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Journal articles on the topic 'Gradient implicite'

Author: Grafiati

Published: 31 August 2024

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1

Weller, Hilary, and Ava Shahrokhi. "Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves." Monthly Weather Review 142, no. 12 (December 1, 2014): 4439–57. http://dx.doi.org/10.1175/mwr-d-14-00054.1.

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Abstract Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modeling flow over orography is introduced that guarantees curl-free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain-following grids. Curl-free gradients are achieved by using the covariant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with NΔt up to at least 10 (where N is the Brunt–Väisälä frequency). A warm bubble rising over orography is simulated and the curl-free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

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Askes, Harm, and Miguel A. Gutiérrez. "Implicit gradient elasticity." International Journal for Numerical Methods in Engineering 67, no. 3 (2006): 400–416. http://dx.doi.org/10.1002/nme.1640.

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3

Haugh, Jason M., Franca Codazzi, Mary Teruel, and Tobias Meyer. "Spatial Sensing in Fibroblasts Mediated by 3′ Phosphoinositides." Journal of Cell Biology 151, no. 6 (December 11, 2000): 1269–80. http://dx.doi.org/10.1083/jcb.151.6.1269.

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The directed movement of fibroblasts towards locally released platelet-derived growth factor (PDGF) is a critical event in wound healing. Although recent studies have implicated polarized activation of phosphoinositide (PI) 3-kinase in G protein-mediated chemotaxis, the role of 3′ PI lipids in tyrosine kinase-triggered chemotaxis is not well understood. Using evanescent wave microscopy and green fluorescent protein–tagged Akt pleckstrin homology domain (GFP–AktPH) as a molecular sensor, we show that application of a shallow PDGF gradient triggers a markedly steeper gradient in 3′ PI lipids in the adhesion zone of fibroblasts. Polar GFP–AktPH gradients, as well as a new type of radial gradient, were measured from front to rear and from the periphery to the center of the adhesion zone, respectively. A strong spatial correlation between polarized 3′ PI production and rapid membrane spreading implicates 3′ PI lipids as a direct mediator of polarized migration. Analysis of the temporal changes of 3′ PI gradients in the adhesion zone revealed a fast diffusion coefficient (0.5 μm2/s) and short lifetime of 3′ PIs of <1 min. Together, this study suggests that the tyrosine kinase-coupled directional movement of fibroblasts and their radial membrane activity are controlled by local generation and rapid degradation of 3′ PI second messengers.

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Minervini, Pasquale, Luca Franceschi, and Mathias Niepert. "Adaptive Perturbation-Based Gradient Estimation for Discrete Latent Variable Models." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 8 (June 26, 2023): 9200–9208. http://dx.doi.org/10.1609/aaai.v37i8.26103.

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The integration of discrete algorithmic components in deep learning architectures has numerous applications. Recently, Implicit Maximum Likelihood Estimation, a class of gradient estimators for discrete exponential family distributions, was proposed by combining implicit differentiation through perturbation with the path-wise gradient estimator. However, due to the finite difference approximation of the gradients, it is especially sensitive to the choice of the finite difference step size, which needs to be specified by the user. In this work, we present Adaptive IMLE (AIMLE), the first adaptive gradient estimator for complex discrete distributions: it adaptively identifies the target distribution for IMLE by trading off the density of gradient information with the degree of bias in the gradient estimates. We empirically evaluate our estimator on synthetic examples, as well as on Learning to Explain, Discrete Variational Auto-Encoders, and Neural Relational Inference tasks. In our experiments, we show that our adaptive gradient estimator can produce faithful estimates while requiring orders of magnitude fewer samples than other gradient estimators.

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Dong, Mingrong, Yixuan Yang, Kai Zeng, Qingwang Wang, and Tao Shen. "Implicit Sharpness-Aware Minimization for Domain Generalization." Remote Sensing 16, no. 16 (August 6, 2024): 2877. http://dx.doi.org/10.3390/rs16162877.

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Domain generalization (DG) aims to learn knowledge from multiple related domains to achieve a robust generalization performance in unseen target domains, which is an effective approach to mitigate domain shift in remote sensing image classification. Although the sharpness-aware minimization (SAM) method enhances DG capability and improves remote sensing image classification performance by promoting the convergence of the loss minimum to a flatter loss surface, the perturbation loss (maximum loss within the neighborhood of a local minimum) of SAM fails to accurately measure the true sharpness of the loss landscape. Furthermore, its variants often overlook gradient conflicts, thereby limiting further improvement in DG performance. In this paper, we introduce implicit sharpness-aware minimization (ISAM), a novel method that addresses the deficiencies of SAM and mitigates gradient conflicts. Specifically, we demonstrate that the discrepancy in training loss during gradient ascent or descent serves as an equivalent measure of the dominant eigenvalue of the Hessian matrix. This discrepancy provides a reliable measure for sharpness. ISAM effectively reduces sharpness and mitigates potential conflicts between gradients by implicitly minimizing the discrepancy between training losses while ensuring a sufficiently low minimum through minimizing perturbation loss. Extensive experiments and analyses demonstrate that ISAM significantly enhances the model’s generalization ability on remote sensing and DG datasets, outperforming existing state-of-the-art methods.

