Identification Of Attractors Research Articles

CosmoMIA: cosmic web-based redshift space halo distribution

Modern galaxy surveys demand extensive survey volumes and resolutions surpassing current dark matter-only simulations' capabilities. To address this, many methods employ effective bias models on the dark matter field to approximate object counts on a grid. However, realistic catalogs necessitate specific coordinates and velocities for a comprehensive understanding of the Universe.In this research, we explore sub-grid modeling to create accurate catalogs, beginning with coarse grid number counts at resolutions of approximately 5.5 h -1 Mpc per side. These resolutions strike a balance between modeling nonlinear damping of baryon acoustic oscillations and facilitating large-volume simulations. Augmented Lagrangian Perturbation Theory (ALPT) is utilized to model the dark matter field and motions, replicating the clustering of a halo catalog derived from a massive simulation at z = 1.1.Our approach involves four key stages: Tracer Assignment: Allocating dark matter particles to tracers based on grid cell counts, generating additional particles to address discrepancies. Attractor Identification: Defining attractors based on particle cosmic web environments, acting as gravitational focal points. Tracer Collapse: Guiding tracers towards attractors, simulating structure collapse. Redshift Space Distortions: Introducing redshift space distortions to simulated catalogs using ALPT and a random dispersion term. Results demonstrate accurate reproduction of monopoles and quadrupoles up to wave numbers of approximately k = 0.6 h Mpc-1. This method holds significant promise for galaxy surveys like DESI, EUCLID, and LSST, enhancing our understanding of the cosmos across scales.

Reduced-order model and attractor identification for large eddy simulation of squirrel cage fan

A large eddy simulation (LES) of a squirrel cage fan (SCF) provides a precise representation of turbulent flows with different degrees of complexity. This study comprehensively analyzes the coherent structures of turbulent flows in an SCF using an LES, proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and multi-resolution dynamic mode decomposition (mrDMD). An intelligent reduced-order model is established by integrating hierarchical deep learning and the sparse identification of nonlinear dynamics. The result shows that the evolution of the global DMD modes is attenuated due to the spatial distribution variations of localized high-frequency mrDMD modes, along with the fragmented and non-steady development of modal patterns. Unlike POD, DMD quantifies the quality of the impeller inlet environment and captures the antisymmetric low-dimensional flows associated with the shedding of rotating vortex structures. The interaction strength between stationary and dynamic rotating areas is accurately represented by attractors characterized by petal-like structures. The trajectory of the attractors faithfully maps the antisymmetric structural attributes, quasi-periodic behavior, and gradual attenuation characteristics exhibited by DMD modes. The number of petal-like systems and their temporal oscillations are in good agreement with the number of fan blades and their rotational cycles. This study provides new insight into fan engineering to advance flow control strategies and improve the understanding of the underlying flow mechanisms.

Pystablemotifs: Python library for attractor identification and control in Boolean networks.

pystablemotifs is a Python 3 library for analyzing Boolean networks. Its non-heuristic and exhaustive attractor identification algorithm was previously presented in Rozum et al. (2021). Here, we illustrate its performance improvements over similar methods and discuss how it uses outputs of the attractor identification process to drive a system to one of its attractors from any initial state. We implement six attractor control algorithms, five of which are new in this work. By design, these algorithms can return different control strategies, allowing for synergistic use. We also give a brief overview of the other tools implemented in pystablemotifs. The source code is on GitHub at https://github.com/jcrozum/pystablemotifs/. Supplementary data are available at Bioinformatics online.

Relationships among generalized positive feedback loops determine possible community outcomes in plant-pollinator interaction networks.

Attractors in Boolean network models representing complex systems such as ecological communities correspond to long-term outcomes (e.g., stable communities) in such systems. As a result, identifying efficient methods to find and characterize these attractors allows for a better understanding of the diversity of possible outcomes. Here we analyze networks that model mutualistic communities of plant and pollinator species governed by Boolean threshold functions. We propose a novel attractor identification method based on generalized positive feedback loops and their functional relationships in such networks. We show that these relationships determine the mechanisms by which groups of stable positive feedback loops collectively trap the system in specific regions of the state space and lead to attractors. Put into the ecological context, we show how survival units-small groups of species in which species can maintain a specific survival state-and their relationships determine the final community outcomes in plant-pollinator networks. We find a remarkable diversity of community outcomes: up to an average of 43 attractors possible for networks with 100 species. This diversity is due to the multiplicity of survival units (up to 34) and stable subcommunities (up to 14). The timing of species influx or outflux does not affect the number of attractors, but it may influence their basins of attraction.

