Perturbation Analysis Research Articles

The onset of penetrative convection in an inclined porous layer

In the present article, a model for penetrative convection in a fluid-saturated inclined porous medium is analyzed. Penetrative convection occurs when an unstably stratified fluid moves into a stably stratified region. In this study, it will be shown that the inclination of the layer plays a relevant role for the penetrative thermal convection of a fluid-saturated porous medium. The results reported in the literature for the limiting case of horizontal layer are recovered and the numerical results for the linear instability, obtained via the Chebyshev-τ method, show that the most destabilizing perturbations are the longitudinal and, as expected, the transverse ones destabilize only up to a certain critical inclination angle of the layer. Moreover, in the numerical analysis of the three-dimensional perturbations, we show that the longitudinal perturbations are the most destabilizing not only with respect to the transverse but also with respect to any general perturbation. We also give nonlinear stability results for the longitudinal perturbations via the weighted energy method.

Ice-flow perturbation analysis: a method to estimate ice-sheet bed topography and conditions from surface datasets

Abstract One of the largest contributors to uncertainty in predictions of sea-level rise from ice-sheet models is a lack of knowledge about the bed topography beneath ice sheets. Bed topography maps are normally made by interpolating between linear radar surveys using methods that include kriging, mass conservation and flowline diffusion, all of which may miss influential mesoscale (2–30 km) bedforms. Previous works have explored an Ice-Flow Perturbation Analysis (IFPA) approach for estimating bed topography using the surface expression of these mesoscale bedforms. Using regions of Pine Island Glacier that have been intensively surveyed by ice-penetrating radar as test sites, and a refined IFPA methodology, we find that IFPA detects bedforms capable of influencing ice flow which are not represented in Bedmachine Antarctica and other interpolated bed products. We further explore the ability of IFPA to estimate relative bed slipperiness, finding higher slipperiness in the main trunk and tributaries. Alongside other methods which estimate ice thickness, bed topography maps from IFPA have the potential to constrain projections of future sea-level rise, especially where radar data are sparse.

Joint Action and Competition between Centrifugal, Magnetorotational, and Magnetic Buoyancy Instabilities

Instabilities driven by some combination of rotation, velocity shear, and magnetic field in a stratified fluid under gravity play an important role in many astrophysical settings. Of particular note are the centrifugal instability, the magnetorotational instability, and magnetic buoyancy instability. Here, we consider a Cartesian model of an equatorial region incorporating all the physical ingredients necessary to study their competition. We investigate the linear instability to interchange (“axisymmetric”) modes of an inviscid, perfectly conducting, isothermal gas, including the effects of rotation, velocity shear, and poloidal and toroidal magnetic fields. The stability problem can be reduced to a second-order boundary value problem, with the growth rate as the eigenvalue. We can make analytic progress through consideration of the physically relevant regime in which the transverse horizontal wavenumber k ≫ 1. Via a perturbation analysis, with 1/k as the small parameter, we can derive the growth rate and the spatial dependence of the eigenfunctions: the unstable modes are strongly localized in the vertical direction, being either wall modes (localized near a boundary of the domain) or body modes (localized in the interior). We describe the conditions under which the joint action of the separate instability mechanisms leads to enhancement or suppression of the instability. Our analytical results are supplemented by numerical solutions of the stability problem. The most unstable mode found analytically is typically in excellent agreement with that found numerically through consideration of a wide range of wavenumbers. Finally, we discuss how our results relate to the solar tachocline.

Numerical study of the hydrodynamic stability of a wind-turbine airfoil with a laminar separation bubble under free-stream turbulence

