Higher-Order Rytov Approximation for Large-Scale and Strong Perturbation Media

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

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Efficient and High-Quality Seeded Graph Matching: Employing Higher-order Structural Information

ACM Transactions on Knowledge Discovery from Data ◽

10.1145/3442340 ◽

2021 ◽

Vol 15 (3) ◽

pp. 1-31

Author(s):

Haida Zhang ◽

Zengfeng Huang ◽

Xuemin Lin ◽

Zhe Lin ◽

Wenjie Zhang ◽

...

Keyword(s):

Large Scale ◽

Graph Matching ◽

Structural Information ◽

Experimental Studies ◽

Higher Order ◽

Personalized Pagerank ◽

Matching Accuracy ◽

Approximation Techniques ◽

Order Of Magnitude ◽

Matching Score

Driven by many real applications, we study the problem of seeded graph matching. Given two graphs and , and a small set of pre-matched node pairs where and , the problem is to identify a matching between and growing from , such that each pair in the matching corresponds to the same underlying entity. Recent studies on efficient and effective seeded graph matching have drawn a great deal of attention and many popular methods are largely based on exploring the similarity between local structures to identify matching pairs. While these recent techniques work provably well on random graphs, their accuracy is low over many real networks. In this work, we propose to utilize higher-order neighboring information to improve the matching accuracy and efficiency. As a result, a new framework of seeded graph matching is proposed, which employs Personalized PageRank (PPR) to quantify the matching score of each node pair. To further boost the matching accuracy, we propose a novel postponing strategy, which postpones the selection of pairs that have competitors with similar matching scores. We show that the postpone strategy indeed significantly improves the matching accuracy. To improve the scalability of matching large graphs, we also propose efficient approximation techniques based on algorithms for computing PPR heavy hitters. Our comprehensive experimental studies on large-scale real datasets demonstrate that, compared with state-of-the-art approaches, our framework not only increases the precision and recall both by a significant margin but also achieves speed-up up to more than one order of magnitude.

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Learning Graph Convolutional Network for Skeleton-Based Human Action Recognition by Neural Searching

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i03.5652 ◽

2020 ◽

Vol 34 (03) ◽

pp. 2669-2676 ◽

Cited By ~ 11

Author(s):

Wei Peng ◽

Xiaopeng Hong ◽

Haoyu Chen ◽

Guoying Zhao

Keyword(s):

Action Recognition ◽

Large Scale ◽

Order Approximation ◽

Human Action Recognition ◽

Search Space ◽

Human Action ◽

Higher Order ◽

Dynamic Graph ◽

Convolutional Network ◽

Representational Capacity

Human action recognition from skeleton data, fuelled by the Graph Convolutional Network (GCN) with its powerful capability of modeling non-Euclidean data, has attracted lots of attention. However, many existing GCNs provide a pre-defined graph structure and share it through the entire network, which can loss implicit joint correlations especially for the higher-level features. Besides, the mainstream spectral GCN is approximated by one-order hop such that higher-order connections are not well involved. All of these require huge efforts to design a better GCN architecture. To address these problems, we turn to Neural Architecture Search (NAS) and propose the first automatically designed GCN for this task. Specifically, we explore the spatial-temporal correlations between nodes and build a search space with multiple dynamic graph modules. Besides, we introduce multiple-hop modules and expect to break the limitation of representational capacity caused by one-order approximation. Moreover, a corresponding sampling- and memory-efficient evolution strategy is proposed to search in this space. The resulted architecture proves the effectiveness of the higher-order approximation and the layer-wise dynamic graph modules. To evaluate the performance of the searched model, we conduct extensive experiments on two very large scale skeleton-based action recognition datasets. The results show that our model gets the state-of-the-art results in term of given metrics.

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Finite-frequency traveltime tomography using the Generalized Rytov approximation

Geophysical Journal International ◽

10.1093/gji/ggaa067 ◽

2020 ◽

Vol 221 (2) ◽

pp. 1412-1426 ◽

Cited By ~ 1

Author(s):

B Feng ◽

W Xu ◽

R S Wu ◽

X B Xie ◽

H Wang

Keyword(s):

