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Wavelet based data reduction and compression scheme for high volume scientific data

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Tongxin Xuebao/Journal on Communication 2008年第SUPPL.期29卷 91-95页

作者： Wu, Guo-Qing Chen, Hong Postgraduate Department China Academic of Engineering Physics Beijing 100088 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

To handle high volume numerical data from simulations, a data reduction and compression scheme based on discrete wavelet transform was presented. By discrete wavelet transform, most energy of scientific data is concentrated into a smaller region. Wavelet coefficients can be selected by thresholded and still retain high percentage of energy of the original data. To optimize the threshold, objection function is constructed to balance model accuracy and data reduction. Reduced coefficients are then quantized and finally entropy encoded. Signal noise ratio and relative energy error are used to evaluate precision loss of data in the whole process. To show applicability of scheme, results obtained with plasma simulation data is presented. Extension of the work leads to efficient analysis and understanding of the GB or TB volume scientific data.

关键词： Discrete wavelet transforms

Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning

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arXiv 2024年

作者： Shah, Ashka DePavia, Adela Hudson, Nathaniel Foster, Ian Stevens, Rick Department of Computer Science University of Chicago ChicagoIL United States Committee on Computational and Applied Mathematics University of Chicago ChicagoIL United States Data Science and Learning Division Argonne National Laboratory LemontIL United States

The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect relationships in a generalized way-without necessarily tailoring to a specific domain. Causal discovery algorithms search over a structured hypothesis space, defined by the set of directed acyclic graphs, to find the graph that best explains the data. For high-dimensional problems, however, this search becomes intractable and scalable algorithms for causal discovery are needed to bridge the gap. In this paper, we define a novel causal graph partition that allows for divide-and-conquer causal discovery with theoretical guarantees. We leverage the idea of a superstructure-a set of learned or existing candidate hypotheses-to partition the search space. We prove under certain assumptions that learning with a causal graph partition always yields the Markov Equivalence Class of the true causal graph. We show our algorithm achieves comparable accuracy and a faster time to solution for biologically-tuned synthetic networks and networks up to 104 variables. This makes our method applicable to gene regulatory network inference and other domains with high-dimensional structured hypothesis spaces. © 2024, CC BY.

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An extended hybrid numerical simulation of isotropic compressible turbulence

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arXiv 2017年

作者： Liu, Luoqin Wang, J.C. Shi, Y.P. Chen, S.Y. He, X.T. State Key Laboratory for Turbulence and Complex Systems Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen518055 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

This paper presents an extension of the hybrid scheme proposed by Wang et al. (J. Comput. Phys. 229 (2010) 169-180) for numerical simulation of compressible isotropic turbulence to flows with higher turbulent Mach numbers. The scheme still utilizes an 8th-order compact scheme with built-in hyperviscosity for smooth regions and a 7th-order WENO scheme for highly compressive regions, but now both in their conservation formulations and for the latter with the Roe type characteristic-wise reconstruction. To enhance the robustness of the WENO scheme without compromising its high-resolution and accuracy, the recursive-order-reduction procedure is adopted, where a new type of reconstruction-failure-detection criterion is constructed. To capture the upwind direction properly in extreme conditions, the global Lax-Friedrichs numerical flux is used. In addition, a new form of cooling function is proposed, which is proved to be positivity-preserving. With these techniques, the new scheme not only inherits the good properties of the original one but also extends largely the computable range of turbulent Mach number, which has been further confirmed by numerical results. Copyright © 2017, The Authors. All rights reserved.

关键词： Turbulence

Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation

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arXiv 2024年

作者： An, Dong Childs, Andrew M. Lin, Lin Ying, Lexing Beijing International Center for Mathematical Research Peking University China Joint Center for Quantum Information and Computer Science University of Maryland College Park United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Department of Mathematics University of California Berkeley United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley United States Challenge Institute for Quantum Computation University of California Berkeley United States Department of Mathematics Stanford University United States Institute for Computational and Mathematical Engineering Stanford University United States

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are well studied, eigenvalue transformations are distinct, especially for non-normal matrices. We propose an efficient quantum algorithm for performing a class of eigenvalue transformations that can be expressed as a certain type of matrix Laplace transformation. This allows us to significantly extend the recently developed linear combination of Hamiltonian simulation (LCHS) method [An, Liu, Lin, Phys. Rev. Lett. 131, 150603, 2023;An, Childs, Lin, arXiv:2312.03916] to represent a wider class of eigenvalue transformations, such as powers of the matrix inverse, A-k, and the exponential of the matrix inverse, e-A-1. The latter can be interpreted as the solution of a mass-matrix differential equation of the form Au′(t) = -u(t). We demonstrate that our eigenvalue transformation approach can solve this problem without explicitly inverting A, reducing the computational complexity. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

Topological coordinates for deformed nanotubes

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AIP Conference Proceedings 2003年第1期685卷 423-426页

作者： István László André Rassat *Department of Theoretical Physics Institute of Physics Budapest University of Technology and Economics BUTE Center for Applied Mathematics and Computational Physics H‐1521 Budapest Hungary †Département de Chimie Ecole Normale Supérieure 24 rue Lhomond 75231 Paris Cedex 05 France

Starting from the topological arrangement of carbon atoms an algorithm is given for the construction of nanotube Cartesian coordinates. The final relaxed structures were obtained by a molecular mechanics calculation where the carbon‐carbon interactions were supposed only between neighboring atoms of the initial tiling. In a given tiling we obtained toroidal or helical structures depending on the special position of the super cell parallelogram.

