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Extremal Values of the Atom-Bond Connectivity Index for Trees with Given Roman Domination Numbers

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arXiv 2024年

Consider that G = (X, Y) is a simple, connected graph with X as the vertex set and Y as the edge set. The atom-bond connectivity (ABC) index is a novel topological index that Estrada introduced in Estrada et al. (1998). It is defined as ABC(G) = xy∈XY (G)s ζx +ζxζζyy− 2 where ζx and ζx represent the degrees of the vertices x and y, respectively. In this work, we explore the behavior of the ABC index for tree graphs. We establish both lower and upper bounds for the ABC index, expressed in terms of the graph’s order and its Roman domination number. Additionally, we characterize the tree structures that correspond to these extremal values, offering a deeper understanding of how the Roman domination number (RDN) influences the ABC index in tree graphs. © 2024, CC BY.

关键词： Trees (mathematics)

Using Information-Theoretic Approaches and Multi-Source data to Explore Inland Arid Region Hydrological Model Systems

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SSRN

SSRN 2023年

作者： Bao, Qingling Ding, Jianli Wang, Jingjie Han, Lijing Key Laboratory of Smart City and Environment Modeling of Higher Education Institute College of resources and Environment Science Xingjiang University Urumqi800046 China Big Data Intelligence Analytics Center of Xinjiang Social Economy College of Statistics and Data Science Xinjiang University of Finance & Economics Urumqi800046 China

Assessing and improving the realistic simulation of water fluxes in each component of the hydrological model is of practical importance for the accurate portrayal of hydrological systems in inland arid regions. Many hydrological modeling studies focused on simulations driven by a single meteorological data source and are evaluated using only classical statistical metrics, thus providing limited insight into model performance at the process level. This study analyzed and compared the applicability of three different meteorologically driven data interpolation methods and satellite reanalysis data in hydrological modeling of arid inland watersheds using the Variable Infiltration Capacity (VIC) model. An information-theoretic-based approach (transfer entropy) was used to quantify the information transfer between hydrological model subsystems for different model settings and combinations of meteorologically driven data. The results showed that (1) Water fluxes simulated by satellite-driven data were more accurately portrayed spatially than interpolated data but did not enhance the runoff simulation. (2) Precipitation and snow water equivalents in the seasonal water balance dominated in the spring and winter months, with runoff and evapotranspiration increasing in the summer and fall. (3) The information transfer rate of each water flux subsystem was lowest between rainfall and snow water equivalent and highest between runoff and soil moisture. (4) The transfer entropy revealed more about the information transfer of individual water fluxes of runoff on the time scale than the Pearson correlation coefficient. (5) The causal relationship between runoff and evapotranspiration and soil moisture was more obvious, while the relationship with snow water equivalent was less obvious. © 2023, The Authors. All rights reserved.

关键词： Runoff

Knee Detection in Bayesian Multi-Objective Optimization Using Thompson Sampling

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IEEE Transactions on Evolutionary Computation 2024年

作者： Heidari, Arash Qing, Jixiang Gonzalez, Sebastian Rojas Branke, Juergen Dhaene, Tom Couckuyt, Ivo Computer Science at IDLab Ghent University Ghent Belgium Imperial College London United Kingdom Department of Computational Mathematics Data Science Institute Belgium Warwick Business School University of Warwick Coventry United Kingdom Computer Modeling and Simulation Research Group University of Antwerp Antwerp Belgium Cluster in IDLab Ghent University Belgium

Real-world problems often consist of multiple conflicting objectives to be optimized simultaneously, featuring a set of Pareto-optimal solutions. Estimating the entire Pareto front can be computationally expensive, and is not always necessary, as decision makers will likely be interested only in specific regions of the Pareto front. In the absence of knowledge about the decision maker preferences, the so-called knees in the Pareto front are considered to be particularly attractive. In this paper, we propose using Thompson Sampling in the Bayesian optimization framework to estimate the location of the knee regions in a data-efficient manner. Our experimental results show that the proposed methods accurately locate the knee regions after a very small number of evaluations, providing a computationally efficient approach to single-and multi-knee detection in multi-objective optimization. © 1997-2012 IEEE.

