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arXiv 2020年

作者： Zhang, Na Li, Qia Department of Applied Mathematics College of Mathematics and Informatics South China Agricultural University Guangzhou510642 China Guangdong Province Key Laboratory of Computational Science School of Data and Computer Sciences Sun Yat-sen University Guangzhou510275 China

We consider in this paper a class of single-ratio fractional minimization problems, in which the numerator part of the objective is the sum of a nonsmooth nonconvex function and a smooth nonconvex function while the denominator part is a nonsmooth convex function. Besides, the three functions involved in the objective are all nonnegative. To the best of our knowledge, this class of problems has seldom been carefully investigated in the literature and existing methods in general fractional optimization are not suitable for solving this problem. In this work, we first derive its first-order necessary optimality condition, by using the first-order operators of the three functions involved. Then we develop first-order algorithms, namely, the proximity-gradient-subgradient algorithm (PGSA), PGSA with monotone line search (PGSA_ML) and PGSA with nonmonotone line search (PGSA_NL). It is shown that any accumulation point of the sequence generated by them is a critical point of the problem under mild assumptions. Moreover, we establish global convergence of the sequence generated by PGSA or PGSA_ML and analyze its convergence rate, by further assuming the local Lipschitz continuity of the nonsmooth function in the numerator part, the smoothness of the denominator part and the Kurdyka-Lojasiewicz property of the objective. The proposed algorithms are applied to the sparse generalized eigenvalue problem associated with a pair of symmetric positive semidefinite matrices and the corresponding convergence results are obtained according to their general convergence theorems. We perform some preliminary numerical experiments to demonstrate the efficiency of the proposed *** Codes 90C26, 90C30, 65K05 Copyright © 2020, The Authors. All rights reserved.

关键词： Optimization

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Estimating axon radius using diffusion-relaxation MRI: Calibrating a surface-based relaxation model with histology

arXiv

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arXiv 2023年

作者： Barakovic, Muhamed Pizzolato, Marco Tax, Chantal M.W. Rudrapatna, Umesh Magon, Stefano Dyrby, Tim B. Granziera, Cristina Thiran, Jean-Philippe Jones, Derek K. Canales-Rodríguez, Erick J. Basel Department of Biomedical Engineering University Hospital Basel University of Basel Basel Switzerland Department of Neurology University Hospital Basel Switzerland Cardiff University Brain Research Imaging Centre Cardiff University Wales Cardiff United Kingdom Lausanne Switzerland Roche Pharma Research & Early Development Neuroscience and Rare Diseases Roche Innovation Center Basel Switzerland Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby Denmark Image Sciences Institute University Medical Center Utrecht Netherlands Danish Research Centre for Magnetic Resonance Centre for Functional and Diagnostic Imaging and Research Copenhagen University Hospital Amager & Hvidovre Hvidovre Denmark University Hospital Basel University of Basel Basel Switzerland Radiology Department Centre Hospitalier Universitaire Vaudois University of Lausanne Lausanne Switzerland EPFL Lausanne Switzerland

Axon radius is a potential biomarker for brain diseases and a crucial tissue microstructure parameter that determines the speed of action potentials. Diffusion MRI (dMRI) allows non-invasive estimation of axon radius, but accurately estimating the radius of axons in the human brain is challenging. Most axons in the brain have a radius below one micrometre, which falls below the sensitivity limit of dMRI signals even when using the most advanced human MRI scanners. Therefore, new MRI methods that are sensitive to small axon radii are needed. In this proof-of-concept investigation, we examine whether a surface-based axonal relaxation process could mediate a relationship between intra-axonal T2 and T1 times and inner axon radius, as measured using postmortem histology. A unique in vivo human diffusion-T1-T2 relaxation dataset was acquired on a 3T MRI scanner with ultra-strong diffusion gradients, using a strong diffusion-weighting (i.e., b=6000 s/mm2) and multiple inversion and echo times. A second reduced diffusion-T2 dataset was collected at various echo times to evaluate the model further. The intra-axonal relaxation times were estimated by fitting a diffusion-relaxation model to the orientation-averaged spherical mean signals. Our analysis revealed that the proposed surface-based relaxation model effectively explains the relationship between the estimated relaxation times and the histological axon radius measured in various corpus callosum regions. Using these histological values, we developed a novel calibration approach to predict axon radius in other areas of the corpus callosum. Notably, the predicted radii and those determined from histological measurements were in close agreement. © 2023, CC BY-NC-ND.

关键词： Magnetic resonance imaging

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High-order semi-Lagrangian kinetic scheme for compressible turbulence

引用

Physical Review E 2021年第2期104卷 025301-025301页

作者： Dominik Wilde Andreas Krämer Dirk Reith Holger Foysi Department of Mechanical Engineering University of Siegen Paul-Bonatz-Straße 9-11 57076 Siegen-Weidenau Germany Institute of Technology Resource and Energy-efficient Engineering (TREE) Bonn-Rhein-Sieg University of Applied Sciences Grantham-Allee 20 53757 Sankt Augustin Germany Department of Mathematics and Computer Science Freie Universität Berlin Arnimallee 6 14195 Berlin Germany Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven 53754 Sankt Augustin Germany

Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time-step size. Exploiting the Lagrangian nature of the Boltzmann equation's material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques other than the filtering introduced by the interpolation, even when the time-step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time-step sizes is dictated by physics rather than spatial discretization.