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Decoherence, entanglement negativity, and circuit complexity for an open quantum system

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Physical Review D 2023年第10期107卷 106007-106007页

作者： Arpan Bhattacharyya Tanvir Hanif S. Shajidul Haque Arpon Paul Indian Institute of Technology Gandhinagar Gujarat-382355 India Department of Theoretical Physics University of Dhaka Dhaka-1000 Bangladesh High Energy Physics Cosmology and Astrophysics Theory Group and The Laboratory for Quantum Gravity and Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town-7700 South Africa National Institute for Theoretical and Computational Sciences (NITheCS) South Africa University of Minnesota Twin Cities Minneapolis Minnesota 55455 USA

In this paper, we compare the saturation timescales for complexity, linear entropy, and entanglement negativity for two open quantum systems. Our first model is a coupled harmonic oscillator, where we treat one of the oscillators as the bath. The second one is a type of Caldeira-Leggett model, where we consider a one-dimensional free scalar field as the bath. Using these open quantum systems, we discovered that both the complexity of purification and the complexity from operator-state mapping is always saturated for a completely mixed state. More explicitly, the saturation timescale for both types of complexity is smaller than the saturation timescale for linear entropy. On top of this, we found that the saturation timescale for linear entropy and entanglement negativity is of the same order for the Caldeira-Leggett model.

关键词： Gauge-gravity dualities Open quantum systems & decoherence computational complexity

SPDE for stochastic SIR epidemic models with infection-age dependent infectivity

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arXiv 2024年

作者： Pang, Guodong Pardoux, Étienne Department of Computational Applied Mathematics and Operations Research George R. Brown School of Engineering Rice University HoustonTX77005 United States Aix–Marseille Univ. CNRS I2M Marseille France

We study the stochastic SIR epidemic model with infection-age dependent infectivity for which a measure-valued process is used to describe the ages of infection for each individual. We establish a functional law large numbers (FLLN) and a functional central limit theorem (FCLT) for the properly scaled measure-valued processes together with the other epidemic processes to describe the evolution dynamics. In the FLLN, assuming that the hazard rate function of the infection periods is bounded and the ages at time 0 of the infections of the initially infected individuals are bounded, we obtain a PDE limit for the LLN-scaled measure-valued process, for which we characterize its solution explicitly. The PDE is linear with a boundary condition given by the unique solution to a set of Volterra-type nonlinear integral equations. In the FCLT, we obtain an SPDE for the CLT-scaled measure-valued process, driven by two independent white noises coming from the infection and recovery processes. The SPDE is also linear and coupled with the solution to a system of stochastic Volterra-type linear integral equations driven by three independent Gaussian noises, one from the random infection functions in addition to the two white noises mentioned above. The solution to the SPDE can be also explicitly characterized, given this auxiliary process. The uniqueness of the SPDE solution is established under stronger assumptions (density and its derivative being locally bounded) on the distribution function of an infectious duration. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Critical mass effect in evolutionary games triggered by zealots

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arXiv 2019年

作者： Cardillo, Alessio Masuda, Naoki Department of Engineering Mathematics University of Bristol BristolBS8 1UB United Kingdom Department of Computer Science and Mathematics University Rovira i Virgili TarragonaE-43007 Spain University of Zaragoza ZaragozaE-50018 Spain Department of Mathematics University at Buffalo BuffaloNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program University at Buffalo State University of New York BuffaloNY14260-5030 United States

Tiny perturbations may trigger large responses in systems near criticality, shifting them across equilibria. Committed minorities are suggested to be responsible for the emergence of collective behaviors in many physical, social, and biological systems. Using evolutionary game theory, we address the question whether a finite fraction of zealots can drive the system to large-scale coordination. We find that a tipping point exists in coordination games, whereas the same phenomenon depends on the selection pressure, update rule, and network structure in other types of games. Our study paves the way to understand social systems driven by the individuals’ benefit in presence of zealots, such as human vaccination behavior or cooperative transports in animal groups. Copyright © 2019, The Authors. All rights reserved.

关键词： Game theory

Solving Constrained Optimization Problems by an Improved Particle Swarm Optimization

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Solving Constrained Optimization Problems by an Improved Par...

International Conference on Innovations in Bio-inspired Computing and Applications (IBICA)

作者： Chaoli Sun Jianchao Zeng Shuchuan Chu John F. Roddick Jengshyang Pan Complex System and Computational Intelligence Laboratory Taiyuan University of Science and Technology Taiyuan Shanxi China School of Computer Science Engineering and Mathematics Flinders University Australia Department of Electronic Engineering National Kaohsiung University of Applied Sciences Kaohsiung Taiwan

Constrained optimization problems compose a large part of real-world applications. More and more attentions have gradually been paid to solve this kind of problems. An improved particle swarm optimization (IPSO) algorithm based on feasibility rules is presented in this paper to solve constrained optimization problems. The average velocity of the swarm and the best history position in the particle's neighborhood are introduced as two turbulence factors, which are considered to influence the fly directions of particles, into the algorithm so as not to converge prematurely. The performance of IPSO algorithm is tested on 13 well-known benchmark functions. The experimental results show that the proposed IPSO algorithm is simple, effective and highly competitive.

关键词： Optimization Particle swarm optimization Algorithm design and analysis Convergence History Educational institutions