The interaction of several instabilities and the influence of free-stream turbulence on laminar-turbulent transition on a 20% thick wind-turbine blade section with a laminar separation bubble (LSB) are investigated with wall-resolved large-eddy simulations (LES). Turbulence intensities (TI) of 0%, 2.2%, 4.5%, 8.6%, and 15.6% at chord Reynolds number 105 are considered. Linear receptivity occurs for the most energetic disturbances; high-frequency perturbations are excited via non-linear mechanisms for TI≥8.6%. Unstable Tollmien–Schlichting (TS) waves appear in the inflectional flow region for TI≤4.5%, shifting to inviscid Kelvin–Helmholtz (KH) modes upon separation and forming spanwise rolls. Sub-harmonic secondary instability occurs for TI=0%, with rolls intertwining before transition. Streaks spanwise modulate the rolls and increase their growth rates with TI for TI≤4.5%, reducing separation and shifting transition upstream. The TI=4.5% case presents the highest perturbations, leading to the smallest LSB and most upstream transition. Earlier inception of TS/KH modes occurs on low-speed streaks, inducing premature transition. However, for TI=8.6%, the effect of the streaks is to stabilize the attached mean flow and front part of the LSB. This occurs due to the near-wall momentum deficit alleviation, leading to the transition delay and larger LSB than TI=4.5%. This also suppresses separation and completely stabilizes TS/KH modes for TI=15.6%. Linear stability theory predicts well the modal evolution for TI≤8.6%. Optimal perturbation analysis accurately computes the streak development upstream of the inflectional flow region but indicates higher amplification than LES downstream due to the capture of low-frequency, oblique modal instabilities from the LSB. Only low-amplitude [O(1%)] streaks displayed exponential growth in the LES since non-linearity precludes the appearance of these modes.

Theoretical investigations on cutoff wave number of quad-polar waveguide

The hollow waveguides with angular deformation are widely used in high power millimeter wave system. In this manuscript, the cutoff wave number of the quad-polar waveguide with a boundary of is theoretically analyzed based on the perturbation analysis. Using the boundary condition and the orthogonal properties of the trigonometric functions, a determinant is obtained and then the exact closed-form expression of cutoff wave number is deduced from the determinant. Based on the cutoff wave number, the eigen field is calculated by nonlinear programming method. The values of the cutoff wavenumbers, eigen fields and surface currents for the first few modes are calculated and compared with the results obtained from simulation software. The high correspondence of the calculated values with the simulated results proves that the proposed method is an appropriate option for fast and precise analyzing quad-polar waveguides.

The environmental performance of plastic packaging waste management in Germany: Current and future key factors

AbstractPlastic is a popular packaging material, but also criticized as a symbol for the make‐use‐dispose economy because of its short lifespan, its dependency on fossil fuels, and its potential contribution to marine litter. To identify current and potential future key factors for the environmental performance of plastic packaging waste (PPW) management in Germany, a life cycle assessment considering five different pathways of PPW (including deposit‐refund systems, separately collected lightweight packaging waste, and treatment of non‐source‐separated residual waste) was performed. The analysis related to the year 2017 and also considered prospective changes in the background system until 2050 by adapting inventories to shared socioeconomic pathways in line with the Paris Agreement. Key factors for the environmental performance were determined by perturbation analysis. Source separation, quality and quantity of recycled plastics, and emissions from the thermal utilization of residues were identified as key factors for the environmental performance of PPW management. While benefits of PPW management are expected to decrease due to prospective system changes, source separation and the separation of plastics from residual waste gain in importance. Potential measures for improving the environmental performance should focus on long‐term key factors, especially separating PPW from the residual waste (in households or in waste treatment facilities) as well as increasing the quantities and qualities of recycled plastics. The present study showed that the evaluation of system performance in view of changing boundary conditions is key to identify optimal configurations of future PPW management.

Interpreting the decisions of CNNs via influence functions.

An understanding of deep neural network decisions is based on the interpretability of model, which provides explanations that are understandable to human beings and helps avoid biases in model predictions. This study investigates and interprets the model output based on images from the training dataset, i.e., to debug the results of a network model in relation to the training dataset. Our objective was to understand the behavior (specifically, class prediction) of deep learning models through the analysis of perturbations of the loss functions. We calculated influence scores for the VGG16 network at different hidden layers across three types of disturbances in the original images of the ImageNet dataset: texture, style, and background elimination. The global and layer-wise influence scores allowed the identification of the most influential training images for the given testing set. We illustrated our findings using influence scores by highlighting the types of disturbances that bias predictions of the network. According to our results, layer-wise influence analysis pairs well with local interpretability methods such as Shapley values to demonstrate significant differences between disturbed image subgroups. Particularly in an image classification task, our layer-wise interpretability approach plays a pivotal role to identify the classification bias in pre-trained convolutional neural networks, thus, providing useful insights to retrain specific hidden layers.

Neural network architectures for optical channel nonlinear compensation in digital subcarrier multiplexing systems.

