A qualitative numerical study of high dimensional dynamical systems
Albers, David James
Since Poincare, the father of modern mathematical dynamical systems, much effort has been exerted to achieve a qualitative understanding of the physical world via a qualitative understanding of the functions we use to model the physical world. In this thesis, we construct a numerical framework suitable for a qualitative, statistical study of dynamical systems using the space of artificial neural networks. We analyze the dynamics along intervals in parameter space, separating the set of neural networks into roughly four regions: the fixed point to the first bifurcation; the route to chaos; the chaotic region; and a transition region between chaos and finite-state neural networks. The study is primarily with respect to high-dimensional dynamical systems. We make the following general conclusions as the dimension of the dynamical system is increased: the probability of the first bifurcation being of type Neimark-Sacker is greater than ninety-percent; the most probable route to chaos is via a cascade of bifurcations of high-period periodic orbits, quasi-periodic orbits, and 2-tori; there exists an interval of parameter space such that hyperbolicity is violated on a countable, Lebesgue measure 0, "increasingly dense" subset; chaos is much more likely to persist with respect to parameter perturbation in the chaotic region of parameter space as the dimension is increased; moreover, as the number of positive Lyapunov exponents is increased, the likelihood that any significant portion of these positive exponents can be perturbed away decreases with increasing dimension. The maximum Kaplan-Yorke dimension and the maximum number of positive Lyapunov exponents increases linearly with dimension. The probability of a dynamical system being chaotic increases exponentially with dimension. The results with respect to the first bifurcation and the route to chaos comment on previous results of Newhouse, Ruelle, Takens, Broer, Chenciner, and Iooss. Moreover, results regarding the high-dimensional
Counting and classifying attractors in high dimensional dynamical systems.
Bagley, R J; Glass, L
1996-12-07
Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the number of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity of deterministic chaos.
Ghosts in high dimensional non-linear dynamical systems: The example of the hypercycle
International Nuclear Information System (INIS)
Sardanyes, Josep
2009-01-01
Ghost-induced delayed transitions are analyzed in high dimensional non-linear dynamical systems by means of the hypercycle model. The hypercycle is a network of catalytically-coupled self-replicating RNA-like macromolecules, and has been suggested to be involved in the transition from non-living to living matter in the context of earlier prebiotic evolution. It is demonstrated that, in the vicinity of the saddle-node bifurcation for symmetric hypercycles, the persistence time before extinction, T ε , tends to infinity as n→∞ (being n the number of units of the hypercycle), thus suggesting that the increase in the number of hypercycle units involves a longer resilient time before extinction because of the ghost. Furthermore, by means of numerical analysis the dynamics of three large hypercycle networks is also studied, focusing in their extinction dynamics associated to the ghosts. Such networks allow to explore the properties of the ghosts living in high dimensional phase space with n = 5, n = 10 and n = 15 dimensions. These hypercyclic networks, in agreement with other works, are shown to exhibit self-maintained oscillations governed by stable limit cycles. The bifurcation scenarios for these hypercycles are analyzed, as well as the effect of the phase space dimensionality in the delayed transition phenomena and in the scaling properties of the ghosts near bifurcation threshold
Geraci, Joseph; Dharsee, Moyez; Nuin, Paulo; Haslehurst, Alexandria; Koti, Madhuri; Feilotter, Harriet E; Evans, Ken
2014-03-01
We introduce a novel method for visualizing high dimensional data via a discrete dynamical system. This method provides a 2D representation of the relationship between subjects according to a set of variables without geometric projections, transformed axes or principal components. The algorithm exploits a memory-type mechanism inherent in a certain class of discrete dynamical systems collectively referred to as the chaos game that are closely related to iterative function systems. The goal of the algorithm was to create a human readable representation of high dimensional patient data that was capable of detecting unrevealed subclusters of patients from within anticipated classifications. This provides a mechanism to further pursue a more personalized exploration of pathology when used with medical data. For clustering and classification protocols, the dynamical system portion of the algorithm is designed to come after some feature selection filter and before some model evaluation (e.g. clustering accuracy) protocol. In the version given here, a univariate features selection step is performed (in practice more complex feature selection methods are used), a discrete dynamical system is driven by this reduced set of variables (which results in a set of 2D cluster models), these models are evaluated for their accuracy (according to a user-defined binary classification) and finally a visual representation of the top classification models are returned. Thus, in addition to the visualization component, this methodology can be used for both supervised and unsupervised machine learning as the top performing models are returned in the protocol we describe here. Butterfly, the algorithm we introduce and provide working code for, uses a discrete dynamical system to classify high dimensional data and provide a 2D representation of the relationship between subjects. We report results on three datasets (two in the article; one in the appendix) including a public lung cancer
High dimensional model representation method for fuzzy structural dynamics
Adhikari, S.; Chowdhury, R.; Friswell, M. I.
2011-03-01
Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the α-cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy.
Analysing spatially extended high-dimensional dynamics by recurrence plots
Energy Technology Data Exchange (ETDEWEB)
Marwan, Norbert, E-mail: marwan@pik-potsdam.de [Potsdam Institute for Climate Impact Research, 14412 Potsdam (Germany); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, 14412 Potsdam (Germany); Humboldt Universität zu Berlin, Institut für Physik (Germany); Nizhny Novgorod State University, Department of Control Theory, Nizhny Novgorod (Russian Federation); Foerster, Saskia [GFZ German Research Centre for Geosciences, Section 1.4 Remote Sensing, Telegrafenberg, 14473 Potsdam (Germany)
2015-05-08
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analysing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world. - Highlights: • We use recurrence plots for analysing partially extended dynamics. • We investigate the high-dimensional chaos of the Lorenz96 model. • The approach distinguishes different spatio-temporal dynamics. • We use the method for studying vegetation cover time series.
Analysis of chaos in high-dimensional wind power system.
Wang, Cong; Zhang, Hongli; Fan, Wenhui; Ma, Ping
2018-01-01
A comprehensive analysis on the chaos of a high-dimensional wind power system is performed in this study. A high-dimensional wind power system is more complex than most power systems. An 11-dimensional wind power system proposed by Huang, which has not been analyzed in previous studies, is investigated. When the systems are affected by external disturbances including single parameter and periodic disturbance, or its parameters changed, chaotic dynamics of the wind power system is analyzed and chaotic parameters ranges are obtained. Chaos existence is confirmed by calculation and analysis of all state variables' Lyapunov exponents and the state variable sequence diagram. Theoretical analysis and numerical simulations show that the wind power system chaos will occur when parameter variations and external disturbances change to a certain degree.
Inference in High-dimensional Dynamic Panel Data Models
DEFF Research Database (Denmark)
Kock, Anders Bredahl; Tang, Haihan
We establish oracle inequalities for a version of the Lasso in high-dimensional fixed effects dynamic panel data models. The inequalities are valid for the coefficients of the dynamic and exogenous regressors. Separate oracle inequalities are derived for the fixed effects. Next, we show how one can...
Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto
2016-12-01
It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low
Supporting Dynamic Quantization for High-Dimensional Data Analytics.
Guzun, Gheorghi; Canahuate, Guadalupe
2017-05-01
Similarity searches are at the heart of exploratory data analysis tasks. Distance metrics are typically used to characterize the similarity between data objects represented as feature vectors. However, when the dimensionality of the data increases and the number of features is large, traditional distance metrics fail to distinguish between the closest and furthest data points. Localized distance functions have been proposed as an alternative to traditional distance metrics. These functions only consider dimensions close to query to compute the distance/similarity. Furthermore, in order to enable interactive explorations of high-dimensional data, indexing support for ad-hoc queries is needed. In this work we set up to investigate whether bit-sliced indices can be used for exploratory analytics such as similarity searches and data clustering for high-dimensional big-data. We also propose a novel dynamic quantization called Query dependent Equi-Depth (QED) quantization and show its effectiveness on characterizing high-dimensional similarity. When applying QED we observe improvements in kNN classification accuracy over traditional distance functions. Gheorghi Guzun and Guadalupe Canahuate. 2017. Supporting Dynamic Quantization for High-Dimensional Data Analytics. In Proceedings of Ex-ploreDB'17, Chicago, IL, USA, May 14-19, 2017, 6 pages. https://doi.org/http://dx.doi.org/10.1145/3077331.3077336.
Quantum correlation of high dimensional system in a dephasing environment
Ji, Yinghua; Ke, Qiang; Hu, Juju
2018-05-01
For a high dimensional spin-S system embedded in a dephasing environment, we theoretically analyze the time evolutions of quantum correlation and entanglement via Frobenius norm and negativity. The quantum correlation dynamics can be considered as a function of the decoherence parameters, including the ratio between the system oscillator frequency ω0 and the reservoir cutoff frequency ωc , and the different environment temperature. It is shown that the quantum correlation can not only measure nonclassical correlation of the considered system, but also perform a better robustness against the dissipation. In addition, the decoherence presents the non-Markovian features and the quantum correlation freeze phenomenon. The former is much weaker than that in the sub-Ohmic or Ohmic thermal reservoir environment.
Statistical mechanics of complex neural systems and high dimensional data
International Nuclear Information System (INIS)
Advani, Madhu; Lahiri, Subhaneil; Ganguli, Surya
2013-01-01
Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparate spatiotemporal scales to solve important computational problems? Second, how can we extract meaningful models of neuronal systems from high dimensional datasets? To aid in these challenges, we give a pedagogical review of a collection of ideas and theoretical methods arising at the intersection of statistical physics, computer science and neurobiology. We introduce the interrelated replica and cavity methods, which originated in statistical physics as powerful ways to quantitatively analyze large highly heterogeneous systems of many interacting degrees of freedom. We also introduce the closely related notion of message passing in graphical models, which originated in computer science as a distributed algorithm capable of solving large inference and optimization problems involving many coupled variables. We then show how both the statistical physics and computer science perspectives can be applied in a wide diversity of contexts to problems arising in theoretical neuroscience and data analysis. Along the way we discuss spin glasses, learning theory, illusions of structure in noise, random matrices, dimensionality reduction and compressed sensing, all within the unified formalism of the replica method. Moreover, we review recent conceptual connections between message passing in graphical models, and neural computation and learning. Overall, these ideas illustrate how statistical physics and computer science might provide a lens through which we can uncover emergent computational functions buried deep within the dynamical complexities of neuronal networks. (paper)
Approximate Dynamic Programming Based on High Dimensional Model Representation
Czech Academy of Sciences Publication Activity Database
Pištěk, Miroslav
2013-01-01
Roč. 49, č. 5 (2013), s. 720-737 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GAP102/11/0437 Institutional support: RVO:67985556 Keywords : approximate dynamic programming * Bellman equation * approximate HDMR minimization * trust region problem Subject RIV: BC - Control Systems Theory Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/pistek-0399560.pdf
Bayesian Inference of High-Dimensional Dynamical Ocean Models
Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.
2015-12-01
This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.
Linear stability theory as an early warning sign for transitions in high dimensional complex systems
International Nuclear Information System (INIS)
Piovani, Duccio; Grujić, Jelena; Jensen, Henrik Jeldtoft
2016-01-01
We analyse in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems by application to the Tangled Nature model of evolutionary ecology and high dimensional replicator systems with a stochastic element. A high dimensional stability matrix is derived in the mean field approximation to the stochastic dynamics. This allows us to determine the stability spectrum about the observed quasi-stable configurations. From overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation, we are able to construct a good early-warning indicator of the transitions occurring intermittently. (paper)
Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has consid...... dimensional reliability problems in structural dynamics.......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...
High-Dimensional Adaptive Particle Swarm Optimization on Heterogeneous Systems
International Nuclear Information System (INIS)
Wachowiak, M P; Sarlo, B B; Foster, A E Lambe
2014-01-01
Much work has recently been reported in parallel GPU-based particle swarm optimization (PSO). Motivated by the encouraging results of these investigations, while also recognizing the limitations of GPU-based methods for big problems using a large amount of data, this paper explores the efficacy of employing other types of parallel hardware for PSO. Most commodity systems feature a variety of architectures whose high-performance capabilities can be exploited. In this paper, high-dimensional problems and those that employ a large amount of external data are explored within the context of heterogeneous systems. Large problems are decomposed into constituent components, and analyses are undertaken of which components would benefit from multi-core or GPU parallelism. The current study therefore provides another demonstration that ''supercomputing on a budget'' is possible when subtasks of large problems are run on hardware most suited to these tasks. Experimental results show that large speedups can be achieved on high dimensional, data-intensive problems. Cost functions must first be analysed for parallelization opportunities, and assigned hardware based on the particular task
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
Energy Technology Data Exchange (ETDEWEB)
Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki [Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); CREST, JST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Shiro, Masanori [Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568 (Japan); Takahashi, Nozomu; Mas, Paloma [Center for Research in Agricultural Genomics (CRAG), Consorci CSIC-IRTA-UAB-UB, Barcelona 08193 (Spain)
2015-01-15
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
International Nuclear Information System (INIS)
Hirata, Yoshito; Aihara, Kazuyuki; Suzuki, Hideyuki; Shiro, Masanori; Takahashi, Nozomu; Mas, Paloma
2015-01-01
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data
Approximating high-dimensional dynamics by barycentric coordinates with linear programming.
Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma
2015-01-01
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks.
Vlachas, Pantelis R; Byeon, Wonmin; Wan, Zhong Y; Sapsis, Themistoklis P; Koumoutsakos, Petros
2018-05-01
We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.
Energy Technology Data Exchange (ETDEWEB)
Tahira, Rabia; Ikram, Manzoor; Zubairy, M Suhail [Centre for Quantum Physics, COMSATS Institute of Information Technology, Islamabad (Pakistan); Bougouffa, Smail [Department of Physics, Faculty of Science, Taibah University, PO Box 30002, Madinah (Saudi Arabia)
2010-02-14
We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.
International Nuclear Information System (INIS)
Tahira, Rabia; Ikram, Manzoor; Zubairy, M Suhail; Bougouffa, Smail
2010-01-01
We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.
Controlling chaos in low and high dimensional systems with periodic parametric perturbations
International Nuclear Information System (INIS)
Mirus, K.A.; Sprott, J.C.
1998-06-01
The effect of applying a periodic perturbation to an accessible parameter of various chaotic systems is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic systems can result in limit cycles for relatively small perturbations. Such perturbations can also control or significantly reduce the dimension of high-dimensional systems. Initial application to the control of fluctuations in a prototypical magnetic fusion plasma device will be reviewed
A novel algorithm of artificial immune system for high-dimensional function numerical optimization
Institute of Scientific and Technical Information of China (English)
DU Haifeng; GONG Maoguo; JIAO Licheng; LIU Ruochen
2005-01-01
Based on the clonal selection theory and immune memory theory, a novel artificial immune system algorithm, immune memory clonal programming algorithm (IMCPA), is put forward. Using the theorem of Markov chain, it is proved that IMCPA is convergent. Compared with some other evolutionary programming algorithms (like Breeder genetic algorithm), IMCPA is shown to be an evolutionary strategy capable of solving complex machine learning tasks, like high-dimensional function optimization, which maintains the diversity of the population and avoids prematurity to some extent, and has a higher convergence speed.
Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical Networks
Directory of Open Access Journals (Sweden)
Simon Rosenfeld
2009-01-01
Full Text Available The question of dynamical stability and stochastic behavior of large biochemical networks is discussed. It is argued that stringent conditions of asymptotic stability have very little chance to materialize in a multidimensional system described by the differential equations of chemical kinetics. The reason is that the criteria of asymptotic stability (Routh- Hurwitz, Lyapunov criteria, Feinberg’s Deficiency Zero theorem would impose the limitations of very high algebraic order on the kinetic rates and stoichiometric coefficients, and there are no natural laws that would guarantee their unconditional validity. Highly nonlinear, dynamically unstable systems, however, are not necessarily doomed to collapse, as a simple Jacobian analysis would suggest. It is possible that their dynamics may assume the form of pseudo-random fluctuations quite similar to a shot noise, and, therefore, their behavior may be described in terms of Langevin and Fokker-Plank equations. We have shown by simulation that the resulting pseudo-stochastic processes obey the heavy-tailed Generalized Pareto Distribution with temporal sequence of pulses forming the set of constituent-specific Poisson processes. Being applied to intracellular dynamics, these properties are naturally associated with burstiness, a well documented phenomenon in the biology of gene expression.
Wang, Zhiping; Chen, Jinyu; Yu, Benli
2017-02-20
We investigate the two-dimensional (2D) and three-dimensional (3D) atom localization behaviors via spontaneously generated coherence in a microwave-driven four-level atomic system. Owing to the space-dependent atom-field interaction, it is found that the detecting probability and precision of 2D and 3D atom localization behaviors can be significantly improved via adjusting the system parameters, the phase, amplitude, and initial population distribution. Interestingly, the atom can be localized in volumes that are substantially smaller than a cubic optical wavelength. Our scheme opens a promising way to achieve high-precision and high-efficiency atom localization, which provides some potential applications in high-dimensional atom nanolithography.
Wu, Shuang; Liu, Zhi-Ping; Qiu, Xing; Wu, Hulin
2014-01-01
The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.
Garashchuk, Sophya; Rassolov, Vitaly A
2008-07-14
Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.
Directory of Open Access Journals (Sweden)
F. C. Cooper
2013-04-01
Full Text Available The fluctuation-dissipation theorem (FDT has been proposed as a method of calculating the response of the earth's atmosphere to a forcing. For this problem the high dimensionality of the relevant data sets makes truncation necessary. Here we propose a method of truncation based upon the assumption that the response to a localised forcing is spatially localised, as an alternative to the standard method of choosing a number of the leading empirical orthogonal functions. For systems where this assumption holds, the response to any sufficiently small non-localised forcing may be estimated using a set of truncations that are chosen algorithmically. We test our algorithm using 36 and 72 variable versions of a stochastic Lorenz 95 system of ordinary differential equations. We find that, for long integrations, the bias in the response estimated by the FDT is reduced from ~75% of the true response to ~30%.
Modeling and simulation of high dimensional stochastic multiscale PDE systems at the exascale
Energy Technology Data Exchange (ETDEWEB)
Zabaras, Nicolas J. [Cornell Univ., Ithaca, NY (United States)
2016-11-08
Predictive Modeling of multiscale and Multiphysics systems requires accurate data driven characterization of the input uncertainties, and understanding of how they propagate across scales and alter the final solution. This project develops a rigorous mathematical framework and scalable uncertainty quantification algorithms to efficiently construct realistic low dimensional input models, and surrogate low complexity systems for the analysis, design, and control of physical systems represented by multiscale stochastic PDEs. The work can be applied to many areas including physical and biological processes, from climate modeling to systems biology.
He, Ling Yan; Wang, Tie-Jun; Wang, Chuan
2016-07-11
High-dimensional quantum system provides a higher capacity of quantum channel, which exhibits potential applications in quantum information processing. However, high-dimensional universal quantum logic gates is difficult to achieve directly with only high-dimensional interaction between two quantum systems and requires a large number of two-dimensional gates to build even a small high-dimensional quantum circuits. In this paper, we propose a scheme to implement a general controlled-flip (CF) gate where the high-dimensional single photon serve as the target qudit and stationary qubits work as the control logic qudit, by employing a three-level Λ-type system coupled with a whispering-gallery-mode microresonator. In our scheme, the required number of interaction times between the photon and solid state system reduce greatly compared with the traditional method which decomposes the high-dimensional Hilbert space into 2-dimensional quantum space, and it is on a shorter temporal scale for the experimental realization. Moreover, we discuss the performance and feasibility of our hybrid CF gate, concluding that it can be easily extended to a 2n-dimensional case and it is feasible with current technology.
Sample-Based Motion Planning in High-Dimensional and Differentially-Constrained Systems
2010-02-01
path planning and motion primitives to enable crawling gaits on rough terrain e.g. [Rebula et al., 2007, Kolter et al., 2008,Pongas et al., 2007,Ratliff...demonstrating robust planning and locomotion over quite challenging terrain (e.g., [Rebula et al., 2007, Kolter et al., 2008, Pongas et al., 2007, Zucker, 2009...and Systems. [ Kolter et al., 2008] Kolter , J. Z., Rodgers, M. P., and Ng, A. Y. (2008). A control architecture for quadruped locomotion over rough
International Nuclear Information System (INIS)
Kim, Do Hun; Mun, Tae Hun; Kim, Dong Hwan
1999-02-01
This book introduces systems thinking and conceptual tool and modeling tool of dynamics system such as tragedy of single thinking, accessible way of system dynamics, feedback structure and causal loop diagram analysis, basic of system dynamics modeling, causal loop diagram and system dynamics modeling, information delay modeling, discovery and application for policy, modeling of crisis of agricultural and stock breeding products, dynamic model and lesson in ecosystem, development and decadence of cites and innovation of education forward system thinking.
Cavaglieri, Daniele; Bewley, Thomas
2015-04-01
Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storage RK schemes are especially effective for time-marching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop and characterize eight new low-storage implicit/explicit RK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep.
Clustering high dimensional data
DEFF Research Database (Denmark)
Assent, Ira
2012-01-01
High-dimensional data, i.e., data described by a large number of attributes, pose specific challenges to clustering. The so-called ‘curse of dimensionality’, coined originally to describe the general increase in complexity of various computational problems as dimensionality increases, is known...... to render traditional clustering algorithms ineffective. The curse of dimensionality, among other effects, means that with increasing number of dimensions, a loss of meaningful differentiation between similar and dissimilar objects is observed. As high-dimensional objects appear almost alike, new approaches...... for clustering are required. Consequently, recent research has focused on developing techniques and clustering algorithms specifically for high-dimensional data. Still, open research issues remain. Clustering is a data mining task devoted to the automatic grouping of data based on mutual similarity. Each cluster...
Sternberg, Shlomo
2010-01-01
Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides for professors and MATLAB exercises.""Even though there are many dynamical systems books on the market, this book is bound to become a classic. The the
Energy Technology Data Exchange (ETDEWEB)
Pavluchenko, Sergey A. [Universidade Federal do Maranhao (UFMA), Programa de Pos-Graduacao em Fisica, Sao Luis, Maranhao (Brazil)
2017-08-15
In this paper we perform a systematic study of spatially flat [(3+D)+1]-dimensional Einstein-Gauss-Bonnet cosmological models with Λ-term. We consider models that topologically are the product of two flat isotropic subspaces with different scale factors. One of these subspaces is three-dimensional and represents our space and the other is D-dimensional and represents extra dimensions. We consider no ansatz of the scale factors, which makes our results quite general. With both Einstein-Hilbert and Gauss-Bonnet contributions in play, D = 3 and the general D ≥ 4 cases have slightly different dynamics due to the different structure of the equations of motion. We analytically study the equations of motion in both cases and describe all possible regimes with special interest on the realistic regimes. Our analysis suggests that the only realistic regime is the transition from high-energy (Gauss-Bonnet) Kasner regime, which is the standard cosmological singularity in that case, to the anisotropic exponential regime with expanding three and contracting extra dimensions. Availability of this regime allows us to put a constraint on the value of Gauss-Bonnet coupling α and the Λ-term - this regime appears in two regions on the (α, Λ) plane: α < 0, Λ > 0, αΛ ≤ -3/2 and α > 0, αΛ ≤ (3D{sup 2} - 7D + 6)/(4D(D-1)), including the entire Λ < 0 region. The obtained bounds are confronted with the restrictions on α and Λ from other considerations, like causality, entropy-to-viscosity ratio in AdS/CFT and others. Joint analysis constrains (α, Λ) even further: α > 0, D ≥ 2 with (3D{sup 2} - 7D + 6)/(4D(D-1)) ≥ αΛ ≥ -(D+2)(D+3)(D{sup 2} + 5D + 12)/(8(D{sup 2} + 3D + 6){sup 2}). (orig.)
CSIR Research Space (South Africa)
Mc
2012-07-01
Full Text Available stream_source_info McLaren_2012.pdf.txt stream_content_type text/plain stream_size 2190 Content-Encoding ISO-8859-1 stream_name McLaren_2012.pdf.txt Content-Type text/plain; charset=ISO-8859-1 High dimensional... entanglement M. McLAREN1,2, F.S. ROUX1 & A. FORBES1,2,3 1. CSIR National Laser Centre, PO Box 395, Pretoria 0001 2. School of Physics, University of the Stellenbosch, Private Bag X1, 7602, Matieland 3. School of Physics, University of Kwazulu...
Model order reduction of large-scale dynamical systems with Jacobi-Davidson style eigensolvers
Benner, P.; Hochstenbach, M.E.; Kürschner, P.
2011-01-01
Many applications concerning physical and technical processes employ dynamical systems for simulation purposes. The increasing demand for a more accurate and detailed description of realistic phenomena leads to high dimensional dynamical systems and hence, simulation often yields an increased
Morecroft, John
System dynamics is an approach for thinking about and simulating situations and organisations of all kinds and sizes by visualising how the elements fit together, interact and change over time. This chapter, written by John Morecroft, describes modern system dynamics which retains the fundamentals developed in the 1950s by Jay W. Forrester of the MIT Sloan School of Management. It looks at feedback loops and time delays that affect system behaviour in a non-linear way, and illustrates how dynamic behaviour depends upon feedback loop structures. It also recognises improvements as part of the ongoing process of managing a situation in order to achieve goals. Significantly it recognises the importance of context, and practitioner skills. Feedback systems thinking views problems and solutions as being intertwined. The main concepts and tools: feedback structure and behaviour, causal loop diagrams, dynamics, are practically illustrated in a wide variety of contexts from a hot water shower through to a symphony orchestra and the practical application of the approach is described through several real examples of its use for strategic planning and evaluation.
Birkhoff, George D
1927-01-01
His research in dynamics constitutes the middle period of Birkhoff's scientific career, that of maturity and greatest power. -Yearbook of the American Philosophical Society The author's great book€¦is well known to all, and the diverse active modern developments in mathematics which have been inspired by this volume bear the most eloquent testimony to its quality and influence. -Zentralblatt MATH In 1927, G. D. Birkhoff wrote a remarkable treatise on the theory of dynamical systems that would inspire many later mathematicians to do great work. To a large extent, Birkhoff was writing about his o
Chernozhukov, Victor; Hansen, Christian; Spindler, Martin
2016-01-01
In this article the package High-dimensional Metrics (\\texttt{hdm}) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence intervals and significance testing for (possibly many) low-dimensional subcomponents of the high-dimensional parameter vector. Efficient estimators and uniformly valid confidence intervals for regression coefficients on target variables (e...
Wang, Wei; Yang, Jiong
With the rapid growth of computational biology and e-commerce applications, high-dimensional data becomes very common. Thus, mining high-dimensional data is an urgent problem of great practical importance. However, there are some unique challenges for mining data of high dimensions, including (1) the curse of dimensionality and more crucial (2) the meaningfulness of the similarity measure in the high dimension space. In this chapter, we present several state-of-art techniques for analyzing high-dimensional data, e.g., frequent pattern mining, clustering, and classification. We will discuss how these methods deal with the challenges of high dimensionality.
Longo, Diane M; Louie, Brent; Ptacek, Jason; Friedland, Greg; Evensen, Erik; Putta, Santosh; Atallah, Michelle; Spellmeyer, David; Wang, Ena; Pos, Zoltan; Marincola, Francesco M; Schaeffer, Andrea; Lukac, Suzanne; Railkar, Radha; Beals, Chan R; Cesano, Alessandra; Carayannopoulos, Leonidas N; Hawtin, Rachael E
2014-06-21
Single-cell network profiling (SCNP) is a multiparametric flow cytometry-based approach that simultaneously measures evoked signaling in multiple cell subsets. Previously, using the SCNP approach, age-associated immune signaling responses were identified in a cohort of 60 healthy donors. In the current study, a high-dimensional analysis of intracellular signaling was performed by measuring 24 signaling nodes in 7 distinct immune cell subsets within PBMCs in an independent cohort of 174 healthy donors [144 elderly (>65 yrs); 30 young (25-40 yrs)]. Associations between age and 9 immune signaling responses identified in the previously published 60 donor cohort were confirmed in the current study. Furthermore, within the current study cohort, 48 additional immune signaling responses differed significantly between young and elderly donors. These associations spanned all profiled modulators and immune cell subsets. These results demonstrate that SCNP, a systems-based approach, can capture the complexity of the cellular mechanisms underlying immunological aging. Further, the confirmation of age associations in an independent donor cohort supports the use of SCNP as a tool for identifying reproducible predictive biomarkers in areas such as vaccine response and response to cancer immunotherapies.
High-dimensional covariance estimation with high-dimensional data
Pourahmadi, Mohsen
2013-01-01
Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and mac
Network Reconstruction From High-Dimensional Ordinary Differential Equations.
Chen, Shizhe; Shojaie, Ali; Witten, Daniela M
2017-01-01
We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.
Modeling high dimensional multichannel brain signals
Hu, Lechuan
2017-03-27
In this paper, our goal is to model functional and effective (directional) connectivity in network of multichannel brain physiological signals (e.g., electroencephalograms, local field potentials). The primary challenges here are twofold: first, there are major statistical and computational difficulties for modeling and analyzing high dimensional multichannel brain signals; second, there is no set of universally-agreed measures for characterizing connectivity. To model multichannel brain signals, our approach is to fit a vector autoregressive (VAR) model with sufficiently high order so that complex lead-lag temporal dynamics between the channels can be accurately characterized. However, such a model contains a large number of parameters. Thus, we will estimate the high dimensional VAR parameter space by our proposed hybrid LASSLE method (LASSO+LSE) which is imposes regularization on the first step (to control for sparsity) and constrained least squares estimation on the second step (to improve bias and mean-squared error of the estimator). Then to characterize connectivity between channels in a brain network, we will use various measures but put an emphasis on partial directed coherence (PDC) in order to capture directional connectivity between channels. PDC is a directed frequency-specific measure that explains the extent to which the present oscillatory activity in a sender channel influences the future oscillatory activity in a specific receiver channel relative all possible receivers in the network. Using the proposed modeling approach, we have achieved some insights on learning in a rat engaged in a non-spatial memory task.
Modeling high dimensional multichannel brain signals
Hu, Lechuan; Fortin, Norbert; Ombao, Hernando
2017-01-01
In this paper, our goal is to model functional and effective (directional) connectivity in network of multichannel brain physiological signals (e.g., electroencephalograms, local field potentials). The primary challenges here are twofold: first, there are major statistical and computational difficulties for modeling and analyzing high dimensional multichannel brain signals; second, there is no set of universally-agreed measures for characterizing connectivity. To model multichannel brain signals, our approach is to fit a vector autoregressive (VAR) model with sufficiently high order so that complex lead-lag temporal dynamics between the channels can be accurately characterized. However, such a model contains a large number of parameters. Thus, we will estimate the high dimensional VAR parameter space by our proposed hybrid LASSLE method (LASSO+LSE) which is imposes regularization on the first step (to control for sparsity) and constrained least squares estimation on the second step (to improve bias and mean-squared error of the estimator). Then to characterize connectivity between channels in a brain network, we will use various measures but put an emphasis on partial directed coherence (PDC) in order to capture directional connectivity between channels. PDC is a directed frequency-specific measure that explains the extent to which the present oscillatory activity in a sender channel influences the future oscillatory activity in a specific receiver channel relative all possible receivers in the network. Using the proposed modeling approach, we have achieved some insights on learning in a rat engaged in a non-spatial memory task.
Chernozhukov, Victor; Hansen, Chris; Spindler, Martin
2016-01-01
The package High-dimensional Metrics (\\Rpackage{hdm}) is an evolving collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence intervals and significance testing for (possibly many) low-dimensional subcomponents of the high-dimensional parameter vector. Efficient estimators and uniformly valid confidence intervals for regression coefficients on target variables (e.g., treatment or poli...
