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Unified Causality Analysis Based on the Degrees of Freedom

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arXiv 2024年

作者： Telcs, András Kurbucz, Marcell T. Jakovác, Antal Department of Computational Sciences Institute for Particle and Nuclear Physics HUN-REN Wigner Research Centre for Physics 29-33 Konkoly-Thege Miklós Street BudapestH-1121 Hungary Department of Statistics Institute of Data Analytics and Information Systems Corvinus University of Budapest 8 Fővám Square BudapestH-1093 Hungary Department of Quantitative Methods Faculty of Business and Economics University of Pannonia 10 Egyetem Street VeszprémH-8200 Hungary

Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved hidden drivers on the observed dynamics. This paper presents a unified method capable of identifying fundamental causal relationships between pairs of systems, whether deterministic or stochastic. Notably, the method also uncovers hidden common causes beyond the observed variables. By analyzing the degrees of freedom in the system, our approach provides a more comprehensive understanding of both causal influence and hidden confounders. This unified framework is validated through theoretical models and simulations, demonstrating its robustness and potential for broader application. © 2024, CC BY-SA.

关键词： Degrees of freedom (mechanics)

LLT: An R package for Linear Law-based Feature Space Transformation

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arXiv 2023年

作者： Kurbucz, Marcell T. Pósfay, Péter Jakovác, Antal Department of Computational Sciences Wigner Research Centre for Physics 29-33 Konkoly-Thege Miklós Street BudapestH-1121 Hungary Institute of Data Analytics and Information Systems Corvinus University of Budapest 8 Fővám Square BudapestH-1093 Hungary

The goal of the linear law-based feature space transformation (LLT) algorithm is to assist with the classification of univariate and multivariate time series. The presented R package, called LLT, implements this algorithm in a flexible yet user-friendly way. This package first splits the instances into training and test sets. It then utilizes time-delay embedding and spectral decomposition techniques to identify the governing patterns (called linear laws) of each input sequence (initial feature) within the training set. Finally, it applies the linear laws of the training set to transform the initial features of the test set. These steps are performed by three separate functions called trainTest, trainLaw, and testTrans. Their application requires a predefined data structure;however, for fast calculation, they use only built-in functions. The LLT R package and a sample dataset with the appropriate data structure are publicly available on *** Codes 62H30, 68T10, 62M10, 60-04 © 2023, CC BY.

关键词： Linear transformations

Energy dissipation in astrophysical simulations: results of the Orszag-Tang test problem

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arXiv 2023年

作者： Kayanikhoo, Fatemeh Čemeljić, Miljenko Wielgus, Maciek Kluz, Wlodek Nicolaus Copernicus Astronomical Center Bartycka 18 Warszaw00-716 Poland Research Centre for Computational Physics and Data Processing Institute of Physics Silesian University in Opava Bezručovo nám. 13 OpavaCZ-746 01 Czech Republic Academia Sinica Institute of Astronomy and Astrophysics P.O. Box 23-141 Taipei106 Taiwan Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany

MSC Codes 85-08The magnetic field through the magnetic reconnection process affects the dynamics and structure of astrophysical systems. Numerical simulations are the tools to study the evolution of these systems. However, the resolution, dimensions, resistivity, and turbulence of the system are some important parameters to take into account in the simulations. In this paper, we investigate the evolution of magnetic energy in astrophysical simulations by performing a standard test problem for MHD codes, Orszag-Tang. We estimate the numerical dissipation in the simulations using state-of-the-art numerical simulation code in astrophysics, PLUTO. The estimated numerical resistivity in 2D simulations corresponds to the Lundquist number ≈ 104 in the resolution of 512 × 512 grid cells. It is also shown that the plasmoid unstable reconnection layer can be resolved with sufficient resolutions. Our analysis demonstrates that in non-relativistic magnetohydrodynamics simulations, magnetic and kinetic energies undergo conversion into internal energy, resulting in plasma heating. Copyright © 2023, The Authors. All rights reserved.

关键词： Energy dissipation

Predicting the Price Movement of Cryptocurrencies Using Linear Law-based Transformation

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arXiv 2023年

The aim of this paper is to investigate the effect of a novel method called linear law-based feature space transformation (LLT) on the accuracy of intraday price movement prediction of cryptocurrencies. To do this, the 1-minute interval price data of Bitcoin, Ethereum, Binance Coin, and Ripple between 1 January 2019 and 22 October 2022 were collected from the Binance cryptocurrency exchange. Then, 14-hour nonoverlapping time windows were applied to sample the price data. The classification was based on the first 12 hours, and the two classes were determined based on whether the closing price rose or fell after the next 2 hours. These price data were first transformed with the LLT, then they were classified by traditional machine learning algorithms with 10-fold cross-validation. Based on the results, LLT greatly increased the accuracy for all cryptocurrencies, which emphasizes the potential of the LLT algorithm in predicting price *** Codes 68T10, 91B84, 62M10, 91-08 © 2023, CC BY.

关键词： Linear transformations

THE MAXIMUM MASS AND DEFORMATION OF ROTATING STRANGE QUARK STARS WITH STRONG MAGNETIC FIELDS

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arXiv 2023年

作者： Kayanikhoo, Fatemeh Kapusta, Mateusz Čemeljić, Miljenko Nicolaus Copernicus Astronomical Center Polish Academy of Sciences Bartycka 18 Warsaw00-716 Poland Astronomical Observatory University of Warsaw Al. Ujazdowskie 4 Warszawa00-478 Poland Research Centre for Computational Physics and Data Processing Institute of Physics Silesian University in Opava Bezručovo nám. 13 OpavaCZ-746 01 Czech Republic Academia Sinica Institute of Astronomy and Astrophysics P.O. Box 23-141 Taipei106 Taiwan

We study the structure and total energy of a strange quark star (SQS) endowed with a strong magnetic field with different rotational frequencies. The MIT bag model is used, with the density-dependent bag constant for the equation of state (EOS). The EOS is computed considering the Landau quantization effect regarding the strong magnetic fields (up to 5 × 1017 G) in the interior of the strange quark star. Using the LORENE library, we calculate the structural parameters of SQS for different setups of magnetic field strengths and rotational frequencies. In each setup, we perform calculations for 51 stellar configurations, with specified central enthalpy values. We investigate the configurations with the maximum gravitational mass of SQS in each setup. Our models of SQSs are compared in the maximum gravitational mass, binding energy, compactness, and deformation of the star. We show that the gravitational mass might exceed 2.3M☉ in some models, which is comparable with the mass of the recently detected "black widow" pulsar PSR J0952-0607 and the mass of GW190814 detected by the LIGO/Virgo collaboration. The deformation and maximum gravitational mass of SQS can be characterized by simple functions that have been fitted to account for variations in both magnetic field strength and frequency. Rapidly rotating strange stars have a minimum gravitational mass given by the equatorial mass-shedding limit. © 2023, CC BY.

关键词： Equations of state

Involution game with spatio-temporal heterogeneity of social resources

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arXiv 2022年

作者： Wang, Chaoqian Szolnoki, Attila Program for Computational Social Science Department of Computational and Data Sciences George Mason University FairfaxVA22030 United States Institute of Technical Physics and Materials Science Centre for Energy Research P.O. Box 49 BudapestH-1525 Hungary

When group members claim a portion of limited resources, it is tempting to invest more effort to get a larger share. However, if everyone acts similarly, they all get the same piece they would obtain without extra effort. This is the involution game dilemma that can be detected in several real-life situations. It is also a realistic assumption that resources are not uniform in space and time, which may influence the system's resulting involution level. We here introduce spatio-temporal heterogeneity of social resources and explore their consequences on involution. When spatial heterogeneity is applied, network reciprocity can mitigate the involution for rich resources, which would be critical otherwise in a homogeneous population. Interestingly, when the resource level is modest, spatial heterogeneity causes more intensive involution in a system where most cooperator agents, who want to keep investment at a low level, are present. This picture is partly the opposite in the extreme case when more investment is less effective. Spatial heterogeneity can also produce a counterintuitive effect when the presence of alternative resource levels cannot explain the emergence of involution. If we apply temporal heterogeneity additionally, then the impact of spatial heterogeneity practically vanishes, and we turn back to the behavior observed in a homogeneous population earlier. Our observations are also supported by solving the corresponding replicator equations numerically. © 2022, CC BY.

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Eigenvalue-Based Randomness Test for Residual Diagnostics in Panel data Models

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arXiv 2025年

作者： Kurbucz, Marcell T. Garrido, Betsabé Pérez Jakovác, Antal Institute for Global Prosperity The Bartlett University College London 149 Tottenham Court Road LondonW1T 7NF United Kingdom Department of Computer Science Institute of Data Analytics and Information Systems Corvinus University of Budapest 8 Fővám Square Budapest1093 Hungary Department of Computational Sciences Institute for Particle and Nuclear Physics HUN-REN Wigner Research Centre for Physics 29-33 Konkoly-Thege Miklós Street Budapest1121 Hungary Department of Statistics Institute of Data Analytics and Information Systems Corvinus University of Budapest 8 Fővám Square Budapest1093 Hungary

This paper introduces the Eigenvalue-Based Randomness (EBR) test—a novel approach rooted in the Tracy-Widom law from random matrix theory—and applies it to the context of residual analysis in panel data models. Unlike traditional methods, which target specific issues like cross-sectional dependence or autocorrelation, the EBR test simultaneously examines multiple assumptions by analyzing the largest eigenvalue of a symmetrized residual matrix. Monte Carlo simulations demonstrate that the EBR test is particularly robust in detecting not only standard violations such as autocorrelation and linear cross-sectional dependence (CSD) but also more intricate non-linear and non-monotonic dependencies, making it a comprehensive and highly flexible tool for enhancing the reliability of panel data *** Codes 62H25, 15B52, 62M10 © 2025, CC BY.

关键词： Eigenvalues and eigenfunctions

Energy distribution and substructure formation in astrophysical MHD simulations

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arXiv 2023年

作者： Kayanikhoo, Fatemeh Čemeljić, Miljenko Wielgus, Maciek Kluźniak, Wlodek Nicolaus Copernicus Astronomical Center The Polish Academy of Sciences Bartycka 18 Warsaw00-716 Poland Research Centre for Computational Physics and Data Processing Institute of Physics Silesian University in Opava Bezručovo nám. 13 OpavaCZ-74601 Czech Republic Academia Sinica Institute of Astronomy and Astrophysics P.O. Box 23-141 Taipei106 Taiwan Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany

During substructure formation in magnetized astrophysical plasma, dissipation of magnetic energy facilitated by magnetic reconnection affects the system dynamics by heating and accelerating the ejected plasmoids. Numerical simulations are a crucial tool for investigating such systems. In astrophysical simulations, the energy dissipation, reconnection rate and substructure formation critically depend on the onset of reconnection of numerical or physical origin. In this paper, we hope to assess the reliability of the state-of-the-art numerical codes, PLUTO and KORAL by quantifying and discussing the impact of dimensionality, resolution, and code accuracy on magnetic energy dissipation, reconnection rate, and substructure formation. We quantitatively compare results obtained with relativistic and non-relativistic, resistive and non-resistive, as well as two- and three-dimensional setups performing the Orszag-Tang test problem. We find sufficient resolution in each model, for which numerical error is negligible and the resolution does not significantly affect the magnetic energy dissipation and reconnection rate. The non-relativistic simulations show that at sufficient resolution, magnetic and kinetic energies convert to internal energy and heat the plasma. In the relativistic system, energy components undergo mutual conversion during the simulation time, which leads to a substantial increase in magnetic energy at 20% and 90% of the total simulation time of 10 light-crossing times—the magnetic field is amplified by a factor of five due to relativistic shocks. We also show that the reconnection rate in all our simulations is higher than 0.1, indicating plasmoid-mediated regime. It is shown that in KORAL simulations more substructures are captured than in PLUTO *** Codes 85-08 © 2023, CC BY.

关键词： Energy dissipation

A reversed form of public goods game: equivalence and difference

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arXiv 2022年

作者： Wang, Chaoqian Szolnoki, Attila Department of Computational and Data Sciences George Mason University FairfaxVA22030 United States Institute of Technical Physics and Materials Science Centre for Energy Research P.O. Box 49 BudapestH-1525 Hungary

According to the public goods game (PGG) protocol, participants decide freely whether they want to contribute to a common pool or not, but the resulting benefit is distributed equally. A conceptually similar dilemma situation may emerge when participants consider if they claim a common resource but the related cost is covered equally by all group members. The latter establishes a reversed form of the original public goods game (R-PGG). In this work, we show that R-PGG is equivalent to PGG in several circumstances, starting from the traditional analysis, via the evolutionary approach in unstructured populations, to Monte Carlo simulations in structured populations. However, there are also cases when the behavior of R-PGG could be surprisingly different from the outcome of PGG. When the key parameters are heterogeneous, for instance, the results of PGG and R-PGG could be diverse even if we apply the same amplitudes of heterogeneity. We find that the heterogeneity in R-PGG generally impedes cooperation, while the opposite is observed for PGG. These diverse system reactions can be understood if we follow how payoff functions change when introducing heterogeneity in the parameter space. This analysis also reveals the distinct roles of cooperator and defector strategies in the mentioned games. Our observations may hopefully stimulate further research to check the potential differences between PGG and R-PGG due to the alternative complexity of conditions. © 2022, CC BY.

关键词： Monte Carlo methods