关键词： Compressible flows Kinetic theory Turbulence Lattice-Boltzmann methods Navier-Stokes equation

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Reduction of Server Load by Means of CMS Drupal

Reduction of Server Load by Means of CMS Drupal

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International Conference on Advanced computer Information Technologies (ACIT)

作者： Viktor Satsyk Roman Grudetsky Olena Kuzmych Nataliia Bahniuk Liudmyla Hlynchuk Yulia Melnychuk Department of Automation and Computer-Integrated Technologies Lutsk National Technical University Lutsk Ukraine Department of Computer Engineering and Cyber Security Lutsk National Technical University Lutsk Ukraine Department of Applied Mathematics Eastern European National University Lutsk Ukraine Department of Computer Science Lutsk National Technical University Lutsk Ukraine

ISBN: (数字)9781728167602

ISBN: (纸本)9781728167619

In this paper description and analysis of simple methods of reducing (neutralization) the server load, as well as methods of optimization of Drupal based on embedded and additionally installed modules is done. An optimization of Drupal configuration and service, server optimization is also proposed. Direct SQL queries and the Drupal Database API has been tested on real-developed XML-PHP interaction web-site. Descriptive and graphical test results are displayed on the webpages of the developed web-site.

关键词： Servers Optimization Databases Task analysis Mirrors IP networks computer security

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Global Guarantees for Blind Demodulation with Generative Priors

arXiv

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arXiv 2019年

作者： Hand, Paul Joshi, Babhru Department of Mathematics College of Computer and Information Science Northeastern University Department of Computational and Applied Mathematics Rice University

We study a deep learning inspired formulation for the blind demodulation problem, which is the task of recovering two unknown vectors from their entrywise multiplication. We consider the case where the unknown vectors are in the range of known deep generative models, G(1) : Rn → R` and G(2) : Rp → R`. In the case when the networks corresponding to the generative models are expansive, the weight matrices are random and the dimension of the unknown vectors satisfy ` = Ω(n2 + p2), up to log factors, we show that the empirical risk objective has a favorable landscape for optimization. That is, the objective function has a descent direction at every point outside of a small neighborhood around four hyperbolic curves. We also characterize the local maximizers of the empirical risk objective and, hence, show that there does not exist any other stationary points outside of these neighborhood around four hyperbolic curves and the set of local maximizers. We also implement a gradient descent scheme inspired by the geometry of the landscape of the objective function. In order to converge to a global minimizer, this gradient descent scheme exploits the fact that exactly one of the hyperbolic curve corresponds to the global minimizer, and thus points near this hyperbolic curve have a lower objective value than points close to the other spurious hyperbolic curves. We show that this gradient descent scheme can effectively remove distortions synthetically introduced to the MNIST dataset. Copyright © 2019, The Authors. All rights reserved.

关键词： Gradient methods

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Multidimensional TV-stokes for image processing

arXiv

引用

arXiv 2020年

作者： Wu, Bin Tai, Xue-Cheng Rahman, Talal Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Inndalsveien 28 Bergen5063 Norway Department of Mathematics University of Bergen Allégaten 41 Bergen5007 Norway

A complete multidimential TV-Stokes model is proposed based on smoothing a gradient field in the first step and reconstruction of the multidimensional image from the gradient field. It is the correct extension of the original two dimensional TV-Stokes to multidimensions. Numerical algorithm using the Chambolle’s semi-implicit dual formula is proposed. Numerical results applied to denoising 3D images and movies are presented. They show excellent performance in avoiding the staircase effect, and preserving fine structures. Copyright © 2020, The Authors. All rights reserved.

关键词： Image reconstruction

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Beyond accuracy: generalization properties of bio-plausible temporal credit assignment rules

arXiv

引用

arXiv 2022年

作者： Liu, Yuhan Helena Ghosh, Arna Richards, Blake A. Shea-Brown, Eric Lajoie, Guillaume Department of Applied Mathematics University of Washington SeattleWA United States Allen Institute for Brain Science 615 Westlake Ave N SeattleWA United States Computational Neuroscience Center University of Washington SeattleWA United States School of Computer Science McGill University MontrealQC Canada Mila - Quebec AI Institute MontrealQC Canada Department of Neurology and Neurosurgery Montreal Neurological Institute McGill University MontrealQC Canada Canada CIFAR AI Chair CIFAR TorontoON Canada Dept. de Mathématiques et Statistiques Université de Montréal MontrealQC Canada