Pilyugin, Sergei Yu
2012-01-01
Dynamical systems are abundant in theoretical physics and engineering. Their understanding, with sufficient mathematical rigor, is vital to solving many problems. This work conveys the modern theory of dynamical systems in a didactically developed fashion.In addition to topological dynamics, structural stability and chaotic dynamics, also generic properties and pseudotrajectories are covered, as well as nonlinearity. The author is an experienced book writer and his work is based on years of teaching.
Gils, S; Hoveijn, I; Takens, F; Nonlinear Dynamical Systems and Chaos
1996-01-01
Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.
Dynamic Systems and Control Engineering
International Nuclear Information System (INIS)
Kim, Jong Seok
1994-02-01
This book deals with introduction of dynamic system and control engineering, frequency domain modeling of dynamic system, temporal modeling of dynamic system, typical dynamic system and automatic control device, performance and stability of control system, root locus analysis, analysis of frequency domain dynamic system, design of frequency domain dynamic system, design and analysis of space, space of control system and digital control system such as control system design of direct digital and digitalization of consecutive control system.
Dynamic Systems and Control Engineering
Energy Technology Data Exchange (ETDEWEB)
Kim, Jong Seok
1994-02-15
This book deals with introduction of dynamic system and control engineering, frequency domain modeling of dynamic system, temporal modeling of dynamic system, typical dynamic system and automatic control device, performance and stability of control system, root locus analysis, analysis of frequency domain dynamic system, design of frequency domain dynamic system, design and analysis of space, space of control system and digital control system such as control system design of direct digital and digitalization of consecutive control system.
Stability of dynamical systems
Liao, Xiaoxin; Yu, P 0
2007-01-01
The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems.ʺ Presents
Modeling High-Dimensional Multichannel Brain Signals
Hu, Lechuan
2017-12-12
Our goal is to model and measure functional and effective (directional) connectivity in multichannel brain physiological signals (e.g., electroencephalograms, local field potentials). The difficulties from analyzing these data mainly come from two aspects: first, there are major statistical and computational challenges for modeling and analyzing high-dimensional multichannel brain signals; second, there is no set of universally agreed measures for characterizing connectivity. To model multichannel brain signals, our approach is to fit a vector autoregressive (VAR) model with potentially high lag order so that complex lead-lag temporal dynamics between the channels can be captured. Estimates of the VAR model will be obtained by our proposed hybrid LASSLE (LASSO + LSE) method which combines regularization (to control for sparsity) and least squares estimation (to improve bias and mean-squared error). Then we employ some measures of connectivity but put an emphasis on partial directed coherence (PDC) which can capture the directional connectivity between channels. PDC is a frequency-specific measure that explains the extent to which the present oscillatory activity in a sender channel influences the future oscillatory activity in a specific receiver channel relative to all possible receivers in the network. The proposed modeling approach provided key insights into potential functional relationships among simultaneously recorded sites during performance of a complex memory task. Specifically, this novel method was successful in quantifying patterns of effective connectivity across electrode locations, and in capturing how these patterns varied across trial epochs and trial types.
International Nuclear Information System (INIS)
Posch, H.A.; Narnhofer, H.; Thirring, W.
1990-01-01
We study the dynamics of classical particles interacting with attractive Gaussian potentials. This system is thermodynamically not stable and exhibits negative specific heat. The results of the computer simulation of the dynamics are discussed in comparison with various theories. In particular, we find that the condensed phase is a stationary solution of the Vlasov equation, but the Vlasov dynamics cannot describe the collapse. 14 refs., 1 tab., 11 figs. (Authors)
Ligterink, N.E.
2007-01-01
Functional system dynamics is the analysis, modelling, and simulation of continuous systems usually described by partial differential equations. From the infinite degrees of freedom of such systems only a finite number of relevant variables have to be chosen for a practical model description. The proper input and output of the system are an important part of the relevant variables.
Shadowing in dynamical systems
Pilyugin, Sergei Yu
1999-01-01
This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.
Modeling High-Dimensional Multichannel Brain Signals
Hu, Lechuan; Fortin, Norbert J.; Ombao, Hernando
2017-01-01
aspects: first, there are major statistical and computational challenges for modeling and analyzing high-dimensional multichannel brain signals; second, there is no set of universally agreed measures for characterizing connectivity. To model multichannel
Invitation to dynamical systems
Scheinerman, Edward R
2012-01-01
This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.
Ligterink, N.E.
2007-01-01
Functional system dynamics is the analysis, modelling, and simulation of continuous systems usually described by partial differential equations. From the infinite degrees of freedom of such systems only a finite number of relevant variables have to be chosen for a practical model description. The
Dynamics of Information Systems
Hirsch, Michael J; Murphey, Robert
2010-01-01
Our understanding of information and information dynamics has outgrown classical information theory. This book presents the research explaining the importance of information in the evolution of a distributed or networked system. It presents techniques for measuring the value or significance of information within the context of a system
High dimensional neurocomputing growth, appraisal and applications
Tripathi, Bipin Kumar
2015-01-01
The book presents a coherent understanding of computational intelligence from the perspective of what is known as "intelligent computing" with high-dimensional parameters. It critically discusses the central issue of high-dimensional neurocomputing, such as quantitative representation of signals, extending the dimensionality of neuron, supervised and unsupervised learning and design of higher order neurons. The strong point of the book is its clarity and ability of the underlying theory to unify our understanding of high-dimensional computing where conventional methods fail. The plenty of application oriented problems are presented for evaluating, monitoring and maintaining the stability of adaptive learning machine. Author has taken care to cover the breadth and depth of the subject, both in the qualitative as well as quantitative way. The book is intended to enlighten the scientific community, ranging from advanced undergraduates to engineers, scientists and seasoned researchers in computational intelligenc...
International Nuclear Information System (INIS)
Cugliandolo, Leticia F.
2003-09-01
These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario for this temporal evolution derived from the solution to some solvable models (p spin and the like) that are intimately connected to the mode coupling approach (and similar ones) to super-cooled liquids. At the end we list a number of open problems of great relevance in this context. These Sections can be read independently of the body of the paper where we present some of the basic analytic techniques used to study the out of equilibrium dynamics of classical and quantum models with and without disorder. We start the technical part by briefly discussing the role played by the environment and by introducing and comparing its representation in the equilibrium and dynamic treatment of classical and quantum systems. We next explain the role played by explicit quenched disorder in both approaches. Later on we focus on analytical techniques; we expand on the dynamic functional methods, and the diagrammatic expansions and resummations used to derive macroscopic equations from the microscopic dynamics. We show why the macroscopic dynamic equations for disordered models and those resulting from self-consistent approximations to non-disordered ones coincide. We review some generic properties of dynamic systems evolving out of equilibrium like the modifications of the fluctuation-dissipation theorem, generic scaling forms of the correlation functions, etc. Finally we solve a family of mean-field models. The connection between the dynamic treatment and the analysis of the free-energy landscape of these models is also presented. We use pedagogical examples all along these lectures to illustrate the properties and results. (author)
Dynamic mode decomposition for compressive system identification
Bai, Zhe; Kaiser, Eurika; Proctor, Joshua L.; Kutz, J. Nathan; Brunton, Steven L.
2017-11-01
Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data. In this work, we integrate and unify two recent innovations that extend DMD to systems with actuation and systems with heavily subsampled measurements. When combined, these methods yield a novel framework for compressive system identification, where it is possible to identify a low-order model from limited input-output data and reconstruct the associated full-state dynamic modes with compressed sensing, providing interpretability of the state of the reduced-order model. When full-state data is available, it is possible to dramatically accelerate downstream computations by first compressing the data. We demonstrate this unified framework on simulated data of fluid flow past a pitching airfoil, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). This example provides a challenging and realistic test-case for the proposed method, and results indicate that the dominant coherent structures and dynamics are well characterized even with heavily subsampled data.
Butschli Dynamic Droplet System
DEFF Research Database (Denmark)
Armstrong, R.; Hanczyc, M.
2013-01-01
Dynamical oil-water systems such as droplets display lifelike properties and may lend themselves to chemical programming to perform useful work, specifically with respect to the built environment. We present Butschli water-in-oil droplets as a model for further investigation into the development...... reconstructed the Butschli system and observed its life span under a light microscope, observing chemical patterns and droplet behaviors in nearly three hundred replicate experiments. Self-organizing patterns were observed, and during this dynamic, embodied phase the droplets provided a means of introducing...... temporal and spatial order in the system with the potential for chemical programmability. The authors propose that the discrete formation of dynamic droplets, characterized by their lifelike behavior patterns, during a variable window of time (from 30 s to 30 min after the addition of alkaline water...
Complexity in Dynamical Systems
Moore, Cristopher David
The study of chaos has shown us that deterministic systems can have a kind of unpredictability, based on a limited knowledge of their initial conditions; after a finite time, the motion appears essentially random. This observation has inspired a general interest in the subject of unpredictability, and more generally, complexity; how can we characterize how "complex" a dynamical system is?. In this thesis, we attempt to answer this question with a paradigm of complexity that comes from computer science, we extract sets of symbol sequences, or languages, from a dynamical system using standard methods of symbolic dynamics; we then ask what kinds of grammars or automata are needed a generate these languages. This places them in the Chomsky heirarchy, which in turn tells us something about how subtle and complex the dynamical system's behavior is. This gives us insight into the question of unpredictability, since these automata can also be thought of as computers attempting to predict the system. In the culmination of the thesis, we find a class of smooth, two-dimensional maps which are equivalent to the highest class in the Chomsky heirarchy, the turning machine; they are capable of universal computation. Therefore, these systems possess a kind of unpredictability qualitatively different from the usual "chaos": even if the initial conditions are known exactly, questions about the system's long-term dynamics are undecidable. No algorithm exists to answer them. Although this kind of unpredictability has been discussed in the context of distributed, many-degree-of -freedom systems (for instance, cellular automata) we believe this is the first example of such phenomena in a smooth, finite-degree-of-freedom system.
Asymptotically Honest Confidence Regions for High Dimensional
DEFF Research Database (Denmark)
Caner, Mehmet; Kock, Anders Bredahl
While variable selection and oracle inequalities for the estimation and prediction error have received considerable attention in the literature on high-dimensional models, very little work has been done in the area of testing and construction of confidence bands in high-dimensional models. However...... develop an oracle inequality for the conservative Lasso only assuming the existence of a certain number of moments. This is done by means of the Marcinkiewicz-Zygmund inequality which in our context provides sharper bounds than Nemirovski's inequality. As opposed to van de Geer et al. (2014) we allow...
Complexified dynamical systems
International Nuclear Information System (INIS)
Bender, Carl M; Holm, Darryl D; Hook, Daniel W
2007-01-01
Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely those having PT symmetry. The condition of PT symmetry selects out complex solutions that are periodic. (fast track communication)
Nonautonomous dynamical systems
Kloeden, Peter E
2011-01-01
The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.
System dynamics with interaction discontinuity
Luo, Albert C J
2015-01-01
This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.
Emergence in Dynamical Systems
Directory of Open Access Journals (Sweden)
John Collier
2013-12-01
Full Text Available Emergence is a term used in many contexts in current science; it has become fashionable. It has a traditional usage in philosophy that started in 1875 and was expanded by J. S. Mill (earlier, under a different term and C. D. Broad. It is this form of emergence that I am concerned with here. I distinguish it from uses like ‘computational emergence,’ which can be reduced to combinations of program steps, or its application to merely surprising new features that appear in complex combinations of parts. I will be concerned specifically with ontological emergence that has the logical properties required by Mill and Broad (though there might be some quibbling about the details of their views. I restrict myself to dynamical systems that are embodied in processes. Everything that we can interact with through sensation or action is either dynamical or can be understood in dynamical terms, so this covers all comprehensible forms of emergence in the strong (nonreducible sense I use. I will give general dynamical conditions that underlie the logical conditions traditionally assigned to emergence in nature.The advantage of this is that, though we cannot test logical conditions directly, we can test dynamical conditions. This gives us an empirical and realistic form of emergence, contrary those who say it is a matter of perspective.
What are System Dynamics Insights?
Stave, K.; Zimmermann, N. S.; Kim, H.
2016-01-01
This paper explores the concept of system dynamics insights. In our field, the term “insight” is generally understood to mean dynamic insight, that is, a deep understanding about the relationship between structure and behavior. We argue this is only one aspect of the range of insights possible from system dynamics activities, and describe a broader range of potential system dynamics insights. We also propose an initial framework for discussion that relates different types of system dynamics a...
Interactive Dynamic-System Simulation
Korn, Granino A
2010-01-01
Showing you how to use personal computers for modeling and simulation, Interactive Dynamic-System Simulation, Second Edition provides a practical tutorial on interactive dynamic-system modeling and simulation. It discusses how to effectively simulate dynamical systems, such as aerospace vehicles, power plants, chemical processes, control systems, and physiological systems. Written by a pioneer in simulation, the book introduces dynamic-system models and explains how software for solving differential equations works. After demonstrating real simulation programs with simple examples, the author
Wisdom, Jack
2002-01-01
In these 18 years, the research has touched every major dynamical problem in the solar system, including: the effect of chaotic zones on the distribution of asteroids, the delivery of meteorites along chaotic pathways, the chaotic motion of Pluto, the chaotic motion of the outer planets and that of the whole solar system, the delivery of short period comets from the Kuiper belt, the tidal evolution of the Uranian arid Galilean satellites, the chaotic tumbling of Hyperion and other irregular satellites, the large chaotic variations of the obliquity of Mars, the evolution of the Earth-Moon system, and the resonant core- mantle dynamics of Earth and Venus. It has introduced new analytical and numerical tools that are in widespread use. Today, nearly every long-term integration of our solar system, its subsystems, and other solar systems uses algorithms that was invented. This research has all been primarily Supported by this sequence of PGG NASA grants. During this period published major investigations of tidal evolution of the Earth-Moon system and of the passage of the Earth and Venus through non-linear core-mantle resonances were completed. It has published a major innovation in symplectic algorithms: the symplectic corrector. A paper was completed on non-perturbative hydrostatic equilibrium.
Quantifying high dimensional entanglement with two mutually unbiased bases
Directory of Open Access Journals (Sweden)
Paul Erker
2017-07-01
Full Text Available We derive a framework for quantifying entanglement in multipartite and high dimensional systems using only correlations in two unbiased bases. We furthermore develop such bounds in cases where the second basis is not characterized beyond being unbiased, thus enabling entanglement quantification with minimal assumptions. Furthermore, we show that it is feasible to experimentally implement our method with readily available equipment and even conservative estimates of physical parameters.
High-dimensional quantum cloning and applications to quantum hacking.
Bouchard, Frédéric; Fickler, Robert; Boyd, Robert W; Karimi, Ebrahim
2017-02-01
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.
Introduction to high-dimensional statistics
Giraud, Christophe
2015-01-01
Ever-greater computing technologies have given rise to an exponentially growing volume of data. Today massive data sets (with potentially thousands of variables) play an important role in almost every branch of modern human activity, including networks, finance, and genetics. However, analyzing such data has presented a challenge for statisticians and data analysts and has required the development of new statistical methods capable of separating the signal from the noise.Introduction to High-Dimensional Statistics is a concise guide to state-of-the-art models, techniques, and approaches for ha
Estimating High-Dimensional Time Series Models
DEFF Research Database (Denmark)
Medeiros, Marcelo C.; Mendes, Eduardo F.
We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. We assume both the number of covariates in the model and candidate variables can increase with the number of observations and the number of candidate variables is, possibly......, larger than the number of observations. We show the adaLASSO consistently chooses the relevant variables as the number of observations increases (model selection consistency), and has the oracle property, even when the errors are non-Gaussian and conditionally heteroskedastic. A simulation study shows...
High dimensional classifiers in the imbalanced case
DEFF Research Database (Denmark)
Bak, Britta Anker; Jensen, Jens Ledet
We consider the binary classification problem in the imbalanced case where the number of samples from the two groups differ. The classification problem is considered in the high dimensional case where the number of variables is much larger than the number of samples, and where the imbalance leads...... to a bias in the classification. A theoretical analysis of the independence classifier reveals the origin of the bias and based on this we suggest two new classifiers that can handle any imbalance ratio. The analytical results are supplemented by a simulation study, where the suggested classifiers in some...
Topology of high-dimensional manifolds
Energy Technology Data Exchange (ETDEWEB)
Farrell, F T [State University of New York, Binghamton (United States); Goettshe, L [Abdus Salam ICTP, Trieste (Italy); Lueck, W [Westfaelische Wilhelms-Universitaet Muenster, Muenster (Germany)
2002-08-15
The School on High-Dimensional Manifold Topology took place at the Abdus Salam ICTP, Trieste from 21 May 2001 to 8 June 2001. The focus of the school was on the classification of manifolds and related aspects of K-theory, geometry, and operator theory. The topics covered included: surgery theory, algebraic K- and L-theory, controlled topology, homology manifolds, exotic aspherical manifolds, homeomorphism and diffeomorphism groups, and scalar curvature. The school consisted of 2 weeks of lecture courses and one week of conference. Thwo-part lecture notes volume contains the notes of most of the lecture courses.
Cosmological dynamical systems
Leon, Genly
2011-01-01
In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and useful tools from the qualitative theory of dynamical systems. They provide the theoretical basis for the qualitative study of concrete cosmological models. Chapters 1 and 2 are a review of well-known results. Chapters 3, 4, 5 and 6 are devoted to our main results. In these chapters are extended and settled in a substantially different, more strict mathematical language, several results obtained by one of us in arXiv:0812.1013 [gr-qc]; arXiv:1009.0689 [gr-qc]; arXiv:0904.1577[gr-qc]; and arXiv:0909.3571 [hep-th]. In chapter 6, we provide a different approach to the subject discussed in astro-ph/0503478. Additionally, we perform a Poincar\\'e compactification process allowing to construct a global phase space containing all the cosmological information in both finite and infinite...
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Synchronization dynamics of two different dynamical systems
International Nuclear Information System (INIS)
Luo, Albert C.J.; Min Fuhong
2011-01-01
Highlights: → Synchronization dynamics of two distinct dynamical systems. → Synchronization, de-synchronization and instantaneous synchronization. → A controlled pendulum synchronizing with the Duffing oscillator. → Synchronization invariant set. → Synchronization parameter map. - Abstract: In this paper, synchronization dynamics of two different dynamical systems is investigated through the theory of discontinuous dynamical systems. The necessary and sufficient conditions for the synchronization, de-synchronization and instantaneous synchronization (penetration or grazing) are presented. Using such a synchronization theory, the synchronization of a controlled pendulum with the Duffing oscillator is systematically discussed as a sampled problem, and the corresponding analytical conditions for the synchronization are presented. The synchronization parameter study is carried out for a better understanding of synchronization characteristics of the controlled pendulum and the Duffing oscillator. Finally, the partial and full synchronizations of the controlled pendulum with periodic and chaotic motions are presented to illustrate the analytical conditions. The synchronization of the Duffing oscillator and pendulum are investigated in order to show the usefulness and efficiency of the methodology in this paper. The synchronization invariant domain is obtained. The technique presented in this paper should have a wide spectrum of applications in engineering. For example, this technique can be applied to the maneuvering target tracking, and the others.
Mitigating the Insider Threat Using High-Dimensional Search and Modeling
National Research Council Canada - National Science Library
Van Den Berg, Eric; Uphadyaya, Shambhu; Ngo, Phi H; Muthukrishnan, Muthu; Palan, Rajago
2006-01-01
In this project a system was built aimed at mitigating insider attacks centered around a high-dimensional search engine for correlating the large number of monitoring streams necessary for detecting insider attacks...
Clustering high dimensional data using RIA
Energy Technology Data Exchange (ETDEWEB)
Aziz, Nazrina [School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia)
2015-05-15
Clustering may simply represent a convenient method for organizing a large data set so that it can easily be understood and information can efficiently be retrieved. However, identifying cluster in high dimensionality data sets is a difficult task because of the curse of dimensionality. Another challenge in clustering is some traditional functions cannot capture the pattern dissimilarity among objects. In this article, we used an alternative dissimilarity measurement called Robust Influence Angle (RIA) in the partitioning method. RIA is developed using eigenstructure of the covariance matrix and robust principal component score. We notice that, it can obtain cluster easily and hence avoid the curse of dimensionality. It is also manage to cluster large data sets with mixed numeric and categorical value.
Chaos for Discrete Dynamical System
Directory of Open Access Journals (Sweden)
Lidong Wang
2013-01-01
Full Text Available We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distributively chaotic in a sequence, when it is chaotic in the strong sense of Li-Yorke.
Dynamical Systems for Creative Technology
van Amerongen, J.
2010-01-01
Dynamical Systems for Creative Technology gives a concise description of the physical properties of electrical, mechanical and hydraulic systems. Emphasis is placed on modelling the dynamical properties of these systems. By using a system’s approach it is shown that a limited number of mathematical
Dutt-Mazumder, Aviroop; Button, Chris; Robins, Anthony; Bartlett, Roger
2011-12-01
Recent studies have explored the organization of player movements in team sports using a range of statistical tools. However, the factors that best explain the performance of association football teams remain elusive. Arguably, this is due to the high-dimensional behavioural outputs that illustrate the complex, evolving configurations typical of team games. According to dynamical system analysts, movement patterns in team sports exhibit nonlinear self-organizing features. Nonlinear processing tools (i.e. Artificial Neural Networks; ANNs) are becoming increasingly popular to investigate the coordination of participants in sports competitions. ANNs are well suited to describing high-dimensional data sets with nonlinear attributes, however, limited information concerning the processes required to apply ANNs exists. This review investigates the relative value of various ANN learning approaches used in sports performance analysis of team sports focusing on potential applications for association football. Sixty-two research sources were summarized and reviewed from electronic literature search engines such as SPORTDiscus, Google Scholar, IEEE Xplore, Scirus, ScienceDirect and Elsevier. Typical ANN learning algorithms can be adapted to perform pattern recognition and pattern classification. Particularly, dimensionality reduction by a Kohonen feature map (KFM) can compress chaotic high-dimensional datasets into low-dimensional relevant information. Such information would be useful for developing effective training drills that should enhance self-organizing coordination among players. We conclude that ANN-based qualitative analysis is a promising approach to understand the dynamical attributes of association football players.
Management of complex dynamical systems
MacKay, R. S.
2018-02-01
Complex dynamical systems are systems with many interdependent components which evolve in time. One might wish to control their trajectories, but a more practical alternative is to control just their statistical behaviour. In many contexts this would be both sufficient and a more realistic goal, e.g. climate and socio-economic systems. I refer to it as ‘management’ of complex dynamical systems. In this paper, some mathematics for management of complex dynamical systems is developed in the weakly dependent regime, and questions are posed for the strongly dependent regime.
High-Dimensional Quantum Information Processing with Linear Optics
Fitzpatrick, Casey A.
Quantum information processing (QIP) is an interdisciplinary field concerned with the development of computers and information processing systems that utilize quantum mechanical properties of nature to carry out their function. QIP systems have become vastly more practical since the turn of the century. Today, QIP applications span imaging, cryptographic security, computation, and simulation (quantum systems that mimic other quantum systems). Many important strategies improve quantum versions of classical information system hardware, such as single photon detectors and quantum repeaters. Another more abstract strategy engineers high-dimensional quantum state spaces, so that each successful event carries more information than traditional two-level systems allow. Photonic states in particular bring the added advantages of weak environmental coupling and data transmission near the speed of light, allowing for simpler control and lower system design complexity. In this dissertation, numerous novel, scalable designs for practical high-dimensional linear-optical QIP systems are presented. First, a correlated photon imaging scheme using orbital angular momentum (OAM) states to detect rotational symmetries in objects using measurements, as well as building images out of those interactions is reported. Then, a statistical detection method using chains of OAM superpositions distributed according to the Fibonacci sequence is established and expanded upon. It is shown that the approach gives rise to schemes for sorting, detecting, and generating the recursively defined high-dimensional states on which some quantum cryptographic protocols depend. Finally, an ongoing study based on a generalization of the standard optical multiport for applications in quantum computation and simulation is reported upon. The architecture allows photons to reverse momentum inside the device. This in turn enables realistic implementation of controllable linear-optical scattering vertices for
Controlling Uncertain Dynamical Systems
Indian Academy of Sciences (India)
Author Affiliations. N Ananthkrishnan1 Rashi Bansal2. Head, CAE Analysis & Design Zeus Numerix Pvt Ltd. M-03, SINE, IIT Bombay Powai Mumbai 400076, India. MTech (Aerospace Engineering) with specialization in Dynamics & Control from IIT Bombay.
Dynamic Reconfiguration in Mobile Systems
Smit, Gerardus Johannes Maria; Glesner, Manfred; Zipf, Peter; Smit, L.T.; Havinga, Paul J.M.; Heysters, P.M.; Renovell, Michel; Rosien, M.A.J.
Dynamically reconfigurable systems have the potential of realising efficient systems as well as providing adaptability to changing system requirements. Such systems are suitable for future mobile multimedia systems that have limited battery resources, must handle diverse data types, and must operate
Ergodic theory and dynamical systems
Coudène, Yves
2016-01-01
This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of commen...
Effective control of complex turbulent dynamical systems through statistical functionals.
Majda, Andrew J; Qi, Di
2017-05-30
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among complex systems in science and engineering, including climate, material, and neural science. Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline. In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy, and new control strategies are needed. The goal of this paper is to propose an effective statistical control strategy for complex turbulent dynamical systems based on a recent statistical energy principle and statistical linear response theory. We illustrate the potential practical efficiency and verify this effective statistical control strategy on the 40D Lorenz 1996 model in forcing regimes with various types of fully turbulent dynamics with nearly one-half of the phase space unstable.
High-dimensional single-cell cancer biology.
Irish, Jonathan M; Doxie, Deon B
2014-01-01
Cancer cells are distinguished from each other and from healthy cells by features that drive clonal evolution and therapy resistance. New advances in high-dimensional flow cytometry make it possible to systematically measure mechanisms of tumor initiation, progression, and therapy resistance on millions of cells from human tumors. Here we describe flow cytometry techniques that enable a "single-cell " view of cancer. High-dimensional techniques like mass cytometry enable multiplexed single-cell analysis of cell identity, clinical biomarkers, signaling network phospho-proteins, transcription factors, and functional readouts of proliferation, cell cycle status, and apoptosis. This capability pairs well with a signaling profiles approach that dissects mechanism by systematically perturbing and measuring many nodes in a signaling network. Single-cell approaches enable study of cellular heterogeneity of primary tissues and turn cell subsets into experimental controls or opportunities for new discovery. Rare populations of stem cells or therapy-resistant cancer cells can be identified and compared to other types of cells within the same sample. In the long term, these techniques will enable tracking of minimal residual disease (MRD) and disease progression. By better understanding biological systems that control development and cell-cell interactions in healthy and diseased contexts, we can learn to program cells to become therapeutic agents or target malignant signaling events to specifically kill cancer cells. Single-cell approaches that provide deep insight into cell signaling and fate decisions will be critical to optimizing the next generation of cancer treatments combining targeted approaches and immunotherapy.
Stochastic runaway of dynamical systems
International Nuclear Information System (INIS)
Pfirsch, D.; Graeff, P.
1984-10-01
One-dimensional, stochastic, dynamical systems are well studied with respect to their stability properties. Less is known for the higher dimensional case. This paper derives sufficient and necessary criteria for the asymptotic divergence of the entropy (runaway) and sufficient ones for the moments of n-dimensional, stochastic, dynamical systems. The crucial implication is the incompressibility of their flow defined by the equations of motion in configuration space. Two possible extensions to compressible flow systems are outlined. (orig.)
Dynamical systems in classical mechanics
Kozlov, V V
1995-01-01
This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include… the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics
DEFF Research Database (Denmark)
Thomsen, Per Grove
1996-01-01
A one-dimensional model with axial discretization of engine components has been formulated using tha balance equations for mass energy and momentum and the ideal gas equation of state. ODE's that govern the dynamic behaviour of the regenerator matrix temperatures are included in the model. Known...
Lectures on chaotic dynamical systems
Afraimovich, Valentin
2002-01-01
This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics. The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.
Dynamics robustness of cascading systems.
Directory of Open Access Journals (Sweden)
Jonathan T Young
2017-03-01
Full Text Available A most important property of biochemical systems is robustness. Static robustness, e.g., homeostasis, is the insensitivity of a state against perturbations, whereas dynamics robustness, e.g., homeorhesis, is the insensitivity of a dynamic process. In contrast to the extensively studied static robustness, dynamics robustness, i.e., how a system creates an invariant temporal profile against perturbations, is little explored despite transient dynamics being crucial for cellular fates and are reported to be robust experimentally. For example, the duration of a stimulus elicits different phenotypic responses, and signaling networks process and encode temporal information. Hence, robustness in time courses will be necessary for functional biochemical networks. Based on dynamical systems theory, we uncovered a general mechanism to achieve dynamics robustness. Using a three-stage linear signaling cascade as an example, we found that the temporal profiles and response duration post-stimulus is robust to perturbations against certain parameters. Then analyzing the linearized model, we elucidated the criteria of when signaling cascades will display dynamics robustness. We found that changes in the upstream modules are masked in the cascade, and that the response duration is mainly controlled by the rate-limiting module and organization of the cascade's kinetics. Specifically, we found two necessary conditions for dynamics robustness in signaling cascades: 1 Constraint on the rate-limiting process: The phosphatase activity in the perturbed module is not the slowest. 2 Constraints on the initial conditions: The kinase activity needs to be fast enough such that each module is saturated even with fast phosphatase activity and upstream changes are attenuated. We discussed the relevance of such robustness to several biological examples and the validity of the above conditions therein. Given the applicability of dynamics robustness to a variety of systems, it
Dynamic Ocean Track System Plus -
Department of Transportation — Dynamic Ocean Track System Plus (DOTS Plus) is a planning tool implemented at the ZOA, ZAN, and ZNY ARTCCs. It is utilized by Traffic Management Unit (TMU) personnel...
Dynamical systems and linear algebra
Colonius, Fritz (Prof.)
2007-01-01
Dynamical systems and linear algebra / F. Colonius, W. Kliemann. - In: Handbook of linear algebra / ed. by Leslie Hogben. - Boca Raton : Chapman & Hall/CRC, 2007. - S. 56,1-56,22. - (Discrete mathematics and its applications)
Directory of Open Access Journals (Sweden)
Z. Ertinger
1995-09-01
Full Text Available Our aim is to present some aspects of the mathematical theory of strange behaviour of nonlinear systems, especially of systems with symmetry. Proofs are emitted, the interested reader is advised to references. Our presentation is inevitably selective. We focus on parts of the theory with possible applications to electronic circuits and systems which may display chaotic behaviour.
Dynamical systems in population biology
Zhao, Xiao-Qiang
2017-01-01
This research monograph provides an introduction to the theory of nonautonomous semiflows with applications to population dynamics. It develops dynamical system approaches to various evolutionary equations such as difference, ordinary, functional, and partial differential equations, and pays more attention to periodic and almost periodic phenomena. The presentation includes persistence theory, monotone dynamics, periodic and almost periodic semiflows, basic reproduction ratios, traveling waves, and global analysis of prototypical population models in ecology and epidemiology. Research mathematicians working with nonlinear dynamics, particularly those interested in applications to biology, will find this book useful. It may also be used as a textbook or as supplementary reading for a graduate special topics course on the theory and applications of dynamical systems. Dr. Xiao-Qiang Zhao is a University Research Professor at Memorial University of Newfoundland, Canada. His main research interests involve applied...