关键词： Multiobjective optimization

System bias correction of short-term hub-height wind forecasts using the Kalman filter

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Protection and Control of Modern Power Systems 2021年第1期6卷 473-481页

作者： Jingjing Xu Ziniu Xiao Zhaohui Lin Ming Li International Center for Climate and Environment Science(ICCES) Institute of Atmospheric PhysicsChinese Academy of ScienceBeijingChina State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG) Institute of Atmospheric PhysicsChinese Academy of SciencesBeijingChina Data61 Commonwealth Scientific and Industrial Research Organization(CSIRO)PerthAustralia

Wind energy is a fluctuating source for power systems, which poses challenges to grid planning for the wind power industry. To improve the short-term wind forecasts at turbine height, the bias correction approach Kalman filter (KF) is applied to 72-h wind speed forecasts from the WRF model in Zhangbei wind farm for a period over two years. The KF approach shows a remarkable ability in improving the raw forecasts by decreasing the root-mean-square error by 16% from 3.58 to 3.01 m s−1, the mean absolute error by 14% from 2.71 to 2.34 m s−1, the bias from 0.22 to − 0.19 m s−1, and improving the correlation from 0.58 to 0.66. The KF significantly reduces random errors of the model, showing the capability to deal with the forecast errors associated with physical processes which cannot be accurately handled by the numerical model. In addition, the improvement of the bias correction is larger for wind speeds sensitive to wind power generation. So the KF approach is suitable for short-term wind power prediction.

关键词： Wind forecasts Wind energy Numerical model Bias correction Kalman filter Atmospheric boundary layer

Jaxsgmc: Modular Stochastic Gradient MCMC in Jax

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SSRN

SSRN 2023年

作者： Thaler, Stephan Fuchs, Paul Cukarska, Ana Zavadlav, Julija Multiscale Modeling of Fluid Materials Department of Engineering Physics and Computation TUM School of Engineering and Design Technical University of Munich Germany Munich Data Science Institute Technical University of Munich Germany

We present JaxSGMC, an application-agnostic library for stochastic gradient Markov chain Monte Carlo (SG-MCMC) in JAX. SG-MCMC schemes are uncertainty quantification (UQ) methods that scale to large datasets and high-dimensional models, enabling trustworthy neural network predictions via Bayesian deep learning. JaxSGMC implements several state-of-the-art SG-MCMC samplers to promote UQ in deep learning by reducing the barriers of entry for switching from stochastic optimization to SG-MCMC sampling. Additionally, JaxSGMC allows users to build custom samplers from standard SG-MCMC building blocks. Due to this modular structure, we anticipate that JaxSGMC will accelerate research into novel SG-MCMC schemes and facilitate their application across a broad range of domains. © 2023, The Authors. All rights reserved.

关键词： Large dataset

H2 optimal model reduction of linear systems with multiple quadratic outputs

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arXiv 2024年

作者： Reiter, Sean Duff, Igor Pontes Gosea, Ion Victor Gugercin, Serkan Department of Mathematics Virginia Tech BlacksburgVA24061 United States Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

In this work, we consider the H2 optimal model reduction of dynamical systems that are linear in the state equation and up to quadratic nonlinearity in the output equation. As our primary theoretical contributions, we derive gradients of the squared H2 system error with respect to the reduced model quantities and, from the stationary points of these gradients, introduce Gramian-based first-order necessary conditions for the H2 optimal approximation of a linear quadratic output (LQO) system. The resulting H2 optimality framework neatly generalizes the analogous Gramian-based optimality framework for purely linear systems. Computationally, we show how to enforce the necessary optimality conditions using Petrov-Galerkin projection;the corresponding projection matrices are obtained from a pair of Sylvester equations. Based on this result, we propose an iteratively corrected algorithm for the H2 model reduction of LQO systems, which we refer to as LQO-TSIA (linear quadratic output two-sided iteration algorithm). Numerical examples are included to illustrate the effectiveness of the proposed computational method against other existing *** Codes 15A24, 46N10, 49K15, 93A15, 93C10, 93C80 Copyright © 2024, The Authors. All rights reserved.