Convergence Rate ◽

Large Scale ◽

Frequency Theory ◽

Seismic Exploration ◽

Finite Frequency ◽

Traveltime Tomography ◽

Sensitivity Kernel ◽

Rytov Approximation ◽

Weak Scattering ◽

Small Phase

SUMMARY Wave-equation-based traveltime tomography has been extensively applied in both global tomography and seismic exploration. Typically, the traveltime Fréchet derivative is obtained using the first-order Born approximation, which is only satisfied for weak velocity perturbations and small phase shifts (i.e. the weak-scattering assumption). Although the small phase-shift restriction can be handled with the Rytov approximation, the weak velocity-perturbation assumption is still a major limitation. The recently developed generalized Rytov approximation (GRA) method can achieve an improved phase accuracy of the forward-scattered wavefield, in the presence of large-scale and strong velocity perturbations. In this paper, we combine GRA with the classical finite-frequency theory and propose a GRA-based traveltime sensitivity kernel (GRA-TSK), which overcomes the weak-scattering limitation of the conventional finite-frequency methods. Numerical examples demonstrate that the accumulated time delay of forward-scattered waves caused by large-scale smooth perturbations can be correctly handled by the GRA-TSK, regardless of the magnitude of the velocity perturbations. Then, we apply the new sensitivity kernel to solve the traveltime inverse problem, and we propose a matrix-free Gauss–Newton method that has a faster convergence rate compared with the gradient-based method. Numerical tests show that, compared with the conventional adjoint traveltime tomography, the proposed GRA-based traveltime tomography can obtain a more accurate model with a faster convergence rate, making it more suited for recovering the large-intermediate scale of the velocity model, even for strong-perturbation and complex subsurface structures.

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Clustered CTCF binding is an evolutionary mechanism to maintain topologically associating domains

Genome Biology ◽

10.1186/s13059-019-1894-x ◽

2020 ◽

Vol 21 (1) ◽

Cited By ~ 13

Author(s):

Elissavet Kentepozidou ◽

Sarah J. Aitken ◽

Christine Feig ◽

Klara Stefflova ◽

Ximena Ibarra-Soria ◽

...

Keyword(s):

Large Scale ◽

Evolutionary Dynamics ◽

Computational Study ◽

Genome Structure ◽

Higher Order ◽

Ctcf Binding ◽

Natural Genetic Variation ◽

Transcription Start Sites ◽

Topologically Associating Domains ◽

Species Specific

Abstract Background CTCF binding contributes to the establishment of a higher-order genome structure by demarcating the boundaries of large-scale topologically associating domains (TADs). However, despite the importance and conservation of TADs, the role of CTCF binding in their evolution and stability remains elusive. Results We carry out an experimental and computational study that exploits the natural genetic variation across five closely related species to assess how CTCF binding patterns stably fixed by evolution in each species contribute to the establishment and evolutionary dynamics of TAD boundaries. We perform CTCF ChIP-seq in multiple mouse species to create genome-wide binding profiles and associate them with TAD boundaries. Our analyses reveal that CTCF binding is maintained at TAD boundaries by a balance of selective constraints and dynamic evolutionary processes. Regardless of their conservation across species, CTCF binding sites at TAD boundaries are subject to stronger sequence and functional constraints compared to other CTCF sites. TAD boundaries frequently harbor dynamically evolving clusters containing both evolutionarily old and young CTCF sites as a result of the repeated acquisition of new species-specific sites close to conserved ones. The overwhelming majority of clustered CTCF sites colocalize with cohesin and are significantly closer to gene transcription start sites than nonclustered CTCF sites, suggesting that CTCF clusters particularly contribute to cohesin stabilization and transcriptional regulation. Conclusions Dynamic conservation of CTCF site clusters is an apparently important feature of CTCF binding evolution that is critical to the functional stability of a higher-order chromatin structure.

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Higher-order massive neutrino perturbations in large-scale structure

Journal of Cosmology and Astroparticle Physics ◽

10.1088/1475-7516/2015/03/046 ◽

2015 ◽

Vol 2015 (03) ◽

pp. 046-046 ◽

Cited By ~ 26

Author(s):

Florian Führer ◽

Yvonne Y.Y. Wong

Keyword(s):

Large Scale ◽

Large Scale Structure ◽

Higher Order ◽

Scale Structure ◽

Massive Neutrino

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A Higher-Order Closure Model with an Explicit PBL Top

Journal of the Atmospheric Sciences ◽

10.1175/2009jas3205.1 ◽

2010 ◽

Vol 67 (3) ◽

pp. 834-850 ◽

Cited By ~ 4

Author(s):

Cara-Lyn Lappen ◽

David Randall ◽

Takanobu Yamaguchi

Keyword(s):