Dynamics of Financial System: A System Dynamics Approach
Girish K. Nair; Lewlyn Lester Raj Rodrigues
2013-01-01
There are several ratios which define the financial health of an organization but the importance of Net cash flow, Gross income, Net income, Pending bills, Receivable bills, Debt, and Book value can never be undermined as they give the exact picture of the financial condition. While there are several approaches to study the dynamics of these variables, system dynamics based modelling and simulation is one of the modern techniques. The paper explores this method to simulate the before mentione...
Self-supervised dynamical systems
International Nuclear Information System (INIS)
Zak, Michail
2004-01-01
A new type of dynamical systems which capture the interactions via information flows typical for active multi-agent systems is introduced. The mathematical formalism is based upon coupling the classical dynamical system (with random components caused by uncertainties in initial conditions as well as by Langevin forces) with the corresponding Liouville or the Fokker-Planck equations describing evolution of these uncertainties in terms of probability density. The coupling is implemented by information-based supervising forces which fundamentally change the patterns of probability evolution. It is demonstrated that the probability density can approach prescribed attractors while exhibiting such patterns as shock waves, solitons and chaos in probability space. Applications of these phenomena to information-based neural nets, expectation-based cooperation, self-programmed systems, control chaos using terminal attractors as well as to games with incomplete information, are addressed. A formal similarity between the mathematical structure of the introduced dynamical systems and quantum mechanics is discussed
Nonlinear dynamics in biological systems
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
Dynamic Stability of Maglev Systems,
1992-04-01
AD-A259 178 ANL-92/21 Materials and Components Dynamic Stability of Technology Division Materials and Components Maglev Systems Technology Division...of Maglev Systems Y. Cai, S. S. Chen, and T. M. Mulcahy Materials and Components Technology Division D. M. Rote Center for Transportation Research...of Maglev System with L-Shaped Guideway ......................................... 6 3 Stability of M aglev System s
Self-Supervised Dynamical Systems
Zak, Michail
2003-01-01
Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and
Dynamically reconfigurable photovoltaic system
Okandan, Murat; Nielson, Gregory N.
2016-05-31
A PV system composed of sub-arrays, each having a group of PV cells that are electrically connected to each other. A power management circuit for each sub-array has a communications interface and serves to connect or disconnect the sub-array to a programmable power grid. The power grid has bus rows and bus columns. A bus management circuit is positioned at a respective junction of a bus column and a bus row and is programmable through its communication interface to connect or disconnect a power path in the grid. As a result, selected sub-arrays are connected by selected power paths to be in parallel so as to produce a low system voltage, and, alternately in series so as to produce a high system voltage that is greater than the low voltage by at least a factor of ten.
Dynamically reconfigurable photovoltaic system
Energy Technology Data Exchange (ETDEWEB)
Okandan, Murat; Nielson, Gregory N.
2016-12-27
A PV system composed of sub-arrays, each having a group of PV cells that are electrically connected to each other. A power management circuit for each sub-array has a communications interface and serves to connect or disconnect the sub-array to a programmable power grid. The power grid has bus rows and bus columns. A bus management circuit is positioned at a respective junction of a bus column and a bus row and is programmable through its communication interface to connect or disconnect a power path in the grid. As a result, selected sub-arrays are connected by selected power paths to be in parallel so as to produce a low system voltage, and, alternately in series so as to produce a high system voltage that is greater than the low voltage by at least a factor of ten.
Howard, Ronald A
2007-01-01
This book is an integrated work published in two volumes. The first volume treats the basic Markov process and its variants; the second, semi-Markov and decision processes. Its intent is to equip readers to formulate, analyze, and evaluate simple and advanced Markov models of systems, ranging from genetics and space engineering to marketing. More than a collection of techniques, it constitutes a guide to the consistent application of the fundamental principles of probability and linear system theory.Author Ronald A. Howard, Professor of Management Science and Engineering at Stanford University
Dynamical system approach to phyllotaxis
DEFF Research Database (Denmark)
D'ovidio, Francesco; Mosekilde, Erik
2000-01-01
and not a dynamical system, mainly because new active elements are added at each step, and thus the dimension of the "natural" phase space is not conserved. Here a construction is presented by which a well defined dynamical system can be obtained, and a bifurcation analysis can be carried out. Stable and unstable...... of the Jacobian, and thus the eigenvalues, is given. It is likely that problems of the above type often arise in biology, and especially in morphogenesis, where growing systems are modeled....
Energy Technology Data Exchange (ETDEWEB)
Dan Maljovec; Bei Wang; Valerio Pascucci; Peer-Timo Bremer; Michael Pernice; Robert Nourgaliev
2013-05-01
The next generation of methodologies for nuclear reactor Probabilistic Risk Assessment (PRA) explicitly accounts for the time element in modeling the probabilistic system evolution and uses numerical simulation tools to account for possible dependencies between failure events. The Monte-Carlo (MC) and the Dynamic Event Tree (DET) approaches belong to this new class of dynamic PRA methodologies. A challenge of dynamic PRA algorithms is the large amount of data they produce which may be difficult to visualize and analyze in order to extract useful information. We present a software tool that is designed to address these goals. We model a large-scale nuclear simulation dataset as a high-dimensional scalar function defined over a discrete sample of the domain. First, we provide structural analysis of such a function at multiple scales and provide insight into the relationship between the input parameters and the output. Second, we enable exploratory analysis for users, where we help the users to differentiate features from noise through multi-scale analysis on an interactive platform, based on domain knowledge and data characterization. Our analysis is performed by exploiting the topological and geometric properties of the domain, building statistical models based on its topological segmentations and providing interactive visual interfaces to facilitate such explorations. We provide a user’s guide to our software tool by highlighting its analysis and visualization capabilities, along with a use case involving dataset from a nuclear reactor safety simulation.
Constraint elimination in dynamical systems
Singh, R. P.; Likins, P. W.
1989-01-01
Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.
Experimental Modeling of Dynamic Systems
DEFF Research Database (Denmark)
Knudsen, Morten Haack
2006-01-01
An engineering course, Simulation and Experimental Modeling, has been developed that is based on a method for direct estimation of physical parameters in dynamic systems. Compared with classical system identification, the method appears to be easier to understand, apply, and combine with physical...
Computable Types for Dynamic Systems
P.J. Collins (Pieter); K. Ambos-Spies; B. Loewe; W. Merkle
2009-01-01
textabstractIn this paper, we develop a theory of computable types suitable for the study of dynamic systems in discrete and continuous time. The theory uses type-two effectivity as the underlying computational model, but we quickly develop a type system which can be manipulated abstractly, but for
Managing Complex Dynamical Systems
Cox, John C.; Webster, Robert L.; Curry, Jeanie A.; Hammond, Kevin L.
2011-01-01
Management commonly engages in a variety of research designed to provide insight into the motivation and relationships of individuals, departments, organizations, etc. This paper demonstrates how the application of concepts associated with the analysis of complex systems applied to such data sets can yield enhanced insights for managerial action.
Parametric Resonance in Dynamical Systems
Nijmeijer, Henk
2012-01-01
Parametric Resonance in Dynamical Systems discusses the phenomenon of parametric resonance and its occurrence in mechanical systems,vehicles, motorcycles, aircraft and marine craft, and micro-electro-mechanical systems. The contributors provide an introduction to the root causes of this phenomenon and its mathematical equivalent, the Mathieu-Hill equation. Also included is a discussion of how parametric resonance occurs on ships and offshore systems and its frequency in mechanical and electrical systems. This book also: Presents the theory and principles behind parametric resonance Provides a unique collection of the different fields where parametric resonance appears including ships and offshore structures, automotive vehicles and mechanical systems Discusses ways to combat, cope with and prevent parametric resonance including passive design measures and active control methods Parametric Resonance in Dynamical Systems is ideal for researchers and mechanical engineers working in application fields such as MEM...
Identification of Complex Dynamical Systems with Neural Networks (2/2)
CERN. Geneva
2016-01-01
The identification and analysis of high dimensional nonlinear systems is obviously a challenging task. Neural networks have been proven to be universal approximators but this still leaves the identification task a hard one. To do it efficiently, we have to violate some of the rules of classical regression theory. Furthermore we should focus on the interpretation of the resulting model to overcome its black box character. First, we will discuss function approximation with 3 layer feedforward neural networks up to new developments in deep neural networks and deep learning. These nets are not only of interest in connection with image analysis but are a center point of the current artificial intelligence developments. Second, we will focus on the analysis of complex dynamical system in the form of state space models realized as recurrent neural networks. After the introduction of small open dynamical systems we will study dynamical systems on manifolds. Here manifold and dynamics have to be identified in parall...
Identification of Complex Dynamical Systems with Neural Networks (1/2)
CERN. Geneva
2016-01-01
The identification and analysis of high dimensional nonlinear systems is obviously a challenging task. Neural networks have been proven to be universal approximators but this still leaves the identification task a hard one. To do it efficiently, we have to violate some of the rules of classical regression theory. Furthermore we should focus on the interpretation of the resulting model to overcome its black box character. First, we will discuss function approximation with 3 layer feedforward neural networks up to new developments in deep neural networks and deep learning. These nets are not only of interest in connection with image analysis but are a center point of the current artificial intelligence developments. Second, we will focus on the analysis of complex dynamical system in the form of state space models realized as recurrent neural networks. After the introduction of small open dynamical systems we will study dynamical systems on manifolds. Here manifold and dynamics have to be identified in parall...
Dynamic state estimation techniques for large-scale electric power systems
International Nuclear Information System (INIS)
Rousseaux, P.; Pavella, M.
1991-01-01
This paper presents the use of dynamic type state estimators for energy management in electric power systems. Various dynamic type estimators have been developed, but have never been implemented. This is primarily because of dimensionality problems posed by the conjunction of an extended Kalman filter with a large scale power system. This paper precisely focuses on how to circumvent the high dimensionality, especially prohibitive in the filtering step, by using a decomposition-aggregation hierarchical scheme; to appropriately model the power system dynamics, the authors introduce new state variables in the prediction step and rely on a load forecasting method. The combination of these two techniques succeeds in solving the overall dynamic state estimation problem not only in a tractable and realistic way, but also in compliance with real-time computational requirements. Further improvements are also suggested, bound to the specifics of the high voltage electric transmission systems
Fuzzy parametric uncertainty analysis of linear dynamical systems: A surrogate modeling approach
Chowdhury, R.; Adhikari, S.
2012-10-01
Uncertainty propagation engineering systems possess significant computational challenges. This paper explores the possibility of using correlated function expansion based metamodelling approach when uncertain system parameters are modeled using Fuzzy variables. In particular, the application of High-Dimensional Model Representation (HDMR) is proposed for fuzzy finite element analysis of dynamical systems. The HDMR expansion is a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The input variables may be either finite-dimensional (i.e., a vector of parameters chosen from the Euclidean space RM) or may be infinite-dimensional as in the function space CM[0,1]. The computational effort to determine the expansion functions using the alpha cut method scales polynomially with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is integrated with a commercial Finite Element software. Modal analysis of a simplified aircraft wing with Fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations.
THE COLORIMETRY WITH A HIGH DIMENSIONAL RESOLUTION
Directory of Open Access Journals (Sweden)
I. E. Zuikov
2013-01-01
Full Text Available The developed method of Objects photometric and colorimetric characteristics measurements on the base of digital cameras are described. Application of the initial samples those are realized as the support of the control points on a non-radiant Object or as primary sources on a radiant Object will provide the metrological traceability and also build a conditional scale in each colour channel and expand the dynamic range of measurements by increasing the reliability and accuracy of measurement results.
The Dynamical Invariant of Open Quantum System
Wu, S. L.; Zhang, X. Y.; Yi, X. X.
2015-01-01
The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...
Dynamic simulation of LMFBR systems
International Nuclear Information System (INIS)
Agrawal, A.K.; Khatib-Rahbar, M.
1980-01-01
This review article focuses on the dynamic analysis of liquid-metal-cooled fast breeder reactor systems in the context of protected transients. Following a brief discussion on various design and simulation approaches, a critical review of various models for in-reactor components, intermediate heat exchangers, heat transport systems and the steam generating system is presented. A brief discussion on choice of fuels as well as core and blanket system designs is also included. Numerical considerations for obtaining system-wide steady-state and transient solutions are discussed, and examples of various system transients are presented. Another area of major interest is verification of phenomenological models. Various steps involved in the code and model verification are briefly outlined. The review concludes by posing some further areas of interest in fast reactor dynamics and safety. (author)
Engineering two-photon high-dimensional states through quantum interference
Zhang, Yingwen; Roux, Filippus S.; Konrad, Thomas; Agnew, Megan; Leach, Jonathan; Forbes, Andrew
2016-01-01
Many protocols in quantum science, for example, linear optical quantum computing, require access to large-scale entangled quantum states. Such systems can be realized through many-particle qubits, but this approach often suffers from scalability problems. An alternative strategy is to consider a lesser number of particles that exist in high-dimensional states. The spatial modes of light are one such candidate that provides access to high-dimensional quantum states, and thus they increase the storage and processing potential of quantum information systems. We demonstrate the controlled engineering of two-photon high-dimensional states entangled in their orbital angular momentum through Hong-Ou-Mandel interference. We prepare a large range of high-dimensional entangled states and implement precise quantum state filtering. We characterize the full quantum state before and after the filter, and are thus able to determine that only the antisymmetric component of the initial state remains. This work paves the way for high-dimensional processing and communication of multiphoton quantum states, for example, in teleportation beyond qubits. PMID:26933685
Combinations of complex dynamical systems
Pilgrim, Kevin M
2003-01-01
This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere. It is intended for researchers interested in the classification of those complex one-dimensional dynamical systems which are in some loose sense tame. The program is motivated by the dictionary between the theories of iterated rational maps and Kleinian groups.
Coherent structures and dynamical systems
Jimenez, Javier
1987-01-01
Any flow of a viscous fluid has a finite number of degrees of freedom, and can therefore be seen as a dynamical system. A coherent structure can be thought of as a lower dimensional manifold in whose neighborhood the dynamical system spends a substantial fraction of its time. If such a manifold exists, and if its dimensionality is substantially lower that that of the full flow, it is conceivable that the flow could be described in terms of the reduced set of degrees of freedom, and that such a description would be simpler than one in which the existence of structure was not recognized. Several examples are briefly summarized.
Effect of Zealotry in High-dimensional Opinion Dynamics Models
2015-02-18
the several platforms for portable computing to choose from, such as Apple iPad, Amazon Kindle, and Samsung Galaxy Note. A third example is the choice... diverse topologies, Chaos 17, 026111 (2007). [16] S. K. Maity, T. V. Manoj, and A. Mukherjee, Opinion formation in time-varying social networks: The case of
Linking PCA and time derivatives of dynamic systems
Stanimirovic, Olja; Hoefsloot, Huub C. J.; de Bokx, Pieter K.; Smilde, Age K.
2006-01-01
Low dimensional approximate descriptions of the high dimensional phase space of dynamic processes are very useful. Principal component analysis (PCA) is the most used technique to find the low dimensional subspace of interest. Here, it will be shown that mean centering of the process data across
Multivariate statistics high-dimensional and large-sample approximations
Fujikoshi, Yasunori; Shimizu, Ryoichi
2010-01-01
A comprehensive examination of high-dimensional analysis of multivariate methods and their real-world applications Multivariate Statistics: High-Dimensional and Large-Sample Approximations is the first book of its kind to explore how classical multivariate methods can be revised and used in place of conventional statistical tools. Written by prominent researchers in the field, the book focuses on high-dimensional and large-scale approximations and details the many basic multivariate methods used to achieve high levels of accuracy. The authors begin with a fundamental presentation of the basic
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-01
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Truly random dynamics generated by autonomous dynamical systems
González, J. A.; Reyes, L. I.
2001-09-01
We investigate explicit functions that can produce truly random numbers. We use the analytical properties of the explicit functions to show that a certain class of autonomous dynamical systems can generate random dynamics. This dynamics presents fundamental differences with the known chaotic systems. We present real physical systems that can produce this kind of random time-series. Some applications are discussed.
Dynamic decoupling of secondary systems
International Nuclear Information System (INIS)
Gupta, A.K.; Tembulkar, J.M.
1984-01-01
The dynamic analysis of primary systems must often be performed decoupled from the secondary system. In doing so, one should assure that the decoupling does not significantly affect the frequencies and the response of the primary systems. The practice consists of heuristic algorithms intended to limit changes in the frequencies. The change in response is not considered. In this paper, changes in both the frequencies and the response are considered. Rational, but simple algorithms are derived to make accurate predictions. Material up to MDOF primary-SDOF secondary system is presented in this paper. MDOF-MDOF systems are treated in a companion paper. (orig.)
Dynamics of Variable Mass Systems
Eke, Fidelis O.
1998-01-01
This report presents the results of an investigation of the effects of mass loss on the attitude behavior of spinning bodies in flight. The principal goal is to determine whether there are circumstances under which the motion of variable mass systems can become unstable in the sense that their transverse angular velocities become unbounded. Obviously, results from a study of this kind would find immediate application in the aerospace field. The first part of this study features a complete and mathematically rigorous derivation of a set of equations that govern both the translational and rotational motions of general variable mass systems. The remainder of the study is then devoted to the application of the equations obtained to a systematic investigation of the effect of various mass loss scenarios on the dynamics of increasingly complex models of variable mass systems. It is found that mass loss can have a major impact on the dynamics of mechanical systems, including a possible change in the systems stability picture. Factors such as nozzle geometry, combustion chamber geometry, propellant's initial shape, size and relative mass, and propellant location can all have important influences on the system's dynamic behavior. The relative importance of these parameters on-system motion are quantified in a way that is useful for design purposes.
2000-01-01
The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.
Controlling dynamics in diatomic systems
Indian Academy of Sciences (India)
WINTEC
Abstract. Controlling molecular energetics using laser pulses is exemplified for nuclear motion in two different diatomic systems. The problem of finding the optimized field for maximizing a desired quantum dynamical target is formulated using an iterative method. The method is applied for two diatomic sys- tems, HF and OH.
Construction of high-dimensional neural network potentials using environment-dependent atom pairs.
Jose, K V Jovan; Artrith, Nongnuch; Behler, Jörg
2012-05-21
An accurate determination of the potential energy is the crucial step in computer simulations of chemical processes, but using electronic structure methods on-the-fly in molecular dynamics (MD) is computationally too demanding for many systems. Constructing more efficient interatomic potentials becomes intricate with increasing dimensionality of the potential-energy surface (PES), and for numerous systems the accuracy that can be achieved is still not satisfying and far from the reliability of first-principles calculations. Feed-forward neural networks (NNs) have a very flexible functional form, and in recent years they have been shown to be an accurate tool to construct efficient PESs. High-dimensional NN potentials based on environment-dependent atomic energy contributions have been presented for a number of materials. Still, these potentials may be improved by a more detailed structural description, e.g., in form of atom pairs, which directly reflect the atomic interactions and take the chemical environment into account. We present an implementation of an NN method based on atom pairs, and its accuracy and performance are compared to the atom-based NN approach using two very different systems, the methanol molecule and metallic copper. We find that both types of NN potentials provide an excellent description of both PESs, with the pair-based method yielding a slightly higher accuracy making it a competitive alternative for addressing complex systems in MD simulations.
Adaptive, dynamic, and resilient systems
Suri, Niranjan
2015-01-01
As the complexity of today's networked computer systems grows, they become increasingly difficult to understand, predict, and control. Addressing these challenges requires new approaches to building these systems. Adaptive, Dynamic, and Resilient Systems supplies readers with various perspectives of the critical infrastructure that systems of networked computers rely on. It introduces the key issues, describes their interrelationships, and presents new research in support of these areas.The book presents the insights of a different group of international experts in each chapter. Reporting on r
High-dimensional quantum cryptography with twisted light
International Nuclear Information System (INIS)
Mirhosseini, Mohammad; Magaña-Loaiza, Omar S; O’Sullivan, Malcolm N; Rodenburg, Brandon; Malik, Mehul; Boyd, Robert W; Lavery, Martin P J; Padgett, Miles J; Gauthier, Daniel J
2015-01-01
Quantum key distribution (QKD) systems often rely on polarization of light for encoding, thus limiting the amount of information that can be sent per photon and placing tight bounds on the error rates that such a system can tolerate. Here we describe a proof-of-principle experiment that indicates the feasibility of high-dimensional QKD based on the transverse structure of the light field allowing for the transfer of more than 1 bit per photon. Our implementation uses the orbital angular momentum (OAM) of photons and the corresponding mutually unbiased basis of angular position (ANG). Our experiment uses a digital micro-mirror device for the rapid generation of OAM and ANG modes at 4 kHz, and a mode sorter capable of sorting single photons based on their OAM and ANG content with a separation efficiency of 93%. Through the use of a seven-dimensional alphabet encoded in the OAM and ANG bases, we achieve a channel capacity of 2.05 bits per sifted photon. Our experiment demonstrates that, in addition to having an increased information capacity, multilevel QKD systems based on spatial-mode encoding can be more resilient against intercept-resend eavesdropping attacks. (paper)
Explorations on High Dimensional Landscapes: Spin Glasses and Deep Learning
Sagun, Levent
This thesis deals with understanding the structure of high-dimensional and non-convex energy landscapes. In particular, its focus is on the optimization of two classes of functions: homogeneous polynomials and loss functions that arise in machine learning. In the first part, the notion of complexity of a smooth, real-valued function is studied through its critical points. Existing theoretical results predict that certain random functions that are defined on high dimensional domains have a narrow band of values whose pre-image contains the bulk of its critical points. This section provides empirical evidence for convergence of gradient descent to local minima whose energies are near the predicted threshold justifying the existing asymptotic theory. Moreover, it is empirically shown that a similar phenomenon may hold for deep learning loss functions. Furthermore, there is a comparative analysis of gradient descent and its stochastic version showing that in high dimensional regimes the latter is a mere speedup. The next study focuses on the halting time of an algorithm at a given stopping condition. Given an algorithm, the normalized fluctuations of the halting time follow a distribution that remains unchanged even when the input data is sampled from a new distribution. Two qualitative classes are observed: a Gumbel-like distribution that appears in Google searches, human decision times, and spin glasses and a Gaussian-like distribution that appears in conjugate gradient method, deep learning with MNIST and random input data. Following the universality phenomenon, the Hessian of the loss functions of deep learning is studied. The spectrum is seen to be composed of two parts, the bulk which is concentrated around zero, and the edges which are scattered away from zero. Empirical evidence is presented for the bulk indicating how over-parametrized the system is, and for the edges that depend on the input data. Furthermore, an algorithm is proposed such that it would
Dynamical systems probabilistic risk assessment
Energy Technology Data Exchange (ETDEWEB)
Denman, Matthew R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ames, Arlo Leroy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2014-03-01
Probabilistic Risk Assessment (PRA) is the primary tool used to risk-inform nuclear power regulatory and licensing activities. Risk-informed regulations are intended to reduce inherent conservatism in regulatory metrics (e.g., allowable operating conditions and technical specifications) which are built into the regulatory framework by quantifying both the total risk profile as well as the change in the risk profile caused by an event or action (e.g., in-service inspection procedures or power uprates). Dynamical Systems (DS) analysis has been used to understand unintended time-dependent feedbacks in both industrial and organizational settings. In dynamical systems analysis, feedback loops can be characterized and studied as a function of time to describe the changes to the reliability of plant Structures, Systems and Components (SSCs). While DS has been used in many subject areas, some even within the PRA community, it has not been applied toward creating long-time horizon, dynamic PRAs (with time scales ranging between days and decades depending upon the analysis). Understanding slowly developing dynamic effects, such as wear-out, on SSC reliabilities may be instrumental in ensuring a safely and reliably operating nuclear fleet. Improving the estimation of a plant's continuously changing risk profile will allow for more meaningful risk insights, greater stakeholder confidence in risk insights, and increased operational flexibility.
Dynamics of immune system vulnerabilities
Stromberg, Sean P.
The adaptive immune system can be viewed as a complex system, which adapts, over time, to reflect the history of infections experienced by the organism. Understanding its operation requires viewing it in terms of tradeoffs under constraints and evolutionary history. It typically displays "robust, yet fragile" behavior, meaning common tasks are robust to small changes but novel threats or changes in environment can have dire consequences. In this dissertation we use mechanistic models to study several biological processes: the immune response, the homeostasis of cells in the lymphatic system, and the process that normally prevents autoreactive cells from entering the lymphatic system. Using these models we then study the effects of these processes interacting. We show that the mechanisms that regulate the numbers of cells in the immune system, in conjunction with the immune response, can act to suppress autoreactive cells from proliferating, thus showing quantitatively how pathogenic infections can suppress autoimmune disease. We also show that over long periods of time this same effect can thin the repertoire of cells that defend against novel threats, leading to an age correlated vulnerability. This vulnerability is shown to be a consequence of system dynamics, not due to degradation of immune system components with age. Finally, modeling a specific tolerance mechanism that normally prevents autoimmune disease, in conjunction with models of the immune response and homeostasis we look at the consequences of the immune system mistakenly incorporating pathogenic molecules into its tolerizing mechanisms. The signature of this dynamic matches closely that of the dengue virus system.
Vehicle systems: coupled and interactive dynamics analysis
Vantsevich, Vladimir V.
2014-11-01
This article formulates a new direction in vehicle dynamics, described as coupled and interactive vehicle system dynamics. Formalised procedures and analysis of case studies are presented. An analytical consideration, which explains the physics of coupled system dynamics and its consequences for dynamics of a vehicle, is given for several sets of systems including: (i) driveline and suspension of a 6×6 truck, (ii) a brake mechanism and a limited slip differential of a drive axle and (iii) a 4×4 vehicle steering system and driveline system. The article introduces a formal procedure to turn coupled system dynamics into interactive dynamics of systems. A new research direction in interactive dynamics of an active steering and a hybrid-electric power transmitting unit is presented and analysed to control power distribution between the drive axles of a 4×4 vehicle. A control strategy integrates energy efficiency and lateral dynamics by decoupling dynamics of the two systems thus forming their interactive dynamics.
Feedback coupling in dynamical systems
Trimper, Steffen; Zabrocki, Knud
2003-05-01
Different evolution models are considered with feedback-couplings. In particular, we study the Lotka-Volterra system under the influence of a cumulative term, the Ginzburg-Landau model with a convolution memory term and chemical rate equations with time delay. The memory leads to a modified dynamical behavior. In case of a positive coupling the generalized Lotka-Volterra system exhibits a maximum gain achieved after a finite time, but the population will die out in the long time limit. In the opposite case, the time evolution is terminated in a crash. Due to the nonlinear feedback coupling the two branches of a bistable model are controlled by the the strength and the sign of the memory. For a negative coupling the system is able to switch over between both branches of the stationary solution. The dynamics of the system is further controlled by the initial condition. The diffusion-limited reaction is likewise studied in case the reacting entities are not available simultaneously. Whereas for an external feedback the dynamics is altered, but the stationary solution remain unchanged, a self-organized internal feedback leads to a time persistent solution.
Hidden attractors in dynamical systems
Dudkowski, Dawid; Jafari, Sajad; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Prasad, Awadhesh
2016-06-01
Complex dynamical systems, ranging from the climate, ecosystems to financial markets and engineering applications typically have many coexisting attractors. This property of the system is called multistability. The final state, i.e., the attractor on which the multistable system evolves strongly depends on the initial conditions. Additionally, such systems are very sensitive towards noise and system parameters so a sudden shift to a contrasting regime may occur. To understand the dynamics of these systems one has to identify all possible attractors and their basins of attraction. Recently, it has been shown that multistability is connected with the occurrence of unpredictable attractors which have been called hidden attractors. The basins of attraction of the hidden attractors do not touch unstable fixed points (if exists) and are located far away from such points. Numerical localization of the hidden attractors is not straightforward since there are no transient processes leading to them from the neighborhoods of unstable fixed points and one has to use the special analytical-numerical procedures. From the viewpoint of applications, the identification of hidden attractors is the major issue. The knowledge about the emergence and properties of hidden attractors can increase the likelihood that the system will remain on the most desirable attractor and reduce the risk of the sudden jump to undesired behavior. We review the most representative examples of hidden attractors, discuss their theoretical properties and experimental observations. We also describe numerical methods which allow identification of the hidden attractors.
Global communication schemes for the numerical solution of high-dimensional PDEs
DEFF Research Database (Denmark)
Hupp, Philipp; Heene, Mario; Jacob, Riko
2016-01-01
The numerical treatment of high-dimensional partial differential equations is among the most compute-hungry problems and in urgent need for current and future high-performance computing (HPC) systems. It is thus also facing the grand challenges of exascale computing such as the requirement...
Dynamical Systems and Motion Vision.
1988-04-01
TASK Artificial Inteligence Laboratory AREA I WORK UNIT NUMBERS 545 Technology Square . Cambridge, MA 02139 C\\ II. CONTROLLING OFFICE NAME ANO0 ADDRESS...INSTITUTE OF TECHNOLOGY ARTIFICIAL INTELLIGENCE LABORATORY A.I.Memo No. 1037 April, 1988 Dynamical Systems and Motion Vision Joachim Heel Abstract: In this... Artificial Intelligence L3 Laboratory of the Massachusetts Institute of Technology. Support for the Laboratory’s [1 Artificial Intelligence Research is
DYNAMICS OF FINANCIAL SYSTEM: A SYSTEM DYNAMICS APPROACH
Directory of Open Access Journals (Sweden)
Girish K Nair
2013-01-01
Full Text Available There are several ratios which define the financial health of an organization but the importance of Net cash flow, Gross income, Net income, Pending bills, Receivable bills, Debt, and Book value can never be undermined as they give the exact picture of the financial condition. While there are several approaches to study the dynamics of these variables, system dynamics based modelling and simulation is one of the modern techniques. The paper explores this method to simulate the before mentioned parameters during production capacity expansion in an electronic industry. Debt and Book value have shown a non-linear pattern of variation which is discussed. The model can be used by the financial experts as a decision support tool in arriving at conclusions in connection to the expansion plans of the organization.
Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.
Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young
2017-03-14
Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.
On Rank Driven Dynamical Systems
Veerman, J. J. P.; Prieto, F. J.
2014-08-01
We investigate a class of models related to the Bak-Sneppen (BS) model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of "complex behavior" such as self-organized criticality that is often observed in physical and biological systems. In this model, random fitnesses in are associated to agents located at the vertices of a graph . Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others with a priori given rank probabilities are replaced by new agents with random fitnesses. We consider two cases: The exogenous case where the new fitnesses are taken from an a priori fixed distribution, and the endogenous case where the new fitnesses are taken from the current distribution as it evolves. We approximate the dynamics by making a simplifying independence assumption. We use Order Statistics and Dynamical Systems to define a rank-driven dynamical system that approximates the evolution of the distribution of the fitnesses in these rank-driven models, as well as in the BS model. For this simplified model we can find the limiting marginal distribution as a function of the initial conditions. Agreement with experimental results of the BS model is excellent.
Directory of Open Access Journals (Sweden)
Enkelejda Miho
2018-02-01
Full Text Available The adaptive immune system recognizes antigens via an immense array of antigen-binding antibodies and T-cell receptors, the immune repertoire. The interrogation of immune repertoires is of high relevance for understanding the adaptive immune response in disease and infection (e.g., autoimmunity, cancer, HIV. Adaptive immune receptor repertoire sequencing (AIRR-seq has driven the quantitative and molecular-level profiling of immune repertoires, thereby revealing the high-dimensional complexity of the immune receptor sequence landscape. Several methods for the computational and statistical analysis of large-scale AIRR-seq data have been developed to resolve immune repertoire complexity and to understand the dynamics of adaptive immunity. Here, we review the current research on (i diversity, (ii clustering and network, (iii phylogenetic, and (iv machine learning methods applied to dissect, quantify, and compare the architecture, evolution, and specificity of immune repertoires. We summarize outstanding questions in computational immunology and propose future directions for systems immunology toward coupling AIRR-seq with the computational discovery of immunotherapeutics, vaccines, and immunodiagnostics.
Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems
Marston, J. B.; Hastings, M. B.
2005-03-01
The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.
Harnessing high-dimensional hyperentanglement through a biphoton frequency comb
Xie, Zhenda; Zhong, Tian; Shrestha, Sajan; Xu, Xinan; Liang, Junlin; Gong, Yan-Xiao; Bienfang, Joshua C.; Restelli, Alessandro; Shapiro, Jeffrey H.; Wong, Franco N. C.; Wei Wong, Chee
2015-08-01
Quantum entanglement is a fundamental resource for secure information processing and communications, and hyperentanglement or high-dimensional entanglement has been separately proposed for its high data capacity and error resilience. The continuous-variable nature of the energy-time entanglement makes it an ideal candidate for efficient high-dimensional coding with minimal limitations. Here, we demonstrate the first simultaneous high-dimensional hyperentanglement using a biphoton frequency comb to harness the full potential in both the energy and time domain. Long-postulated Hong-Ou-Mandel quantum revival is exhibited, with up to 19 time-bins and 96.5% visibilities. We further witness the high-dimensional energy-time entanglement through Franson revivals, observed periodically at integer time-bins, with 97.8% visibility. This qudit state is observed to simultaneously violate the generalized Bell inequality by up to 10.95 standard deviations while observing recurrent Clauser-Horne-Shimony-Holt S-parameters up to 2.76. Our biphoton frequency comb provides a platform for photon-efficient quantum communications towards the ultimate channel capacity through energy-time-polarization high-dimensional encoding.
Substitution dynamical systems spectral analysis
Queffélec, Martine
2010-01-01
This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many...
System dynamics in hydropower plants
Energy Technology Data Exchange (ETDEWEB)
Stuksrud, Dag Birger
1998-12-31
The main purpose of this thesis on system dynamics in hydropower plants was to establish new models of a hydropower system where the turbine/conduits and the electricity supply and generation are connected together as one unit such that possible interactions between the two power regimes can be studied. In order to describe the system dynamics as well as possible, a previously developed analytic model of high-head Francis turbines is improved. The model includes the acceleration resistance in the turbine runner and the draft tube. Expressions for the loss coefficients in the model are derived in order to obtain a purely analytic model. The necessity of taking the hydraulic inertia into account is shown by means of simulations. Unstable behaviour and a higher transient turbine speed than expected may occur for turbines with steep characteristics or large draft tubes. The turbine model was verified previously with respect to a high-head Francis turbine; the thesis performs an experimental verification on a low-head Francis turbine and compares the measurements with simulations from the improved turbine model. It is found that the dynamic turbine model is, after adjustment, capable of describing low-head machines as well with satisfying results. The thesis applies a method called the ``Limited zero-pole method`` to obtain new rational approximations of the elastic behaviour in the conduits with frictional damping included. These approximations are used to provide an accurate state space formulation of a hydropower plant. Simulations performed with the new computer programs show that hydraulic transients such as water-hammer and mass oscillations are reflected in the electric grid. Unstable governing performance in the electric and hydraulic parts also interact. This emphasizes the need for analysing the whole power system as a unit. 63 refs., 149 figs., 4 tabs.
High-dimensional model estimation and model selection
CERN. Geneva
2015-01-01
I will review concepts and algorithms from high-dimensional statistics for linear model estimation and model selection. I will particularly focus on the so-called p>>n setting where the number of variables p is much larger than the number of samples n. I will focus mostly on regularized statistical estimators that produce sparse models. Important examples include the LASSO and its matrix extension, the Graphical LASSO, and more recent non-convex methods such as the TREX. I will show the applicability of these estimators in a diverse range of scientific applications, such as sparse interaction graph recovery and high-dimensional classification and regression problems in genomics.
Power system dynamics and control
Kwatny, Harry G
2016-01-01
This monograph explores a consistent modeling and analytic framework that provides the tools for an improved understanding of the behavior and the building of efficient models of power systems. It covers the essential concepts for the study of static and dynamic network stability, reviews the structure and design of basic voltage and load-frequency regulators, and offers an introduction to power system optimal control with reliability constraints. A set of Mathematica tutorial notebooks providing detailed solutions of the examples worked-out in the text, as well as a package that will enable readers to work out their own examples and problems, supplements the text. A key premise of the book is that the design of successful control systems requires a deep understanding of the processes to be controlled; as such, the technical discussion begins with a concise review of the physical foundations of electricity and magnetism. This is followed by an overview of nonlinear circuits that include resistors, inductors, ...
Nonlinear transport of dynamic system phase space
International Nuclear Information System (INIS)
Xie Xi; Xia Jiawen
1993-01-01
The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example
Musashi dynamic image processing system
International Nuclear Information System (INIS)
Murata, Yutaka; Mochiki, Koh-ichi; Taguchi, Akira
1992-01-01
In order to produce transmitted neutron dynamic images using neutron radiography, a real time system called Musashi dynamic image processing system (MDIPS) was developed to collect, process, display and record image data. The block diagram of the MDIPS is shown. The system consists of a highly sensitive, high resolution TV camera driven by a custom-made scanner, a TV camera deflection controller for optimal scanning, which adjusts to the luminous intensity and the moving speed of an object, a real-time corrector to perform the real time correction of dark current, shading distortion and field intensity fluctuation, a real time filter for increasing the image signal to noise ratio, a video recording unit and a pseudocolor monitor to realize recording in commercially available products and monitoring by means of the CRTs in standard TV scanning, respectively. The TV camera and the TV camera deflection controller utilized for producing still images can be applied to this case. The block diagram of the real-time corrector is shown. Its performance is explained. Linear filters and ranked order filters were developed. (K.I.)
Quantum Dynamics in Biological Systems
Shim, Sangwoo
In the first part of this dissertation, recent efforts to understand quantum mechanical effects in biological systems are discussed. Especially, long-lived quantum coherences observed during the electronic energy transfer process in the Fenna-Matthews-Olson complex at physiological condition are studied extensively using theories of open quantum systems. In addition to the usual master equation based approaches, the effect of the protein structure is investigated in atomistic detail through the combined application of quantum chemistry and molecular dynamics simulations. To evaluate the thermalized reduced density matrix, a path-integral Monte Carlo method with a novel importance sampling approach is developed for excitons coupled to an arbitrary phonon bath at a finite temperature. In the second part of the thesis, simulations of molecular systems and applications to vibrational spectra are discussed. First, the quantum dynamics of a molecule is simulated by combining semiclassical initial value representation and density funcitonal theory with analytic derivatives. A computationally-tractable approximation to the sum-of-states formalism of Raman spectra is subsequently discussed.
On some dynamical chameleon systems
Burkin, I. M.; Kuznetsova, O. I.
2018-03-01
It is now well known that dynamical systems can be categorized into systems with self-excited attractors and systems with hidden attractors. A self-excited attractor has a basin of attraction that is associated with an unstable equilibrium, while a hidden attractor has a basin of attraction that does not intersect with small neighborhoods of any equilibrium points. Hidden attractors play the important role in engineering applications because they allow unexpected and potentially disastrous responses to perturbations in a structure like a bridge or an airplane wing. In addition, complex behaviors of chaotic systems have been applied in various areas from image watermarking, audio encryption scheme, asymmetric color pathological image encryption, chaotic masking communication to random number generator. Recently, researchers have discovered the so-called “chameleon systems”. These systems were so named because they demonstrate self-excited or hidden oscillations depending on the value of parameters. The present paper offers a simple algorithm of synthesizing one-parameter chameleon systems. The authors trace the evolution of Lyapunov exponents and the Kaplan-Yorke dimension of such systems which occur when parameters change.
System Dynamics and Serious Games
Van Daalen, C.; Schaffernicht, M.; Mayer, I.
2014-01-01
This paper deals with the relationship between serious games and system dynamics. Games have been used in SD since the beginning. However, the field of serious gaming also has its own development. The purpose of this contribution is to provide a broad overview of the combination of serious gaming and SD and discuss the state of the art and promise. We first define serious game, simulation and case study and then point out how SD overlaps with them. Then we move on to define the basic componen...
Directory of Open Access Journals (Sweden)
Xiaodian Sun
2016-10-01
Full Text Available Background: Gene regulatory networks are complex dynamic systems and the reverse-engineering of such networks from high-dimensional time course transcriptomic data have attracted researchers from various fields. It is also interesting and important to study the behavior of the reconstructed networks on the basis of dynamic models and the biological mechanisms. We focus on the gene regulatory networks reconstructed using the ordinary differential equation (ODE modelling approach and investigate the properties of these networks. Results: Controllability and stability analyses are conducted for the reconstructed gene response networks of 17 influenza infected subjects based on ODE models. Symptomatic subjects tend to have larger numbers of driver nodes, higher proportions of critical links and lower proportions of redundant links than asymptomatic subjects. We also show that the degree distribution, rather than the structure of networks, plays an important role in controlling the network in response to influenza infection. In addition, we find that the stability of high-dimensional networks is very sensitive to randomness in the reconstructed systems brought by errors in measurements and parameter estimation. Conclusions: The gene response networks of asymptomatic subjects are easier to be controlled than those of symptomatic subjects. This may indicate that the regulatory systems of asymptomatic subjects are easier to recover from disease stimulations, so these subjects are less likely to develop symptoms. Our results also suggest that stability constraint should be considered in the modelling of high-dimensional networks and the estimation of network parameters.
Dynamical habitability of planetary systems.
Dvorak, Rudolf; Pilat-Lohinger, Elke; Bois, Eric; Schwarz, Richard; Funk, Barbara; Beichman, Charles; Danchi, William; Eiroa, Carlos; Fridlund, Malcolm; Henning, Thomas; Herbst, Tom; Kaltenegger, Lisa; Lammer, Helmut; Léger, Alain; Liseau, René; Lunine, Jonathan; Paresce, Francesco; Penny, Alan; Quirrenbach, Andreas; Röttgering, Huub; Selsis, Frank; Schneider, Jean; Stam, Daphne; Tinetti, Giovanna; White, Glenn J
2010-01-01
The problem of the stability of planetary systems, a question that concerns only multiplanetary systems that host at least two planets, is discussed. The problem of mean motion resonances is addressed prior to discussion of the dynamical structure of the more than 350 known planets. The difference with regard to our own Solar System with eight planets on low eccentricity is evident in that 60% of the known extrasolar planets have orbits with eccentricity e > 0.2. We theoretically highlight the studies concerning possible terrestrial planets in systems with a Jupiter-like planet. We emphasize that an orbit of a particular nature only will keep a planet within the habitable zone around a host star with respect to the semimajor axis and its eccentricity. In addition, some results are given for individual systems (e.g., Gl777A) with regard to the stability of orbits within habitable zones. We also review what is known about the orbits of planets in double-star systems around only one component (e.g., gamma Cephei) and around both stars (e.g., eclipsing binaries).
Topological dimension and dynamical systems
Coornaert, Michel
2015-01-01
Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner’s characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active ar...
System dynamics for mechanical engineers
Davies, Matthew
2015-01-01
This textbook is ideal for mechanical engineering students preparing to enter the workforce during a time of rapidly accelerating technology, where they will be challenged to join interdisciplinary teams. It explains system dynamics using analogies familiar to the mechanical engineer while introducing new content in an intuitive fashion. The fundamentals provided in this book prepare the mechanical engineer to adapt to continuous technological advances with topics outside traditional mechanical engineering curricula by preparing them to apply basic principles and established approaches to new problems. This book also: · Reinforces the connection between the subject matter and engineering reality · Includes an instructor pack with the online publication that describes in-class experiments with minimal preparation requirements · Provides content dedicated to the modeling of modern interdisciplinary technological subjects, including opto-mechanical systems, high...
Dynamics of complex quantum systems
Akulin, Vladimir M
2014-01-01
This book gathers together a range of similar problems that can be encountered in different fields of modern quantum physics and that have common features with regard to multilevel quantum systems. The main motivation was to examine from a uniform standpoint various models and approaches that have been developed in atomic, molecular, condensed matter, chemical, laser and nuclear physics in various contexts. The book should help senior-level undergraduate, graduate students and researchers putting particular problems in these fields into a broader scientific context and thereby taking advantage of well-established techniques used in adjacent fields. This second edition has been expanded to include substantial new material (e.g. new sections on Dynamic Localization and on Euclidean Random Matrices and new chapters on Entanglement, Open Quantum Systems, and Coherence Protection). It is based on the author’s lectures at the Moscow Institute of Physics and Technology, at the CNRS Aimé Cotton Laboratory, and on ...
Nonlinear dynamics non-integrable systems and chaotic dynamics
Borisov, Alexander
2017-01-01
This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.
A hybridized K-means clustering approach for high dimensional ...
African Journals Online (AJOL)
International Journal of Engineering, Science and Technology ... Due to incredible growth of high dimensional dataset, conventional data base querying methods are inadequate to extract useful information, so researchers nowadays ... Recently cluster analysis is a popularly used data analysis method in number of areas.
On Robust Information Extraction from High-Dimensional Data
Czech Academy of Sciences Publication Activity Database
Kalina, Jan
2014-01-01
Roč. 9, č. 1 (2014), s. 131-144 ISSN 1452-4864 Grant - others:GA ČR(CZ) GA13-01930S Institutional support: RVO:67985807 Keywords : data mining * high-dimensional data * robust econometrics * outliers * machine learning Subject RIV: IN - Informatics, Computer Science
Pricing High-Dimensional American Options Using Local Consistency Conditions
Berridge, S.J.; Schumacher, J.M.
2004-01-01
We investigate a new method for pricing high-dimensional American options. The method is of finite difference type but is also related to Monte Carlo techniques in that it involves a representative sampling of the underlying variables.An approximating Markov chain is built using this sampling and
Irregular grid methods for pricing high-dimensional American options
Berridge, S.J.
2004-01-01
This thesis proposes and studies numerical methods for pricing high-dimensional American options; important examples being basket options, Bermudan swaptions and real options. Four new methods are presented and analysed, both in terms of their application to various test problems, and in terms of
Stability in dynamical systems I
International Nuclear Information System (INIS)
Courant, E.D.; Ruth, R.D.; Weng, W.T.
1984-08-01
We have reviewed some of the basic techniques which can be used to analyze stability in nonlinear dynamical systems, particularly in circular particle accelerators. We have concentrated on one-dimensional systems in the examples in order to simply illustrate the general techniques. We began with a review of Hamiltonian dynamics and canonical transformations. We then reviewed linear equations with periodic coefficients using the basic techniques from accelerator theory. To handle nonlinear terms we developed a canonical perturbation theory. From this we calculated invariants and the amplitude dependence of the frequency. This led us to resonances. We studied the cubic resonance in detail by using a rotating coordinate system in phase space. We then considered a general isolated nonlinear resonance. In this case we calculated the width of the resonance and estimated the spacing of resonances in order to use the Chirikov criterion to restrict the validity of the analysis. Finally the resonance equation was reduced to the pendulum equation, and we examined the motion on a separatrix. This brought us to the beginnings of stochastic behavior in the neighborhood of the separatrix. It is this complex behavior in the neighborhood of the separatrix which causes the perturbation theory used here to diverge in many cases. In spite of this the methods developed here have been and are used quite successfully to study nonlinear effects in nearly integrable systems. When used with caution and in conjunction with numerical work they give tremendous insight into the nature of the phase space structure and the stability of nonlinear differential equations. 14 references
Data-Driven Modeling of Complex Systems by means of a Dynamical ANN
Seleznev, A.; Mukhin, D.; Gavrilov, A.; Loskutov, E.; Feigin, A.
2017-12-01
The data-driven methods for modeling and prognosis of complex dynamical systems become more and more popular in various fields due to growth of high-resolution data. We distinguish the two basic steps in such an approach: (i) determining the phase subspace of the system, or embedding, from available time series and (ii) constructing an evolution operator acting in this reduced subspace. In this work we suggest a novel approach combining these two steps by means of construction of an artificial neural network (ANN) with special topology. The proposed ANN-based model, on the one hand, projects the data onto a low-dimensional manifold, and, on the other hand, models a dynamical system on this manifold. Actually, this is a recurrent multilayer ANN which has internal dynamics and capable of generating time series. Very important point of the proposed methodology is the optimization of the model allowing us to avoid overfitting: we use Bayesian criterion to optimize the ANN structure and estimate both the degree of evolution operator nonlinearity and the complexity of nonlinear manifold which the data are projected on. The proposed modeling technique will be applied to the analysis of high-dimensional dynamical systems: Lorenz'96 model of atmospheric turbulence, producing high-dimensional space-time chaos, and quasi-geostrophic three-layer model of the Earth's atmosphere with the natural orography, describing the dynamics of synoptical vortexes as well as mesoscale blocking systems. The possibility of application of the proposed methodology to analyze real measured data is also discussed. The study was supported by the Russian Science Foundation (grant #16-12-10198).
Genuinely high-dimensional nonlocality optimized by complementary measurements
International Nuclear Information System (INIS)
Lim, James; Ryu, Junghee; Yoo, Seokwon; Lee, Changhyoup; Bang, Jeongho; Lee, Jinhyoung
2010-01-01
Qubits exhibit extreme nonlocality when their state is maximally entangled and this is observed by mutually unbiased local measurements. This criterion does not hold for the Bell inequalities of high-dimensional systems (qudits), recently proposed by Collins-Gisin-Linden-Massar-Popescu and Son-Lee-Kim. Taking an alternative approach, called the quantum-to-classical approach, we derive a series of Bell inequalities for qudits that satisfy the criterion as for the qubits. In the derivation each d-dimensional subsystem is assumed to be measured by one of d possible measurements with d being a prime integer. By applying to two qubits (d=2), we find that a derived inequality is reduced to the Clauser-Horne-Shimony-Holt inequality when the degree of nonlocality is optimized over all the possible states and local observables. Further applying to two and three qutrits (d=3), we find Bell inequalities that are violated for the three-dimensionally entangled states but are not violated by any two-dimensionally entangled states. In other words, the inequalities discriminate three-dimensional (3D) entanglement from two-dimensional (2D) entanglement and in this sense they are genuinely 3D. In addition, for the two qutrits we give a quantitative description of the relations among the three degrees of complementarity, entanglement and nonlocality. It is shown that the degree of complementarity jumps abruptly to very close to its maximum as nonlocality starts appearing. These characteristics imply that complementarity plays a more significant role in the present inequality compared with the previously proposed inequality.
Dynamical systems of algebraic origin
Schmidt, Klaus
1995-01-01
Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting...
Advanced data assimilation in strongly nonlinear dynamical systems
Miller, Robert N.; Ghil, Michael; Gauthiez, Francois
1994-01-01
Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.
Dynamical Signatures of Living Systems
Zak, M.
1999-01-01
One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion
Dynamics of Large Systems of Nonlinearly Evolving Units
Lu, Zhixin
The dynamics of large systems of many nonlinearly evolving units is a general research area that has great importance for many areas in science and technology, including biology, computation by artificial neural networks, statistical mechanics, flocking in animal groups, the dynamics of coupled neurons in the brain, and many others. While universal principles and techniques are largely lacking in this broad area of research, there is still one particular phenomenon that seems to be broadly applicable. In particular, this is the idea of emergence, by which is meant macroscopic behaviors that "emerge" from a large system of many "smaller or simpler entities such that...large entities" [i.e., macroscopic behaviors] arise which "exhibit properties the smaller/simpler entities do not exhibit." In this thesis we investigate mechanisms and manifestations of emergence in four dynamical systems consisting many nonlinearly evolving units. These four systems are as follows. (a) We first study the motion of a large ensemble of many noninteracting particles in a slowly changing Hamiltonian system that undergoes a separatrix crossing. In such systems, we find that separatrix-crossing induces a counterintuitive effect. Specifically, numerical simulation of two sets of densely sprinkled initial conditions on two energy curves appears to suggest that the two energy curves, one originally enclosing the other, seemingly interchange their positions. This, however, is topologically forbidden. We resolve this paradox by introducing a numerical simulation method we call "robust" and study its consequences. (b) We next study the collective dynamics of oscillatory pacemaker neurons in Suprachiasmatic Nucleus (SCN), which, through synchrony, govern the circadian rhythm of mammals. We start from a high-dimensional description of the many coupled oscillatory neuronal units within the SCN. This description is based on a forced Kuramoto model. We then reduce the system dimensionality by using
Distribution of high-dimensional entanglement via an intra-city free-space link.
Steinlechner, Fabian; Ecker, Sebastian; Fink, Matthias; Liu, Bo; Bavaresco, Jessica; Huber, Marcus; Scheidl, Thomas; Ursin, Rupert
2017-07-24
Quantum entanglement is a fundamental resource in quantum information processing and its distribution between distant parties is a key challenge in quantum communications. Increasing the dimensionality of entanglement has been shown to improve robustness and channel capacities in secure quantum communications. Here we report on the distribution of genuine high-dimensional entanglement via a 1.2-km-long free-space link across Vienna. We exploit hyperentanglement, that is, simultaneous entanglement in polarization and energy-time bases, to encode quantum information, and observe high-visibility interference for successive correlation measurements in each degree of freedom. These visibilities impose lower bounds on entanglement in each subspace individually and certify four-dimensional entanglement for the hyperentangled system. The high-fidelity transmission of high-dimensional entanglement under real-world atmospheric link conditions represents an important step towards long-distance quantum communications with more complex quantum systems and the implementation of advanced quantum experiments with satellite links.
Dynamical System Approaches to Combinatorial Optimization
DEFF Research Database (Denmark)
Starke, Jens
2013-01-01
of large times as an asymptotically stable point of the dynamics. The obtained solutions are often not globally optimal but good approximations of it. Dynamical system and neural network approaches are appropriate methods for distributed and parallel processing. Because of the parallelization......Several dynamical system approaches to combinatorial optimization problems are described and compared. These include dynamical systems derived from penalty methods; the approach of Hopfield and Tank; self-organizing maps, that is, Kohonen networks; coupled selection equations; and hybrid methods...... thereof can be used as models for many industrial problems like manufacturing planning and optimization of flexible manufacturing systems. This is illustrated for an example in distributed robotic systems....
High Dimensional Modulation and MIMO Techniques for Access Networks
DEFF Research Database (Denmark)
Binti Othman, Maisara
Exploration of advanced modulation formats and multiplexing techniques for next generation optical access networks are of interest as promising solutions for delivering multiple services to end-users. This thesis addresses this from two different angles: high dimensionality carrierless...... the capacity per wavelength of the femto-cell network. Bit rate up to 1.59 Gbps with fiber-wireless transmission over 1 m air distance is demonstrated. The results presented in this thesis demonstrate the feasibility of high dimensionality CAP in increasing the number of dimensions and their potentially......) optical access network. 2 X 2 MIMO RoF employing orthogonal frequency division multiplexing (OFDM) with 5.6 GHz RoF signaling over all-vertical cavity surface emitting lasers (VCSEL) WDM passive optical networks (PONs). We have employed polarization division multiplexing (PDM) to further increase...
HSM: Heterogeneous Subspace Mining in High Dimensional Data
DEFF Research Database (Denmark)
Müller, Emmanuel; Assent, Ira; Seidl, Thomas
2009-01-01
Heterogeneous data, i.e. data with both categorical and continuous values, is common in many databases. However, most data mining algorithms assume either continuous or categorical attributes, but not both. In high dimensional data, phenomena due to the "curse of dimensionality" pose additional...... challenges. Usually, due to locally varying relevance of attributes, patterns do not show across the full set of attributes. In this paper we propose HSM, which defines a new pattern model for heterogeneous high dimensional data. It allows data mining in arbitrary subsets of the attributes that are relevant...... for the respective patterns. Based on this model we propose an efficient algorithm, which is aware of the heterogeneity of the attributes. We extend an indexing structure for continuous attributes such that HSM indexing adapts to different attribute types. In our experiments we show that HSM efficiently mines...
HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.
Fan, Jianqing; Liao, Yuan; Mincheva, Martina
2011-01-01
The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.
From globally coupled maps to complex-systems biology
Energy Technology Data Exchange (ETDEWEB)
Kaneko, Kunihiko, E-mail: kaneko@complex.c.u-tokyo.ac.jp [Research Center for Complex Systems Biology, Graduate School of Arts and Sciences, The University of Tokyo 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902 (Japan)
2015-09-15
Studies of globally coupled maps, introduced as a network of chaotic dynamics, are briefly reviewed with an emphasis on novel concepts therein, which are universal in high-dimensional dynamical systems. They include clustering of synchronized oscillations, hierarchical clustering, chimera of synchronization and desynchronization, partition complexity, prevalence of Milnor attractors, chaotic itinerancy, and collective chaos. The degrees of freedom necessary for high dimensionality are proposed to equal the number in which the combinatorial exceeds the exponential. Future analysis of high-dimensional dynamical systems with regard to complex-systems biology is briefly discussed.
High-dimensional data in economics and their (robust) analysis
Czech Academy of Sciences Publication Activity Database
Kalina, Jan
2017-01-01
Roč. 12, č. 1 (2017), s. 171-183 ISSN 1452-4864 R&D Projects: GA ČR GA17-07384S Institutional support: RVO:67985556 Keywords : econometrics * high-dimensional data * dimensionality reduction * linear regression * classification analysis * robustness Subject RIV: BA - General Mathematics OBOR OECD: Business and management http://library.utia.cas.cz/separaty/2017/SI/kalina-0474076.pdf
High-dimensional Data in Economics and their (Robust) Analysis
Czech Academy of Sciences Publication Activity Database
Kalina, Jan
2017-01-01
Roč. 12, č. 1 (2017), s. 171-183 ISSN 1452-4864 R&D Projects: GA ČR GA17-07384S Grant - others:GA ČR(CZ) GA13-01930S Institutional support: RVO:67985807 Keywords : econometrics * high-dimensional data * dimensionality reduction * linear regression * classification analysis * robustness Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability
High Dimensional Classification Using Features Annealed Independence Rules.
Fan, Jianqing; Fan, Yingying
2008-01-01
Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is largely poorly understood. In a seminal paper, Bickel and Levina (2004) show that the Fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem. We first demonstrate that even for the independence classification rule, classification using all the features can be as bad as the random guessing due to noise accumulation in estimating population centroids in high-dimensional feature space. In fact, we demonstrate further that almost all linear discriminants can perform as bad as the random guessing. Thus, it is paramountly important to select a subset of important features for high-dimensional classification, resulting in Features Annealed Independence Rules (FAIR). The conditions under which all the important features can be selected by the two-sample t-statistic are established. The choice of the optimal number of features, or equivalently, the threshold value of the test statistics are proposed based on an upper bound of the classification error. Simulation studies and real data analysis support our theoretical results and demonstrate convincingly the advantage of our new classification procedure.
Dynamic Stability Experiment of Maglev Systems,
1995-04-01
This report summarizes the research performed on maglev vehicle dynamic stability at Argonne National Laboratory during the past few years. It also... maglev system, it is important to consider this phenomenon in the development of all maglev systems. This report presents dynamic stability experiments...on maglev systems and compares their numerical simulation with predictions calculated by a nonlinear dynamic computer code. Instabilities of an
Attractors for discrete periodic dynamical systems
John E. Franke; James F. Selgrade
2003-01-01
A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the unin of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an...
An Axiomatic Representation of System Dynamics
Baianu, I
2004-01-01
An axiomatic representation of system dynamics is introduced in terms of categories, functors, organismal supercategories, limits and colimits of diagrams. Specific examples are considered in Complex Systems Biology, such as ribosome biogenesis and Hormonal Control in human subjects. "Fuzzy" Relational Structures are also proposed for flexible representations of biological system dynamics and organization.
Controlling chaos in discontinuous dynamical systems
International Nuclear Information System (INIS)
Danca, Marius-F.
2004-01-01
In this paper we consider the possibility to implement the technique of changes in the system variables to control the chaos introduced by Gueemez and Matias for continuous dynamical systems to a class of discontinuous dynamical systems. The approach is realized via differential inclusions following the Filippov theory. Three practical examples are considered
Dynamism in Electronic Performance Support Systems.
Laffey, James
1995-01-01
Describes a model for dynamic electronic performance support systems based on NNAble, a system developed by the training group at Apple Computer. Principles for designing dynamic performance support are discussed, including a systems approach, performer-centered design, awareness of situated cognition, organizational memory, and technology use.…
The Episodic Nature of Experience: A Dynamical Systems Analysis.
Sreekumar, Vishnu; Dennis, Simon; Doxas, Isidoros
2017-07-01
Context is an important construct in many domains of cognition, including learning, memory, and emotion. We used dynamical systems methods to demonstrate the episodic nature of experience by showing a natural separation between the scales over which within-context and between-context relationships operate. To do this, we represented an individual's emails extending over about 5 years in a high-dimensional semantic space and computed the dimensionalities of the subspaces occupied by these emails. Personal discourse has a two-scaled geometry with smaller within-context dimensionalities than between-context dimensionalities. Prior studies have shown that reading experience (Doxas, Dennis, & Oliver, 2010) and visual experience (Sreekumar, Dennis, Doxas, Zhuang, & Belkin, 2014) have a similar two-scaled structure. Furthermore, the recurrence plot of the emails revealed that experience is predictable and hierarchical, supporting the constructs of some influential theories of memory. The results demonstrate that experience is not scale-free and provide an important target for accounts of how experience shapes cognition. Copyright © 2016 Cognitive Science Society, Inc.
A Shell Multi-dimensional Hierarchical Cubing Approach for High-Dimensional Cube
Zou, Shuzhi; Zhao, Li; Hu, Kongfa
The pre-computation of data cubes is critical for improving the response time of OLAP systems and accelerating data mining tasks in large data warehouses. However, as the sizes of data warehouses grow, the time it takes to perform this pre-computation becomes a significant performance bottleneck. In a high dimensional data warehouse, it might not be practical to build all these cuboids and their indices. In this paper, we propose a shell multi-dimensional hierarchical cubing algorithm, based on an extension of the previous minimal cubing approach. This method partitions the high dimensional data cube into low multi-dimensional hierarchical cube. Experimental results show that the proposed method is significantly more efficient than other existing cubing methods.
Attachment is a dynamic system
Directory of Open Access Journals (Sweden)
Zlatka Cugmas
2003-04-01
Full Text Available On the basis of the study of recent scientific literature about the development of attachment, the author answers the following questions: which are the postulates the theory of attachment has about the stability of the patterns of attachment, which level of stability in the patterns of attachment from infancy to adulthood these studies illuminate and which factors significantly influence the (instability of the patterns of attachment in time. The theory of attachment assumes that normal circumstances elicit stability. Changes, however, can be the result of important events influencing the sensitivity of the object of attachment. Agreement has not yet been reached regarding the percentage of stability in the patterns of attachment. There is more agreement regarding attachment in adulthood than that in childhood. The results depend on the size and characteristics of the subjects of the research, the measuring instruments, type of data analysis etc. The author concludes that attachment is a dynamic system influenced by significant changes in life (the cognitive development of the child, external care, parents' divorce, different stressful situations. As the influence of stressful events on the individual person' s quality of attachment is examined, it is necessary to consider also his/her temperamental characteristics, role of other people in their lives, etc.
Reinforcement learning on slow features of high-dimensional input streams.
