Now showing items 21-40 of 54927

    • Uncertain logistic and Box-Cox regression analysis with maximum likelihood estimation

      Fang, Liang; Hong, Yiping; Zhou, Zaiying; Chen, Wenhui (Communications in Statistics - Theory and Methods, Informa UK Limited, 2021-09-12) [Article]
      Although the maximum likelihood estimation (MLE) for the uncertain discrete models has long been an academic interest, it has yet to be proposed in the literature. Thus, this study proposes the uncertain MLE for discrete models in the framework of the uncertainty theory, such as the uncertain logistic regression model. We also generalize the estimation proposed by Lio and Liu and obtain the uncertain MLE for non-linear continuous models, such as the uncertain Box-Cox regression model. Our proposed methods provide a useful tool for making inferences regarding non-linear data that is precisely or imprecisely observed, especially data based on degrees of belief, such as an expert’s experimental data. We demonstrate our methodology by calculating proposed estimates and providing forecast values and confidence intervals for numerical examples. Moreover, we evaluate our proposed models via residual analysis and the cross-validation method. The study enriches the definition of the uncertain MLE, thus making it easy to construct estimation and prediction methods for general uncertainty models.
    • H2Opus: A distributed-memory multi-GPU software package for non-local operators

      Zampini, Stefano; Boukaram, Wagih Halim; Turkiyyah, George; Knio, Omar; Keyes, David E. (arXiv, 2021-09-12) [Preprint]
      Hierarchical $\mathcal{H}^2$-matrices are asymptotically optimal representations for the discretizations of non-local operators such as those arising in integral equations or from kernel functions. Their $O(N)$ complexity in both memory and operator application makes them particularly suited for large-scale problems. As a result, there is a need for software that provides support for distributed operations on these matrices to allow large-scale problems to be represented. In this paper, we present high-performance, distributed-memory GPU-accelerated algorithms and implementations for matrix-vector multiplication and matrix recompression of hierarchical matrices in the $\mathcal{H}^2$ format. The algorithms are a new module of H2Opus, a performance-oriented package that supports a broad variety of $\mathcal{H}^2$-matrix operations on CPUs and GPUs. Performance in the distributed GPU setting is achieved by marshaling the tree data of the hierarchical matrix representation to allow batched kernels to be executed on the individual GPUs. MPI is used for inter-process communication. We optimize the communication data volume and hide much of the communication cost with local compute phases of the algorithms. Results show near-ideal scalability up to 1024 NVIDIA V100 GPUs on Summit, with performance exceeding 2.3 Tflop/s/GPU for the matrix-vector multiplication, and 670 Gflops/s/GPU for matrix compression, which involves batched QR and SVD operations. We illustrate the flexibility and efficiency of the library by solving a 2D variable diffusivity integral fractional diffusion problem with an algebraic multigrid-preconditioned Krylov solver and demonstrate scalability up to 16M degrees of freedom problems on 64 GPUs.
    • Naturally Extracted Hydrophobic Solvent and Self-Assembly in Interfacial Polymerization

      Falca, Gheorghe; Musteata, Valentina-Elena; Chisca, Stefan; Hedhili, Mohamed N.; Ong, Chi Siang; Nunes, Suzana Pereira (ACS Applied Materials & Interfaces, American Chemical Society (ACS), 2021-09-12) [Article]
      Pharmaceutical, chemical, and food industries are actively implementing membrane nanofiltration modules in their processes to separate valuable products and recover solvents. Interfacial polymerization (IP) is the most widely used method to produce thin-film composite membranes for nanofiltration and reverse osmosis processes. Although membrane processes are considered green and environmentally friendly, membrane fabrication has still to be further developed in such direction. For instance, the emission of volatile solvents during membrane production in the industry has to be carefully controlled for health reasons. Greener solvents are being proposed for phase-separation membrane manufacture. For the IP organic phase, the proposition of greener alternatives is in an early stage. In this work, we demonstrate the preparation of a high-performing composite membrane employing zero vapor pressure and naturally extracted oleic acid as the IP organic phase. Its long hydrophobic chain ensures intrinsic low volatility and acid monomer dissolution, while the polar head induces a unique self-assembly structure during the film formation. Membranes prepared by this technique were selective for small molecules with a molecular weight cutoff of 650 g mol–1 and a high permeance of ∼57 L m–2 h–1 bar–1.
    • Check Your Other Door! Establishing Backdoor Attacks in the Frequency Domain