In this work, we propose to use various artificial neural network (ANN) structures for modeling and compensation of intra- and inter-subcarrier fiber nonlinear interference in digital subcarrier multiplexing (DSCM) optical transmission systems. We perform nonlinear channel equalization by employing different ANN cores including convolutional neural networks (CNN) and long short-term memory (LSTM) layers. First, we develop a fiber nonlinearity compensation for DSCM systems based on a fully-connected network across all subcarriers. In subsequent steps, and borrowing from the perturbation analysis of fiber nonlinearity, we gradually upgrade proposed designs towards modular structures with better performance-complexity advantages. Our study shows that putting proper macro structures in design of ANN nonlinear equalizers in DSCM systems can be crucial in development of practical solutions for future generations of coherent optical transceivers.

On a multiple time-scales perturbation analysis of a Stefan problem with a time-dependent Dirichlet boundary condition

In this paper, a classical Stefan problem with a prescribed and small time-dependent temperature at the boundary is studied. By using a multiple time-scales perturbation method, it is shown analytically how the moving boundary profile is influenced by the prescribed temperature at the boundary and the initial conditions. Only a few exact solutions are available for this type of problems and it turns out that the constructed approximations agree very well with these exact solutions. In particular, approximations of solutions for this type of problems, with periodic and decaying temperatures at the boundary, are constructed. Furthermore, these approximations are valid on a long time scale, and seems to be not available in the literature.

Topology optimization of microstructures with perturbation analysis and penalty methods

Topology optimization at the continuum nano/microscale is of wide interest in designing and developing more efficient micro/nano electromechanical systems. This paper presents a new methodology for topology optimization of microstructures that is based on perturbation analysis and the penalty methods. The homogenized material coefficients are numerically computed based on perturbation analysis, and periodic boundary conditions are imposed by the penalty methods. The sensitivity analysis is implemented directly without the adjoint method. The extension of the proposed method to the design of components for multi-field analysis is straightforward. The capability and performance of the presented methodology are demonstrated through several numerical examples.

A Boolean model of the oncogene role of FAM111B in lung adenocarcinoma

The ultimate goal of this study is to analyze the gene regulation between FAM111B and p53 in lung adenocarcinoma using Boolean networks. Recent studies have shown that downregulation of FAM111B enhances the G2/M cell cycle checkpoint in the respective cell lines. Upregulation of p53 directly downregulates FAM111B, which is directed to affect cell cycle controllers Cdc25C and Cdk1/CyclinB, thereby controlling G2/M cell cycle arrest. As for apoptosis, down-regulation of FAM111B by p53 directly regulates the BAG3/Bcl-2 axis, which triggers apoptotic cell death. However, the molecular mechanisms involving p53 and FAM111B in G2/M checkpoint regulation are still unknown. Thus, we present a Boolean model of the G2/M checkpoint considering the effect of p53 and FAM111B. Our model indicates that the cell fate between the two cellular phenotypes, arrest, and apoptosis, at the G2/M checkpoint is non-deterministic and is controlled by p53. The model was compared with the experimental data involving gain- or loss-of-function genes and achieved a fair agreement. The model predicts a positive circuit involving p53/FAM111B/BAG3. Our circuit perturbation analysis suggests that this circuit may be essential for controlling cell-fate decisions at the G2/M checkpoint. Our model supports that FAM111B is an engaging target for drug development in lung adenocarcinoma.

Electroencephalography Network Indices as Biomarkers of Upper Limb Impairment in Chronic Stroke.

Alteration of electroencephalography (EEG) signals during task-specific movement of the impaired limb has been reported as a potential biomarker for the severity of motor impairment and for the prediction of motor recovery in individuals with stroke. When implementing EEG experiments, detailed paradigms and well-organized experiment protocols are required to obtain robust and interpretable results. In this protocol, we illustrate a task-specific paradigm with upper limb movement and methods and techniques needed for the acquisition and analysis of EEG data. The paradigm consists of 1 min of rest followed by 10 trials comprising alternating 5 s and 3 s of resting and task (hand extension)-states, respectively, over 4 sessions. EEG signals were acquired using 32 Ag/AgCl scalp electrodes at a sampling rate of 1,000 Hz. Event-related spectral perturbation analysis associated with limb movement and functional network analyses at the global level in the low-beta (12-20 Hz) frequency band were performed. Representative results showed an alteration of the functional network of low-beta EEG frequency bands during movement of the impaired upper limb, and the altered functional network was associated with the degree of motor impairment in chronic stroke patients. The results demonstrate the feasibility of the experimental paradigm in EEG measurements during upper limb movement in individuals with stroke. Further research using this paradigm is needed to determine the potential value of EEG signals as biomarkers of motor impairment and recovery.