Directory of Open Access Journals (Sweden)
Robert Legenstein
Full Text Available Humans and animals are able to learn complex behaviors based on a massive stream of sensory information from different modalities. Early animal studies have identified learning mechanisms that are based on reward and punishment such that animals tend to avoid actions that lead to punishment whereas rewarded actions are reinforced. However, most algorithms for reward-based learning are only applicable if the dimensionality of the state-space is sufficiently small or its structure is sufficiently simple. Therefore, the question arises how the problem of learning on high-dimensional data is solved in the brain. In this article, we propose a biologically plausible generic two-stage learning system that can directly be applied to raw high-dimensional input streams. The system is composed of a hierarchical slow feature analysis (SFA network for preprocessing and a simple neural network on top that is trained based on rewards. We demonstrate by computer simulations that this generic architecture is able to learn quite demanding reinforcement learning tasks on high-dimensional visual input streams in a time that is comparable to the time needed when an explicit highly informative low-dimensional state-space representation is given instead of the high-dimensional visual input. The learning speed of the proposed architecture in a task similar to the Morris water maze task is comparable to that found in experimental studies with rats. This study thus supports the hypothesis that slowness learning is one important unsupervised learning principle utilized in the brain to form efficient state representations for behavioral learning.
Multibody system dynamics, robotics and control
Gerstmayr, Johannes
2013-01-01
The volume contains 19 contributions by international experts in the field of multibody system dynamics, robotics and control. The book aims to bridge the gap between the modeling of mechanical systems by means of multibody dynamics formulations and robotics. In the classical approach, a multibody dynamics model contains a very high level of detail, however, the application of such models to robotics or control is usually limited. The papers aim to connect the different scientific communities in multibody dynamics, robotics and control. Main topics are flexible multibody systems, humanoid robots, elastic robots, nonlinear control, optimal path planning, and identification.
Crisis-induced unstable dimension variability in a dynamical system
International Nuclear Information System (INIS)
Kubo, Geraldo T.; Viana, Ricardo L.; Lopes, Sergio R.; Grebogi, Celso
2008-01-01
Unstable dimension variability is an extreme form of non-hyperbolic behavior in chaotic systems whose attractors have periodic orbits with a different number of unstable directions. We propose a new mechanism for the onset of unstable dimension variability based on an interior crisis, or a collision between a chaotic attractor and an unstable periodic orbit. We give a physical example by considering a high-dimensional dissipative physical system driven by impulsive periodic forcing
Adaptive Integration of Nonsmooth Dynamical Systems
2017-10-11
2017 W911NF-12-R-0012-03: Adaptive Integration of Nonsmooth Dynamical Systems The views, opinions and/or findings contained in this report are those of...Integration of Nonsmooth Dynamical Systems Report Term: 0-Other Email: drum@gwu.edu Distribution Statement: 1-Approved for public release; distribution is...classdrake_1_1systems_1_1_integrator_base.html ; 3) a solver for dynamical systems with arbitrary unilateral and bilateral constraints (the key component of the time stepping systems )- see
Nonautonomous dynamical systems in the life sciences
Pötzsche, Christian
2013-01-01
Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.
Logical entropy of quantum dynamical systems
Directory of Open Access Journals (Sweden)
Ebrahimzadeh Abolfazl
2016-01-01
Full Text Available This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.
Incorporating Dynamical Systems into the Traditional Curriculum.
Natov, Jonathan
2001-01-01
Presents a brief overview of dynamical systems. Gives examples from dynamical systems and where they fit into the current curriculum. Points out that these examples are accessible to undergraduate freshmen and sophomore students, add continuity to the standard curriculum, and are worth including in classes. (MM)
Reconceptualizing Learning as a Dynamical System.
Ennis, Catherine D.
1992-01-01
Dynamical systems theory can increase our understanding of the constantly evolving learning process. Current research using experimental and interpretive paradigms focuses on describing the attractors and constraints stabilizing the educational process. Dynamical systems theory focuses attention on critical junctures in the learning process as…
Dynamics and control of hybrid mechanical systems
Leonov, G.A.; Nijmeijer, H.; Pogromski, A.Y.; Fradkov, A.L.
2010-01-01
The papers in this edited volume aim to provide a better understanding of the dynamics and control of a large class of hybrid dynamical systems that are described by different models in different state space domains. They not only cover important aspects and tools for hybrid systems analysis and
Dynamical entropy for infinite quantum systems
International Nuclear Information System (INIS)
Hudetz, T.
1990-01-01
We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)
System dynamics modelling of situation awareness
CSIR Research Space (South Africa)
Oosthuizen, R
2015-11-01
Full Text Available . The feedback loops and delays in the Command and Control system also contribute to the complex dynamic behavior. This paper will build on existing situation awareness models to develop a System Dynamics model to support a qualitative investigation through...
Systems-Dynamic Analysis for Neighborhood Study
Systems-dynamic analysis (or system dynamics (SD)) helps planners identify interrelated impacts of transportation and land-use policies on neighborhood-scale economic outcomes for households and businesses, among other applications. This form of analysis can show benefits and tr...
Narcissistic group dynamics of multiparty systems
Schruijer, S.G.L.
2015-01-01
Purpose – This paper aims to introduce and illustrate the notion of narcissistic group dynamics. It is claimed that narcissism does not simply reside within individuals but can be characteristic of groups and social systems. In this case, the focus is on narcissistic dynamics in multiparty systems.
Bifurcation Control of Chaotic Dynamical Systems
National Research Council Canada - National Science Library
Wang, Hua O; Abed, Eyad H
1992-01-01
A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems...
Chaotic systems are dynamically random
International Nuclear Information System (INIS)
Svozil, K.
1988-01-01
The idea is put forward that the significant route to chaos is driven by recursive iterations of suitable evolution functions. The corresponding formal notion of randomness is not based on dynamic complexity rather than on static complexity. 24 refs. (Author)
Dynamical systems on 2- and 3-manifolds
Grines, Viacheslav Z; Pochinka, Olga V
2016-01-01
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. < The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are present...
Partial dynamical systems, fell bundles and applications
Exel, Ruy
2017-01-01
Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C*-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of "partiality". One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product. Running in parallel with partial dynamica...
Dynamics of vehicle-road coupled system
Yang, Shaopu; Li, Shaohua
2015-01-01
Vehicle dynamics and road dynamics are usually considered to be two largely independent subjects. In vehicle dynamics, road surface roughness is generally regarded as random excitation of the vehicle, while in road dynamics, the vehicle is generally regarded as a moving load acting on the pavement. This book suggests a new research concept to integrate the vehicle and the road system with the help of a tire model, and establishes a cross-subject research framework dubbed vehicle-pavement coupled system dynamics. In this context, the dynamics of the vehicle, road and the vehicle-road coupled system are investigated by means of theoretical analysis, numerical simulations and field tests. This book will be a valuable resource for university professors, graduate students and engineers majoring in automotive design, mechanical engineering, highway engineering and other related areas. Shaopu Yang is a professor and deputy president of Shijiazhuang Tiedao University, China; Liqun Chen is a professor at Shanghai Univ...
Hawking radiation of a high-dimensional rotating black hole
Energy Technology Data Exchange (ETDEWEB)
Zhao, Ren; Zhang, Lichun; Li, Huaifan; Wu, Yueqin [Shanxi Datong University, Institute of Theoretical Physics, Department of Physics, Datong (China)
2010-01-15
We extend the classical Damour-Ruffini method and discuss Hawking radiation spectrum of high-dimensional rotating black hole using Tortoise coordinate transformation defined by taking the reaction of the radiation to the spacetime into consideration. Under the condition that the energy and angular momentum are conservative, taking self-gravitation action into account, we derive Hawking radiation spectrums which satisfy unitary principle in quantum mechanics. It is shown that the process that the black hole radiates particles with energy {omega} is a continuous tunneling process. We provide a theoretical basis for further studying the physical mechanism of black-hole radiation. (orig.)
On spectral distribution of high dimensional covariation matrices
DEFF Research Database (Denmark)
Heinrich, Claudio; Podolskij, Mark
In this paper we present the asymptotic theory for spectral distributions of high dimensional covariation matrices of Brownian diffusions. More specifically, we consider N-dimensional Itô integrals with time varying matrix-valued integrands. We observe n equidistant high frequency data points...... of the underlying Brownian diffusion and we assume that N/n -> c in (0,oo). We show that under a certain mixed spectral moment condition the spectral distribution of the empirical covariation matrix converges in distribution almost surely. Our proof relies on method of moments and applications of graph theory....
The additive hazards model with high-dimensional regressors
DEFF Research Database (Denmark)
Martinussen, Torben; Scheike, Thomas
2009-01-01
This paper considers estimation and prediction in the Aalen additive hazards model in the case where the covariate vector is high-dimensional such as gene expression measurements. Some form of dimension reduction of the covariate space is needed to obtain useful statistical analyses. We study...... model. A standard PLS algorithm can also be constructed, but it turns out that the resulting predictor can only be related to the original covariates via time-dependent coefficients. The methods are applied to a breast cancer data set with gene expression recordings and to the well known primary biliary...
High-dimensional quantum channel estimation using classical light
CSIR Research Space (South Africa)
Mabena, Chemist M
2017-11-01
Full Text Available stream_source_info Mabena_20007_2017.pdf.txt stream_content_type text/plain stream_size 960 Content-Encoding UTF-8 stream_name Mabena_20007_2017.pdf.txt Content-Type text/plain; charset=UTF-8 PHYSICAL REVIEW A 96, 053860... (2017) High-dimensional quantum channel estimation using classical light Chemist M. Mabena CSIR National Laser Centre, P.O. Box 395, Pretoria 0001, South Africa and School of Physics, University of the Witwatersrand, Johannesburg 2000, South...
Data analysis in high-dimensional sparse spaces
DEFF Research Database (Denmark)
Clemmensen, Line Katrine Harder
classification techniques for high-dimensional problems are presented: Sparse discriminant analysis, sparse mixture discriminant analysis and orthogonality constrained support vector machines. The first two introduces sparseness to the well known linear and mixture discriminant analysis and thereby provide low...... are applied to classifications of fish species, ear canal impressions used in the hearing aid industry, microbiological fungi species, and various cancerous tissues and healthy tissues. In addition, novel applications of sparse regressions (also called the elastic net) to the medical, concrete, and food...
Nonlinear dynamics of fractional order Duffing system
International Nuclear Information System (INIS)
Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian
2015-01-01
In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.
Dynamics of Open Systems with Affine Maps
International Nuclear Information System (INIS)
Zhang Da-Jian; Liu Chong-Long; Tong Dian-Min
2015-01-01
Many quantum systems of interest are initially correlated with their environments and the reduced dynamics of open systems are an interesting while challenging topic. Affine maps, as an extension of completely positive maps, are a useful tool to describe the reduced dynamics of open systems with initial correlations. However, it is unclear what kind of initial state shares an affine map. In this study, we give a sufficient condition of initial states, in which the reduced dynamics can always be described by an affine map. Our result shows that if the initial states of the combined system constitute a convex set, and if the correspondence between the initial states of the open system and those of the combined system, defined by taking the partial trace, is a bijection, then the reduced dynamics of the open system can be described by an affine map. (paper)
Transcribing the balanced scorecard into system dynamics
DEFF Research Database (Denmark)
Nielsen, Steen; Nielsen, Erland Hejn
2013-01-01
The purpose of this paper is to show how a System Dynamics Modelling approach can be integrated into the Balanced Scorecard (BSC) for a case company with special focus on the handling of causality in a dynamic perspective. The BSC model includes five perspectives and a number of financial and non...... the cause-and-effect relationships of an integrated BSC model. Including dynamic aspects of BSCs into the discussion is only in its infancy, so the aim of our work is also to contribute to both scholars’ and practitioners’ general understanding of how such delayed dynamic effects propagate through system...
Dynamical systems, attractors, and neural circuits.
Miller, Paul
2016-01-01
Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic-they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.
Optimal reduction of flexible dynamic system
International Nuclear Information System (INIS)
Jankovic, J.
1994-01-01
Dynamic system reduction is basic procedure in various problems of active control synthesis of flexible structures. In this paper is presented direct method for system reduction by explicit extraction of modes included in reduced model form. Criterion for optimal system discrete approximation in synthesis reduced dynamic model is also presented. Subjected method of system decomposition is discussed in relation to the Schur method of solving matrix algebraic Riccati equation as condition for system reduction. By using exposed method procedure of flexible system reduction in addition with corresponding example is presented. Shown procedure is powerful in problems of active control synthesis of flexible system vibrations
Scalable Nearest Neighbor Algorithms for High Dimensional Data.
Muja, Marius; Lowe, David G
2014-11-01
For many computer vision and machine learning problems, large training sets are key for good performance. However, the most computationally expensive part of many computer vision and machine learning algorithms consists of finding nearest neighbor matches to high dimensional vectors that represent the training data. We propose new algorithms for approximate nearest neighbor matching and evaluate and compare them with previous algorithms. For matching high dimensional features, we find two algorithms to be the most efficient: the randomized k-d forest and a new algorithm proposed in this paper, the priority search k-means tree. We also propose a new algorithm for matching binary features by searching multiple hierarchical clustering trees and show it outperforms methods typically used in the literature. We show that the optimal nearest neighbor algorithm and its parameters depend on the data set characteristics and describe an automated configuration procedure for finding the best algorithm to search a particular data set. In order to scale to very large data sets that would otherwise not fit in the memory of a single machine, we propose a distributed nearest neighbor matching framework that can be used with any of the algorithms described in the paper. All this research has been released as an open source library called fast library for approximate nearest neighbors (FLANN), which has been incorporated into OpenCV and is now one of the most popular libraries for nearest neighbor matching.
Manifold learning to interpret JET high-dimensional operational space
International Nuclear Information System (INIS)
Cannas, B; Fanni, A; Pau, A; Sias, G; Murari, A
2013-01-01
In this paper, the problem of visualization and exploration of JET high-dimensional operational space is considered. The data come from plasma discharges selected from JET campaigns from C15 (year 2005) up to C27 (year 2009). The aim is to learn the possible manifold structure embedded in the data and to create some representations of the plasma parameters on low-dimensional maps, which are understandable and which preserve the essential properties owned by the original data. A crucial issue for the design of such mappings is the quality of the dataset. This paper reports the details of the criteria used to properly select suitable signals downloaded from JET databases in order to obtain a dataset of reliable observations. Moreover, a statistical analysis is performed to recognize the presence of outliers. Finally data reduction, based on clustering methods, is performed to select a limited and representative number of samples for the operational space mapping. The high-dimensional operational space of JET is mapped using a widely used manifold learning method, the self-organizing maps. The results are compared with other data visualization methods. The obtained maps can be used to identify characteristic regions of the plasma scenario, allowing to discriminate between regions with high risk of disruption and those with low risk of disruption. (paper)
Elucidating high-dimensional cancer hallmark annotation via enriched ontology.
Yan, Shankai; Wong, Ka-Chun
2017-09-01
Cancer hallmark annotation is a promising technique that could discover novel knowledge about cancer from the biomedical literature. The automated annotation of cancer hallmarks could reveal relevant cancer transformation processes in the literature or extract the articles that correspond to the cancer hallmark of interest. It acts as a complementary approach that can retrieve knowledge from massive text information, advancing numerous focused studies in cancer research. Nonetheless, the high-dimensional nature of cancer hallmark annotation imposes a unique challenge. To address the curse of dimensionality, we compared multiple cancer hallmark annotation methods on 1580 PubMed abstracts. Based on the insights, a novel approach, UDT-RF, which makes use of ontological features is proposed. It expands the feature space via the Medical Subject Headings (MeSH) ontology graph and utilizes novel feature selections for elucidating the high-dimensional cancer hallmark annotation space. To demonstrate its effectiveness, state-of-the-art methods are compared and evaluated by a multitude of performance metrics, revealing the full performance spectrum on the full set of cancer hallmarks. Several case studies are conducted, demonstrating how the proposed approach could reveal novel insights into cancers. https://github.com/cskyan/chmannot. Copyright © 2017 Elsevier Inc. All rights reserved.
Stochastic Thermodynamics: A Dynamical Systems Approach
Directory of Open Access Journals (Sweden)
Tanmay Rajpurohit
2017-12-01
Full Text Available In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time.
Information Processing Capacity of Dynamical Systems
Dambre, Joni; Verstraeten, David; Schrauwen, Benjamin; Massar, Serge
2012-07-01
Many dynamical systems, both natural and artificial, are stimulated by time dependent external signals, somehow processing the information contained therein. We demonstrate how to quantify the different modes in which information can be processed by such systems and combine them to define the computational capacity of a dynamical system. This is bounded by the number of linearly independent state variables of the dynamical system, equaling it if the system obeys the fading memory condition. It can be interpreted as the total number of linearly independent functions of its stimuli the system can compute. Our theory combines concepts from machine learning (reservoir computing), system modeling, stochastic processes, and functional analysis. We illustrate our theory by numerical simulations for the logistic map, a recurrent neural network, and a two-dimensional reaction diffusion system, uncovering universal trade-offs between the non-linearity of the computation and the system's short-term memory.
Information Processing Capacity of Dynamical Systems
Dambre, Joni; Verstraeten, David; Schrauwen, Benjamin; Massar, Serge
2012-01-01
Many dynamical systems, both natural and artificial, are stimulated by time dependent external signals, somehow processing the information contained therein. We demonstrate how to quantify the different modes in which information can be processed by such systems and combine them to define the computational capacity of a dynamical system. This is bounded by the number of linearly independent state variables of the dynamical system, equaling it if the system obeys the fading memory condition. It can be interpreted as the total number of linearly independent functions of its stimuli the system can compute. Our theory combines concepts from machine learning (reservoir computing), system modeling, stochastic processes, and functional analysis. We illustrate our theory by numerical simulations for the logistic map, a recurrent neural network, and a two-dimensional reaction diffusion system, uncovering universal trade-offs between the non-linearity of the computation and the system's short-term memory. PMID:22816038
System Dynamics Modelling for a Balanced Scorecard
DEFF Research Database (Denmark)
Nielsen, Steen; Nielsen, Erland Hejn
2008-01-01
/methodology/approach - We use a case study model to develop time or dynamic dimensions by using a System Dynamics modelling (SDM) approach. The model includes five perspectives and a number of financial and non-financial measures. All indicators are defined and related to a coherent number of different cause...... have a major influence on other indicators and profit and may be impossible to predict without using a dynamic model. Practical implications - The model may be used as the first step in quantifying the cause-and-effect relationships of an integrated BSC model. Using the System Dynamics model provides......Purpose - To construct a dynamic model/framework inspired by a case study based on an international company. As described by the theory, one of the main difficulties of BSC is to foresee the time lag dimension of different types of indicators and their combined dynamic effects. Design...
Modeling the Dynamic Digestive System Microbiome†
Estes, Anne M.
2015-01-01
“Modeling the Dynamic Digestive System Microbiome” is a hands-on activity designed to demonstrate the dynamics of microbiome ecology using dried pasta and beans to model disturbance events in the human digestive system microbiome. This exercise demonstrates how microbiome diversity is influenced by: 1) niche availability and habitat space and 2) a major disturbance event, such as antibiotic use. Students use a pictorial key to examine prepared models of digestive system microbiomes to determi...
Session 6: Dynamic Modeling and Systems Analysis
Csank, Jeffrey; Chapman, Jeffryes; May, Ryan
2013-01-01
These presentations cover some of the ongoing work in dynamic modeling and dynamic systems analysis. The first presentation discusses dynamic systems analysis and how to integrate dynamic performance information into the systems analysis. The ability to evaluate the dynamic performance of an engine design may allow tradeoffs between the dynamic performance and operability of a design resulting in a more efficient engine design. The second presentation discusses the Toolbox for Modeling and Analysis of Thermodynamic Systems (T-MATS). T-MATS is a Simulation system with a library containing the basic building blocks that can be used to create dynamic Thermodynamic Systems. Some of the key features include Turbo machinery components, such as turbines, compressors, etc., and basic control system blocks. T-MAT is written in the Matlab-Simulink environment and is open source software. The third presentation focuses on getting additional performance from the engine by allowing the limit regulators only to be active when a limit is danger of being violated. Typical aircraft engine control architecture is based on MINMAX scheme, which is designed to keep engine operating within prescribed mechanical/operational safety limits. Using a conditionally active min-max limit regulator scheme, additional performance can be gained by disabling non-relevant limit regulators
q-entropy for symbolic dynamical systems
International Nuclear Information System (INIS)
Zhao, Yun; Pesin, Yakov
2015-01-01
For symbolic dynamical systems we use the Carathéodory construction as described in (Pesin 1997 Dimension Theory in Dynamical Systems, ConTemporary Views and Applications (Chicago: University of Chicago Press)) to introduce the notions of q-topological and q-metric entropies. We describe some basic properties of these entropies and in particular, discuss relations between q-metric entropy and local metric entropy. Both q-topological and q-metric entropies are new invariants respectively under homeomorphisms and metric isomorphisms of dynamical systems. (paper)
Planar dynamical systems selected classical problems
Liu, Yirong; Huang, Wentao
2014-01-01
This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert's 16th problem. This book is intended for graduate students, post-doctors and researchers in the area of theories and applications of dynamical systems. For all engineers who are interested the theory of dynamical systems, it is also a reasona
Collective Dynamics of Nonlinear and Disordered Systems
Radons, G; Just, W
2005-01-01
Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.
SIAM conference on applications of dynamical systems
Energy Technology Data Exchange (ETDEWEB)
1992-01-01
A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.
Fault diagnosis for dynamic power system
International Nuclear Information System (INIS)
Thabet, A.; Abdelkrim, M.N.; Boutayeb, M.; Didier, G.; Chniba, S.
2011-01-01
The fault diagnosis problem for dynamic power systems is treated, the nonlinear dynamic model based on a differential algebraic equations is transformed with reduced index to a simple dynamic model. Two nonlinear observers are used for generating the fault signals for comparison purposes, one of them being an extended Kalman estimator and the other a new extended kalman filter with moving horizon with a study of convergence based on the choice of matrix of covariance of the noises of system and measurements. The paper illustrates a simulation study applied on IEEE 3 buses test system.
The fractional dynamics of quantum systems
Lu, Longzhao; Yu, Xiangyang
2018-05-01
The fractional dynamic process of a quantum system is a novel and complicated problem. The establishment of a fractional dynamic model is a significant attempt that is expected to reveal the mechanism of fractional quantum system. In this paper, a generalized time fractional Schrödinger equation is proposed. To study the fractional dynamics of quantum systems, we take the two-level system as an example and derive the time fractional equations of motion. The basic properties of the system are investigated by solving this set of equations in the absence of light field analytically. Then, when the system is subject to the light field, the equations are solved numerically. It shows that the two-level system described by the time fractional Schrödinger equation we proposed is a confirmable system.
Dynamics of mechanical systems with variable mass
Belyaev, Alexander
2014-01-01
The book presents up-to-date and unifying formulations for treating dynamics of different types of mechanical systems with variable mass. The starting point is overview of the continuum mechanics relations of balance and jump for open systems from which extended Lagrange and Hamiltonian formulations are derived. Corresponding approaches are stated at the level of analytical mechanics with emphasis on systems with a position-dependent mass and at the level of structural mechanics. Special emphasis is laid upon axially moving structures like belts and chains, and on pipes with an axial flow of fluid. Constitutive relations in the dynamics of systems with variable mass are studied with particular reference to modeling of multi-component mixtures. The dynamics of machines with a variable mass are treated in detail and conservation laws and the stability of motion will be analyzed. Novel finite element formulations for open systems in coupled fluid and structural dynamics are presented.
Coherent regimes of globally coupled dynamical systems
DEFF Research Database (Denmark)
de Monte, Silvia; D'ovidio, Francesco; Mosekilde, Erik
2003-01-01
This Letter presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to populations of any size and functional form in the region...
An Integrative Dynamical Systems Perspective on Emotions
Treur, J.
2013-01-01
Within cognitive, affective and social neuroscience more and more mechanisms are found that suggest how emotions relate in a bidirectional manner to many other mental processes and behaviour. Based on this, in this paper a neurologically inspired dynamical systems approach on the dynamics and
Directory of Open Access Journals (Sweden)
Elmar eRückert
2013-10-01
Full Text Available A salient feature of human motor skill learning is the ability to exploitsimilarities across related tasks.In biological motor control, it has been hypothesized that muscle synergies,coherent activations of groups of muscles, allow for exploiting shared knowledge.Recent studies have shown that a rich set of complex motor skills can be generated bya combination of a small number of muscle synergies.In robotics, dynamic movement primitives are commonlyused for motor skill learning. This machine learning approach implements a stable attractor systemthat facilitates learning and it can be used in high-dimensional continuous spaces. However, it does not allow for reusing shared knowledge, i.e. for each task an individual set of parameters has to be learned.We propose a novel movement primitive representationthat employs parametrized basis functions, which combines the benefits of muscle synergiesand dynamic movement primitives. For each task asuperposition of synergies modulates a stable attractor system.This approach leads to a compact representation of multiple motor skills andat the same time enables efficient learning in high-dimensional continuous systems.The movement representation supports discrete and rhythmic movements andin particular includes the dynamic movement primitive approach as a special case.We demonstrate the feasibility of the movement representation in three multi-task learning simulated scenarios.First, the characteristics of the proposed representation are illustrated in a point-mass task.Second, in complex humanoid walking experiments,multiple walking patterns with different step heights are learned robustly and efficiently.Finally, in a multi-directional reaching task simulated with a musculoskeletal modelof the human arm, we show how the proposed movement primitives can be used tolearn appropriate muscle excitation patterns and to generalize effectively to new reaching skills.
Class prediction for high-dimensional class-imbalanced data
Directory of Open Access Journals (Sweden)
Lusa Lara
2010-10-01
Full Text Available Abstract Background The goal of class prediction studies is to develop rules to accurately predict the class membership of new samples. The rules are derived using the values of the variables available for each subject: the main characteristic of high-dimensional data is that the number of variables greatly exceeds the number of samples. Frequently the classifiers are developed using class-imbalanced data, i.e., data sets where the number of samples in each class is not equal. Standard classification methods used on class-imbalanced data often produce classifiers that do not accurately predict the minority class; the prediction is biased towards the majority class. In this paper we investigate if the high-dimensionality poses additional challenges when dealing with class-imbalanced prediction. We evaluate the performance of six types of classifiers on class-imbalanced data, using simulated data and a publicly available data set from a breast cancer gene-expression microarray study. We also investigate the effectiveness of some strategies that are available to overcome the effect of class imbalance. Results Our results show that the evaluated classifiers are highly sensitive to class imbalance and that variable selection introduces an additional bias towards classification into the majority class. Most new samples are assigned to the majority class from the training set, unless the difference between the classes is very large. As a consequence, the class-specific predictive accuracies differ considerably. When the class imbalance is not too severe, down-sizing and asymmetric bagging embedding variable selection work well, while over-sampling does not. Variable normalization can further worsen the performance of the classifiers. Conclusions Our results show that matching the prevalence of the classes in training and test set does not guarantee good performance of classifiers and that the problems related to classification with class
High-dimensional change-point estimation: Combining filtering with convex optimization
Soh, Yong Sheng; Chandrasekaran, Venkat
2017-01-01
We consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they have undesirable scaling behavior in the high-dimensional setting. However, many high-dimensional signals encountered in practice frequently possess latent low-dimensional structure. Motivated by this observation, we propose a technique for high-dimensional...
Constraint Embedding for Multibody System Dynamics
Jain, Abhinandan
2009-01-01
This paper describes a constraint embedding approach for the handling of local closure constraints in multibody system dynamics. The approach uses spatial operator techniques to eliminate local-loop constraints from the system and effectively convert the system into tree-topology systems. This approach allows the direct derivation of recursive O(N) techniques for solving the system dynamics and avoiding the expensive steps that would otherwise be required for handling the closedchain dynamics. The approach is very effective for systems where the constraints are confined to small-subgraphs within the system topology. The paper provides background on the spatial operator O(N) algorithms, the extensions for handling embedded constraints, and concludes with some examples of such constraints.
Understanding and Modeling Teams As Dynamical Systems
Gorman, Jamie C.; Dunbar, Terri A.; Grimm, David; Gipson, Christina L.
2017-01-01
By its very nature, much of teamwork is distributed across, and not stored within, interdependent people working toward a common goal. In this light, we advocate a systems perspective on teamwork that is based on general coordination principles that are not limited to cognitive, motor, and physiological levels of explanation within the individual. In this article, we present a framework for understanding and modeling teams as dynamical systems and review our empirical findings on teams as dynamical systems. We proceed by (a) considering the question of why study teams as dynamical systems, (b) considering the meaning of dynamical systems concepts (attractors; perturbation; synchronization; fractals) in the context of teams, (c) describe empirical studies of team coordination dynamics at the perceptual-motor, cognitive-behavioral, and cognitive-neurophysiological levels of analysis, and (d) consider the theoretical and practical implications of this approach, including new kinds of explanations of human performance and real-time analysis and performance modeling. Throughout our discussion of the topics we consider how to describe teamwork using equations and/or modeling techniques that describe the dynamics. Finally, we consider what dynamical equations and models do and do not tell us about human performance in teams and suggest future research directions in this area. PMID:28744231
Solved problems in dynamical systems and control
Tenreiro-Machado, J; Valério, Duarte; Galhano, Alexandra M
2016-01-01
This book presents a collection of exercises on dynamical systems, modelling and control. Each topic covered includes a summary of the theoretical background, problems with solutions, and further exercises.
International Nuclear Information System (INIS)
Tripathy, Rohit; Bilionis, Ilias; Gonzalez, Marcial
2016-01-01
Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the
Tripathy, Rohit; Bilionis, Ilias; Gonzalez, Marcial
2016-09-01
Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the
Energy Technology Data Exchange (ETDEWEB)
Tripathy, Rohit, E-mail: rtripath@purdue.edu; Bilionis, Ilias, E-mail: ibilion@purdue.edu; Gonzalez, Marcial, E-mail: marcial-gonzalez@purdue.edu
2016-09-15
Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the
Individual-based models for adaptive diversification in high-dimensional phenotype spaces.
Ispolatov, Iaroslav; Madhok, Vaibhav; Doebeli, Michael
2016-02-07
Most theories of evolutionary diversification are based on equilibrium assumptions: they are either based on optimality arguments involving static fitness landscapes, or they assume that populations first evolve to an equilibrium state before diversification occurs, as exemplified by the concept of evolutionary branching points in adaptive dynamics theory. Recent results indicate that adaptive dynamics may often not converge to equilibrium points and instead generate complicated trajectories if evolution takes place in high-dimensional phenotype spaces. Even though some analytical results on diversification in complex phenotype spaces are available, to study this problem in general we need to reconstruct individual-based models from the adaptive dynamics generating the non-equilibrium dynamics. Here we first provide a method to construct individual-based models such that they faithfully reproduce the given adaptive dynamics attractor without diversification. We then show that a propensity to diversify can be introduced by adding Gaussian competition terms that generate frequency dependence while still preserving the same adaptive dynamics. For sufficiently strong competition, the disruptive selection generated by frequency-dependence overcomes the directional evolution along the selection gradient and leads to diversification in phenotypic directions that are orthogonal to the selection gradient. Copyright © 2015 Elsevier Ltd. All rights reserved.
Variance inflation in high dimensional Support Vector Machines
DEFF Research Database (Denmark)
Abrahamsen, Trine Julie; Hansen, Lars Kai
2013-01-01
Many important machine learning models, supervised and unsupervised, are based on simple Euclidean distance or orthogonal projection in a high dimensional feature space. When estimating such models from small training sets we face the problem that the span of the training data set input vectors...... the case of Support Vector Machines (SVMS) and we propose a non-parametric scheme to restore proper generalizability. We illustrate the algorithm and its ability to restore performance on a wide range of benchmark data sets....... follow a different probability law with less variance. While the problem and basic means to reconstruct and deflate are well understood in unsupervised learning, the case of supervised learning is less well understood. We here investigate the effect of variance inflation in supervised learning including...