Large Scale ◽

Computational Cost ◽

Higher Order ◽

Entrainment Rate ◽

Time Step ◽

Vertical Coordinate ◽

Second Moments ◽

Scale Models ◽

Vertical Grid ◽

Flux Model

Abstract In 2001, the authors presented a higher-order mass-flux model called “assumed distributions with higher-order closure” (ADHOC 1), which represents the large eddies of the planetary boundary layer (PBL) in terms of an assumed joint distribution of the vertical velocity and scalars. In a subsequent version (ADHOC 2) the authors incorporated vertical momentum fluxes and second moments involving pressure perturbations into the framework. These versions of ADHOC, as well as all other higher-order closure models, are not suitable for use in large-scale models because of the high vertical and temporal resolution that is required. This high resolution is needed mainly because higher-order closure (HOC) models must resolve discontinuities at the PBL top, which can occur anywhere on a model’s Eulerian vertical grid. This paper reports the development of ADHOC 3, in which the computational cost of the model is reduced by introducing the PBL depth as an explicit prognostic variable. ADHOC 3 uses a stretched vertical coordinate that is attached to the PBL top. The discontinuous jumps at the PBL top are “hidden” in the layer edge that represents the PBL top. This new HOC model can use much coarser vertical resolution and a longer time step and is thus suitable for use in large-scale models. To predict the PBL depth, an entrainment parameterization is needed. In the development of the model, the authors have been led to a new view of the old problem of entrainment parameterization. The relatively detailed information available in the HOC model is used to parameterize the entrainment rate. The present approach thus borrows ideas from mixed-layer modeling to create a new, more economical type of HOC model that is better suited for use as a parameterization in large-scale models.

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Reduction of higher order mode generation in large scale gravitational wave interferometers by central heating residual aberration correction

Physical Review D ◽

10.1103/physrevd.87.082003 ◽

2013 ◽

Vol 87 (8) ◽

Cited By ~ 16

Author(s):

R. A. Day ◽

G. Vajente ◽

M. Kasprzack ◽

J. Marque

Keyword(s):

Gravitational Wave ◽

Large Scale ◽

Higher Order ◽

Aberration Correction ◽

Order Mode ◽

Central Heating ◽

Residual Aberration ◽

Higher Order Mode ◽

Mode Generation

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Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method

Advances in Radio Science ◽

10.5194/ars-12-1-2014 ◽

2014 ◽

Vol 12 ◽

pp. 1-11

Author(s):

L. Li ◽

K. Wang ◽

H. Li ◽

T. F. Eibert

Keyword(s):

Finite Element ◽

Large Scale ◽

Higher Order ◽

Boundary Integral ◽

Basis Functions ◽

Boundary Integral Method ◽

Matrix Elements ◽

Matrix Assembly ◽

Time Accuracy ◽

Element Boundary

Abstract. A hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This assembly procedure applys to both, the FE part as well as the BI part of the algorithm. The geometry is meshed into three-dimensional tetrahedra as finite elements and nearly orthogonal hierarchical basis functions are employed. The boundary conditions are implemented in a strong sense such that the boundary values of the volume basis functions are directly utilized within the BI, either for the tangential electric and magnetic fields or for the asssociated equivalent surface current densities by applying a cross product with the unit surface normals. The self-identified method for the global matrix assembly automatically discerns the global order of the basis functions for generating the matrix elements. Higher order basis functions do need more unknowns for each single FE, however, fewer FEs are needed to achieve the same satisfiable accuracy. This improvement provides a lot more flexibility for meshing and allows the mesh size to raise up to λ/3. The performance of the implemented system is evaluated in terms of computation time, accuracy and memory occupation, where excellent results with respect to precision and computation times of large scale simulations are found.

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Higher order schemes in time for the surface quasi-geostrophic system under location uncertainty

10.5194/egusphere-egu21-10935 ◽

2021 ◽

Author(s):

Camilla Fiorini ◽

Long Li ◽

Étienne Mémin

Keyword(s):

Fluid Dynamics ◽

Large Scale ◽

Higher Order ◽

Small Scale ◽

Milstein Scheme ◽

Location Uncertainty ◽

Stochastic Transport ◽

Smooth Component ◽

Lagrangian Velocity ◽

Optimal Polynomial

In this work we consider the surface quasi-geostrophic (SQG) system under location uncertainty (LU) and propose a Milstein-type scheme for these equations. The LU framework, first introduced in [1], is based on the decomposition of the Lagrangian velocity into two components: a large-scale smooth component and a small-scale stochastic one. This decomposition leads to a stochastic transport operator, and one can, in turn, derive the stochastic LU version of every classical fluid-dynamics system.&#160;&#160; &#160; SQG is a simple 2D oceanic model with one partial differential equation, which models the stochastic transport of the buoyancy, and an operator which relies the velocity and the buoyancy.&#160; &#160; For this kinds of equations, the Euler-Maruyama scheme converges with weak order 1 and strong order 0.5. Our aim is to develop higher order schemes in time: the first step is to consider Milstein scheme, which improves the strong convergence to the order 1. To do this, it is necessary to simulate or estimate the L&#233;vy area [2].&#160; &#160; We show with some numerical results how the Milstein scheme is able to capture some of the smaller structures of the dynamic even at a poor resolution.&#160;References[1] E. M&#233;min. Fluid flow dynamics under location uncertainty. Geophysical & Astrophysical Fluid Dynamics, 108.2 (2014): 119-146.&#160;[2] J. Foster, T. Lyons and H. Oberhauser. An optimal polynomial approximation of Brownian motion. SIAM Journal on Numerical Analysis 58.3 (2020): 1393-1421.

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