Method to determine the centration of a lenticule of tissue extracted from a cornea.

A simple and novel method to analyse the centration of a lenticule of tissue extracted from a cornea has been developed, in which the centre of "mass" of the individual differences between post and preoperative maps of several corneal metrics represents the lenticule centration and its spatial distance to a reference point (aimed centration) determines the decentration. Different parameters have been evaluated to weight the centre of "mass". The robustness of the methods has been evaluated using perturbation analysis (adding white-noise to the data) based on realistic uncertainties. A clipped analysis has been performed to prevent large, localised areas of lacking/missing data from affecting the centre of "mass". The method has been tested on a pilot cohort of clinical data showing 30% and 63% of the treatments within 200 µm of decentration for corneal thickness and refractive equivalent power, respectively. Except for anterior elevation with a total standard deviation of 17 µm, all other metrics show excellent precision of ∼5 µm. The method provides a reliable and objective way to determine the centration of a lenticule of tissue extracted from a cornea and it can be applied to any topo- or tomographic derived metric.

Perturbation analysis of the euclidean distance matrix optimization problem and its numerical implications

Perturbation analysis of the euclidean distance matrix optimization problem and its numerical implications

Discovering Venom-Derived Drug Candidates Using Differential Gene Expression.

Venoms are a diverse and complex group of natural toxins that have been adapted to treat many types of human disease, but rigorous computational approaches for discovering new therapeutic activities are scarce. We have designed and validated a new platform-named VenomSeq-to systematically identify putative associations between venoms and drugs/diseases via high-throughput transcriptomics and perturbational differential gene expression analysis. In this study, we describe the architecture of VenomSeq and its evaluation using the crude venoms from 25 diverse animal species and 9 purified teretoxin peptides. By integrating comparisons to public repositories of differential expression, associations between regulatory networks and disease, and existing knowledge of venom activity, we provide a number of new therapeutic hypotheses linking venoms to human diseases supported by multiple layers of preliminary evidence.

Chiral perturbative relation for neutrino masses in the type-I seesaw mechanism

In this letter, we perform a perturbative analysis by the lightest singular value mD1 of the Dirac mass matrix mD in the type-I seesaw mechanism. A mass relation M1=mD12/|(mν)11| is obtained for the lightest mass M1 of the right-handed neutrino νR1 and the mass matrix of the left-handed neutrinos mν in the diagonal basis of mD. This relation is rather stable under renormalization because it is gauge-invariant in the SM and associates with the approximate chiral symmetry of νR1.If diagonalization of the Yukawa matrices of leptons Yν,e has only small mixings, the value (mν)11 is close to the effective mass mee of the neutrinoless double beta decay. By assuming mD1≃mu,e≃0.5 MeV, the lightest mass is about M1≳O(100) TeV in the normal hierarchy and M1∼O(10) TeV in the inverted hierarchy. Such a νR1 with a tiny Yukawa coupling yν1∼O(10−5) can indirectly influence various observations.On the other hand, the famous bound of the thermal leptogenesis M1≳109 GeV that requires mD1≳30 MeV seems to be difficult to reconcile with a simple unified theory without a special condition.

On the stability of distributed secondary control for DC microgrids with grid-forming and grid-feeding converters

This paper investigates the stability problem of a single-bus DC microgrid with mixed grid-forming/grid-feeding converters and the constant impedance, constant current, and constant power (ZIP) loads. Considering the different output properties of grid-forming and grid-feeding converters, distributed secondary controllers with mixed V–I droop and I–V droop controllers are designed to achieve accurate bidirectional current sharing and voltage regulation. As few converters have access to the information of the common bus, an observer is designed for each local controller to estimate the bus voltage. Then, the observer state is used to generate voltage correction term in the feedback loop, which gets potential faster regulation compared with the existing approaches that use pinning gains. Based on the rank-one perturbation analysis, a stability criterion of DC microgrid is given for the case of ZI load, where global voltage regulation and current sharing are guaranteed. Then, the stability criterion is extended to the case of ZIP load, where local stability of the DC microgrid is guaranteed. Both numerical examples and experimental tests are given to verify the effectiveness of the theoretical results.