Applying recursive numerical integration techniques for solving high dimensional integrals
International Nuclear Information System (INIS)
Ammon, Andreas; Genz, Alan; Hartung, Tobias; Jansen, Karl; Volmer, Julia; Leoevey, Hernan
2016-11-01
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with N samples behaves like 1/√(N). This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points m that is at least exponential.
High-dimensional cluster analysis with the Masked EM Algorithm
Kadir, Shabnam N.; Goodman, Dan F. M.; Harris, Kenneth D.
2014-01-01
Cluster analysis faces two problems in high dimensions: first, the “curse of dimensionality” that can lead to overfitting and poor generalization performance; and second, the sheer time taken for conventional algorithms to process large amounts of high-dimensional data. We describe a solution to these problems, designed for the application of “spike sorting” for next-generation high channel-count neural probes. In this problem, only a small subset of features provide information about the cluster member-ship of any one data vector, but this informative feature subset is not the same for all data points, rendering classical feature selection ineffective. We introduce a “Masked EM” algorithm that allows accurate and time-efficient clustering of up to millions of points in thousands of dimensions. We demonstrate its applicability to synthetic data, and to real-world high-channel-count spike sorting data. PMID:25149694
Evaluating Clustering in Subspace Projections of High Dimensional Data
DEFF Research Database (Denmark)
Müller, Emmanuel; Günnemann, Stephan; Assent, Ira
2009-01-01
Clustering high dimensional data is an emerging research field. Subspace clustering or projected clustering group similar objects in subspaces, i.e. projections, of the full space. In the past decade, several clustering paradigms have been developed in parallel, without thorough evaluation...... and comparison between these paradigms on a common basis. Conclusive evaluation and comparison is challenged by three major issues. First, there is no ground truth that describes the "true" clusters in real world data. Second, a large variety of evaluation measures have been used that reflect different aspects...... of the clustering result. Finally, in typical publications authors have limited their analysis to their favored paradigm only, while paying other paradigms little or no attention. In this paper, we take a systematic approach to evaluate the major paradigms in a common framework. We study representative clustering...
Applying recursive numerical integration techniques for solving high dimensional integrals
Energy Technology Data Exchange (ETDEWEB)
Ammon, Andreas [IVU Traffic Technologies AG, Berlin (Germany); Genz, Alan [Washington State Univ., Pullman, WA (United States). Dept. of Mathematics; Hartung, Tobias [King' s College, London (United Kingdom). Dept. of Mathematics; Jansen, Karl; Volmer, Julia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leoevey, Hernan [Humboldt Univ. Berlin (Germany). Inst. fuer Mathematik
2016-11-15
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with N samples behaves like 1/√(N). This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points m that is at least exponential.
Reduced order surrogate modelling (ROSM) of high dimensional deterministic simulations
Mitry, Mina
Often, computationally expensive engineering simulations can prohibit the engineering design process. As a result, designers may turn to a less computationally demanding approximate, or surrogate, model to facilitate their design process. However, owing to the the curse of dimensionality, classical surrogate models become too computationally expensive for high dimensional data. To address this limitation of classical methods, we develop linear and non-linear Reduced Order Surrogate Modelling (ROSM) techniques. Two algorithms are presented, which are based on a combination of linear/kernel principal component analysis and radial basis functions. These algorithms are applied to subsonic and transonic aerodynamic data, as well as a model for a chemical spill in a channel. The results of this thesis show that ROSM can provide a significant computational benefit over classical surrogate modelling, sometimes at the expense of a minor loss in accuracy.
Asymptotics of empirical eigenstructure for high dimensional spiked covariance.
Wang, Weichen; Fan, Jianqing
2017-06-01
We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those in Paul (2007) to a more general setting and solve the rates of convergence problems in Shen et al. (2013). They also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called shrinkage principal orthogonal complement thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks of large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies.
Dynamical Systems Approach to Endothelial Heterogeneity
Regan, Erzsébet Ravasz; Aird, William C.
2012-01-01
Rationale Objective Here we reexamine our current understanding of the molecular basis of endothelial heterogeneity. We introduce multistability as a new explanatory framework in vascular biology. Methods We draw on the field of non-linear dynamics to propose a dynamical systems framework for modeling multistability and its derivative properties, including robustness, memory, and plasticity. Conclusions Our perspective allows for both a conceptual and quantitative description of system-level features of endothelial regulation. PMID:22723222
Nonlinear and Complex Dynamics in Real Systems
William Barnett; Apostolos Serletis; Demitre Serletis
2005-01-01
This paper was produced for the El-Naschie Symposium on Nonlinear Dynamics in Shanghai in December 2005. In this paper we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems with nonlinear chaotic dynamics and discuss some techniques used in distinguishing between stochastic and deterministic behavior. Moreover, we look at the issue of where and when the ideas of chaos could p...
Dynamic Double Curvature Mould System
DEFF Research Database (Denmark)
Jepsen, Christian Raun; Kristensen, Mathias Kræmmergaard; Kirkegaard, Poul Henning
2011-01-01
The present paper describes a concept for a reconfigurable mould surface which is designed to fit the needs of contemporary architecture. The core of the concept presented is a dynamic surface manipulated into a given shape using a digital signal created directly from the CAD drawing of the design....... This happens fast, automatic and without production of waste, and the manipulated surface is fair and robust, eliminating the need for additional, manual treatment. Limitations to the possibilities of the flexible form are limited curvature and limited level of detail, making it especially suited for larger...
Attractors and basins of dynamical systems
Directory of Open Access Journals (Sweden)
Attila Dénes
2011-03-01
Full Text Available There are several programs for studying dynamical systems, but none of them is very useful for investigating basins and attractors of higher dimensional systems. Our goal in this paper is to show a new algorithm for finding even chaotic attractors and their basins for these systems. We present an implementation and examples for the use of this program.
High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments.
Babazadeh, Amin; Erhard, Manuel; Wang, Feiran; Malik, Mehul; Nouroozi, Rahman; Krenn, Mario; Zeilinger, Anton
2017-11-03
Transformations on quantum states form a basic building block of every quantum information system. From photonic polarization to two-level atoms, complete sets of quantum gates for a variety of qubit systems are well known. For multilevel quantum systems beyond qubits, the situation is more challenging. The orbital angular momentum modes of photons comprise one such high-dimensional system for which generation and measurement techniques are well studied. However, arbitrary transformations for such quantum states are not known. Here we experimentally demonstrate a four-dimensional generalization of the Pauli X gate and all of its integer powers on single photons carrying orbital angular momentum. Together with the well-known Z gate, this forms the first complete set of high-dimensional quantum gates implemented experimentally. The concept of the X gate is based on independent access to quantum states with different parities and can thus be generalized to other photonic degrees of freedom and potentially also to other quantum systems.
The brain as a dynamic physical system.
McKenna, T M; McMullen, T A; Shlesinger, M F
1994-06-01
The brain is a dynamic system that is non-linear at multiple levels of analysis. Characterization of its non-linear dynamics is fundamental to our understanding of brain function. Identifying families of attractors in phase space analysis, an approach which has proven valuable in describing non-linear mechanical and electrical systems, can prove valuable in describing a range of behaviors and associated neural activity including sensory and motor repertoires. Additionally, transitions between attractors may serve as useful descriptors for analysing state changes in neurons and neural ensembles. Recent observations of synchronous neural activity, and the emerging capability to record the spatiotemporal dynamics of neural activity by voltage-sensitive dyes and electrode arrays, provide opportunities for observing the population dynamics of neural ensembles within a dynamic systems context. New developments in the experimental physics of complex systems, such as the control of chaotic systems, selection of attractors, attractor switching and transient states, can be a source of powerful new analytical tools and insights into the dynamics of neural systems.
Dynamics and control of technical systems
Balthazar, José M; Kaczmarczyk, Stefan
2014-01-01
The main topics of this Special Issue are linear and, mainly, nonlinear dynamics, chaos and control of systems and structures and their applications in different field of science and engineering. According to the goal of the Special Issue, the selected contributions are divided into three major parts: ""Vibration Problems in Vertical Transportation Systems"", ""Nonlinear Dynamics, Chaos and Control of Elastic Structures"" and ""New Strategies and Challenges for Aerospace and Ocean Structures Dynamics and Control"". The discussion of real problems in aerospace and how these problems can be unde
Tao, Chenyang; Nichols, Thomas E; Hua, Xue; Ching, Christopher R K; Rolls, Edmund T; Thompson, Paul M; Feng, Jianfeng
2017-01-01
We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data the effective dimensionality of the data, and then jointly performs dimension reduction of the covariates, dynamic identification of latent factors, and nonparametric estimation of both covariate and latent response fields. After accounting for the latent and covariate effects, GRLLF performs a nonparametric test on the remaining factor of interest. GRRLF provides a better factorization of the signals compared with common solutions, and is less susceptible to overfitting because it exploits the effective dimensionality. The generality and the flexibility of GRRLF also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed. Within the field of neuroimaging, it improves the sensitivity for weak signals and is a promising alternative to existing approaches. The operation of the framework is demonstrated with both synthetic datasets and a real-world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured, and the results compared favorably with those from existing approaches. Copyright © 2016. Published by Elsevier Inc.
Dynamical systems examples of complex behaviour
Jost, Jürgen
2005-01-01
Our aim is to introduce, explain, and discuss the fundamental problems, ideas, concepts, results, and methods of the theory of dynamical systems and to show how they can be used in speci?c examples. We do not intend to give a comprehensive overview of the present state of research in the theory of dynamical systems, nor a detailed historical account of its development. We try to explain the important results, often neglecting technical re?nements 1 and, usually, we do not provide proofs. One of the basic questions in studying dynamical systems, i.e. systems that evolve in time, is the construction of invariants that allow us to classify qualitative types of dynamical evolution, to distinguish between qualitatively di?erent dynamics, and to studytransitions between di?erent types. Itis also important to ?nd out when a certain dynamic behavior is stable under small perturbations, as well as to understand the various scenarios of instability. Finally, an essential aspect of a dynamic evolution is the transformat...
Lectures on fractal geometry and dynamical systems
Pesin, Yakov
2009-01-01
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular "chaotic" motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory--Cantor sets, Hausdorff dimension, box dimension--using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples o...
System dynamics an introduction for mechanical engineers
Seeler, Karl A
2014-01-01
This essential textbook takes the student from the initial steps in modeling a dynamic system through development of the mathematical models needed for feedback control. The generously-illustrated, student-friendly text focuses on fundamental theoretical development rather than the application of commercial software. Practical details of machine design are included to motivate the non-mathematically inclined student. This book also: Emphasizes the linear graph method for modeling dynamic systems Offers a systematic approach for creating an engineering model, extracting information, and formulating mathematical analyses Adopts a unifying theme of power flow as the dynamic agent that eases analysis of hybrid systems, such as machinery Presents differential equations as dynamic operators and stresses input/output relationships Introduces Mathcad and programming in MATLAB Allows for use of Open Source Computational Software (R or C) Features over 1000 illustrations
Dynamic memory management for embedded systems
Atienza Alonso, David; Poucet, Christophe; Peón-Quirós, Miguel; Bartzas, Alexandros; Catthoor, Francky; Soudris, Dimitrios
2015-01-01
This book provides a systematic and unified methodology, including basic principles and reusable processes, for dynamic memory management (DMM) in embedded systems. The authors describe in detail how to design and optimize the use of dynamic memory in modern, multimedia and network applications, targeting the latest generation of portable embedded systems, such as smartphones. Coverage includes a variety of design and optimization topics in electronic design automation of DMM, from high-level software optimization to microarchitecture-level hardware support. The authors describe the design of multi-layer dynamic data structures for the final memory hierarchy layers of the target portable embedded systems and how to create a low-fragmentation, cost-efficient, dynamic memory management subsystem out of configurable components for the particular memory allocation and de-allocation patterns for each type of application. The design methodology described in this book is based on propagating constraints among de...
Error modeling for surrogates of dynamical systems using machine learning
Trehan, Sumeet; Carlberg, Kevin T.; Durlofsky, Louis J.
2017-12-01
A machine-learning-based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (e.g., random forests, LASSO) to map a large set of inexpensively computed `error indicators' (i.e., features) produced by the surrogate model at a given time instance to a prediction of the surrogate-model error in a quantity of interest (QoI). This eliminates the need for the user to hand-select a small number of informative features. The methodology requires a training set of parameter instances at which the time-dependent surrogate-model error is computed by simulating both the high-fidelity and surrogate models. Using these training data, the method first determines regression-model locality (via classification or clustering), and subsequently constructs a `local' regression model to predict the time-instantaneous error within each identified region of feature space. We consider two uses for the resulting error model: (1) as a correction to the surrogate-model QoI prediction at each time instance, and (2) as a way to statistically model arbitrary functions of the time-dependent surrogate-model error (e.g., time-integrated errors). We apply the proposed framework to model errors in reduced-order models of nonlinear oil--water subsurface flow simulations. The reduced-order models used in this work entail application of trajectory piecewise linearization with proper orthogonal decomposition. When the first use of the method is considered, numerical experiments demonstrate consistent improvement in accuracy in the time-instantaneous QoI prediction relative to the original surrogate model, across a large number of test cases. When the second use is considered, results show that the proposed method provides accurate statistical predictions of the time- and well-averaged errors.
System crash as dynamics of complex networks.
Yu, Yi; Xiao, Gaoxi; Zhou, Jie; Wang, Yubo; Wang, Zhen; Kurths, Jürgen; Schellnhuber, Hans Joachim
2016-10-18
Complex systems, from animal herds to human nations, sometimes crash drastically. Although the growth and evolution of systems have been extensively studied, our understanding of how systems crash is still limited. It remains rather puzzling why some systems, appearing to be doomed to fail, manage to survive for a long time whereas some other systems, which seem to be too big or too strong to fail, crash rapidly. In this contribution, we propose a network-based system dynamics model, where individual actions based on the local information accessible in their respective system structures may lead to the "peculiar" dynamics of system crash mentioned above. Extensive simulations are carried out on synthetic and real-life networks, which further reveal the interesting system evolution leading to the final crash. Applications and possible extensions of the proposed model are discussed.
On-chip generation of high-dimensional entangled quantum states and their coherent control.
Kues, Michael; Reimer, Christian; Roztocki, Piotr; Cortés, Luis Romero; Sciara, Stefania; Wetzel, Benjamin; Zhang, Yanbing; Cino, Alfonso; Chu, Sai T; Little, Brent E; Moss, David J; Caspani, Lucia; Azaña, José; Morandotti, Roberto
2017-06-28
Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics, for increasing the sensitivity of quantum imaging schemes, for improving the robustness and key rate of quantum communication protocols, for enabling a richer variety of quantum simulations, and for achieving more efficient and error-tolerant quantum computation. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2). Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode.
Modular interdependency in complex dynamical systems.
Watson, Richard A; Pollack, Jordan B
2005-01-01
Herbert A. Simon's characterization of modularity in dynamical systems describes subsystems as having dynamics that are approximately independent of those of other subsystems (in the short term). This fits with the general intuition that modules must, by definition, be approximately independent. In the evolution of complex systems, such modularity may enable subsystems to be modified and adapted independently of other subsystems, whereas in a nonmodular system, modifications to one part of the system may result in deleterious side effects elsewhere in the system. But this notion of modularity and its effect on evolvability is not well quantified and is rather simplistic. In particular, modularity need not imply that intermodule dependences are weak or unimportant. In dynamical systems this is acknowledged by Simon's suggestion that, in the long term, the dynamical behaviors of subsystems do interact with one another, albeit in an "aggregate" manner--but this kind of intermodule interaction is omitted in models of modularity for evolvability. In this brief discussion we seek to unify notions of modularity in dynamical systems with notions of how modularity affects evolvability. This leads to a quantifiable measure of modularity and a different understanding of its effect on evolvability.
International Nuclear Information System (INIS)
Sidlichovsky, M.
1987-01-01
The conference proceedings contains a total of 31 papers of which 7 have not been incorporated in INIS. The papers mainly discuss the mathematical methods of calculating the movement of planets, their satellites and asteroids in the solar system and the mathematical modelling of the past development of the solar system. Great attention is also devoted to resonance in the solar system and to the study of many celestial bodies. Four papers are devoted to planetary rings and three to modern astrometry. (M.D.). 63 figs., 10 tabs., 520 refs
Dynamics of Multibody Systems Near Lagrangian Points
Wong, Brian
This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the Lagrangian points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid Lagrangian point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. Numerical simulations are used to study the long term
Hybrid dynamical systems observation and control
Defoort, Michael
2015-01-01
This book is a collection of contributions defining the state of current knowledge and new trends in hybrid systems – systems involving both continuous dynamics and discrete events – as described by the work of several well-known groups of researchers. Hybrid Dynamical Systems presents theoretical advances in such areas as diagnosability, observability and stabilization for various classes of system. Continuous and discrete state estimation and self-triggering control of nonlinear systems are advanced. The text employs various methods, among them, high-order sliding modes, Takagi–Sugeno representation and sampled-data switching to achieve its ends. The many applications of hybrid systems from power converters to computer science are not forgotten; studies of flexible-joint robotic arms and – as representative biological systems – the behaviour of the human heart and vasculature, demonstrate the wide-ranging practical significance of control in hybrid systems. The cross-disciplinary origins of study ...
Dynamic of small photovoltaic systems
Mehrmann, A.; Kleinkauf, W.; Pigorsch, W.; Steeb, H.
The results of 1.5 yr of field-testing of two photovoltaic (PV) power plants, one equipped with an electrolyzer and H2 storage, are reported. Both systems were interconnected with the grid and featured the PV module, a power conditioning unit, ac and dc load connections, and control units. The rated power of both units was 100 Wp. The system with electrolysis was governed by control laws which maximized the electrolyzer current. The tests underscored the preference for a power conditioning unit, rather than direct output to load connections. A 1 kWp system was developed in a follow-up program and will be tested in concert with electrolysis and interconnection with several grid customers. The program is geared to eventual development of larger units for utility-size applications.
Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks.
Arampatzis, Georgios; Katsoulakis, Markos A; Pantazis, Yannis
2015-01-01
Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially) sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in "sloppy" systems. In particular, the computational acceleration is quantified by the ratio between the total number of parameters over the
Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks.
Directory of Open Access Journals (Sweden)
Georgios Arampatzis
Full Text Available Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in "sloppy" systems. In particular, the computational acceleration is quantified by the ratio between the total number of
Problems of classical dynamical systems
International Nuclear Information System (INIS)
Thirring, W.
1975-01-01
After a brief survey of Hamiltonian theory and of relevant notions of set theory and manifolds, these lecture notes present some general properties of orbits, paying special attention to integrable systems. This is followed by a discussion of the Kolmogorov-Arnol'd-Moser theorem, dealing with the stability of orbits under small perturbations, and its importance for ergodic theory. Ergodicity and mixing are then treated in detail. In particular, the ergodic theorem of von Neumann is derived, and a specific example is given of a (strongly) mixing system. (author)
Topological theory of dynamical systems recent advances
Aoki, N
1994-01-01
This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments. This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book. Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.
Controllable Subspaces of Open Quantum Dynamical Systems
International Nuclear Information System (INIS)
Zhang Ming; Gong Erling; Xie Hongwei; Hu Dewen; Dai Hongyi
2008-01-01
This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.
Linear dynamic coupling in geared rotor systems
David, J. W.; Mitchell, L. D.
1986-01-01
The effects of high frequency oscillations caused by the gear mesh, on components of a geared system that can be modeled as rigid discs are analyzed using linear dynamic coupling terms. The coupled, nonlinear equations of motion for a disc attached to a rotating shaft are presented. The results of a trial problem analysis show that the inclusion of the linear dynamic coupling terms can produce significant changes in the predicted response of geared rotor systems, and that the produced sideband responses are greater than the unbalanced response. The method is useful in designing gear drives for heavy-lift helicopters, industrial speed reducers, naval propulsion systems, and heavy off-road equipment.
Dynamic modeling of the INAPRO aquaponic system
Karimanzira, Divas; Keesman, Karel J.; Kloas, Werner; Baganz, Daniela; Rauschenbach, Thomas
2016-01-01
The use of modeling techniques to analyze aquaponics systems is demonstrated with an example of dynamic modeling for the production of Nile tilapia (Oreochromis niloticus) and tomatoes (Solanum lycopersicon) using the innovative double recirculating aquaponic system ASTAF-PRO. For the management
Dynamic Systems Theory and Team Sport Coaching
Gréhaigne, Jean-Francis; Godbout, Paul
2014-01-01
This article examines the theory of dynamic systems and its use in the domains of the study and coaching of team sports. The two teams involved in a match are looked at as two interacting systems in movement, where opposition is paramount. A key element for the observation of game play is the notion of configuration of play and its ever-changing…
Reaction dynamics in polyatomic molecular systems
Energy Technology Data Exchange (ETDEWEB)
Miller, W.H. [Lawrence Berkeley Laboratory, CA (United States)
1993-12-01
The goal of this program is the development of theoretical methods and models for describing the dynamics of chemical reactions, with specific interest for application to polyatomic molecular systems of special interest and relevance. There is interest in developing the most rigorous possible theoretical approaches and also in more approximate treatments that are more readily applicable to complex systems.
Dynamic MR imaging of the musculoskeletal system
International Nuclear Information System (INIS)
Shah, A.S.; Hylton, H.; Hentz, V.R.; Schattner, P.
1991-01-01
This paper reports on dynamic MR imaging which is an MR technique that allows imaging of the musculoskeletal system in motion. Current methods for observing the articulation of muscles and joints are limited to acquisition of stationary images at different spatial orientations. These images are then replayed from computer memory to simulate motion. Unlike stationary acquisition, dynamic MR imaging allows the volume of interest to be subjected to motion and dynamic stress, which is important for detecting stress-induced pathology. To demonstrate the utility of dynamic MR imaging, a system for imaging a moving wrist has been developed. The system consists of apparatus capable of providing simultaneous radialulnar deviation and flexion-extension, and hardware for system control and acquisition gating. The apparatus is mounted on the patient bed and is transferable to a variety of standard clinical MR imaging systems. Images were obtained during motion, and the ability of dynamic MR imaging to accurately image the moving wrist with very little motion artifact was demonstrated
Solar dynamic power system definition study
Wallin, Wayne E.; Friefeld, Jerry M.
1988-01-01
The solar dynamic power system design and analysis study compared Brayton, alkali-metal Rankine, and free-piston Stirling cycles with silicon planar and GaAs concentrator photovoltaic power systems for application to missions beyond the Phase 2 Space Station level of technology for all power systems. Conceptual designs for Brayton and Stirling power systems were developed for 35 kWe and 7 kWe power levels. All power systems were designed for 7-year end-of-life conditions in low Earth orbit. LiF was selected for thermal energy storage for the solar dynamic systems. Results indicate that the Stirling cycle systems have the highest performance (lowest weight and area) followed by the Brayton cycle, with photovoltaic systems considerably lower in performance. For example, based on the performance assumptions used, the planar silicon power system weight was 55 to 75 percent higher than for the Stirling system. A technology program was developed to address areas wherein significant performance improvements could be realized relative to the current state-of-the-art as represented by Space Station. In addition, a preliminary evaluation of hardenability potential found that solar dynamic systems can be hardened beyond the hardness inherent in the conceptual designs of this study.
Near Identifiability of Dynamical Systems
Hadaegh, F. Y.; Bekey, G. A.
1987-01-01
Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.
Dynamic Systems Modeling in Educational System Design & Policy
Groff, Jennifer Sterling
2013-01-01
Over the last several hundred years, local and national educational systems have evolved from relatively simple systems to incredibly complex, interdependent, policy-laden structures, to which many question their value, effectiveness, and direction they are headed. System Dynamics is a field of analysis used to guide policy and system design in…
Energy Efficient MAC Scheme for Wireless Sensor Networks with High-Dimensional Data Aggregate
Directory of Open Access Journals (Sweden)
Seokhoon Kim
2015-01-01
Full Text Available This paper presents a novel and sustainable medium access control (MAC scheme for wireless sensor network (WSN systems that process high-dimensional aggregated data. Based on a preamble signal and buffer threshold analysis, it maximizes the energy efficiency of the wireless sensor devices which have limited energy resources. The proposed group management MAC (GM-MAC approach not only sets the buffer threshold value of a sensor device to be reciprocal to the preamble signal but also sets a transmittable group value to each sensor device by using the preamble signal of the sink node. The primary difference between the previous and the proposed approach is that existing state-of-the-art schemes use duty cycle and sleep mode to save energy consumption of individual sensor devices, whereas the proposed scheme employs the group management MAC scheme for sensor devices to maximize the overall energy efficiency of the whole WSN systems by minimizing the energy consumption of sensor devices located near the sink node. Performance evaluations show that the proposed scheme outperforms the previous schemes in terms of active time of sensor devices, transmission delay, control overhead, and energy consumption. Therefore, the proposed scheme is suitable for sensor devices in a variety of wireless sensor networking environments with high-dimensional data aggregate.
Progress in high-dimensional percolation and random graphs
Heydenreich, Markus
2017-01-01
This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study. Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4–9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dimensiona l percolation. Part III, consist...
Effects of dependence in high-dimensional multiple testing problems
Directory of Open Access Journals (Sweden)
van de Wiel Mark A
2008-02-01
Full Text Available Abstract Background We consider effects of dependence among variables of high-dimensional data in multiple hypothesis testing problems, in particular the False Discovery Rate (FDR control procedures. Recent simulation studies consider only simple correlation structures among variables, which is hardly inspired by real data features. Our aim is to systematically study effects of several network features like sparsity and correlation strength by imposing dependence structures among variables using random correlation matrices. Results We study the robustness against dependence of several FDR procedures that are popular in microarray studies, such as Benjamin-Hochberg FDR, Storey's q-value, SAM and resampling based FDR procedures. False Non-discovery Rates and estimates of the number of null hypotheses are computed from those methods and compared. Our simulation study shows that methods such as SAM and the q-value do not adequately control the FDR to the level claimed under dependence conditions. On the other hand, the adaptive Benjamini-Hochberg procedure seems to be most robust while remaining conservative. Finally, the estimates of the number of true null hypotheses under various dependence conditions are variable. Conclusion We discuss a new method for efficient guided simulation of dependent data, which satisfy imposed network constraints as conditional independence structures. Our simulation set-up allows for a structural study of the effect of dependencies on multiple testing criterions and is useful for testing a potentially new method on π0 or FDR estimation in a dependency context.
Inference for High-dimensional Differential Correlation Matrices.
Cai, T Tony; Zhang, Anru
2016-01-01
Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed.
Efficient Smoothed Concomitant Lasso Estimation for High Dimensional Regression
Ndiaye, Eugene; Fercoq, Olivier; Gramfort, Alexandre; Leclère, Vincent; Salmon, Joseph
2017-10-01
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider ℓ 1 penalty to enforce sparsity in such scenarios. Sparsity enforcing methods, the Lasso being a canonical example, are popular candidates to address high dimension. For efficiency, they rely on tuning a parameter trading data fitting versus sparsity. For the Lasso theory to hold this tuning parameter should be proportional to the noise level, yet the latter is often unknown in practice. A possible remedy is to jointly optimize over the regression parameter as well as over the noise level. This has been considered under several names in the literature: Scaled-Lasso, Square-root Lasso, Concomitant Lasso estimation for instance, and could be of interest for uncertainty quantification. In this work, after illustrating numerical difficulties for the Concomitant Lasso formulation, we propose a modification we coined Smoothed Concomitant Lasso, aimed at increasing numerical stability. We propose an efficient and accurate solver leading to a computational cost no more expensive than the one for the Lasso. We leverage on standard ingredients behind the success of fast Lasso solvers: a coordinate descent algorithm, combined with safe screening rules to achieve speed efficiency, by eliminating early irrelevant features.
Bayesian Subset Modeling for High-Dimensional Generalized Linear Models
Liang, Faming
2013-06-01
This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online. © 2013 American Statistical Association.
The literary uses of high-dimensional space
Directory of Open Access Journals (Sweden)
Ted Underwood
2015-12-01
Full Text Available Debates over “Big Data” shed more heat than light in the humanities, because the term ascribes new importance to statistical methods without explaining how those methods have changed. What we badly need instead is a conversation about the substantive innovations that have made statistical modeling useful for disciplines where, in the past, it truly wasn’t. These innovations are partly technical, but more fundamentally expressed in what Leo Breiman calls a new “culture” of statistical modeling. Where 20th-century methods often required humanists to squeeze our unstructured texts, sounds, or images into some special-purpose data model, new methods can handle unstructured evidence more directly by modeling it in a high-dimensional space. This opens a range of research opportunities that humanists have barely begun to discuss. To date, topic modeling has received most attention, but in the long run, supervised predictive models may be even more important. I sketch their potential by describing how Jordan Sellers and I have begun to model poetic distinction in the long 19th century—revealing an arc of gradual change much longer than received literary histories would lead us to expect.
Dynamics Explorer science data processing system
International Nuclear Information System (INIS)
Smith, P.H.; Freeman, C.H.; Hoffman, R.A.
1981-01-01
The Dynamics Explorer project has acquired the ground data processing system from the Atmosphere Explorer project to provide a central computer facility for the data processing, data management and data analysis activities of the investigators. Access to this system is via remote terminals at the investigators' facilities, which provide ready access to the data sets derived from groups of instruments on both spacecraft. The original system has been upgraded with both new hardware and enhanced software systems. These new systems include color and grey scale graphics terminals, an augmentation computer, micrographies facility, a versatile data base with a directory and data management system, and graphics display software packages. (orig.)
Stirling Engine Dynamic System Modeling
Nakis, Christopher G.
2004-01-01
The Thermo-Mechanical systems branch at the Glenn Research Center focuses a large amount time on Stirling engines. These engines will be used on missions where solar power is inefficient, especially in deep space. I work with Tim Regan and Ed Lewandowski who are currently developing and validating a mathematical model for the Stirling engines. This model incorporates all aspects of the system including, mechanical, electrical and thermodynamic components. Modeling is done through Simplorer, a program capable of running simulations of the model. Once created and then proven to be accurate, a model is used for developing new ideas for engine design. My largest specific project involves varying key parameters in the model and quantifying the results. This can all be done relatively trouble-free with the help of Simplorer. Once the model is complete, Simplorer will do all the necessary calculations. The more complicated part of this project is determining which parameters to vary. Finding key parameters depends on the potential for a value to be independently altered in the design. For example, a change in one dimension may lead to a proportional change to the rest of the model, and no real progress is made. Also, the ability for a changed value to have a substantial impact on the outputs of the system is important. Results will be condensed into graphs and tables with the purpose of better communication and understanding of the data. With the changing of these parameters, a more optimal design can be created without having to purchase or build any models. Also, hours and hours of results can be simulated in minutes. In the long run, using mathematical models can save time and money. Along with this project, I have many other smaller assignments throughout the summer. My main goal is to assist in the processes of model development, validation and testing.
Dynamics of Nonlinear Time-Delay Systems
Lakshmanan, Muthusamy
2010-01-01
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...
On non-stationarity of dynamic systems
DEFF Research Database (Denmark)
Høskuldsson, Agnar
2004-01-01
. Covariance structure of dynamic systems tends to vary over time. Here some procedures to find stable solutions to linear dynamic systems with low rank are presented. Subsets of variables and samples to be included in a model are considered. The procedures are based on the H-principle of mathematical...... that are based on exact solutions. With in few seconds the algorithms can provide with solutions of models having hundreds or thousands of variables. The procedure is described mathematically and demonstrated for a dynamic industrial case. It is shown how the algorithms can provide solutions involving NIR data...... for process control. The method is simple to apply and the motivation of the procedure is obvious for industrial applications. It can be used, e.g., when modelling on-line systems....
Supervised Learning for Dynamical System Learning.
