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Highly accurate σ- and τ-functionals for beyond-RPA methods with approximate exchange kernels

JOURNAL OF CHEMICAL PHYSICS 2023年第19期159卷 194104页

作者： Lemke, Yannick Ochsenfeld, Christian Ludwig Maximilians Univ Munchen LMU Chair Theoret Chem Dept Chem Butenandtstr 5-13 D-81377 Munich Germany Max Planck Inst Solid State Res Heisenbergstr 1 D-70569 Stuttgart Germany

sigma-Functionals are promising new developments for the Kohn-Sham correlation energy based upon the direct Random Phase approximation (dRPA) within the adiabatic connection formalism, providing impressive improvements over dRPA for a broad range of benchmarks. However, sigma-functionals exhibit a high amount of self-interaction inherited from the approximations made within dRPA. Inclusion of an exchange kernel in deriving the coupling-strength-dependent density-density response function leads to so-called tau-functionals, which - apart from a fourth-order Taylor series expansion - have only been realized in an approximate fashion so far to the best of our knowledge, most notably in the form of scaled sigma-functionals. In this work, we derive, optimize, and benchmark three types of sigma- and tau-functionals including approximate exchange effects in the form of an antisymmetrized Hartree kernel. These functionals, based on a second-order screened exchange type contribution in the adiabatic connection formalism, the electron-hole time-dependent Hartree-Fock kernel (eh-TDHF) otherwise known as RPA with exchange (RPAx), and an approximation thereof known as approximate exchange kernel (AXK), are optimized on the ASCDB database using two new parametrizations named A1 and A2. In addition, we report a first full evaluation of sigma- and tau-functionals on the GMTKN55 database, revealing our exchange-including functionals to considerably outperform existing sigma-functionals while being highly competitive with some of the best double-hybrid functionals of the original GMTKN55 publication. In particular, the sigma-functionals based on AXK and tau-functionals based on RPAx with PBE0 reference stand out as highly accurate approaches for a wide variety of chemically relevant problems.

关键词： approximation algorithms

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Monochromatic partitioning of colored points by lines

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INFORMATION PROCESSING LETTERS 2023年 182卷

作者： Jowhari, Hossein Rezapour, Mohsen KN Toosi Univ Technol Fac Math Dept Comp Sci & Stat Tehran Iran

Given a set of n colored points in the plane, we consider the problem of partitioning the underlying space of the points into monochromatic regions using the minimum number of lines. This is a generalized version of the problem of separating non-colored points by lines studied by Har-Peled and Jones in SODA'18. We propose the first approximation algorithm for the problem. Our algorithm returns an O (log n) factor approximation in O (mn2 sigma log n) time, where sigma is the optimal number of lines and m is the number of colors.(c) 2023 Elsevier B.V. All rights reserved.

关键词： approximation algorithms Computational geometry Covering

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Min-max latency walks: approximation algorithms for monitoring vertex-weighted graphs

Springer Tracts in Advanced Robotics

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Springer Tracts in Advanced Robotics 2013年 86卷 139-155页

作者： Alamdari, Soroush Fata, Elaheh Smith, Stephen L. Cheriton School of Computer Science University of Waterloo WaterlooONN2L 3G1 Canada Department of Electrical and Computer Engineering University of Waterloo WaterlooONN2L 3G1 Canada

ISBN: (纸本)9783642362781

In this paper, we consider the problem of planning a path for a robot to monitor a known set of features of interest in an *** represent the environment as a vertex- and edge-weighted graph, where vertices represent features or regions of interest. The edge weights give travel times between regions, and the vertex weights give the importance of each region. If the robot repeatedly performs a closed walk on the graph, then we can define the latency of a vertex to be the maximum time between visits to that vertex, weighted by the importance (vertex weight) of that vertex. Our goal in this paper is to find the closed walk that minimizes the maximum weighted latency of any vertex. We show that there does not always exist an optimal walk of polynomial size. We then prove that for any graph there exist a constant approximation walk of size O(n2), where n is the number of vertices. We provide two approximation algorithms;an O(logn)-approximation and an O(logρ)-approximation, where ρ is the ratio between the maximum and minimum vertex weight. We provide simulation results which demonstrate that our algorithms can be applied to problems consisting of thousands of vertices. © Springer-Verlag Berlin Heidelberg 2013.

关键词： approximation algorithms

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Measuring the impact of influence on individuals: roadmap to quantifying attitude

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SOCIAL NETWORK ANALYSIS AND MINING 2021年第1期11卷 1-20页

作者： Fu, Xiaoyun Padmanabhan, Madhavan Kumar, Raj Gaurav Basu, Samik Dorius, Shawn Pavan, A. Iowa State Univ Ames IA 50011 USA

Diffusion of information in social network has been the focus of intense research in the recent past decades due to its significant impact in shaping public discourse through group/individual influence. Existing research primarily models influence as a binary property of entities: influenced or not influenced. While this is a useful abstraction, it discards the notion of degree of influence, i.e., certain individuals may be influenced "more" than others. We introduce the notion of attitude, which, as described in social psychology, is the degree by which an entity is influenced by the information. Intuitively, attitude captures the number of distinct neighbors of an entity influencing the latter. We present an information diffusion model (AIC model) that quantifies the degree of influence, i.e., attitude of individuals, in a social network. With this model, we formulate and study attitude maximization problem. We prove that the function for computing attitude is monotonic and sub-modular, and the attitude maximization problem is NP-Hard. We present a greedy algorithm for maximization with an approximation guarantee of (1 - 1/e). In the context of AIC model, we study two problems, with the aim to investigate the scenarios where attaining individuals with high attitude is objectively more important than maximizing the attitude of the entire network. In the first problem, we introduce the notion of actionable attitude;intuitively, individuals with actionable attitude are likely to "act" on their attained attitude. We show that the function for computing actionable attitude, unlike that for computing attitude, is non-submodular and however is approximately submodular. We present approximation algorithm for maximizing actionable attitude in a network. In the second problem, we consider identifying the number of individuals in the network with attitude above a certain value, a threshold. In this context, the function for computing the number of individuals with attitude a

关键词： approximation algorithms

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Track Mis-Registration Estimator Based on K-Means Algorithm for Bit-Patterned Media Recording

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IEEE TRANSACTIONS ON MAGNETICS 2023年第3期59卷

作者： Jeong, Seongkwon Lee, Jaejin Soongsil Univ Sch Elect Engn Seoul 06978 South Korea

Bit-patterned media recording (BPMR) has been considered among the key technologies to extend recording densities to 1 Tb/in(2) and beyond. However, the BPMR system encounters the challenges of two-dimensional intersymbol interference and track mis-registration (TMR). In this article, we propose a TMR estimator based on the K-means algorithm for estimating the TMR levels and preventing the performance degradation of the BPMR system. The TMR estimator calculates the distances between the centroid of the readback signal and predetermined centroids according to the TMR level. The equalizer coefficients and partial response target are adjusted to the corresponding TMR level. At a bit error rate of 10(-3) and a TMR of 10%, the proposed detection scheme performs better by approximately 1 dB in comparison with the conventional detection.

关键词： Equalizers Clustering algorithms Magnetic recording Signal to noise ratio Partitioning algorithms Manganese approximation algorithms Bit-patterned media recording (BPMR) centroid K-means algorithm track mis-registration (TMR)

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How Do You Want Your Greedy: Simultaneous or Repeated?

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JOURNAL OF MACHINE LEARNING RESEARCH 2023年 24卷 1-87页

作者： Feldman, Moran Harshaw, Christopher Karbasi, Amin Univ Haifa Dept Comp Sci Haifa Israel Univ Calif Berkeley Simons Inst Berkeley CA USA Yale Univ Dept Elect Engeering New Haven CT USA Yale Univ Dept Comp Sci New Haven CT USA Yale Univ Dept Stat & Data Sci New Haven CT USA

We present SIMULTANEOUSGREEDYS, a deterministic algorithm for constrained submodular maximization. At a high level, the algorithm maintains l solutions and greedily updates them in a simultaneous fashion. SIMULTANEOUSGREEDYS achieves the tightest known which are (k + 1)2/k = k + O(1) and (1 + root k + 2)2 = k + O( approximation guarantees for both k-extendible systems and the more general k-systems, root k), respectively. We also improve the analysis of REPEATEDGREEDY, showing that it achieves an approximation root root ratio of k+O( k) for k-systems when allowed to run for O( k) iterations, an improvement in both the runtime and approximation over previous analyses. We demonstrate that both algorithms may be modified to run in nearly linear time with an arbitrarily small loss in the approximation. Both SIMULTANEOUSGREEDYS and REPEATEDGREEDY are flexible enough to incor-porate the intersection of m additional knapsack constraints, while retaining similar ap-proximation guarantees: both algorithms yield an approximation guarantee of roughly k + 2m + O(root k + m) for k-systems and SIMULTANEOUSGREEDYS enjoys an improved ap-proximation guarantee of k + 2m + O(root m) for k-extendible systems. To complement our algorithmic contributions, we prove that no algorithm making polynomially many oracle queries can achieve an approximation better than k + 1/2 - epsilon. We also present ***, a Julia package which implements these algorithms. Finally, we test these algorithms on real datasets.

关键词： Submodular maximization k-systems k-extendible systems approximation algorithms

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Time-Delay Estimation of Microseismic DAS Data Using Band-Limited Phase-Only Correlation

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2023年 61卷

作者： Wu, Shaojiang Wang, Yibo Liang, Xing Chinese Acad Sci Key Lab Petr Resource Res Inst Geol & Geophys Beijing 100029 Peoples R China Chinese Acad Sci Innovat Acad Earth Sci Beijing 100029 Peoples R China PetroChina Zhejiang Oilfield Co Hangzhou 311100 Peoples R China

Time-delay estimation is a critical step in many geophysical applications. Conventional approaches are mainly based on the cross correlation of waveforms in time domain but show strong distortions with multiple oscillations and side lobes. We propose a band-limited phase-only correlation (POC) algorithm for time-delay estimation. The algorithm involves the following key steps: 1) transforming 1-D waveform into 2-D time-frequency spectra using S-transform;2) calculating the band-limited POC function of the transformed spectra;and 3) measuring time delays by analyzing POC coefficient. We demonstrate the effectiveness of the proposed algorithm using synthetic and real microseismic fiber-optic distributed acoustic sensing (DAS) datasets. Results show that POC can effectively and accurately estimate the time delays of waveforms. Compared with the performance of the conventional cross correlation method in time domain, the proposed method has three main advantages: 1) better identification of event and noise waveforms;2) lower uncertainty of narrow correlation peaks;and 3) weaker distortions with small oscillations and side lobes.

关键词： Estimation Correlation Uncertainty Oscillators Acoustic distortion Time-domain analysis Receivers approximation algorithms inverse problems mathematical model reliability

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Escaping Braess's paradox through approximate Caratheodory's theorem

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INFORMATION PROCESSING LETTERS 2023年 179卷

作者： Dimos, Sotirios Fotakis, Dimitris Lianeas, Thanasis Sergis, Kyriakos Natl Tech Univ Athens Sch Elect & Comp Engn 9 Iroon Polytech St Athens 15780 Greece