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Bertei, Antonio, Andrea Lamorgese, and Roberto Mauri. "Constitutive Relations of Thermal and Mass Diffusion." Journal of Non-Equilibrium Thermodynamics 45, no. 1 (January 28, 2020): 27–38. http://dx.doi.org/10.1515/jnet-2019-0055.

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AbstractNon-equilibrium thermodynamics provides a general framework for the description of mass and thermal diffusion, thereby including also cross-thermal and material diffusion effects, which are generally modeled through the Onsager coupling terms within the constitutive equations relating heat and mass flux to the gradients of temperature and chemical potential. These so-called Soret and Dufour coefficients are not uniquely defined, though, as they can be derived by adopting one of the several constitutive relations satisfying the principles of non-equilibrium thermodynamics. Therefore, mass diffusion induced by a temperature gradient and heat conduction induced by a composition gradient can be implicitly, and unexpectedly, predicted even in the absence of coupling terms. This study presents a critical analysis of different formulations of the constitutive relations, with special focus on regular binary mixtures. It is shown that, among the different formulations presented, the one which adopts the chemical potential gradient at constant temperature as the driving force for mass diffusion allows for the implicit thermo-diffusion effect to be strictly absent while the resulting Dufour effect is negligibly small. Such a formulation must be preferred to the other ones since cross-coupling effects are predicted only if explicitly introduced via Onsager coupling coefficients.

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Nishikawa, Hiroaki. "From hyperbolic diffusion scheme to gradient method: Implicit Green–Gauss gradients for unstructured grids." Journal of Computational Physics 372 (November 2018): 126–60. http://dx.doi.org/10.1016/j.jcp.2018.06.019.

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8

Gourmel, Olivier, Loic Barthe, Marie-Paule Cani, Brian Wyvill, Adrien Bernhardt, Mathias Paulin, and Herbert Grasberger. "A gradient-based implicit blend." ACM Transactions on Graphics 32, no. 2 (April 2013): 1–12. http://dx.doi.org/10.1145/2451236.2451238.

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9

Dandi, Yatin, Luis Barba, and Martin Jaggi. "Implicit Gradient Alignment in Distributed and Federated Learning." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 6 (June 28, 2022): 6454–62. http://dx.doi.org/10.1609/aaai.v36i6.20597.

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A major obstacle to achieving global convergence in distributed and federated learning is the misalignment of gradients across clients or mini-batches due to heterogeneity and stochasticity of the distributed data. In this work, we show that data heterogeneity can in fact be exploited to improve generalization performance through implicit regularization. One way to alleviate the effects of heterogeneity is to encourage the alignment of gradients across different clients throughout training. Our analysis reveals that this goal can be accomplished by utilizing the right optimization method that replicates the implicit regularization effect of SGD, leading to gradient alignment as well as improvements in test accuracies. Since the existence of this regularization in SGD completely relies on the sequential use of different mini-batches during training, it is inherently absent when training with large mini-batches. To obtain the generalization benefits of this regularization while increasing parallelism, we propose a novel GradAlign algorithm that induces the same implicit regularization while allowing the use of arbitrarily large batches in each update. We experimentally validate the benefits of our algorithm in different distributed and federated learning settings.

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10

Nelson, J. Bradley. "An alternate derivation of the three‐dimensional Hilbert transform relations from first principles." GEOPHYSICS 51, no. 4 (April 1986): 1014–15. http://dx.doi.org/10.1190/1.1442141.

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Several techniques for determining the location, geometry, and strength of a source are based on a knowledge of the magnetic gradients generated by that source. Hood (1965), Bhattacharyya (1966), and Rao et al. (1981) detailed three of these gradient methods. For many years, geophysicists have used the two‐dimensional (2-D) Hilbert transform to approximate the vertical gradient from measurements of the horizontal gradient in the magnetic‐field intensity (Nabighian, 1972; Stanley and Green, 1976; Stanley, 1977; Mohan et al., 1982). This technique is of limited applicability because of the implicit assumption that the source is a linear, 2-D body oriented at right angles to the profile direction.

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Goodhill, Geoffrey J., and Herwig Baier. "Axon Guidance: Stretching Gradients to the Limit." Neural Computation 10, no. 3 (April 1, 1998): 521–27. http://dx.doi.org/10.1162/089976698300017638.

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Neuronal growth cones, the sensory-motile structures at the tips of developing axons, navigate to their targets over distances that can be many times greater than their diameter. They may accomplish this impressive task by following spatial gradients of axon guidance molecules in their environment (Bonhoeffer & Gierer, 1984; Tessier-Lavigne & Placzek, 1991; Baier & Bonhoeffer, 1994). We calculate the optimal shape of a gradient and the distance over which it can be detected by a growth cone for two competing mechanistic models of axon guidance. The results are surprisingly simple: Regardless of the mechanism, the maximum distance is about 1 cm. Since gradients and growth cones have coevolved, we suggest that the shape of the gradient in situ will predict the mechanism of gradient detection. In addition, we show that the experimentally determined dissociation constants for receptor-ligand complexes implicated in axon guidance are about optimal with respect to maximizing guidance distance. The relevance of these results to the retinotectal system is discussed.

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12

Brown, James William L., Azmain Chowdhury, Baris Kanber, Ferran Prados Carrasco, Arman Eshaghi, Carole H. Sudre, Matteo Pardini, et al. "Magnetisation transfer ratio abnormalities in primary and secondary progressive multiple sclerosis." Multiple Sclerosis Journal 26, no. 6 (April 8, 2019): 679–87. http://dx.doi.org/10.1177/1352458519841810.

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Background: In relapse-onset multiple sclerosis (MS), tissue abnormality – as assessed with magnetisation transfer ratio (MTR) imaging – is greater in the outer cortical and inner periventricular layers. The cause of this remains unknown but meningeal inflammation has been implicated, particularly lymphoid follicles, which are seen in secondary progressive (SP) but not primary progressive (PP) MS. Cortical and periventricular MTR gradients might, therefore, differ in PPMS and SPMS if these follicles are responsible. Objective: We assessed cortical and periventricular MTR gradients in PPMS, and compared gradients between people with PPMS and SPMS. Methods: Using an optimised processing pipeline, periventricular normal-appearing white matter and cortical grey-matter MTR gradients were compared between 51 healthy controls and 63 people with progressive MS (28 PPMS, 35 SPMS). Results: The periventricular gradient was significantly shallower in healthy controls (0.122 percentage units (pu)/band) compared to PPMS (0.952 pu/band, p < 0.0001) and SPMS (1.360 pu/band, p < 0.0001). The cortical gradient was also significantly shallower in healthy controls (−2.860 pu/band) compared to PPMS (−3.214 pu/band, p = 0.038) and SPMS (−3.328 pu/band, p = 0.016). Conclusion: Abnormal periventricular and cortical MTR gradients occur in both PPMS and SPMS, suggesting comparable underlying pathological processes.

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13

Simone, Angelo. "Explicit and implicit gradient-enhanced damage models." Revue Européenne de Génie Civil 11, no. 7-8 (August 2007): 1023–44. http://dx.doi.org/10.1080/17747120.2007.9692975.

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14

Yang, Zhuang. "Variance reduced optimization with implicit gradient transport." Knowledge-Based Systems 212 (January 2021): 106626. http://dx.doi.org/10.1016/j.knosys.2020.106626.

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Simone, Angelo. "Explicit and implicit gradient-enhanced damage models." Revue européenne de génie civil 11, no. 7-8 (October 1, 2007): 1023–44. http://dx.doi.org/10.3166/regc.11.1023-1044.

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16

Liu, Jinze. "The advance of underdetermined linear regression optimization based on implicit bias." Journal of Physics: Conference Series 2580, no. 1 (September 1, 2023): 012008. http://dx.doi.org/10.1088/1742-6596/2580/1/012008.

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Abstract The gradient descent method has the characteristics of easy realization and simple structure. The traditional gradient descent method has many advantages, especially in solving convex optimization problems. In recent years, some researchers have noticed that the gradient descent algorithm is helpful to solve the problem of underdetermined linear regression optimization. Therefore, in order to explore the specific relationship between gradient descent and under-determined linear regression optimization, this paper focuses on a case with a unique finite root loss function and discusses in detail the working principles of the natural-gradient-descent, mirror-descent, and gradient-descent in this case, and proves the auxiliary effect of gradient descent on under-determined linear regression optimization theoretically. How to use the characteristics of the gradient descent algorithm to design a suitable model, and how do we use the idea of the gradient descent algorithm to find an answer for problem of under determined linear regression optimization in the practical application will be the future research work to continue to advance.