Hefny, Ahmed; Downey, Carlton; Gordon, Geoffrey J
2015-01-01
Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporate prior information such as sparsity or structure. To address this problem, we present a new view of dynamical system learning: we show how to learn dynamical systems by solving a sequence of ordinary supervised learning problems, thereby allowing users to incorporate prior knowledge via standard techniques such as L 1 regularization. Many existing spectral methods are special cases of this new framework, using linear regression as the supervised learner. We demonstrate the effectiveness of our framework by showing examples where nonlinear regression or lasso let us learn better state representations than plain linear regression does; the correctness of these instances follows directly from our general analysis.
Uncertain dynamical systems: A differential game approach
Gutman, S.
1976-01-01
A class of dynamical systems in a conflict situation is formulated and discussed, and the formulation is applied to the study of an important class of systems in the presence of uncertainty. The uncertainty is deterministic and the only assumption is that its value belongs to a known compact set. Asymptotic stability is fully discussed with application to variable structure and model reference control systems.
Nonlinear Dynamics, Chaotic and Complex Systems
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
International Nuclear Information System (INIS)
Tendler, M.
1986-04-01
The behaviour of the plasma in the EXTRAP device was found to differ drastically from the conventional Z-pinch discharges. The comparative discussion on the properties of these two configurations is presented. It is shown that the energy mechanism is responsible for the arising difference between them. Given the lack of experimental data on the confinement of the peripheral plasma, in the present study we suggest a scaling for the net energy loss with plasma density and temperature. Using self-similar methods, we show that strongly non-linear damped oscillations arise as a result of our scaling. Some preliminary results on the stability of this system are reported. Finally, some technical recommendations for the design of the toroidal device EXTRAP T1 are put forward. In particular the scheme, allowing the extension of the pulse duration, which is rather limited in the present version, is suggested. (Author)
System Dynamics Modeling of Multipurpose Reservoir Operation
Directory of Open Access Journals (Sweden)
Ebrahim Momeni
2006-03-01
Full Text Available System dynamics, a feedback – based object – oriented simulation approach, not only represents complex dynamic systemic systems in a realistic way but also allows the involvement of end users in model development to increase their confidence in modeling process. The increased speed of model development, the possibility of group model development, the effective communication of model results, and the trust developed in the model due to user participation are the main strengths of this approach. The ease of model modification in response to changes in the system and the ability to perform sensitivity analysis make this approach more attractive compared with systems analysis techniques for modeling water management systems. In this study, a system dynamics model was developed for the Zayandehrud basin in central Iran. This model contains river basin, dam reservoir, plains, irrigation systems, and groundwater. Current operation rule is conjunctive use of ground and surface water. Allocation factor for each irrigation system is computed based on the feedback from groundwater storage in its zone. Deficit water is extracted from groundwater.The results show that applying better rules can not only satisfy all demands such as Gawkhuni swamp environmental demand, but it can also prevent groundwater level drawdown in future.
Robust control synthesis for uncertain dynamical systems
Byun, Kuk-Whan; Wie, Bong; Sunkel, John
1989-01-01
This paper presents robust control synthesis techniques for uncertain dynamical systems subject to structured parameter perturbation. Both QFT (quantitative feedback theory) and H-infinity control synthesis techniques are investigated. Although most H-infinity-related control techniques are not concerned with the structured parameter perturbation, a new way of incorporating the parameter uncertainty in the robust H-infinity control design is presented. A generic model of uncertain dynamical systems is used to illustrate the design methodologies investigated in this paper. It is shown that, for a certain noncolocated structural control problem, use of both techniques results in nonminimum phase compensation.
Topological equivalence of nonlinear autonomous dynamical systems
International Nuclear Information System (INIS)
Nguyen Huynh Phan; Tran Van Nhung
1995-12-01
We show in this paper that the autonomous nonlinear dynamical system Σ(A,B,F): x' = Ax+Bu+F(x) is topologically equivalent to the linear dynamical system Σ(A,B,O): x' = Ax+Bu if the projection of A on the complement in R n of the controllable vectorial subspace is hyperbolic and if lipschitz constant of F is sufficiently small ( * ) and F(x) = 0 when parallel x parallel is sufficiently large ( ** ). In particular, if Σ(A,B,O) is controllable, it is topologically equivalent to Σ(A,B,F) when it is only that F satisfy ( ** ). (author). 18 refs
Dynamic Control Based Photovoltaic Illuminating System
Directory of Open Access Journals (Sweden)
Zhang Chengkai
2016-01-01
Full Text Available Smart LED illumination system can use the power from whether the photovoltaic cell or the power grid automatically based on the SOC (State Of Charge of the photovoltaic cell. This paper proposes a feedback control of the photovoltaic cells and a dynamic control strategy for the Energy system. The dynamic control strategy is used to determine the switching state of the photovoltaic cell based on the illumination load in the past one hour and the battery capacity. These controls are manifested by experimental prototype that the control scheme is correct and effective.
High dynamic range coding imaging system
Wu, Renfan; Huang, Yifan; Hou, Guangqi
2014-10-01
We present a high dynamic range (HDR) imaging system design scheme based on coded aperture technique. This scheme can help us obtain HDR images which have extended depth of field. We adopt Sparse coding algorithm to design coded patterns. Then we utilize the sensor unit to acquire coded images under different exposure settings. With the guide of the multiple exposure parameters, a series of low dynamic range (LDR) coded images are reconstructed. We use some existing algorithms to fuse and display a HDR image by those LDR images. We build an optical simulation model and get some simulation images to verify the novel system.
Trust dynamics in a large system implementation
DEFF Research Database (Denmark)
Schlichter, Bjarne Rerup; Rose, Jeremy
2013-01-01
outcomes, but largely ignored the dynamics of trust relations. Giddens, as part of his study of modernity, theorises trust dynamics in relation to abstract social systems, though without focusing on information systems. We use Giddens’ concepts to investigate evolving trust relationships in a longitudinal......A large information systems implementation (such as Enterprise Resource Planning systems) relies on the trust of its stakeholders to succeed. Such projects impact diverse groups of stakeholders, each with their legitimate interests and expectations. Levels of stakeholder trust can be expected...... case analysis of a large Integrated Hospital System implementation for the Faroe Islands. Trust relationships suffered a serious breakdown, but the project was able to recover and meet its goals. We develop six theoretical propositions theorising the relationship between trust and project outcomes...
Constraint Embedding Technique for Multibody System Dynamics
Woo, Simon S.; Cheng, Michael K.
2011-01-01
Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with
Do dynamical systems follow Benford's law?
International Nuclear Information System (INIS)
Tolle, Charles R.; Budzien, Joanne L.; LaViolette, Randall A.
2000-01-01
Data compiled from a variety of sources follow Benford's law, which gives a monotonically decreasing distribution of the first digit (1 through 9). We examine the frequency of the first digit of the coordinates of the trajectories generated by some common dynamical systems. One-dimensional cellular automata fulfill the expectation that the frequency of the first digit is uniform. The molecular dynamics of fluids, on the other hand, provides trajectories that follow Benford's law. Finally, three chaotic systems are considered: Lorenz, Henon, and Roessler. The Lorenz system generates trajectories that follow Benford's law. The Henon system generates trajectories that resemble neither the uniform distribution nor Benford's law. Finally, the Roessler system generates trajectories that follow the uniform distribution for some parameters choices, and Benford's law for others. (c) 2000 American Institute of Physics
Complex and adaptive dynamical systems a primer
Gros, Claudius
2007-01-01
We are living in an ever more complex world, an epoch where human actions can accordingly acquire far-reaching potentialities. Complex and adaptive dynamical systems are ubiquitous in the world surrounding us and require us to adapt to new realities and the way of dealing with them. This primer has been developed with the aim of conveying a wide range of "commons-sense" knowledge in the field of quantitative complex system science at an introductory level, providing an entry point to this both fascinating and vitally important subject. The approach is modular and phenomenology driven. Examples of emerging phenomena of generic importance treated in this book are: -- The small world phenomenon in social and scale-free networks. -- Phase transitions and self-organized criticality in adaptive systems. -- Life at the edge of chaos and coevolutionary avalanches resulting from the unfolding of all living. -- The concept of living dynamical systems and emotional diffusive control within cognitive system theory. Techn...
Complex and Adaptive Dynamical Systems A Primer
Gros, Claudius
2011-01-01
We are living in an ever more complex world, an epoch where human actions can accordingly acquire far-reaching potentialities. Complex and adaptive dynamical systems are ubiquitous in the world surrounding us and require us to adapt to new realities and the way of dealing with them. This primer has been developed with the aim of conveying a wide range of "commons-sense" knowledge in the field of quantitative complex system science at an introductory level, providing an entry point to this both fascinating and vitally important subject. The approach is modular and phenomenology driven. Examples of emerging phenomena of generic importance treated in this book are: -- The small world phenomenon in social and scale-free networks. -- Phase transitions and self-organized criticality in adaptive systems. -- Life at the edge of chaos and coevolutionary avalanches resulting from the unfolding of all living. -- The concept of living dynamical systems and emotional diffusive control within cognitive system theory. Techn...
Cardea: Dynamic Access Control in Distributed Systems
Lepro, Rebekah
2004-01-01
Modern authorization systems span domains of administration, rely on many different authentication sources, and manage complex attributes as part of the authorization process. This . paper presents Cardea, a distributed system that facilitates dynamic access control, as a valuable piece of an inter-operable authorization framework. First, the authorization model employed in Cardea and its functionality goals are examined. Next, critical features of the system architecture and its handling of the authorization process are then examined. Then the S A M L and XACML standards, as incorporated into the system, are analyzed. Finally, the future directions of this project are outlined and connection points with general components of an authorization system are highlighted.
Solar dynamic power systems for space station
Irvine, Thomas B.; Nall, Marsha M.; Seidel, Robert C.
1986-01-01
The Parabolic Offset Linearly Actuated Reflector (POLAR) solar dynamic module was selected as the baseline design for a solar dynamic power system aboard the space station. The POLAR concept was chosen over other candidate designs after extensive trade studies. The primary advantages of the POLAR concept are the low mass moment of inertia of the module about the transverse boom and the compactness of the stowed module which enables packaging of two complete modules in the Shuttle orbiter payload bay. The fine pointing control system required for the solar dynamic module has been studied and initial results indicate that if disturbances from the station are allowed to back drive the rotary alpha joint, pointing errors caused by transient loads on the space station can be minimized. This would allow pointing controls to operate in bandwidths near system structural frequencies. The incorporation of the fine pointing control system into the solar dynamic module is fairly straightforward for the three strut concentrator support structure. However, results of structural analyses indicate that this three strut support is not optimum. Incorporation of a vernier pointing system into the proposed six strut support structure is being studied.
Reducing the Complexity of Genetic Fuzzy Classifiers in Highly-Dimensional Classification Problems
Directory of Open Access Journals (Sweden)
DimitrisG. Stavrakoudis
2012-04-01
Full Text Available This paper introduces the Fast Iterative Rule-based Linguistic Classifier (FaIRLiC, a Genetic Fuzzy Rule-Based Classification System (GFRBCS which targets at reducing the structural complexity of the resulting rule base, as well as its learning algorithm's computational requirements, especially when dealing with high-dimensional feature spaces. The proposed methodology follows the principles of the iterative rule learning (IRL approach, whereby a rule extraction algorithm (REA is invoked in an iterative fashion, producing one fuzzy rule at a time. The REA is performed in two successive steps: the first one selects the relevant features of the currently extracted rule, whereas the second one decides the antecedent part of the fuzzy rule, using the previously selected subset of features. The performance of the classifier is finally optimized through a genetic tuning post-processing stage. Comparative results in a hyperspectral remote sensing classification as well as in 12 real-world classification datasets indicate the effectiveness of the proposed methodology in generating high-performing and compact fuzzy rule-based classifiers, even for very high-dimensional feature spaces.
Tikhonov, Mikhail; Monasson, Remi
2018-01-01
Much of our understanding of ecological and evolutionary mechanisms derives from analysis of low-dimensional models: with few interacting species, or few axes defining "fitness". It is not always clear to what extent the intuition derived from low-dimensional models applies to the complex, high-dimensional reality. For instance, most naturally occurring microbial communities are strikingly diverse, harboring a large number of coexisting species, each of which contributes to shaping the environment of others. Understanding the eco-evolutionary interplay in these systems is an important challenge, and an exciting new domain for statistical physics. Recent work identified a promising new platform for investigating highly diverse ecosystems, based on the classic resource competition model of MacArthur. Here, we describe how the same analytical framework can be used to study evolutionary questions. Our analysis illustrates how, at high dimension, the intuition promoted by a one-dimensional (scalar) notion of fitness can become misleading. Specifically, while the low-dimensional picture emphasizes organism cost or efficiency, we exhibit a regime where cost becomes irrelevant for survival, and link this observation to generic properties of high-dimensional geometry.
Operationalizing sustainability in urban coastal systems: a system dynamics analysis.
Mavrommati, Georgia; Bithas, Kostas; Panayiotidis, Panayiotis
2013-12-15
We propose a system dynamics approach for Ecologically Sustainable Development (ESD) in urban coastal systems. A systematic analysis based on theoretical considerations, policy analysis and experts' knowledge is followed in order to define the concept of ESD. The principles underlying ESD feed the development of a System Dynamics Model (SDM) that connects the pollutant loads produced by urban systems' socioeconomic activities with the ecological condition of the coastal ecosystem that it is delineated in operational terms through key biological elements defined by the EU Water Framework Directive. The receiving waters of the Athens Metropolitan area, which bears the elements of typical high population density Mediterranean coastal city but which currently has also new dynamics induced by the ongoing financial crisis, are used as an experimental system for testing a system dynamics approach to apply the concept of ESD. Systems' thinking is employed to represent the complex relationships among the components of the system. Interconnections and dependencies that determine the potentials for achieving ESD are revealed. The proposed system dynamics analysis can facilitate decision makers to define paths of development that comply with the principles of ESD. Copyright © 2013 Elsevier Ltd. All rights reserved.
High-dimensional statistical inference: From vector to matrix
Zhang, Anru
Statistical inference for sparse signals or low-rank matrices in high-dimensional settings is of significant interest in a range of contemporary applications. It has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. In this thesis, we consider several problems in including sparse signal recovery (compressed sensing under restricted isometry) and low-rank matrix recovery (matrix recovery via rank-one projections and structured matrix completion). The first part of the thesis discusses compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key technical tool which represents points in a polytope by convex combinations of sparse vectors. The technique is elementary while leads to sharp results. It is shown that, in compressed sensing, delta kA 0, delta kA < 1/3 + epsilon, deltak A + thetak,kA < 1 + epsilon, or deltatkA< √(t - 1) / t + epsilon are not sufficient to guarantee the exact recovery of all k-sparse signals for large k. Similar result also holds for matrix recovery. In addition, the conditions delta kA<1/3, deltak A+ thetak,kA<1, delta tkA < √(t - 1)/t and deltarM<1/3, delta rM+ thetar,rM<1, delta trM< √(t - 1)/ t are also shown to be sufficient respectively for stable recovery of approximately sparse signals and low-rank matrices in the noisy case. For the second part of the thesis, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is adaptive to the rank and robust against small perturbations. Both upper and lower bounds for the estimation accuracy under the Frobenius norm loss are obtained. The proposed estimator is shown to be rate-optimal under certain conditions. The
Approximation of High-Dimensional Rank One Tensors
Bachmayr, Markus
2013-11-12
Many real world problems are high-dimensional in that their solution is a function which depends on many variables or parameters. This presents a computational challenge since traditional numerical techniques are built on model classes for functions based solely on smoothness. It is known that the approximation of smoothness classes of functions suffers from the so-called \\'curse of dimensionality\\'. Avoiding this curse requires new model classes for real world functions that match applications. This has led to the introduction of notions such as sparsity, variable reduction, and reduced modeling. One theme that is particularly common is to assume a tensor structure for the target function. This paper investigates how well a rank one function f(x 1,...,x d)=f 1(x 1)⋯f d(x d), defined on Ω=[0,1]d can be captured through point queries. It is shown that such a rank one function with component functions f j in W∞ r([0,1]) can be captured (in L ∞) to accuracy O(C(d,r)N -r) from N well-chosen point evaluations. The constant C(d,r) scales like d dr. The queries in our algorithms have two ingredients, a set of points built on the results from discrepancy theory and a second adaptive set of queries dependent on the information drawn from the first set. Under the assumption that a point z∈Ω with nonvanishing f(z) is known, the accuracy improves to O(dN -r). © 2013 Springer Science+Business Media New York.
Quality and efficiency in high dimensional Nearest neighbor search
Tao, Yufei; Yi, Ke; Sheng, Cheng; Kalnis, Panos
2009-01-01
Nearest neighbor (NN) search in high dimensional space is an important problem in many applications. Ideally, a practical solution (i) should be implementable in a relational database, and (ii) its query cost should grow sub-linearly with the dataset size, regardless of the data and query distributions. Despite the bulk of NN literature, no solution fulfills both requirements, except locality sensitive hashing (LSH). The existing LSH implementations are either rigorous or adhoc. Rigorous-LSH ensures good quality of query results, but requires expensive space and query cost. Although adhoc-LSH is more efficient, it abandons quality control, i.e., the neighbor it outputs can be arbitrarily bad. As a result, currently no method is able to ensure both quality and efficiency simultaneously in practice. Motivated by this, we propose a new access method called the locality sensitive B-tree (LSB-tree) that enables fast highdimensional NN search with excellent quality. The combination of several LSB-trees leads to a structure called the LSB-forest that ensures the same result quality as rigorous-LSH, but reduces its space and query cost dramatically. The LSB-forest also outperforms adhoc-LSH, even though the latter has no quality guarantee. Besides its appealing theoretical properties, the LSB-tree itself also serves as an effective index that consumes linear space, and supports efficient updates. Our extensive experiments confirm that the LSB-tree is faster than (i) the state of the art of exact NN search by two orders of magnitude, and (ii) the best (linear-space) method of approximate retrieval by an order of magnitude, and at the same time, returns neighbors with much better quality. © 2009 ACM.
Approximation of High-Dimensional Rank One Tensors
Bachmayr, Markus; Dahmen, Wolfgang; DeVore, Ronald; Grasedyck, Lars
2013-01-01
Many real world problems are high-dimensional in that their solution is a function which depends on many variables or parameters. This presents a computational challenge since traditional numerical techniques are built on model classes for functions based solely on smoothness. It is known that the approximation of smoothness classes of functions suffers from the so-called 'curse of dimensionality'. Avoiding this curse requires new model classes for real world functions that match applications. This has led to the introduction of notions such as sparsity, variable reduction, and reduced modeling. One theme that is particularly common is to assume a tensor structure for the target function. This paper investigates how well a rank one function f(x 1,...,x d)=f 1(x 1)⋯f d(x d), defined on Ω=[0,1]d can be captured through point queries. It is shown that such a rank one function with component functions f j in W∞ r([0,1]) can be captured (in L ∞) to accuracy O(C(d,r)N -r) from N well-chosen point evaluations. The constant C(d,r) scales like d dr. The queries in our algorithms have two ingredients, a set of points built on the results from discrepancy theory and a second adaptive set of queries dependent on the information drawn from the first set. Under the assumption that a point z∈Ω with nonvanishing f(z) is known, the accuracy improves to O(dN -r). © 2013 Springer Science+Business Media New York.
An exploration of dynamical systems and chaos
Argyris, John H; Haase, Maria; Friedrich, Rudolf
2015-01-01
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlar...
Brand Equity Evolution: a System Dynamics Model
Directory of Open Access Journals (Sweden)
Edson Crescitelli
2009-04-01
Full Text Available One of the greatest challenges in brand management lies in monitoring brand equity over time. This paper aimsto present a simulation model able to represent this evolution. The model was drawn on brand equity concepts developed by Aaker and Joachimsthaler (2000, using the system dynamics methodology. The use ofcomputational dynamic models aims to create new sources of information able to sensitize academics and managers alike to the dynamic implications of their brand management. As a result, an easily implementable model was generated, capable of executing continuous scenario simulations by surveying casual relations among the variables that explain brand equity. Moreover, the existence of a number of system modeling tools will allow extensive application of the concepts used in this study in practical situations, both in professional and educational settings
Integrability of dynamical systems algebra and analysis
Zhang, Xiang
2017-01-01
This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the center—focus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology. Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems.
Controlling Complex Systems and Developing Dynamic Technology
Avizienis, Audrius Victor
In complex systems, control and understanding become intertwined. Following Ilya Prigogine, we define complex systems as having control parameters which mediate transitions between distinct modes of dynamical behavior. From this perspective, determining the nature of control parameters and demonstrating the associated dynamical phase transitions are practically equivalent and fundamental to engaging with complexity. In the first part of this work, a control parameter is determined for a non-equilibrium electrochemical system by studying a transition in the morphology of structures produced by an electroless deposition reaction. Specifically, changing the size of copper posts used as the substrate for growing metallic silver structures by the reduction of Ag+ from solution under diffusion-limited reaction conditions causes a dynamical phase transition in the crystal growth process. For Cu posts with edge lengths on the order of one micron, local forces promoting anisotropic growth predominate, and the reaction produces interconnected networks of Ag nanowires. As the post size is increased above 10 microns, the local interfacial growth reaction dynamics couple with the macroscopic diffusion field, leading to spatially propagating instabilities in the electrochemical potential which induce periodic branching during crystal growth, producing dendritic deposits. This result is interesting both as an example of control and understanding in a complex system, and as a useful combination of top-down lithography with bottom-up electrochemical self-assembly. The second part of this work focuses on the technological development of devices fabricated using this non-equilibrium electrochemical process, towards a goal of integrating a complex network as a dynamic functional component in a neuromorphic computing device. Self-assembled networks of silver nanowires were reacted with sulfur to produce interfacial "atomic switches": silver-silver sulfide junctions, which exhibit
State dynamics of a double sandbar system
Price, T.D.; Ruessink, B.G.
2011-01-01
A 9.3-year dataset of low-tide time-exposure images from Surfers Paradise, Northern Gold Coast, Australia was used to characterise the state dynamics of a double sandbar system. The morphology of the nearshore sandbars was described by means of the sequential bar state classification scheme of
Geometric analysis of nondeterminacy in dynamical systems
DEFF Research Database (Denmark)
Wisniewski, Rafal; Raussen, Martin Hubert
2007-01-01
This article intends to provide some new insights into concurrency using ideas from the theory of dynamical systems. Inherently discrete concurrency corresponds to a parallel continuous concept: a discrete state space corresponds to a differential manifold, an execution path corresponds to a flow...
Invariant of dynamical systems: A generalized entropy
International Nuclear Information System (INIS)
Meson, A.M.; Vericat, F.
1996-01-01
In this work the concept of entropy of a dynamical system, as given by Kolmogorov, is generalized in the sense of Tsallis. It is shown that this entropy is an isomorphism invariant, being complete for Bernoulli schemes. copyright 1996 American Institute of Physics
Dynamical Systems Approaches to Emotional Development
Camras, Linda A.; Witherington, David C.
2005-01-01
Within the last 20 years, transitions in the conceptualization of emotion and its development have given rise to calls for an explanatory framework that captures emotional development in all its organizational complexity and variability. Recent attempts have been made to couch emotional development in terms of a dynamical systems approach through…
Organizing Performance Requirements For Dynamical Systems
Malchow, Harvey L.; Croopnick, Steven R.
1990-01-01
Paper describes methodology for establishing performance requirements for complicated dynamical systems. Uses top-down approach. In series of steps, makes connections between high-level mission requirements and lower-level functional performance requirements. Provides systematic delineation of elements accommodating design compromises.
Improving homogeneity by dynamic speed limit systems.
Nes, N. van Brandenberg, S. & Twisk, D.A.M.
2010-01-01
Homogeneity of driving speeds is an important variable in determining road safety; more homogeneous driving speeds increase road safety. This study investigates the effect of introducing dynamic speed limit systems on homogeneity of driving speeds. A total of 46 subjects twice drove a route along 12
The Self as a Complex Dynamic System
Mercer, Sarah
2011-01-01
This article explores the potential offered by complexity theories for understanding language learners' sense of self and attempts to show how the self might usefully be conceived of as a complex dynamic system. Rather than presenting empirical findings, the article discusses existent research on the self and aims at outlining a conceptual…
The dynamics of antilock brake systems
Denny, Mark
2005-11-01
The nonlinear dynamics of automobile braking are investigated. Nonlinearity arises because of the manner in which the friction coefficient between vehicle tyres and road surface depends upon vehicle speed and wheel angular speed. We show how antilock brake systems approach optimum braking performance.
Book Review: Dynamic Systems for Everyone
Asish Ghosh starts the epilogue of the second edition of Dynamic Systems for Everyone with this quote: “We are now witnessing major technological advancements in areas, like artificial intelligence, robotics and self driven cars. …The pace of change is accelerating, ...
On multi-dissipative dynamic systems
DEFF Research Database (Denmark)
Thygesen, Uffe Høgsbro
1999-01-01
We consider deterministic dynamic systems with state space representations which are dissipative in the sense of Willems (1972) with respect to several supply rates. This property is of interest in robustness analysis and in multi-objective control. We give conditions under which the convex cone...
Induced topological pressure for topological dynamical systems
International Nuclear Information System (INIS)
Xing, Zhitao; Chen, Ercai
2015-01-01
In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure
Stochastic properties of the Friedman dynamical system
International Nuclear Information System (INIS)
Szydlowski, M.; Heller, M.; Golda, Z.
1985-01-01
Some mathematical aspects of the stochastic cosmology are discussed in the corresponding ordinary Friedman world models. In particulare, it is shown that if the strong and Lorentz energy conditions are known, or the potential function is given, or a stochastic measure is suitably defined then the structure of the phase plane of the Friedman dynamical system is determined. 11 refs., 2 figs. (author)
Abstraction of Dynamical Systems by Timed Automata
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2011-01-01
To enable formal verification of a dynamical system, given by a set of differential equations, it is abstracted by a finite state model. This allows for application of methods for model checking. Consequently, it opens the possibility of carrying out the verification of reachability and timing re...
The dynamics of surge in compression systems
Indian Academy of Sciences (India)
is of interest to study compression-system surge to understand its dynamics in order ... Internal problems like compressor going into rotating stall, resulting in loss of ... of water column, was used for mass-flow measurement at the impeller entry.
LOCAL ENTROPY FUNCTION OF DYNAMICAL SYSTEM
Directory of Open Access Journals (Sweden)
İsmail TOK
2013-05-01
Full Text Available In this work, we first,define the entropy function of the topological dynamical system and investigate basic properties of this function without going into details. Let (X,A,T be a probability measure space and consider P = { pl5p2,...,pn} a finite measurable partition of all sub-sets of topological dynamical system (X,T.Then,the quantity H (P = ^ zpt is called the i=1 entropy function of finite measurable partition P.Where f-1 log t if 0 0.If diam(P < s,then the quantity L^ (T = h^ (T - h^ (T,P is called a local entropy function of topological dynamical system (X,T . In conclusion, Let (X,T and (Y,S be two topological dynamical system. If TxS is a transformation defined on the product space (XxY,TxS with (TxS(x , y = (Tx,Sy for all (x,y X x Y.Then L ^^ (TxS = L^d(T + L (S .and, we prove some fundamental properties of this function.
Design tools for complex dynamic security systems.
Energy Technology Data Exchange (ETDEWEB)
Byrne, Raymond Harry; Rigdon, James Brian; Rohrer, Brandon Robinson; Laguna, Glenn A.; Robinett, Rush D. III (.; ); Groom, Kenneth Neal; Wilson, David Gerald; Bickerstaff, Robert J.; Harrington, John J.
2007-01-01
The development of tools for complex dynamic security systems is not a straight forward engineering task but, rather, a scientific task where discovery of new scientific principles and math is necessary. For years, scientists have observed complex behavior but have had difficulty understanding it. Prominent examples include: insect colony organization, the stock market, molecular interactions, fractals, and emergent behavior. Engineering such systems will be an even greater challenge. This report explores four tools for engineered complex dynamic security systems: Partially Observable Markov Decision Process, Percolation Theory, Graph Theory, and Exergy/Entropy Theory. Additionally, enabling hardware technology for next generation security systems are described: a 100 node wireless sensor network, unmanned ground vehicle and unmanned aerial vehicle.
Dynamics of quasi-stable dissipative systems
Chueshov, Igor
2015-01-01
This book is devoted to background material and recently developed mathematical methods in the study of infinite-dimensional dissipative systems. The theory of such systems is motivated by the long-term goal to establish rigorous mathematical models for turbulent and chaotic phenomena. The aim here is to offer general methods and abstract results pertaining to fundamental dynamical systems properties related to dissipative long-time behavior. The book systematically presents, develops and uses the quasi-stability method while substantially extending it by including for consideration new classes of models and PDE systems arising in Continuum Mechanics. The book can be used as a textbook in dissipative dynamics at the graduate level. Igor Chueshov is a Professor of Mathematics at Karazin Kharkov National University in Kharkov, Ukraine.
Quantum speed limits in open system dynamics
del Campo, A.; Egusquiza, I. L.; Plenio, M. B.; Huelga, S. F.
2012-01-01
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive and trace preserving (CPT) evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the ...
Dynamic Properties of Impulse Measuring Systems
DEFF Research Database (Denmark)
Pedersen, A.; Lausen, P.
1971-01-01
After some basic considerations the dynamic properties of the measuring system are subjected to a general examination based on a number of responses, characteristic of the system. It is demonstrated that an impulse circuit has an internal impedance different from zero, for which reason...... the interaction between the generator and the measuring circuit is of paramount importance to the voltage across the test object. Based on the measured values the determination of the applied voltage is considered....
Coherence and chaos in extended dynamical systems
International Nuclear Information System (INIS)
Bishop, A.R.
1994-01-01
Coherence, chaos, and pattern formation are characteristic elements of the nonequilibrium statistical mechanics controlling mesoscopic order and disorder in many-degree-of-freedom nonlinear dynamical systems. Competing length scales and/or time scales are the underlying microscopic driving forces for many of these aspects of ''complexity.'' We illustrate the basic concepts with some model examples of classical and quantum, ordered and disordered, nonlinear systems
Chaos control of Chen chaotic dynamical system
International Nuclear Information System (INIS)
Yassen, M.T.
2003-01-01
This paper is devoted to study the problem of controlling chaos in Chen chaotic dynamical system. Two different methods of control, feedback and nonfeedback methods are used to suppress chaos to unstable equilibria or unstable periodic orbits (UPO). The Lyapunov direct method and Routh-Hurwitz criteria are used to study the conditions of the asymptotic stability of the steady states of the controlled system. Numerical simulations are presented to show these results
Automated design of complex dynamic systems.
Directory of Open Access Journals (Sweden)
Michiel Hermans
Full Text Available Several fields of study are concerned with uniting the concept of computation with that of the design of physical systems. For example, a recent trend in robotics is to design robots in such a way that they require a minimal control effort. Another example is found in the domain of photonics, where recent efforts try to benefit directly from the complex nonlinear dynamics to achieve more efficient signal processing. The underlying goal of these and similar research efforts is to internalize a large part of the necessary computations within the physical system itself by exploiting its inherent non-linear dynamics. This, however, often requires the optimization of large numbers of system parameters, related to both the system's structure as well as its material properties. In addition, many of these parameters are subject to fabrication variability or to variations through time. In this paper we apply a machine learning algorithm to optimize physical dynamic systems. We show that such algorithms, which are normally applied on abstract computational entities, can be extended to the field of differential equations and used to optimize an associated set of parameters which determine their behavior. We show that machine learning training methodologies are highly useful in designing robust systems, and we provide a set of both simple and complex examples using models of physical dynamical systems. Interestingly, the derived optimization method is intimately related to direct collocation a method known in the field of optimal control. Our work suggests that the application domains of both machine learning and optimal control have a largely unexplored overlapping area which envelopes a novel design methodology of smart and highly complex physical systems.