      Hammoud, Hasan Abed Al Kader; Ghanem, Bernard (arXiv, 2021-09-12) [Preprint]
      Deep Neural Networks (DNNs) have been utilized in various applications ranging from image classification and facial recognition to medical imagery analysis and real-time object detection. As our models become more sophisticated and complex, the computational cost of training such models becomes a burden for small companies and individuals; for this reason, outsourcing the training process has been the go-to option for such users. Unfortunately, outsourcing the training process comes at the cost of vulnerability to backdoor attacks. These attacks aim at establishing hidden backdoors in the DNN such that the model performs well on benign samples but outputs a particular target label when a trigger is applied to the input. Current backdoor attacks rely on generating triggers in the image/pixel domain; however, as we show in this paper, it is not the only domain to exploit and one should always "check the other doors". In this work, we propose a complete pipeline for generating a dynamic, efficient, and invisible backdoor attack in the frequency domain. We show the advantages of utilizing the frequency domain for establishing undetectable and powerful backdoor attacks through extensive experiments on various datasets and network architectures. The backdoored models are shown to break various state-of-the-art defences. We also show two possible defences that succeed against frequency-based backdoor attacks and possible ways for the attacker to bypass them. We conclude the work with some remarks regarding a network's learning capacity and the capability of embedding a backdoor attack in the model.
    • MovieCuts: A New Dataset and Benchmark for Cut Type Recognition

      Pardo, Alejandro; Heilbron, Fabian Caba; Alcázar, Juan León; Thabet, Ali Kassem; Ghanem, Bernard (arXiv, 2021-09-12) [Preprint]
      Understanding movies and their structural patterns is a crucial task to decode the craft of video editing. While previous works have developed tools for general analysis such as detecting characters or recognizing cinematography properties at the shot level, less effort has been devoted to understanding the most basic video edit, the Cut. This paper introduces the cut type recognition task, which requires modeling of multi-modal information. To ignite research in the new task, we construct a large-scale dataset called MovieCuts, which contains more than 170K videoclips labeled among ten cut types. We benchmark a series of audio-visual approaches, including some that deal with the problem's multi-modal and multi-label nature. Our best model achieves 45.7% mAP, which suggests that the task is challenging and that attaining highly accurate cut type recognition is an open research problem.
    • Cancer-associated mutations in the p85α N-terminal SH2 domain activate a spectrum of receptor tyrosine kinases.

      Li, Xinran; Lau, Amy Y T; Ng, Angel S N; Aldehaiman, Abdullah; Zhou, Yuan; Ng, Patrick K S; Arold, Stefan T.; Cheung, Lydia W T (Proceedings of the National Academy of Sciences of the United States of America, 2021-09-11) [Article]
      The phosphoinositide 3-kinase regulatory subunit p85α is a key regulator of kinase signaling and is frequently mutated in cancers. In the present study, we showed that in addition to weakening the inhibitory interaction between p85α and p110α, a group of driver mutations in the p85α N-terminal SH2 domain activated EGFR, HER2, HER3, c-Met, and IGF-1R in a p110α-independent manner. Cancer cells expressing these mutations exhibited the activation of p110α and the AKT pathway. Interestingly, the activation of EGFR, HER2, and c-Met was attributed to the ability of driver mutations to inhibit HER3 ubiquitination and degradation. The resulting increase in HER3 protein levels promoted its heterodimerization with EGFR, HER2, and c-Met, as well as the allosteric activation of these dimerized partners; however, HER3 silencing abolished this transactivation. Accordingly, inhibitors of either AKT or the HER family reduced the oncogenicity of driver mutations. The combination of these inhibitors resulted in marked synergy. Taken together, our findings provide mechanistic insights and suggest therapeutic strategies targeting a class of recurrent p85α mutations.
    • Pulsating CO2 nucleation radically improves the efficiency of membrane backwash