Analysing nystagmus waveforms: a computational framework

We present a new computational approach to analyse nystagmus waveforms. Our framework is designed to fully characterise the state of the nystagmus, aid clinical diagnosis and to quantify the dynamical changes in the oscillations over time. Both linear and nonlinear analyses of time series were used to determine the regularity and complexity of a specific homogenous phenotype of nystagmus. Two-dimensional binocular eye movement recordings were carried out on 5 adult subjects who exhibited a unilateral, uniplanar, vertical nystagmus secondary to a monocular late-onset severe visual loss in the oscillating eye (the Heimann-Bielschowsky Phenomenon). The non-affected eye held a central gaze in both horizontal and vertical planes (± 10 min. of arc). All affected eyes exhibited vertical oscillations, with mean amplitudes and frequencies ranging from 2.0°–4.0° to 0.25–1.5 Hz, respectively. Unstable periodic orbit analysis revealed only 1 subject exhibited a periodic oscillation. The remaining subjects were found to display quasiperiodic (n = 1) and nonperiodic (n = 3) oscillations. Phase space reconstruction allowed attractor identification and the computation of a time series complexity measure—the permutation entropy. The entropy measure was found to be able to distinguish between a periodic oscillation associated with a limit cycle attractor, a quasiperiodic oscillation associated with a torus attractor and nonperiodic oscillations associated with higher-dimensional attractors. Importantly, the permutation entropy was able to rank the oscillations, thereby providing an objective index of nystagmus complexity (range 0.15–0.21) that could not be obtained via unstable periodic orbit analysis or attractor identification alone. These results suggest that our framework provides a comprehensive methodology for characterising nystagmus, aiding differential diagnosis and also permitting investigation of the waveforms over time, thereby facilitating the quantification of future therapeutic managements. In addition, permutation entropy could provide an additional tool for future oculomotor modelling.

Dynamical attractors of memristors and their networks

It is shown that the time-averaged dynamics of memristors and their networks periodically driven by alternating-polarity pulses may converge to fixed-point attractors. Starting with a general memristive system model, we derive basic equations describing the fixed-point attractors and investigate attractors in the dynamics of ideal, threshold-type and second-order memristors, and memristive networks. A memristor potential function is introduced, and it is shown that in some cases the attractor identification problem can be mapped to the problem of potential function minimization. Importantly, the fixed-point attractors may only exist if the function describing the internal state dynamics depends on an internal state variable. Our findings may be used to tune the states of analog memristors, and also be relevant to memristive synapses subjected to forward- and back-propagating spikes.

BioLQM: A Java Toolkit for the Manipulation and Conversion of Logical Qualitative Models of Biological Networks.

Here we introduce bioLQM, a new Java software toolkit for the conversion, modification, and analysis of Logical Qualitative Models of biological regulatory networks. BioLQM provides core modeling operations as building blocks for the development of integrated modeling software, or for the assembly of heterogeneous analysis workflows involving several complementary tools. Based on the definition of multi-valued logical models, bioLQM implements import and export facilities, notably for the recent SBML qual exchange format, as well as for formats used by several popular tools, facilitating the design of workflows combining these tools. Model modifications enable the definition of various perturbations, as well as model reduction, easing the analysis of large models. Another modification enables the study of multi-valued models with tools limited to the Boolean case. Finally, bioLQM provides a framework for the development of novel analysis tools. The current version implements various updating modes for model simulation (notably synchronous, asynchronous, and random asynchronous), as well as some static analysis features for the identification of attractors. The bioLQM software can be integrated into analysis workflows through command line and scripting interfaces. As a Java library, it further provides core data structures to the GINsim and EpiLog interactive tools, which supply graphical interfaces and additional analysis methods for cellular and multi-cellular qualitative models.

Chaotic behavior of light-assisted physical aging in arsenoselenide glasses.

The theory of strange attractors is shown to be adequately applicable for analyzing the kinetics of light-assisted physical aging revealed in structural relaxation of Se-rich As-Se glasses below glass transition. Kinetics of enthalpy losses is used to determine the phase space reconstruction parameters. Observed chaotic behaviour (involving chaos and fractal consideration such as detrended fluctuation analysis, attractor identification using phase space representation, delay coordinates, mutual information, false nearest neighbours, etc.) reconstructed via the TISEAN program package is treated within a microstructure model describing multistage aging behaviour in arsenoselenide glasses. This simulation testifies that photoexposure acts as an initiating factor only at the beginning stage of physical aging, thus facilitating further atomic shrinkage of a glassy backbone.

Natural physical aging in glassy As–Se: A comparative study of chaotic behavior with enhanced results analysis

Theory of chaos is shown to be adequately applied to analyze kinetics of natural physical aging revealed in structural relaxation of Se-rich As–Se glasses below glass transition. Kinetics of enthalpy losses induced by prolonged storage in natural conditions is used to determine phase space reconstruction parameters. The observed chaotic behavior (involving chaos and fractal consideration such as detrended fluctuation analysis, attractor identification using phase space representation, delay coordinates, mutual information, and false nearest neighbors) reconstructed via TISEAN is treated within potential energy landscape as diversity of multiple transitions between different basins–metabasins towards more thermodynamically equilibrium state, minimizing the free energy of the system. Natural physical aging, facilitates further atomic shrinkage of the glass backbone.

Adaptive and phase transition behavior in performance of discrete multi-articular actions by degenerate neurobiological systems

The identification of attractors is one of the key tasks in studies of neurobiological coordination from a dynamical systems perspective, with a considerable body of literature resulting from this task. However, with regards to typical movement models investigated, the overwhelming majority of actions studied previously belong to the class of continuous, rhythmical movements. In contrast, very few studies have investigated coordination of discrete movements, particularly multi-articular discrete movements. In the present study, we investigated phase transition behavior in a basketball throwing task where participants were instructed to shoot at the basket from different distances. Adopting the ubiquitous scaling paradigm, throwing distance was manipulated as a candidate control parameter. Using a cluster analysis approach, clear phase transitions between different movement patterns were observed in performance of only two of eight participants. The remaining participants used a single movement pattern and varied it according to throwing distance, thereby exhibiting hysteresis effects. Results suggested that, in movement models involving many biomechanical degrees of freedom in degenerate systems, greater movement variation across individuals is available for exploitation. This observation stands in contrast to movement variation typically observed in studies using more constrained bi-manual movement models. This degenerate system behavior provides new insights and poses fresh challenges to the dynamical systems theoretical approach, requiring further research beyond conventional movement models.

Complexity, self-organisation and variation in behaviour in meandering rivers

River meanders are natural features on the surface of Earth that present some degree of regularity of form. They range from being highly dynamic to being stable under present conditions. Conventional theory is that meanders develop to an equilibrium form which is related to discharge and sediment load. Other research has demonstrated that many highly active meanders exhibit a continuous evolution over time and a non-linearity in rate of development. Ideas of autogenesis and of self-organised criticality as being an explanation of some meander changes have been proposed. In this paper data from rivers around the world are examined for further evidence of autogenic, self-organised or non-linear behaviour through analysis of change in sinuosity over time for reaches and change in individual bend form, particularly bend curvature and bend elongation. Some examples do exhibit trends of increasing sinuosity over time and a few show limits from which large decreases occur. Several case studies show non-linearity of behaviour and increasing complexity of form. Other case studies, however, do not exhibit such trends. Phase space plots are used to help uncover emergent behaviour but show a variety of patterns. The example of a reach in which multiple cut-offs occurred is analysed for mechanisms of self-organisation of the planform and in the pool-riffle pattern. Riffles are more closely spaced and also more transient in the more rapidly changing and higher sinuosity parts of the channel. Hypothetical trajectories of different meander behaviour, including for bedrock meanders, are plotted but the challenge remains to uncover the conditions for occurrence and for divergence of tendencies to stability and instability. Identification of attractors and phase space of behaviour of different meandering systems offer the potential for application to sustainable channel management.

The Theory of Process Integrity and Global Analysis for Process Monitoring and Diagnosis

Process supervision is generally static and begins when deviations from admissible limits are detected. This paper develops a predictive measure of process integrity as a dynamic safety metric which includes a measure of distance to failure and the capacity to recover. It is aided by dynamic models, state and parameter estimation and global analysis. The identification of attractors and the domains of attraction is performed by cell mapping. The adaptive technique locates attractors and domains of attraction with multi level localized mapping in state space.