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17

Kolahdouz, Ebrahim M., and David Salac. "A Semi-implicit Gradient Augmented Level Set Method." SIAM Journal on Scientific Computing 35, no. 1 (January 2013): A231—A254. http://dx.doi.org/10.1137/120871237.

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18

Titscher, Thomas, Javier Oliver, and Jörg F. Unger. "Implicit–Explicit Integration of Gradient-Enhanced Damage Models." Journal of Engineering Mechanics 145, no. 7 (July 2019): 04019040. http://dx.doi.org/10.1061/(asce)em.1943-7889.0001608.

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19

Burago, N. G., and I. S. Nikitin. "Matrix-Free Conjugate Gradient Implementation of Implicit Schemes." Computational Mathematics and Mathematical Physics 58, no. 8 (August 2018): 1247–58. http://dx.doi.org/10.1134/s0965542518080043.

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20

Askes, H., and L. J. Sluys. "Explicit and implicit gradient series in damage mechanics." European Journal of Mechanics - A/Solids 21, no. 3 (January 2002): 379–90. http://dx.doi.org/10.1016/s0997-7538(02)01214-7.

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21

Gairre, L., and E. Mosca. "Implicit predictive adaptive control with stochastic gradient identifiers." IEEE Transactions on Automatic Control 38, no. 7 (July 1993): 1135–39. http://dx.doi.org/10.1109/9.231472.

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22

Vernay, Aurélia, Sébastien Schaub, Isabelle Guillas, Martine Bassilana, and Robert A. Arkowitz. "A steep phosphoinositide bis-phosphate gradient forms during fungal filamentous growth." Journal of Cell Biology 198, no. 4 (August 13, 2012): 711–30. http://dx.doi.org/10.1083/jcb.201203099.

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Membrane lipids have been implicated in many critical cellular processes, yet little is known about the role of asymmetric lipid distribution in cell morphogenesis. The phosphoinositide bis-phosphate PI(4,5)P2 is essential for polarized growth in a range of organisms. Although an asymmetric distribution of this phospholipid has been observed in some cells, long-range gradients of PI(4,5)P2 have not been observed. Here, we show that in the human pathogenic fungus Candida albicans a steep, long-range gradient of PI(4,5)P2 occurs concomitant with emergence of the hyphal filament. Both sufficient PI(4)P synthesis and the actin cytoskeleton are necessary for this steep PI(4,5)P2 gradient. In contrast, neither microtubules nor asymmetrically localized mRNAs are critical. Our results indicate that a gradient of PI(4,5)P2, crucial for filamentous growth, is generated and maintained by the filament tip–localized PI(4)P-5-kinase Mss4 and clearing of this lipid at the back of the cell. Furthermore, we propose that slow membrane diffusion of PI(4,5)P2 contributes to the maintenance of such a gradient.

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Ellison, David, Andrew Mugler, Matthew D. Brennan, Sung Hoon Lee, Robert J. Huebner, Eliah R. Shamir, Laura A. Woo, et al. "Cell–cell communication enhances the capacity of cell ensembles to sense shallow gradients during morphogenesis." Proceedings of the National Academy of Sciences 113, no. 6 (January 20, 2016): E679—E688. http://dx.doi.org/10.1073/pnas.1516503113.

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Collective cell responses to exogenous cues depend on cell–cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and little is known about how multicellular signal processing modulates single-cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored whether cell–cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow epidermal growth factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.

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Hickel, S., and N. A. Adams. "Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence." International Journal of Heat and Fluid Flow 29, no. 3 (June 2008): 626–39. http://dx.doi.org/10.1016/j.ijheatfluidflow.2008.03.008.

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Poh, L. H., R. H. J. Peerlings, M. G. D. Geers, and S. Swaddiwudhipong. "An implicit tensorial gradient plasticity model – Formulation and comparison with a scalar gradient model." International Journal of Solids and Structures 48, no. 18 (September 2011): 2595–604. http://dx.doi.org/10.1016/j.ijsolstr.2011.05.019.

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26

Fan, Xiaomeng, Yuwei Wu, Zhi Gao, Yunde Jia, and Mehrtash Harandi. "Efficient Riemannian Meta-Optimization by Implicit Differentiation." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (June 28, 2022): 3733–40. http://dx.doi.org/10.1609/aaai.v36i4.20287.

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To solve optimization problems with nonlinear constrains, the recently developed Riemannian meta-optimization methods show promise, which train neural networks as an optimizer to perform optimization on Riemannian manifolds. A key challenge is the heavy computational and memory burdens, because computing the meta-gradient with respect to the optimizer involves a series of time-consuming derivatives, and stores large computation graphs in memory. In this paper, we propose an efficient Riemannian meta-optimization method that decouples the complex computation scheme from the meta-gradient. We derive Riemannian implicit differentiation to compute the meta-gradient by establishing a link between Riemannian optimization and the implicit function theorem. As a result, the updating our optimizer is only related to the final two iterations, which in turn speeds up our method and reduces the memory footprint significantly. We theoretically study the computational load and memory footprint of our method for long optimization trajectories, and conduct an empirical study to demonstrate the benefits of the proposed method. Evaluations of three optimization problems on different Riemannian manifolds show that our method achieves state-of-the-art performance in terms of the convergence speed and the quality of optima.

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Buell, Thomas J., Daniel M. S. Raper, Dale Ding, Ching-Jen Chen, Tony R. Wang, Davis G. Taylor, Adeel Ilyas, et al. "Concurrent Venous Stenting of the Transverse and Occipito-Marginal Sinuses: An Analogy with Parallel Hemodynamic Circuits." Journal of Neurosciences in Rural Practice 10, no. 02 (April 2019): 334–38. http://dx.doi.org/10.4103/jnrp.jnrp_259_18.

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ABSTRACTNonthrombotic intracranial venous occlusive disease (NIVOD) has been implicated in the pathophysiology of idiopathic intracranial hypertension (IIH) and various non-IIH headache syndromes. Endovascular stenting of stenotic, dominant transverse sinuses (TSs) may reduce trans-stenosis pressure gradients, decrease intracranial pressure, and alleviate symptoms in a subset of NIVOD patients. We present a case in which concurrent stenting of the occipito-marginal sinus obliterated the residual trans-stenosis pressure gradient across an initially stented dominant TS. We hypothesize that this observation may be explained using an electric-hydraulic analogy, and that this patient’s dominant TS and occipito-marginal sinus may be modeled as a parallel hemodynamic circuit. Neurointerventionalists should be aware of parallel hemodynamic drainage patterns and consider manometry and possibly additional stenting of stenotic, parallel venous outflow pathways if TS stenting alone fails to obliterate the trans-stenosis pressure gradient.

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Paramanantham, SalaiSargunan S., Dong-Hyun Kim, and Warn-Gyu Park. "Numerical Study of Bubble Behavior under Gradient Flows during Subcooled Flow Boiling in Vertical Flow Channel." Symmetry 12, no. 4 (April 12, 2020): 611. http://dx.doi.org/10.3390/sym12040611.

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In this study, we examined the condensing behavior of single and multiple bubbles of pure steam in a subcooled liquid phase using a fully compressible two-phase homogeneous mixture method that is solved by an implicit dual-time preconditioned technique. The interface between the liquid and vapor phases was determined by the advection equations using a compressive high-resolution interfacing capturing method. The spurious current reduced near the interface, a smoothing filter is applied to the progress curvature calculation. The sensitivity study carried out to predict the empirical constant by using Lee’s mass transfer model. A comparison of the numerical and experimental results highlighted that the proposed model accurately predicted the behavior of the definite condensing bubble. Furthermore, the single and multiple bubble condensation behaviors were investigated for different initial subcooled temperatures, and bubble diameters under various gradient flow, such as velocity gradient, temperature gradient, and velocity and temperature gradients. Subsequently, the effect of multiple bubbles flows in different bubble pattern forms, and their condensation was studied. The coalescence of bubbles depends on the subcooled temperature. Furthermore, the bubble diameter, the gap between the bubbles, and the flow rate of the bubbles were also observed.

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Li, Ye, Song-Can Chen, and Sheng-Jun Huang. "Implicit Stochastic Gradient Descent for Training Physics-Informed Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 7 (June 26, 2023): 8692–700. http://dx.doi.org/10.1609/aaai.v37i7.26046.

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Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit stochastic gradient descent (ISGD) method to train PINNs for improving the stability of training process. We heuristically analyze how ISGD overcome stiffness in the gradient flow dynamics of PINNs, especially for problems with multi-scale solutions. We theoretically prove that for two-layer fully connected neural networks with large hidden nodes, randomly initialized ISGD converges to a globally optimal solution for the quadratic loss function. Empirical results demonstrate that ISGD works well in practice and compares favorably to other gradient-based optimization methods such as SGD and Adam, while can also effectively address the numerical stiffness in training dynamics via gradient descent.