To unveil how the brain learns, ongoing work seeks biologically-plausible approximations of gradient descent algorithms for training recurrent neural networks (RNNs). Yet, beyond task accuracy, it is unclear if such learning rules converge to solutions that exhibit different levels of generalization than their non-biologically-plausible counterparts. Leveraging results from deep learning theory based on loss landscape curvature, we ask: how do biologically-plausible gradient approximations affect generalization? We first demonstrate that state-of-the-art biologically-plausible learning rules for training RNNs exhibit worse and more variable generalization performance compared to their machine learning counterparts that follow the true gradient more closely. Next, we verify that such generalization performance is correlated significantly with loss landscape curvature, and we show that biologically-plausible learning rules tend to approach high-curvature regions in synaptic weight space. Using tools from dynamical systems, we derive theoretical arguments and present a theorem explaining this phenomenon. This predicts our numerical results, and explains why biologically-plausible rules lead to worse and more variable generalization properties. Finally, we suggest potential remedies that could be used by the brain to mitigate this effect. To our knowledge, our analysis is the first to identify the reason for this generalization gap between artificial and biologically-plausible learning rules, which can help guide future investigations into how the brain learns solutions that generalize. © 2022, CC BY-NC-SA.

关键词： Recurrent neural networks

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Alternating minimization for a single step tv-stokes model for image denoising

arXiv

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arXiv 2020年

The paper presents a fully coupled TV-Stokes model, and propose an algorithm based on an alternating minimization of the objective functional, whose first iteration is exactly the same as the modified TV-Stokes model proposed earlier. The model is also a generalization of the second order Total Generalized Variation model. A convergence analysis is given. Copyright © 2020, The Authors. All rights reserved.

关键词： Image denoising

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Explaining heterogeneity in medial entorhinal cortex with task-driven neural networks 21

Explaining heterogeneity in medial entorhinal cortex with ta...

引用

Proceedings of the 35th International Conference on Neural Information Processing Systems

作者： Aran Nayebi Alexander Attinger Malcolm G. Campbell Kiah Hardcastle Isabel I.C. Low Caitlin S. Mallory Gabriel C. Mel Ben Sorscher Alex H. Williams Surya Ganguli Lisa M. Giocomo Daniel L.K. Yamins Neurosciences Ph.D. Program Stanford University Department of Neurobiology Stanford University Neurosciences Ph.D. Program Stanford University and Department of Neurobiology Stanford University and Wu Tsai Neurosciences Institute Stanford University Department of Applied Physics Stanford University Department of Statistics Stanford University and Wu Tsai Neurosciences Institute Stanford University Department of Applied Physics Stanford University and Wu Tsai Neurosciences Institute Stanford University and Facebook AI Research Facebook Inc. Department of Neurobiology Stanford University and Wu Tsai Neurosciences Institute Stanford University Department of Computer Science Stanford University and Department of Psychology Stanford University and Wu Tsai Neurosciences Institute Stanford University

ISBN: (纸本)9781713845393

Medial entorhinal cortex (MEC) supports a wide range of navigational and memory related behaviors. Well-known experimental results have revealed specialized cell types in MEC — e.g. grid, border, and head-direction cells — whose highly stereotypical response profiles are suggestive of the role they might play in supporting MEC functionality. However, the majority of MEC neurons do not exhibit stereotypical firing patterns. How should the response profiles of these more "heterogeneous" cells be described, and how do they contribute to behavior? In this work, we took a computational approach to addressing these questions. We first performed a statistical analysis that shows that heterogeneous MEC cells are just as reliable in their response patterns as the more stereotypical cell types, suggesting that they have a coherent functional role. Next, we evaluated a spectrum of candidate models in terms of their ability to describe the response profiles of both stereotypical and heterogeneous MEC cells. We found that recently developed task-optimized neural network models are substantially better than traditional grid cell-centric models at matching most MEC neuronal response profiles — including those of grid cells themselves — despite not being explicitly trained for this purpose. Specific choices of network architecture (such as gated nonlinearities and an explicit intermediate place cell representation) have an important effect on the ability of the model to generalize to novel scenarios, with the best of these models closely approaching the noise ceiling of the data itself. We then performed in silico experiments on this model to address questions involving the relative functional relevance of various cell types, finding that heterogeneous cells are likely to be just as involved in downstream functional outcomes (such as path integration) as grid and border cells. Finally, inspired by recent data showing that, going beyond their spatial response selectivity, MEC cells

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Sparse-data based 3d surface reconstruction with vector matching

arXiv

引用

arXiv 2020年

Three dimensional surface reconstruction based on two dimensional sparse information in the form of only a small number of level lines of the surface with moderately complex structures, containing both structured and unstructured geometries, is considered in this paper. A new model has been proposed which is based on the idea of using normal vector matching combined with a first order and a second order total variation regularizers. A fast algorithm based on the augmented Lagrangian is also proposed. Numerical experiments are provided showing the effectiveness of the model and the algorithm in reconstructing surfaces with detailed features and complex structures for both synthetic and real world digital maps. Copyright © 2020, The Authors. All rights reserved.

关键词： Constrained optimization

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