      Al Ghamdi, Mohanned; Alpatova, Alla; Alhadidi, Abdulsalam; Ghaffour, NorEddine (Desalination, Elsevier BV, 2021-09-11) [Article]
      Although membrane filtration became a dominant water treatment technology globally, it suffers from membrane fouling which aggravates with time and imposes severe adverse effects on process performance, permeate quality and, eventually, its related costs. In this work, we introduce pulsating CO2 solution backwash with intermittent pressure drops to maximize CO2 bubbles yield and radically enhance membrane cleaning. The novel backwash technique was probed during ultrafiltration (UF) of feed waters containing sodium alginate, a model polysaccharide foulants, sea salts enriched in Ca2+, and SiO2. Transmembrane pressures (TMP) observed during the experiments with pulsating CO2 backwash acquired an up/down profile indicating that a considerable portion of TMP was recovered after each backwash cycle, in contrast to insufficient fouling removal and subsequent TMP build-up observed with continuous CO2 and Milli-Q backwashes. Notably, pulsating CO2 backwash alleviated irreversible membrane fouling in highly saline conditions with 30 g/L of sea salts and when it is combined with 1 mg/L of SiO2 (i.e., when conventional membrane backwash was not effective). Furthermore, intense cleaning of the membrane surface and its pores was resembled by a lower fouling resistance in the subsequent UF cycles implying potentially longer operation time with less cleaning frequency and substantial energy savings.
    • Symbiodinium microadriaticum (coral microalgal endosymbiont)

      Voolstra, Christian R.; Aranda, Manuel; Zhan, Ye; Dekker, Job (Trends in Genetics, Elsevier BV, 2021-09-11) [Article]
      Photosynthetic microalgae, from the family Symbiodiniaceae, engage in endosymbioses with marine invertebrates, including stony corals. More generally, dinoflagellates are ubiquitous protists and the main primary producers in the oceans. Despite their ecological and economic importance, their biology remains enigmatic. Here we assembled 94 chromosome-scale scaffolds of the ancestral Symbiodiniaceae species Symbiodinium microadriaticum. Contrary to the random order of genes typically found in eukaryotic cells, genes are enriched toward the ends of chromosomes in alternating unidirectional blocks that are sometimes enriched for genes of specific biological processes. These gene blocks are coexpressed and separated by structural boundaries where transcription converges. These structural domains, in turn, comprise the transcription-dependent basic building blocks of the chromosomes that fold as linear rods. Such a highly ordered structure linking gene orientation, transcription, and spatial organization of chromosomes is exceptional.
    • Doubly Adaptive Scaled Algorithm for Machine Learning Using Second-Order Information

      Jahani, Majid; Rusakov, Sergey; Shi, Zheng; Richtarik, Peter; Mahoney, Michael W.; Takáč, Martin (arXiv, 2021-09-11) [Preprint]
      We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods.
    • Relative Importance of Stochastic Assembly Process of Membrane Biofilm Increased as Biofilm Aged

      Matar, Gerald; Ali, Muhammad; Bagchi, Samik; Nunes, Suzana Pereira; Liu, Wen-Tso; Saikaly, Pascal (Frontiers in Microbiology, Frontiers Media SA, 2021-09-10) [Article]
      The relative importance of different ecological processes controlling biofilm community assembly over time on membranes with different surface characteristics has never been investigated in membrane bioreactors (MBRs). In this study, five ultrafiltration hollow-fiber membranes – having identical nominal pore size (0.1μm) but different hydrophobic or hydrophilic surface characteristics – were operated simultaneously in the same MBR tank with a constant flux of 10 liters per square meter per hour (LMH). In parallel, membrane modules operated without permeate flux (0 LMH) were submerged in the same MBR tank, to investigate the passive microbial adsorption onto different hydrophobic or hydrophilic membranes. Samples from the membrane biofilm were collected after 1, 10, 20, and 30days of continuous filtration. The membrane biofilm microbiome were investigated using 16S rRNA gene amplicon sequencing from DNA and cDNA samples. Similar beta diversity trends were observed for both DNA- and cDNA-based analyses. Beta diversity analyses revealed that the nature of the membrane surface (i.e., hydrophobic vs. hydrophilic) did not seem to have an effect in shaping the bacterial community, and a similar biofilm microbiome evolved for all types of membranes. Similarly, membrane modules operated with and without permeate flux did not significantly influence alpha and beta diversity of the membrane biofilm. Nevertheless, different-aged membrane biofilm samples exhibited significant differences. Proteobacteria was the most dominant phylum in early-stage membrane biofilm after 1 and 10days of filtration. Subsequently, the relative reads abundance of the phyla Bacteroidetes and Firmicutes increased within the membrane biofilm communities after 20 and 30days of filtration, possibly due to successional steps that lead to the formation of a relatively aged biofilm. Our findings indicate distinct membrane biofilm assembly patterns with different-aged biofilm. Ecological null model analyses revealed that the assembly of early-stage biofilm community developed after 1 and 10days of filtration was mainly governed by homogenous selection. As the biofilm aged (days 20 and 30), stochastic processes (e.g., ecological drift) started to become important in shaping the assembly of biofilm community.
    • A numerical method for self-similar solutions of the ideal magnetohydrodynamics