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Singh, Manish K., N. Munikrishna, V. Ramesh, and N. Balakrishnan. "Implicit gradient reconstruction (IGR) method for compressible flow simulation." Journal of Physics: Conference Series 822 (April 11, 2017): 012030. http://dx.doi.org/10.1088/1742-6596/822/1/012030.

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31

Fang, Yixin. "Scalable statistical inference for averaged implicit stochastic gradient descent." Scandinavian Journal of Statistics 46, no. 4 (February 4, 2019): 987–1002. http://dx.doi.org/10.1111/sjos.12378.

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Feng, Decheng, Xiaodan Ren, and Jie Li. "Implicit Gradient Delocalization Method for Force-Based Frame Element." Journal of Structural Engineering 142, no. 2 (February 2016): 04015122. http://dx.doi.org/10.1061/(asce)st.1943-541x.0001397.

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33

Tovo, R., and P. Livieri. "An implicit gradient application to fatigue of complex structures." Engineering Fracture Mechanics 75, no. 7 (May 2008): 1804–14. http://dx.doi.org/10.1016/j.engfracmech.2007.01.020.

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34

Zreid, Imadeddin, and Michael Kaliske. "An implicit gradient formulation for microplane Drucker-Prager plasticity." International Journal of Plasticity 83 (August 2016): 252–72. http://dx.doi.org/10.1016/j.ijplas.2016.04.013.

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Bui, Q. V. "Initiation of damage with implicit gradient-enhanced damage models." International Journal of Solids and Structures 47, no. 18-19 (September 2010): 2425–35. http://dx.doi.org/10.1016/j.ijsolstr.2010.05.003.

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Hadjidimos, A., and M. Lapidakis. "Optimal Alternating Direction Implicit Preconditioners for Conjugate Gradient methods." Applied Mathematics and Computation 183, no. 1 (December 2006): 559–74. http://dx.doi.org/10.1016/j.amc.2006.05.101.

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Zaitzeff, Alexander, Selim Esedoḡlu, and Krishna Garikipati. "Variational Extrapolation of Implicit Schemes for General Gradient Flows." SIAM Journal on Numerical Analysis 58, no. 5 (January 2020): 2799–817. http://dx.doi.org/10.1137/19m1283963.

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38

Geers, M. G. D., R. H. J. Peerlings, W. A. M. Brekelmans, and R. de Borst. "Phenomenological nonlocal approaches based on implicit gradient-enhanced damage." Acta Mechanica 144, no. 1-2 (March 2000): 1–15. http://dx.doi.org/10.1007/bf01181824.

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Simone, A., H. Askes, R. H. J. Peerlings, and L. J. Sluys. "Interpolation requirements for implicit gradient-enhanced continuum damage models." Communications in Numerical Methods in Engineering 19, no. 7 (April 9, 2003): 563–72. http://dx.doi.org/10.1002/cnm.597.

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Simone, A., H. Askes, R. H. J. Peerlings, and L. J. Sluys. "‘Interpolation requirements for implicit gradient-enhanced continuum damage models’." Communications in Numerical Methods in Engineering 20, no. 2 (January 21, 2004): 163–65. http://dx.doi.org/10.1002/cnm.663.

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41

Duan, Guangtao, and Bin Chen. "Comparison of parallel solvers for Moving Particle Semi-Implicit method." Engineering Computations 32, no. 3 (May 5, 2015): 834–62. http://dx.doi.org/10.1108/ec-02-2014-0029.

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Purpose – The purpose of this paper is to find the best solver for parallelizing particle methods based on solving Pressure Poisson Equation (PPE) by taking Moving Particle Semi-Implicit (MPS) method as an example because the solution for PPE is usually the most time-consuming part difficult to parallelize. Design/methodology/approach – To find the best solver, the authors compare six Krylov solvers, namely, Conjugate Gradient method (CG), Scaled Conjugate Gradient method (SCG), Bi-Conjugate Gradient Stabilized (BiCGStab) method, Conjugate Gradient Squared (CGS) method with Symmetric Lanczos Algorithm (SLA) method and Incomplete Cholesky Conjugate Gradient method (ICCG) in terms of convergence, time consumption, parallel efficiency and memory consumption for the semi-implicit particle method. The MPS method is parallelized by the hybrid Open Multi-Processing (OpenMP)/Message Passing Interface (MPI) model. The dam-break flow and channel flow simulations are used to evaluate the performance of different solvers. Findings – It is found that CG converges stably, runs fastest in the serial way, uses the least memory and has highest OpenMP parallel efficiency, but its MPI parallel efficiency is lower than SLA because SLA requires less synchronization than CG. Originality/value – With all these criteria considered and weighed, the recommended parallel solver for the MPS method is CG.