关键词： Linear systems

Accurate machine learning force fields via experimental and simulation data fusion

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arXiv 2023年

作者： Röcken, Sebastien Zavadlav, Julija Multiscale Modeling of Fluid Materials Department of Engineering Physics and Computation TUM School of Engineering and Design Technical University of Munich Germany Munich Data Science Institute Technical University of Munich Germany

Machine Learning (ML)-based force fields are attracting ever-increasing interest due to their capacity to span spatiotemporal scales of classical interatomic potentials at quantum-level accuracy. They can be trained based on high-fidelity simulations or experiments, the former being the common case. However, both approaches are impaired by scarce and erroneous data resulting in models that either do not agree with well-known experimental observations or are under-constrained and only reproduce some properties. Here we leverage both Density Functional Theory (DFT) calculations and experimentally measured mechanical properties and lattice parameters to train an ML potential of titanium. We demonstrate that the fused data learning strategy can concurrently satisfy all target objectives, thus resulting in a molecular model of higher accuracy compared to the models trained with a single data source. The inaccuracies of DFT functionals at target experimental properties were corrected, while the investigated off-target properties remained largely unperturbed. Our approach is applicable to any material and can serve as a general strategy to obtain highly accurate ML potentials. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

LinkMed: Entity Recognition and Relation Extraction from Clinical Notes in Spanish

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LinkMed: Entity Recognition and Relation Extraction from Cli...

2023 Iberian Languages Evaluation Forum, IberLEF 2023

作者： Muñoz-Castro, Carlos Carvallo, Andrés Rojas, Matías Aracena, Claudio Guerra, Rodrigo Pizarro, Benjamín Dunstan, Jocelyn National Center for Artificial Intelligence Chile Faculty of Physical and Mathematical Sciences Universidad de Chile Chile Department of Computer Science Pontificia Universidad Católica de Chile Chile Institute for Mathematical and Computational Engineering Pontificia Universidad Católica de Chile Chile Center for Mathematical Modeling Universidad de Chile Chile Millenium Institute Foundational Research on Data Chile

Relation extraction is an essential component of Natural Language Processing (NLP) and significantly influences information retrieval and structured information extraction. Within clinical notes, the task is needed to establish connections among illnesses, therapies, indications, and other medical concepts. Motivated by the above, in this work, we propose a two-step model approach for entity linking;in the first step, we solve entity recognition, and in the second, a relation classification approach. We evaluated our approach in a Spanish corpus of the TESTLINK challenge in IberLEF2023 (Iberian Languages Evaluation Forum), comprising 81 clinical notes to train and 80 clinical notes to test. Our results show competitive performance with a precision of 0.47, recall of 0.43, and F1-score of 0.45, presenting an effective strategy for relation extraction from clinical notes in Spanish. © 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

关键词： Information retrieval

Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback controller design

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arXiv 2024年

作者： Heiland, Jan Kim, Yongho Werner, Steffen W.R. Department of Mathematics and Natural Sciences Institute of Mathematics Technische Universität Ilmenau Germany Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstraße 1 Magdeburg39106 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Polytopic autoencoders provide low-dimensional parametrizations of states in a polytope. For nonlinear PDEs, this is readily applied to low-dimensional linear parameter-varying (LPV) approximations as they have been exploited for efficient nonlinear controller design via series expansions of the solution to the state-dependent Riccati equation. In this work, we develop a polytopic autoencoder for control applications and show how it improves on standard linear approaches in view of LPV approximations of nonlinear systems. We discuss how the particular architecture enables exact representation of target states and higher order series expansions of the nonlinear feedback law at little extra computational effort in the online phase and how the linear though high-dimensional and nonstandard Lyapunov equations are efficiently computed during the offline phase. In a numerical study, we illustrate the procedure and how this approach can reliably outperform the standard linear-quadratic regulator *** Codes 34H05, 37N35, 65F45, 76D55, 93B52 Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations