathrusts. The physical properties of asperities and barriers affect model seismic behavior. Asperities with similar properties and low yield strength fail preferentially in a simultaneous manner. The combination of all those characteristics suggests that Foamquake is a valuable tool for investigating megathrust seismicity and seismic processes that depend on the 3D nature of the subduction environment
Powerful enhanced Jaya algorithm for efficiently optimizing numerical and engineering problems
No full textOver the last decade, the size and complexity of real-world problems have grown dramatically, necessitating more effective tools. Nature-inspired metaheuristic algorithms have proven to be a promising tool for solving such problems due to their performance in a variety of fields. JAYA algorithm is a novel population-based algorithm which could have been able to present reliable results. This is because it does not need any parameters to be set other than the population size and the maximum number of iteration. Despite its positive feedbacks, this algorithm should be modified to witness more efficiency. This paper aims to amend the original version of Jaya to present a high-efficiency version named Powerful Enhanced Jaya (PEJAYA). In other words, the methodology of updating position in Jaya is modified to enhance the convergence and search capabilities. This approach is assessed according to solve 20 well-known benchmark functions, feature selection, and statistical tests. The output results of proposed optimization algorithm are then evaluated by comparing it with other recent algorithms including crow search algorithm (CSA), standard version of JAYA, particle swarm optimization (PSO), dragonfly algorithm (DA), grasshopper optimization algorithm (GOA), moth-flame optimization (MFO) and sine–cosine algorithm (SCA). Solving a real-world problem is another way of checking the efficiency of this approach with other published works. Prompt escape from local minima, superior convergence, and stability demonstrate that the suggested approach is a very powerful instrument that may be employed in a variety of optimization situations
Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces
No full textWe analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear S(P)DEs with multiplicative noise based on balanced truncation. For the first time, we include in this study the analysis of non-zero initial conditions. We moreover allow for feedback-controlled dynamics for solving stochastic optimal control problems with reduced-order models and prove novel error bounds for a class of linear quadratic regulator problems. We provide numerical evidence for the bounds and discuss the application of our approach to enhanced sampling methods from non-equilibrium statistical mechanics