      Chen, Fang; Samtaney, Ravi (Journal of Computational Physics, Elsevier BV, 2021-09-10) [Article]
      We present a numerical method to obtain self-similar solutions of the ideal magnetohydrodynamics (MHD) equations. Under a self-similar transformation, the initial value problem (IVP) is converted into a boundary value prob1 lem (BVP) by eliminating time and transforming the system to self-similar coordinates (ξ ≡ x/t, η ≡ y/t). The ideal MHD system of equations is augmented by a generalized Lagrange multiplier (GLM) to maintain the solenoidal condition on the magnetic field. The self-similar solution to the BVP is solved using an iterative method, and implemented using the p4est adaptive mesh refinement (AMR) framework. Existing Riemann solvers (e.g., Roe, HLLD etc.) can be modified in a relatively straightforward manner and used in the present method. Numerical tests numerical tests illustrate that the present self-similar solution to the BVP exhibits sharper discontinuities than the corresponding one solved by the IVP. We compare and contrast the IVP and BVP solutions in several one dimensional shock-tube test problem and two dimensional test cases include shock wave refraction at a contact discontinuity, reflection at a solid wall, and shock wave diffraction over a right angle corner.
    • Thermo-Responsive Membranes from Blends of PVDF and PNIPAM-b-PVDF Block Copolymers with Linear and Star Architectures

      Algarni, Fatimah; Musteata, Valentina-Elena; Falca, Gheorghe; Chisca, Stefan; Hadjichristidis, Nikos; Nunes, Suzana Pereira (Macromolecules, American Chemical Society (ACS), 2021-09-10) [Article]
      We report the synthesis of poly(n-isopropylacrylamide)-b-poly(vinylidene fluoride), (PNIPAM-b-PVDF), copolymers with linear and star structures, as well as the self-assembly and fabrication of thermo-responsive membranes from blends of these block copolymers and a linear PVDF homopolymer. The synthesis was achieved by reversible addition–fragmentation chain-transfer sequential copolymerization using mono- or multifunctional transfer agents. The self-assembly in bulk and selective solvents was investigated. The PVDF blocks are crystallizable and hydrophobic and the PNIPAM thermo-responsive in water. The morphology is dominated by the breakout crystallization of the PVDF block. Nanoporous membranes were fabricated by non-solvent-induced phase-separation method. The membranes revealed a macroscale zig–zag morphology, which is dependent on the block copolymer architecture. Due to the presence of PNIPAM, these membranes exhibited thermo-responsive behavior with water permeability and rejection alternately varying with the operating temperature, which is reversible in multiple heating–cooling cycles.
    • Effects of ammonia and hydrogen on the sooting characteristics of laminar coflow flames of ethylene and methane