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42

Vardi, Gal. "On the Implicit Bias in Deep-Learning Algorithms." Communications of the ACM 66, no. 6 (May 24, 2023): 86–93. http://dx.doi.org/10.1145/3571070.

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Guo, Minghao, and Yan Gao. "Adaptive Approximate Implicitization of Planar Parametric Curves via Asymmetric Gradient Constraints." Symmetry 15, no. 9 (September 11, 2023): 1738. http://dx.doi.org/10.3390/sym15091738.

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Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, existing methods mostly suffer from the problems of maintaining geometric features and choosing a reasonable implicit degree. The present paper has two contributions. We first introduce a new regularization constraint (called the asymmetric gradient constraint) for both polynomial and non-polynomial curves, which efficiently possesses shape-preserving. We then propose two adaptive algorithms of approximate implicitization for polynomial and non-polynomial curves respectively, which find the “optimal” implicit degree based on the behavior of the asymmetric gradient constraint. More precisely, the idea is gradually increasing the implicit degree, until there is no obvious improvement in the asymmetric gradient loss of the outputs. Experimental results have shown the effectiveness and high quality of our proposed methods.

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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. "Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2239 (July 2020): 20200334. http://dx.doi.org/10.1098/rspa.2020.0334.

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We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

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Zhang, Yilang, Bingcong Li, Shijian Gao, and Georgios B. Giannakis. "Scalable Bayesian Meta-Learning through Generalized Implicit Gradients." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 9 (June 26, 2023): 11298–306. http://dx.doi.org/10.1609/aaai.v37i9.26337.

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Meta-learning owns unique effectiveness and swiftness in tackling emerging tasks with limited data. Its broad applicability is revealed by viewing it as a bi-level optimization problem. The resultant algorithmic viewpoint however, faces scalability issues when the inner-level optimization relies on gradient-based iterations. Implicit differentiation has been considered to alleviate this challenge, but it is restricted to an isotropic Gaussian prior, and only favors deterministic meta-learning approaches. This work markedly mitigates the scalability bottleneck by cross-fertilizing the benefits of implicit differentiation to probabilistic Bayesian meta-learning. The novel implicit Bayesian meta-learning (iBaML) method not only broadens the scope of learnable priors, but also quantifies the associated uncertainty. Furthermore, the ultimate complexity is well controlled regardless of the inner-level optimization trajectory. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one. Extensive numerical tests are also carried out to empirically validate the performance of the proposed method.

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Piersanti, Eleonora, Marie E. Rognes, and Vegard Vinje. "Are brain displacements and pressures within the parenchyma induced by surface pressure differences? A computational modelling study." PLOS ONE 18, no. 12 (December 27, 2023): e0288668. http://dx.doi.org/10.1371/journal.pone.0288668.

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The intracranial pressure is implicated in many homeostatic processes in the brain and is a fundamental parameter in several diseases such as e.g. idiopathic normal pressure hydrocephalus. The presence of a small but persistent pulsatile intracranial pulsatile transmantle pressure gradient (on the order of a few mmHg/m at peak) has recently been demonstrated in hydrocephalus subjects. A key question is whether pulsatile intracranial pressure and displacements can be induced by a small pressure gradient originating from the brain surface alone. In this study, we model the brain parenchyma as either a linearly elastic or a poroelastic medium, and impose a pulsatile pressure gradient acting between the ventricular and the pial surfaces but no additional external forces. Using this high-resolution physics-based model, we use in vivo pulsatile pressure gradients from subjects with idiopathic normal pressure hydrocephalus to compute parenchyma displacement, volume change, fluid pressure, and fluid flux. The resulting displacement field is pulsatile and in qualitatively and quantitatively good agreement with the literature, both with elastic and poroelastic models. However, the pulsatile forces on the boundaries are not sufficient for pressure pulse propagation through the brain parenchyma. Our results suggest that pressure differences at the brain surface, originating e.g. from pulsating arteries surrounding the brain, are not alone sufficient to drive interstitial fluid flow within the brain parenchyma and that potential pressure gradients found within the parenchyma rather arise from a large portion of the blood vessel network, including smaller blood vessels within the brain parenchyma itself.

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Buell, Thomas J., Daniel M. S. Raper, I. Jonathan Pomeraniec, Dale Ding, Ching-Jen Chen, Davis G. Taylor, and Kenneth C. Liu. "Transient resolution of venous sinus stenosis after high-volume lumbar puncture in a patient with idiopathic intracranial hypertension." Journal of Neurosurgery 129, no. 1 (July 2018): 153–56. http://dx.doi.org/10.3171/2017.3.jns163181.