Motion-compensated scheme for sequential scanned statistical iterative dual-energy CT reconstruction

Objective. Dual-energy computed tomography (DECT) has been widely used to reconstruct numerous types of images due its ability to better discriminate tissue properties. Sequential scanning is a popular dual-energy data acquisition method as it requires no specialized hardware. However, patient motion between two sequential scans may lead to severe motion artifacts in DECT statistical iterative reconstructions (SIR) images. The objective is to reduce the motion artifacts in such reconstructions. Approach. We propose a motion-compensation scheme that incorporates a deformation vector field into any DECT SIR. The deformation vector field is estimated via the multi-modality symmetric deformable registration method. The precalculated registration mapping and its inverse or adjoint are then embedded into each iteration of the iterative DECT algorithm. Main results. Results from a simulated and clinical case show that the proposed framework is capable of reducing motion artifacts in DECT SIRs. Percentage mean square errors in regions of interest in the simulated and clinical cases were reduced from 4.6% to 0.5% and 6.8% to 0.8%, respectively. A perturbation analysis was then performed to determine errors in approximating the continuous deformation by using the deformation field and interpolation. Our findings show that errors in our method are mostly propagated through the target image and amplified by the inverse matrix of the combination of the Fisher information and Hessian of the penalty term. Significance. We have proposed a novel motion-compensation scheme to incorporate a 3D registration method into the joint statistical iterative DECT algorithm in order to reduce motion artifacts caused by inter-scan motion, and successfully demonstrate that interscan motion corrections can be integrated into the DECT SIR process, enabling accurate imaging of radiological quantities on conventional SECT scanners, without significant loss of either computational efficiency or accuracy.

WindowSHAP: An efficient framework for explaining time-series classifiers based on Shapley values

Unpacking and comprehending how black-box machine learning algorithms (such as deep learning models) make decisions has been a persistent challenge for researchers and end-users. Explaining time-series predictive models is useful for clinical applications with high stakes to understand the behavior of prediction models, e.g., to determine how different variables and time points influence the clinical outcome. However, existing approaches to explain such models are frequently unique to architectures and data where the features do not have a time-varying component. In this paper, we introduce WindowSHAP, a model-agnostic framework for explaining time-series classifiers using Shapley values. We intend for WindowSHAP to mitigate the computational complexity of calculating Shapley values for long time-series data as well as improve the quality of explanations. WindowSHAP is based on partitioning a sequence into time windows. Under this framework, we present three distinct algorithms of Stationary, Sliding and Dynamic WindowSHAP, each evaluated against baseline approaches, KernelSHAP and TimeSHAP, using perturbation and sequence analyses metrics. We applied our framework to clinical time-series data from both a specialized clinical domain (Traumatic Brain Injury - TBI) as well as a broad clinical domain (critical care medicine). The experimental results demonstrate that, based on the two quantitative metrics, our framework is superior at explaining clinical time-series classifiers, while also reducing the complexity of computations. We show that for time-series data with 120 time steps (hours), merging 10 adjacent time points can reduce the CPU time of WindowSHAP by 80 % compared to KernelSHAP. We also show that our Dynamic WindowSHAP algorithm focuses more on the most important time steps and provides more understandable explanations. As a result, WindowSHAP not only accelerates the calculation of Shapley values for time-series data, but also delivers more understandable explanations with higher quality.

AdS2 holography and ModMax

We present a JT gravity set up in the presence of projected ModMax corrections in two dimensions. Our starting point is the Einstein’s gravity in four dimensions accompanied by the ModMax Lagrangian. The 2D gravity action is obtained following a suitable dimensional reduction which contains a 2D image of the 4D ModMax Lagrangian. We carry out a perturbative analysis to find out the vacuum structure of the theory which asymptotes to AdS2 in the absence of U(1) gauge fields. We estimate the holographic central charge and obtain corrections perturbatively upto quadratic order in the ModMax and the U(1) coupling. We also find out ModMax corrected 2D black hole solutions and discuss their extremal limits.