      Steinmetz, S.A.; Ahmed, H.A.; Boyette, Wesley; Dunn, M.J.; Roberts, William L.; Masri, A.R. (Fuel, Elsevier BV, 2021-09-10) [Article]
      Hydrogen and its derivatives, including ammonia, are gaining increasing attention as carbon-neutral fuel alternatives. An intermediate step in the transition to hydrogen and ammonia is the blending of these fuels with hydrocarbons, introducing the challenge of soot formation. The impact of ammonia on soot formation has recently been the focus of several studies, but a complete understanding of its chemical effects is lacking. Hydrogen, by comparison, has received significant attention from the soot community. However, controversy remains with regards to hydrogen’s chemical impact, and the dependence of this impact on fuel and flame configuration. This work investigates the effect of both hydrogen and ammonia on soot formation in laminar coflow flames of both ethylene and methane. Hydrogen or ammonia are introduced either by addition or substitution, with parallel studies of helium and argon, in order to isolate their chemical effects. Time- and spectrally-resolved laser-induced emissions from UV and IR excitation are used to quantify differences in soot and soot precursor formation. Additionally, chemical kinetics calculations and analyses are used to elucidate the effects of ammonia introduction to ethylene flames. Ammonia is found to chemically inhibit soot when mixed with either ethylene or methane, with increasing effects on larger precursors. Calculations suggest that this suppression is due to carbon consumption in the formation of HCN and CN. Hydrogen is found to chemically enhance soot formation in both ethylene and methane flames.
    • IntraTomo: Self-supervised Learning-based Tomography via Sinogram Synthesis and Prediction

      Zang, Guangming; Idoughi, Ramzi; Li, Rui; Wonka, Peter; Heidrich, Wolfgang (IEEE, 2021-09-10) [Conference Paper]
      We propose IntraTomo, a powerful framework that combines the benefits of learning-based and model-based approaches for solving highly ill-posed inverse problems, in the Computed Tomography (CT) context. IntraTomo is composed of two core modules: a novel sinogram prediction module and a geometry refinement module, which are applied iteratively. In the first module, the unknown density field is represented as a continuous and differentiable function, parameterized by a deep neural network. This network is learned, in a self-supervised fashion, from the incomplete or/and degraded input sinogram. After getting estimated through the sinogram prediction module, the density field is consistently refined in the second module using local and non-local geometrical priors. With these two core modules, we show that IntraTomo significantly outperforms existing approaches on several ill-posed inverse problems, such as limited angle tomography with a range of 45 degrees, sparse view tomographic reconstruction with as few as eight views, or super-resolution tomography with eight times increased resolution. The experiments on simulated and real data show that our approach can achieve results of unprecedented quality.
    • Influences of ALD Al2O3 on the surface band-bending of c-plane, Ga-face GaN and the implication to GaN-collector npn heterojunction bipolar transistors

      Gong, Jiarui; Kim, Jisoo; Ng, Tien Khee; Lu, Kuangye; Kim, Donghyeok; Zhou, Jie; Liu, Dong; Kim, Jeehwan; Ooi, Boon S.; Ma, Zhenqiang (arXiv, 2021-09-10) [Preprint]
      Due to the lack of effective p-type doping in GaN and the adverse effects of surface band-bending of GaN on electron transport, developing practical GaN heterojunction bipolar transistors has been impossible. The recently demonstrated approach of grafting n-type GaN with p-type semiconductors, like Si and GaAs, by employing ultrathin (UO) Al2O3 at the interface of Si/GaN and GaAs/GaN, has shown the feasibility to overcome the poor p-type doping challenge of GaN by providing epitaxy-like interface quality. However, the surface band-bending of GaN that could be influenced by the UO Al2O3 has been unknown. In this work, the band-bending of c-plane, Ga-face GaN with UO Al2O3 deposition at the surface of GaN was studied using X-ray photoelectron spectroscopy (XPS). The study shows that the UO Al2O3 can help in suppressing the upward band-bending of the c-plane, Ga-face GaN with a monotonic reduction trend of the upward band-bending energy from 0.48 eV down to 0.12 eV as the number of UO Al2O3 deposition cycles is increased from 0 to 20 cycles. The study further shows that the band-bending can be mostly recovered after removing the Al2O3 layer, concurring that the change in the density of fixed charge at the GaN surface caused by UO Al2O3 is the main reason for the surface band-bending modulation. The potential implication of the surface band-bending results of AlGaAs/GaAs/GaN npn heterojunction bipolar transistor (HBT) was preliminarily studied via Silvaco® simulations.
    • Cycle-skipping mitigation using misfit measurements based on differentiable dynamic time warping