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Stenosis of the transverse sinus (TS) and sigmoid sinus (SS), with a trans-stenosis pressure gradient, has been implicated in the pathophysiology of idiopathic intracranial hypertension (IIH). MRI has shown improvement in TS and SS stenosis after high-volume lumbar puncture (HVLP) in a subset of patients with IIH. The authors present the first report of an IIH patient with immediate post-HVLP TS and SS trans-stenosis pressure gradient reduction and an attendant increase in TS and SS cross-sectional area confirmed using intravascular ultrasonography (IVUS). Recurrence of the patient’s TS-SS stenosis coincided with elevated HVLP opening pressure, and venous sinus stent placement resulted in clinical improvement. This report suggests that TS and SS stenosis may be a downstream effect of elevated intracranial pressure in IIH, rather than its principal etiological mechanism. However, the authors hypothesize that endovascular stenting may obliterate a positive feedback loop involving trans-stenosis pressure gradients, and still benefit appropriately selected patients.

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Gerencser, G. A., and B. R. Stevens. "Energetics of sodium-coupled active transport mechanisms in invertebrate epithelia." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 257, no. 3 (September 1, 1989): R461—R472. http://dx.doi.org/10.1152/ajpregu.1989.257.3.r461.

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The Na+ gradient has been implicated as the sole or primary energy source for accumulative transport of organic solutes (e.g., sugars, amino acids) across the mucosal membrane of a variety of epithelial cells. A basic question concerning the Na+-coupled transport process in epithelia is whether the energy available from the transmucosal Na+ electrochemical difference is sufficient to sustain an accumulated organic solute steady-state level. Measurements of Na+ activities, with Na+-sensitive microelectrodes, gave accurate estimates of the Na+ electrochemical potential difference across the mucosal membrane of Aplysia californica gut. The results suggest that the transmucosal Na+ gradient can furnish sufficient energy to sustain the observed intracellular levels of the cotransported species. Many other species sustain large intracellular-extracellular gradients (less than 10(6):1) of free solutes. Theoretical models suggest that secondary active transport mechanisms in these epithelia operate by energetic multiple coupling to the Na+ electrochemical gradient; coupling coefficients of approximately 3 may represent an evolutionary optimization of these epithelial cotransporters. To properly investigate the cotransport mechanisms and energetics in invertebrate membranes, prototype mammalian vesicle experiments should be extended to the invertebrate laboratory.

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Amid, Ehsan, and Manfred K. Warmuth. "An Implicit Form of Krasulina's k-PCA Update without the Orthonormality Constraint." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 3179–86. http://dx.doi.org/10.1609/aaai.v34i04.5715.

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We shed new insights on the two commonly used updates for the online k-PCA problem, namely, Krasulina's and Oja's updates. We show that Krasulina's update corresponds to a projected gradient descent step on the Stiefel manifold of orthonormal k-frames, while Oja's update amounts to a gradient descent step using the unprojected gradient. Following these observations, we derive a more implicit form of Krasulina's k-PCA update, i.e. a version that uses the information of the future gradient as much as possible. Most interestingly, our implicit Krasulina update avoids the costly QR-decomposition step by bypassing the orthonormality constraint. A related update, called the Sanger's rule, can be seen as an explicit approximation of our implicit update. We show that the new update in fact corresponds to an online EM step applied to a probabilistic k-PCA model. The probabilistic view of the update allows us to combine multiple models in a distributed setting. We show experimentally that the implicit Krasulina update yields superior convergence while being significantly faster. We also give strong evidence that the new update can benefit from parallelism and is more stable w.r.t. tuning of the learning rate.

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50

Bansal, Anand, and P. Chaturani. "APPLYING INVERSE WOMERSLEY PROBLEM FOR INDIRECT DATA INTO GOOD QUALITY INPUT DATA FOR MATHEMATICAL MODELS OF BLOOD FLOW IN HUMAN." Jnanabha 51, no. 01 (2021): 232–38. http://dx.doi.org/10.58250/jnanabha.2021.51128.

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The aim of this investigation is to convert experimental flow rate profiles of human cardiovascular system (CVS) (Hwang and Normann [7], Tsangaris and Stergiopulos [11] and Milnor [15]) i.e. indirect input data to direct input data (pressure gradient) using implicit technique of finite difference in inverse Womersley problem. Further pressure gradient profiles have been presented into mathematical form in terms of Fourier series and shown through Figures. Fourier coefficients of pressure gradient profiles are given through Tables. The computer program has been prepared using the finite difference implicit technique and is presented through Appendix.

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