In selfish routing, Braess's paradox demonstrates the counterintuitive fact that removing a part of a network may improve the players' cost at equilibrium. In this work, we use the approximate version of Caratheodory's theorem (Barman, SICOMP 2018) and show how to efficiently approximate the best subnetwork on selfish routing instances with relatively short paths and Lipschitz continuous cost functions. Restriction to networks with short paths is necessary to escape the strong inapproximability result of (Roughgarden, JCSS 2006). We present the first polynomial-time algorithm that approximates (in a certain relaxed sense) the best subnetwork problem on such instances. Specifically, for any constant epsilon > 0, our algorithm computes an epsilon-Nash flow with maximum latency at most (1 + epsilon)L* + epsilon, where L* is the equilibrium latency of the best subnetwork. Moreover, our algorithm runs in quasipolynomial time on networks with polylogarithmically long paths. As a corollary, we obtain the first polynomial-time approximation scheme for the best subnetwork in the class of random Gn,p instances proven prone to Braess's paradox by (Roughgarden and Valiant, RSA 2010) and (Chung Graham et al., RSA 2012). (c) 2022 Elsevier B.V. All rights reserved.

关键词： Braess paradox Congestion games Selfish routing Best subnetwork approximation algorithms

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The p-center problem under locational uncertainty of demand points

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DISCRETE OPTIMIZATION 2023年 47卷

作者： Ataei, Homa Davoodi, Mansoor Inst Adv Studies Basic Sci IASBS Zanjan Iran Ctr Adv Syst Understanding CASUS Helmholtz Zent Dresden Rossendorf Gorlitz Germany

The p-center problem is finding the location of p facilities among a set of n demand points such that the maximum distance between any demand point and its nearest facility is minimized. In this paper, we study this problem in the context of uncertainty, that is, the location of the demand points may change in a region like a disk or a segment, or belong to a finite set of points. We introduce Max-p-center and Min-p-center problems which are the worst and the best possible solutions for the p-center problem under such locational uncertainty. We propose approximation and parameterized algorithms to solve these problems under the Euclidean metric. Further, we study the MinMax Regret 1-center problem under uncertainty and propose a linear-time algorithm to solve it under the Manhattan metric as well as an O(n4) time algorithm under the Euclidean metric.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Facility location Uncertainty Regret Robustness approximation algorithms p-center

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Hybrid Quantum Approximate Optimization Algorithm (HQAOA) for Efficient Blockchain Transaction Scheduling

Hybrid Quantum Approximate Optimization Algorithm (HQAOA) fo...

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International Symposium on Advanced Computing and Communication (ISACC)

作者： Soumyadip Paul Sarit Chakraborty Dept. Of Information Technology Government College of Engg. & Ceramic Technology Kolkata WB India Dept. of Computer Science and Engineering Government College of Engineering and Leather Technology Kolkata WB India

ISBN: (数字)9798331523893

ISBN: (纸本)9798331523909

Quantum technology offers a transformative approach to solving complex computational challenges in decentralized systems, particularly in blockchain transaction scheduling. Efficient transaction scheduling is critical in distributed ledger systems, which often face challenges like dynamic transaction loads. This work proposes a novel approach namely Hybrid Quantum Approximate Optimization Algorithm (HQAOA) which combines Multi-Agent QAOA (MA-QAOA) and Adaptive Layer QAOA (AL-QAOA) to provide a robust solution to such issues. HQAOA leverages a decentralized optimization framework where multiple agents, each representing a node in the network, optimize local transaction scheduling while considering global constraints. Additionally, HQAOA adapts to varying transaction loads by dynamically adjusting the number of quantum layers for each agent, ensuring computational efficiency under different conditions. Such dynamic layer adjustment mechanisms mitigate the adverse effects of quantum noise and ensures optimal performance in scenarios with fluctuating transaction loads. In contrast to traditional QAOA, which struggles with noise and scaling issues, HQAOA provides improved performance by balancing the complexity of the problem with available quantum resources. Experimental results signify the future potential of HQAOA to outperform QAOA, particularly in noisy environments and irregular transaction conditions. This work demonstrates the potential of HQAOA to optimize blockchain transaction scheduling in decentralized systems.

关键词： Quantum computing Distributed ledger Processor scheduling Heuristic algorithms Scalability Noise Dynamic scheduling approximation algorithms Blockchains Complexity theory

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