      chen, fuqiang; Peter, Daniel; Ravasi, Matteo (arXiv, 2021-09-09) [Preprint]
      The dynamic time warping (DTW) distance has been used as a misfit function for wave-equation inversion to mitigate the local minima issue. However, the original DTW distance is not smooth; therefore it can yield a strong discontinuity in the adjoint source. Such a weakness does not help nonlinear inverse problems converge to a plausible minimum by any means. We therefore introduce for the first time in geophysics the smooth DTW distance, which has demonstrated its performance in time series classification, clustering, and prediction as the loss function. The fundamental idea of such a distance is to replace the $\min$ operator with its smooth relaxation. Then it becomes possible to define the analytic derivative of DTW distance. The new misfit function is entitled to the differentiable DTW distance. Moreover, considering that the warping path is an indicator of the traveltime difference between the observed and synthetic trace, a penalization term is constructed based on the warping path such that the misfit accumulation by the penalized differentiable DTW distance is weighted in favor of the traveltime difference. Numerical examples demonstrate the advantage of the penalized differentiable DTW misfit function over the conventional non-differentiable one.
    • 3-D Modeling of Ultrathin Solar Cells with Nanostructured Dielectric Passivation: Case Study of Chalcogenide Solar Cells

      Raja, Waseem; Aydin, Erkan; Allen, Thomas; De Wolf, Stefaan (Advanced Theory and Simulations, Wiley, 2021-09-09) [Article]
      Ultrathin solar cells can be a path forward to low-cost photovoltaics due to their reduced material consumption and shorter required deposition times. With excellent surface passivation, such devices may feature higher open-circuit voltages (VOC). However, their short-circuit current density (JSC) may be reduced due to decreased light absorption. This mandates implementation of efficient light-trapping structures. To design efficient ultrathin solar cells that combine surface-passivation and light-trapping features, accurate 3-D modeling is necessary. To this end, a novel 3-D optoelectrical finite-element model is developed to analyze the performance of ultrathin solar cells. The model is applied to the case of ultrathin (<500 nm) chalcogenide solar cells (copper indium gallium (di) selenide, CIGSe), rear-passivated with nanostructured Al2O3 to circumvent optical and electrical losses. It is found that such a nanopatterned dielectric passivation scheme enhances broadband light-trapping with reduced rear-surface recombination, resulting in an absolute power conversion efficiency enhancement of 3.9%, compared to cells without passivation structure. Overall, the work shows how 3-D finite element modeling can aid in analyzing and developing new optical and electrical solar cell designs for ultrathin solar cells such as those based on chalcogenides and perovskites.
    • Real-time membrane fouling analysis for the assessment of reclamation potential of textile wastewater processed by membrane distillation

      Elcik, Harun; Fortunato, Luca; Vrouwenvelder, Johannes S.; Ghaffour, NorEddine (Journal of Water Process Engineering, Elsevier BV, 2021-09-09) [Article]
      Understanding the factors that specify the fouling development in membrane distillation (MD) plays a key role to develop effective control strategies with the aim of providing its widespread use in industrial applications, such as textile industry. The present study investigated the fouling mechanisms in textile wastewater treatment by direct contact MD (DCMD), employing an advanced in-situ optical coherence tomography (OCT) technology allowing to monitor MD fouling in real-time. The OCT analysis enabled evaluating the effect of feed temperature, flow rate, dye concentration on the membrane fouling and the long-term performance of MD operation that includes a periodical water flushing. The permeate flux decrease during the initial stages of experiments was attributed to the existence of attractive hydrophobic-hydrophobic interaction between the membrane and dye molecules as no cake fouling was observed at the early stages. Then, a flat and homogeneous cake layer was developed with time in all the fouled membranes regardless of the cake layer thickness. The long-term experiment resulted in both reversible and irreversible fouling and showed that water flushing had limited efficacy against reversible fouling. Additionally, electrostatic repulsive forces occurring between the membrane and textile dye molecules influenced the permeate flux depending on the dye concentration. Finally, among all the operating parameters, feed temperature had the highest impact on the membrane fouling and process performance, changed the heat transfer activity at the membrane-liquid frontier zone, in turn, leading to variations in the flux.