Some problems of dynamical systems on three dimensional manifolds
International Nuclear Information System (INIS)
Dong Zhenxie.
1985-08-01
It is important to study the dynamical systems on 3-dimensional manifolds, its importance is showing up in its close relation with our life. Because of the complication of topological structure of Dynamical systems on 3-dimensional manifolds, generally speaking, the search for 3-dynamical systems is not easier than 2-dynamical systems. This paper is a summary of the partial result of dynamical systems on 3-dimensional manifolds. (author)
Parameter identifiability of linear dynamical systems
Glover, K.; Willems, J. C.
1974-01-01
It is assumed that the system matrices of a stationary linear dynamical system were parametrized by a set of unknown parameters. The question considered here is, when can such a set of unknown parameters be identified from the observed data? Conditions for the local identifiability of a parametrization are derived in three situations: (1) when input/output observations are made, (2) when there exists an unknown feedback matrix in the system and (3) when the system is assumed to be driven by white noise and only output observations are made. Also a sufficient condition for global identifiability is derived.
Nonlinear dynamic macromodeling techniques for audio systems
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
Scalable Molecular Dynamics for Large Biomolecular Systems
Directory of Open Access Journals (Sweden)
Robert K. Brunner
2000-01-01
Full Text Available We present an optimized parallelization scheme for molecular dynamics simulations of large biomolecular systems, implemented in the production-quality molecular dynamics program NAMD. With an object-based hybrid force and spatial decomposition scheme, and an aggressive measurement-based predictive load balancing framework, we have attained speeds and speedups that are much higher than any reported in literature so far. The paper first summarizes the broad methodology we are pursuing, and the basic parallelization scheme we used. It then describes the optimizations that were instrumental in increasing performance, and presents performance results on benchmark simulations.
Structural dynamics of electronic and photonic systems
Suhir, Ephraim; Steinberg, David S
2011-01-01
The proposed book will offer comprehensive and versatile methodologies and recommendations on how to determine dynamic characteristics of typical micro- and opto-electronic structural elements (printed circuit boards, solder joints, heavy devices, etc.) and how to design a viable and reliable structure that would be able to withstand high-level dynamic loading. Particular attention will be given to portable devices and systems designed for operation in harsh environments (such as automotive, aerospace, military, etc.) In-depth discussion from a mechanical engineer's viewpoint will be conducte
Nonlinear dynamical system approaches towards neural prosthesis
International Nuclear Information System (INIS)
Torikai, Hiroyuki; Hashimoto, Sho
2011-01-01
An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.
Order in cold ionic systems: Dynamic effects
International Nuclear Information System (INIS)
Schiffer, J.P.
1988-01-01
The present state and recent developments in Molecular Dynamics calculations modeling cooled heavy-ion beams are summarized. First, a frame of reference is established, summarizing what has happened in the past; then the properties of model systems of cold ions studied in Molecular Dynamics calculations are reviewed, with static boundary conditions with which an ordered state is revealed; finally, more recent results on such modelling, adding the complications in the (time-dependent) boundary conditions that begin to approach real storage rings (ion traps) are reported. 14 refs., 19 figs., 2 tabs
Dynamical systems with applications using Maple
Lynch, Stephen
2001-01-01
"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple." —UK Nonlinear News (Review of First Edition) "The book will be useful for all kinds of dynamical systems courses…. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. … [It] is well written and a pleasure to read, which is helped by its attention to historical background." —Mathematical Reviews (Review of First Edition) Since the first edition of this book was published in 2001, Maple™ has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural n...
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Dynamic behavior of district heating systems
International Nuclear Information System (INIS)
Kunz, J.
1994-01-01
The goal of this study is to develop a simulation model of a hot water system taking into account the time dependent phenomena which are important for the operational management of such a system. A state of the art literature review has shown that there is no such model considering all parts from the generation of the heat at the plant to its consumption in the connected buildings so far. First, an exhaustive list of all dynamic phenomena occurring in district heating systems has been drawn and analyzed. Considering this list, this thesis proposes that a model which satisfies the criteria listed above can be developed by superposing four sub-models which are a dynamic model of the heat generation plant, a steady state model of the hydraulic calculation of the distribution network, a dynamic model of the thermal behavior of the network and a dynamic model of the heat consumers. The development of the four sub-models starts from the fundamental conservation equations for fluid systems, i.e. the conservation of mass, momentum and energy. The transformations of those general equations into simple calculation formulas show and justify the hypotheses made in the modeling process. The heat generation plant model itself is a set of sub-models: the models for steam boilers, hot water boilers and heat accumulators which take account of the dynamic evolution of the water temperature by a simple form of the energy conservation equation, as well as the steady state models for circulation pumps and pressurizers. Since the velocities in the network pipes are small, a consideration of steady states is adopted. A network model allowing to calculate the hydraulic variables in every point is adopted from the graph theory. The pressures and flow rates in the network are calculated at discrete time steps and they are considered to be constant for the duration between the time steps. (author) figs., tabs., refs
Dynamical systems on networks a tutorial
Porter, Mason A
2016-01-01
This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on “simple” situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks. Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow of Somerville College. James P. Gleeson is Professor of Industrial and Appli...
Epidemic Dynamics in Open Quantum Spin Systems
Pérez-Espigares, Carlos; Marcuzzi, Matteo; Gutiérrez, Ricardo; Lesanovsky, Igor
2017-10-01
We explore the nonequilibrium evolution and stationary states of an open many-body system that displays epidemic spreading dynamics in a classical and a quantum regime. Our study is motivated by recent experiments conducted in strongly interacting gases of highly excited Rydberg atoms where the facilitated excitation of Rydberg states competes with radiative decay. These systems approximately implement open quantum versions of models for population dynamics or disease spreading where species can be in a healthy, infected or immune state. We show that in a two-dimensional lattice, depending on the dominance of either classical or quantum effects, the system may display a different kind of nonequilibrium phase transition. We moreover discuss the observability of our findings in laser driven Rydberg gases with particular focus on the role of long-range interactions.
Keystroke Dynamics-Based Credential Hardening Systems
Bartlow, Nick; Cukic, Bojan
abstract Keystroke dynamics are becoming a well-known method for strengthening username- and password-based credential sets. The familiarity and ease of use of these traditional authentication schemes combined with the increased trustworthiness associated with biometrics makes them prime candidates for application in many web-based scenarios. Our keystroke dynamics system uses Breiman’s random forests algorithm to classify keystroke input sequences as genuine or imposter. The system is capable of operating at various points on a traditional ROC curve depending on application-specific security needs. As a username/password authentication scheme, our approach decreases the system penetration rate associated with compromised passwords up to 99.15%. Beyond presenting results demonstrating the credential hardening effect of our scheme, we look into the notion that a user’s familiarity to components of a credential set can non-trivially impact error rates.
Brayton dynamic isotope power systems update
International Nuclear Information System (INIS)
Davis, K.A.; Pietsch, A.; Casagrande, R.D.
1986-01-01
Brayton dynamic power systems are uniquely suited for space applications. They are compact and highly efficient, offer inherent reliability due to only one moving part, and utilize a single phase and inert working fluid. Additional features include gas bearings, constant speed, and operation at essentially constant temperature. The design, utilizing an inert gas working fluid and gas bearing, is unaffected by zero gravity and can be easily started and restarted in space at low temperatures. This paper describes the salient features of the BIPS as a Dynamic Isotope Power System (DIPS), summarizes the development work to date, establishes the maturity of the design, provides an update on materials technology, and reviews systems integration considerations
Dynamic graph system for a semantic database
Mizell, David
2015-01-27
A method and system in a computer system for dynamically providing a graphical representation of a data store of entries via a matrix interface is disclosed. A dynamic graph system provides a matrix interface that exposes to an application program a graphical representation of data stored in a data store such as a semantic database storing triples. To the application program, the matrix interface represents the graph as a sparse adjacency matrix that is stored in compressed form. Each entry of the data store is considered to represent a link between nodes of the graph. Each entry has a first field and a second field identifying the nodes connected by the link and a third field with a value for the link that connects the identified nodes. The first, second, and third fields represent the rows, column, and elements of the adjacency matrix.
Individual heterogeneity generating explosive system network dynamics.
Manrique, Pedro D; Johnson, Neil F
2018-03-01
Individual heterogeneity is a key characteristic of many real-world systems, from organisms to humans. However, its role in determining the system's collective dynamics is not well understood. Here we study how individual heterogeneity impacts the system network dynamics by comparing linking mechanisms that favor similar or dissimilar individuals. We find that this heterogeneity-based evolution drives an unconventional form of explosive network behavior, and it dictates how a polarized population moves toward consensus. Our model shows good agreement with data from both biological and social science domains. We conclude that individual heterogeneity likely plays a key role in the collective development of real-world networks and communities, and it cannot be ignored.
Individual heterogeneity generating explosive system network dynamics
Manrique, Pedro D.; Johnson, Neil F.
2018-03-01
Individual heterogeneity is a key characteristic of many real-world systems, from organisms to humans. However, its role in determining the system's collective dynamics is not well understood. Here we study how individual heterogeneity impacts the system network dynamics by comparing linking mechanisms that favor similar or dissimilar individuals. We find that this heterogeneity-based evolution drives an unconventional form of explosive network behavior, and it dictates how a polarized population moves toward consensus. Our model shows good agreement with data from both biological and social science domains. We conclude that individual heterogeneity likely plays a key role in the collective development of real-world networks and communities, and it cannot be ignored.
Geometry and dynamics of integrable systems
Matveev, Vladimir
2016-01-01
Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mir...
Nonlinear PDEs a dynamical systems approach
Schneider, Guido
2017-01-01
This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced...
The dynamical crossover in attractive colloidal systems
Energy Technology Data Exchange (ETDEWEB)
Mallamace, Francesco [Dipartimento di Fisica e Scienze della Terra, Università di Messina and CNISM, I-98168 Messina (Italy); Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Corsaro, Carmelo [Dipartimento di Fisica e Scienze della Terra, Università di Messina and CNISM, I-98168 Messina (Italy); Stanley, H. Eugene [Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215 (United States); Mallamace, Domenico [Dipartimento di Scienze dell’Ambiente, della Sicurezza, del Territorio, degli Alimenti e della Salute, Università di Messina, I-98166 Messina (Italy); Chen, Sow-Hsin [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2013-12-07
We study the dynamical arrest in an adhesive hard-sphere colloidal system. We examine a micellar suspension of the Pluronic-L64 surfactant in the temperature (T) and volume fraction (ϕ) phase diagram. According to mode-coupling theory (MCT), this system is characterized by a cusp-like singularity and two glassy phases: an attractive glass (AG) phase and a repulsive glass (RG) phase. The T − ϕ phase diagram of this system as confirmed by a previous series of scattering data also exhibits a Percolation Threshold (PT) line, a reentrant behavior (AG-liquid-RG), and a glass-to-glass transition. The AG phase can be generated out of the liquid phase by using T and ϕ as control parameters. We utilize viscosity and nuclear magnetic resonance (NMR) techniques. NMR data confirm all the characteristic properties of the colloidal system phase diagram and give evidence of the onset of a fractal-like percolating structure at a precise threshold. The MCT scaling laws used to study the shear viscosity as a function of ϕ and T show in both cases a fragile-to-strong liquid glass-forming dynamic crossover (FSC) located near the percolation threshold where the clustering process is fully developed. These results suggest a larger thermodynamic generality for this phenomenon, which is usually studied only as a function of the temperature. We also find that the critical values of the control parameters, coincident with the PT line, define the locus of the FSC. In the region between the FSC and the glass transition lines the system dynamics are dominated by clustering effects. We thus demonstrate that it is possible, using the conceptual framework provided by extended mode-coupling theory, to describe the way a system approaches dynamic arrest, taking into account both cage and hopping effects.
uncertain dynamic systems on time scales
Directory of Open Access Journals (Sweden)
V. Lakshmikantham
1995-01-01
Full Text Available A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.
Lectures on Dynamics of Stochastic Systems
Klyatskin, Valery I
2010-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data. This book is a revised a
Entanglement dynamics of J-aggregate systems
Energy Technology Data Exchange (ETDEWEB)
Thilagam, A, E-mail: Thilagam.Lohe@unisa.edu.au [Information Technology, Engineering and the Environment, Mawson Institute, University of South Australia, South Australia 5095 (Australia)
2011-04-01
The entanglement dynamics of one-dimensional J-aggregate systems are examined using entanglement measures such as the von Neumann entropy and Wootters concurrence. The effect of dispersion and resonance terms associated with the exciton-phonon interaction are analyzed using Green's function formalism. A probability propagator term, derived using the Markovian approximation, presents J-aggregate systems as potential channels for large scale energy propagation for a select range of parameters. We highlight the role of a critical number of coherently coupled monomer sites and two-exciton states in determining superradiance in J-aggregate systems.
Control theory of digitally networked dynamic systems
Lunze, Jan
2013-01-01
The book gives an introduction to networked control systems and describes new modeling paradigms, analysis methods for event-driven, digitally networked systems, and design methods for distributed estimation and control. Networked model predictive control is developed as a means to tolerate time delays and packet loss brought about by the communication network. In event-based control the traditional periodic sampling is replaced by state-dependent triggering schemes. Novel methods for multi-agent systems ensure complete or clustered synchrony of agents with identical or with individual dynamic
Classical dynamics of particles and systems
Marion, Jerry B
1965-01-01
Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handl
Network Physiology: How Organ Systems Dynamically Interact.
Bartsch, Ronny P; Liu, Kang K L; Bashan, Amir; Ivanov, Plamen Ch
2015-01-01
We systematically study how diverse physiologic systems in the human organism dynamically interact and collectively behave to produce distinct physiologic states and functions. This is a fundamental question in the new interdisciplinary field of Network Physiology, and has not been previously explored. Introducing the novel concept of Time Delay Stability (TDS), we develop a computational approach to identify and quantify networks of physiologic interactions from long-term continuous, multi-channel physiological recordings. We also develop a physiologically-motivated visualization framework to map networks of dynamical organ interactions to graphical objects encoded with information about the coupling strength of network links quantified using the TDS measure. Applying a system-wide integrative approach, we identify distinct patterns in the network structure of organ interactions, as well as the frequency bands through which these interactions are mediated. We establish first maps representing physiologic organ network interactions and discover basic rules underlying the complex hierarchical reorganization in physiologic networks with transitions across physiologic states. Our findings demonstrate a direct association between network topology and physiologic function, and provide new insights into understanding how health and distinct physiologic states emerge from networked interactions among nonlinear multi-component complex systems. The presented here investigations are initial steps in building a first atlas of dynamic interactions among organ systems.
Network Physiology: How Organ Systems Dynamically Interact
Bartsch, Ronny P.; Liu, Kang K. L.; Bashan, Amir; Ivanov, Plamen Ch.
2015-01-01
We systematically study how diverse physiologic systems in the human organism dynamically interact and collectively behave to produce distinct physiologic states and functions. This is a fundamental question in the new interdisciplinary field of Network Physiology, and has not been previously explored. Introducing the novel concept of Time Delay Stability (TDS), we develop a computational approach to identify and quantify networks of physiologic interactions from long-term continuous, multi-channel physiological recordings. We also develop a physiologically-motivated visualization framework to map networks of dynamical organ interactions to graphical objects encoded with information about the coupling strength of network links quantified using the TDS measure. Applying a system-wide integrative approach, we identify distinct patterns in the network structure of organ interactions, as well as the frequency bands through which these interactions are mediated. We establish first maps representing physiologic organ network interactions and discover basic rules underlying the complex hierarchical reorganization in physiologic networks with transitions across physiologic states. Our findings demonstrate a direct association between network topology and physiologic function, and provide new insights into understanding how health and distinct physiologic states emerge from networked interactions among nonlinear multi-component complex systems. The presented here investigations are initial steps in building a first atlas of dynamic interactions among organ systems. PMID:26555073
Q-deformed systems and constrained dynamics
International Nuclear Information System (INIS)
Shabanov, S.V.
1993-01-01
It is shown that quantum theories of the q-deformed harmonic oscillator and one-dimensional free q-particle (a free particle on the 'quantum' line) can be obtained by the canonical quantization of classical Hamiltonian systems with commutative phase-space variables and a non-trivial symplectic structure. In the framework of this approach, classical dynamics of a particle on the q-line coincides with the one of a free particle with friction. It is argued that q-deformed systems can be treated as ordinary mechanical systems with the second-class constraints. In particular, second-class constrained systems corresponding to the q-oscillator and q-particle are given. A possibility of formulating q-deformed systems via gauge theories (first-class constrained systems) is briefly discussed. (orig.)
International Conference on Dynamical Systems : Theory and Applications
2016-01-01
The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Lódz, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.
International Conference on Dynamical Systems : Theory and Applications
2016-01-01
The book is the second volume of a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Lódz, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.
Using system dynamics simulation for assessment of hydropower system safety
King, L. M.; Simonovic, S. P.; Hartford, D. N. D.
2017-08-01
Hydropower infrastructure systems are complex, high consequence structures which must be operated safely to avoid catastrophic impacts to human life, the environment, and the economy. Dam safety practitioners must have an in-depth understanding of how these systems function under various operating conditions in order to ensure the appropriate measures are taken to reduce system vulnerability. Simulation of system operating conditions allows modelers to investigate system performance from the beginning of an undesirable event to full system recovery. System dynamics simulation facilitates the modeling of dynamic interactions among complex arrangements of system components, providing outputs of system performance that can be used to quantify safety. This paper presents the framework for a modeling approach that can be used to simulate a range of potential operating conditions for a hydropower infrastructure system. Details of the generic hydropower infrastructure system simulation model are provided. A case study is used to evaluate system outcomes in response to a particular earthquake scenario, with two system safety performance measures shown. Results indicate that the simulation model is able to estimate potential measures of system safety which relate to flow conveyance and flow retention. A comparison of operational and upgrade strategies is shown to demonstrate the utility of the model for comparing various operational response strategies, capital upgrade alternatives, and maintenance regimes. Results show that seismic upgrades to the spillway gates provide the largest improvement in system performance for the system and scenario of interest.
Emulation tool of dynamic systems via internet
Directory of Open Access Journals (Sweden)
Daniel Ruiz Olaya
2015-11-01
Full Text Available The experimentation laboratories for the studies of control system courses can become expensive, either in its acquisition, operation or maintenance. An alternative resource have been the remote laboratories. However, not always is possible to get complex systems. A solution to this matter are the remote emulation laboratories. In this paper describes the development of a Web application for the emulation of dynamic systems using a free-distribution software tool of rapid control prototyping based on Linux/RTAI. This application is focused especially for the experimentation with dynamic systems that are not available easily in a laboratory where the model have been configured by the user. The design of the front-end and the back-end are presented. The latency times of the real-time operating system and the ability of the system to reproduce similar signals to a real system from an emulated model were verified. An example, to test the functionality of the application the model of an evaporator was used. One of the advantages of the application is the work methodology which is based on the development of blocks in Scicos. This allows the user to reuse those parameters and the code that was implemented to build a block on the Scicos toolbox with the Linux/RTAI/ScicosLab environment. Moreover, only a web-browser and the Java Virtual Machine are required.
DYNAMIC MAGNIFICATION OF BIOMECHANICAL SYSTEM MOTION
Directory of Open Access Journals (Sweden)
A. E. Pokatilov
2017-01-01
Full Text Available Methods for estimation of dynamic magnification pertaining to motion in biomechanics have been developed and approbаted in the paper. It has been ascertained that widely-used characteristics for evaluation of motion influence on mechanisms and machinery such as a dynamic coefficient and acceleration capacity factor become irrelevant while investigating human locomotion under elastic support conditions. The reason is an impossibility to compare human motion in case when there is a contact with elastic and rigid supports because while changing rigidity of the support exercise performing technique is also changing. In this case the technique still depends on a current state of a specific sportsman. Such situation is observed in sports gymnastics. Structure of kinematic and dynamic models for human motion has been investigated in the paper. It has been established that properties of an elastic support are reflected in models within two aspects: in an explicit form, when models have parameters of dynamic deformation for a gymnastic apparatus, and in an implicit form, when we have numerically changed parameters of human motion. The first part can be evaluated quantitatively while making comparison with calculations made in accordance with complete models. For this reason notions of selected and complete models have been introduced in the paper. It has been proposed to specify models for support and models of biomechanical system that represent models pertaining only to human locomotor system. It has been revealed that the selected models of support in kinematics and dynamics have structural difference. Kinematics specifies only parameters of elastic support deformation and dynamics specifies support parameters in an explicit form and additionally in models of human motion in an explicit form as well. Quantitative estimation of a dynamic motion magnification in kinematics and dynamics models has been given while using computing experiment for grand
Dynamically variable spot size laser system
Gradl, Paul R. (Inventor); Hurst, John F. (Inventor); Middleton, James R. (Inventor)
2012-01-01
A Dynamically Variable Spot Size (DVSS) laser system for bonding metal components includes an elongated housing containing a light entry aperture coupled to a laser beam transmission cable and a light exit aperture. A plurality of lenses contained within the housing focus a laser beam from the light entry aperture through the light exit aperture. The lenses may be dynamically adjusted to vary the spot size of the laser. A plurality of interoperable safety devices, including a manually depressible interlock switch, an internal proximity sensor, a remotely operated potentiometer, a remotely activated toggle and a power supply interlock, prevent activation of the laser and DVSS laser system if each safety device does not provide a closed circuit. The remotely operated potentiometer also provides continuous variability in laser energy output.
A Type System for Dynamic Web Documents
DEFF Research Database (Denmark)
Schwartzbach, Michael Ignatieff; Sandholm, Anders
2000-01-01
Many interactive Web services use the CGI interface for communication with clients. They will dynamically create HTML documents that are presented to the client who then resumes the interaction by submitting data through incorporated form fields. This protocol is difficult to statically type-chec...... system is based on a flow analysis of which we prove soundness. We present an efficient runtime implementation that respects the semantics of only well-typed programs. This work is fully implemented as part of the system for defining interactive Web services.......Many interactive Web services use the CGI interface for communication with clients. They will dynamically create HTML documents that are presented to the client who then resumes the interaction by submitting data through incorporated form fields. This protocol is difficult to statically type...
Dynamical systems with applications using MATLAB
Lynch, Stephen
2014-01-01
This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB®, Simulink®, the Image Processing Toolbox™, and the Symbolic Math Toolbox™, including MuPAD. Features new to the second edition include, sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization; chapters on image processing and binary oscillator computing; hundreds of new illustrations, examples, and exercises with solutions; and over eighty up-to-date MATLAB® program files and Simulink model files available online. These files were voted MATLAB® Central Pick of the Week in July 2013. The hands-on approach of Dynamical Systems with Applications using MATLAB®, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equ...
Quantum speed limits in open system dynamics.
del Campo, A; Egusquiza, I L; Plenio, M B; Huelga, S F
2013-02-01
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics, and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive, and trace preserving evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the role of the Hamiltonian being played by the adjoint of the generator of the dynamical semigroup. The utility of the new bound is exemplified in different scenarios, ranging from the estimation of the passage time to the determination of precision limits for quantum metrology in the presence of dephasing noise.
Introduction to differential equations with dynamical systems
Campbell, Stephen L
2011-01-01
Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.
The dynamic state monitoring of bearings system
Directory of Open Access Journals (Sweden)
Marek Krynke
2015-03-01
Full Text Available The article discusses the methods of dynamic state monitoring of bearings system. A vibration signal contains important technical information about the machine condition and is currently the most frequently used in diagnostic bearings systems. One of the main ad-vantages of machine condition monitoring is identifying the cause of failure of the bearings and taking preventative measures, otherwise the operation of such a machine will lead to frequent replacement of the bearings. Monitoring changes in the course of the operation of machin-ery repair strategies allows keeping the conditioned state of dynamic failure conditioned preventive repairs and repairs after-failure time. In addition, the paper also presents the fundamental causes of bearing failure and identifies mechanisms related to the creation of any type of damage.
Matrix correlations for high-dimensional data: The modified RV-coefficient
Smilde, A.K.; Kiers, H.A.L.; Bijlsma, S.; Rubingh, C.M.; Erk, M.J. van
2009-01-01
Motivation: Modern functional genomics generates high-dimensional datasets. It is often convenient to have a single simple number characterizing the relationship between pairs of such high-dimensional datasets in a comprehensive way. Matrix correlations are such numbers and are appealing since they
Systemic Liquidity Crisis with Dynamic Haircuts
Sever, Can
2014-01-01
In this paper, using network tools, I analyse systemic impacts of liquidity shocks in interbank market in case of endogenous haircuts. Gai, Haldane and Kapadia (2011) introduce a benchmark for liquidity crisis following haircut shocks, and Gorton and Metrick (2010) reveal the evidence from 2007-09 crisis for increasing haircuts with banking panic. In the benchmark model, I endogenize and update haircuts dynamically during the period of stress. The results significantly differ from...
High Performance Interactive System Dynamics Visualization
Energy Technology Data Exchange (ETDEWEB)
Bush, Brian W [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Brunhart-Lupo, Nicholas J [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Gruchalla, Kenny M [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Duckworth, Jonathan C [National Renewable Energy Laboratory (NREL), Golden, CO (United States)
2017-09-14
This brochure describes a system dynamics simulation (SD) framework that supports an end-to-end analysis workflow that is optimized for deployment on ESIF facilities(Peregrine and the Insight Center). It includes (I) parallel and distributed simulation of SD models, (ii) real-time 3D visualization of running simulations, and (iii) comprehensive database-oriented persistence of simulation metadata, inputs, and outputs.
High Performance Interactive System Dynamics Visualization
Energy Technology Data Exchange (ETDEWEB)
Bush, Brian W [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Brunhart-Lupo, Nicholas J [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Gruchalla, Kenny M [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Duckworth, Jonathan C [National Renewable Energy Laboratory (NREL), Golden, CO (United States)
2017-09-14
This presentation describes a system dynamics simulation (SD) framework that supports an end-to-end analysis workflow that is optimized for deployment on ESIF facilities(Peregrine and the Insight Center). It includes (I) parallel and distributed simulation of SD models, (ii) real-time 3D visualization of running simulations, and (iii) comprehensive database-oriented persistence of simulation metadata, inputs, and outputs.
Cosmic infinity: A dynamical system approach
Bouhmadi-López, Mariam; Marto, João; Morais, João; Silva, César M.
2016-01-01
Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse the asymptotic behaviour of the universe. On this paper, we show how this can be carried out for 3-forms model. In fact, we show that there are fixed points at infinity mainly by introducing appropriate compactifications and defining a new time variable tha...
Introduction to turbulent dynamical systems in complex systems
Majda, Andrew J
2016-01-01
This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which are of central importance to the field. The contents cover general framework, concrete examples, and instructive qualitative models. Accessible open problems are mentioned throughout. Topics covered include: · Geophysical flows with rotation, topography, deterministic and random forcing · New statistical energy principles for general turbulent dynamical systems, with applications · Linear statistical response theory combined with information theory to cope with model errors · Reduced low order models · Recent mathematical strategies for online data assimilation of turbulent dynamical systems as well as rigorous results for finite ensemble Kalman filters The volume wi...
Statistical dynamics of ultradiffusion in hierarchical systems
International Nuclear Information System (INIS)
Gardner, S.
1987-01-01
In many types of disordered systems which exhibit frustration and competition, an ultrametric topology is found to exist in the space of allowable states. This ultrametric topology of states is associated with a hierarchical relaxation process called ultradiffusion. Ultradiffusion occurs in hierarchical non-linear (HNL) dynamical systems when constraints cause large scale, slow modes of motion to be subordinated to small scale, fast modes. Examples of ultradiffusion are found throughout condensed matter physics and critical phenomena (e.g. the states of spin glasses), in biophysics (e.g. the states of Hopfield networks) and in many other fields including layered computing based upon nonlinear dynamics. The statistical dynamics of ultradiffusion can be treated as a random walk on an ultrametric space. For reversible bifurcating ultrametric spaces the evolution equation governing the probability of a particle being found at site i at time t has a highly degenerate transition matrix. This transition matrix has a fractal geometry similar to the replica form proposed for spin glasses. The authors invert this fractal matrix using a recursive quad-tree (QT) method. Possible applications of hierarchical systems to communications and symbolic computing are discussed briefly
Dynamic optical coupled system employing Dammann gratings
Di, Caihui; Zhou, Changhe; Ru, Huayi
2004-10-01
With the increasing of the number of users in optical fiber communications, fiber-to-home project has a larger market value. Then the need of dynamic optical couplers, especially of N broad-band couplers, becomes greater. Though some advanced fiber fusion techniques have been developed, they still have many shortcomings. In this paper we propose a dynamic optical coupled system employing even-numbered Dammann gratings, which have the characteristic that the phase distribution in the first half-period accurately equals to that in the second-period with π phase inversion. In our experiment, we divide a conventional even-numbered Dammann grating into two identical gratings. The system can achieve the beam splitter and combiner as the switch between them according to the relative shift between two complementary gratings. When there is no shift between the gratings, the demonstrated 1×8 dynamic optical coupler achieves good uniformity of 0.06 and insertion loss of around 10.8 dB for each channel as a splitter. When the two gratings have an accurate shift of a half-period between them, our system has a low insertion loss of 0.46 dB as a combiner at a wavelength of 1550 nm.
Dissipative dynamics of superconducting hybrid qubit systems
International Nuclear Information System (INIS)
Montes, Enrique; Calero, Jesus M; Reina, John H
2009-01-01
We perform a theoretical study of composed superconducting qubit systems for the case of a coupled qubit configuration based on a hybrid qubit circuit made of both charge and phase qubits, which are coupled via a σ x x σ z interaction. We compute the system's eigen-energies in terms of the qubit transition frequencies and the strength of the inter-qubit coupling, and describe the sensitivity of the energy crossing/anti-crossing features to such coupling. We compute the hybrid system's dissipative dynamics for the cases of i) collective and ii) independent decoherence, whereby the system interacts with one common and two different baths of harmonic oscillators, respectively. The calculations have been performed within the Bloch-Redfield formalism and we report the solutions for the populations and the coherences of the system's reduced density matrix. The dephasing and relaxation rates are explicitly calculated as a function of the heat bath temperature.
Thermospheric dynamics - A system theory approach
Codrescu, M.; Forbes, J. M.; Roble, R. G.
1990-01-01
A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.
Complex and adaptive dynamical systems a primer
Gros, Claudius
2013-01-01
Complex system theory is rapidly developing and gaining importance, providing tools and concepts central to our modern understanding of emergent phenomena. This primer offers an introduction to this area together with detailed coverage of the mathematics involved. All calculations are presented step by step and are straightforward to follow. This new third edition comes with new material, figures and exercises. Network theory, dynamical systems and information theory, the core of modern complex system sciences, are developed in the first three chapters, covering basic concepts and phenomena like small-world networks, bifurcation theory and information entropy. Further chapters use a modular approach to address the most important concepts in complex system sciences, with the emergence and self-organization playing a central role. Prominent examples are self-organized criticality in adaptive systems, life at the edge of chaos, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase...
High dimensional biological data retrieval optimization with NoSQL technology
2014-01-01
Background High-throughput transcriptomic data generated by microarray experiments is the most abundant and frequently stored kind of data currently used in translational medicine studies. Although microarray data is supported in data warehouses such as tranSMART, when querying relational databases for hundreds of different patient gene expression records queries are slow due to poor performance. Non-relational data models, such as the key-value model implemented in NoSQL databases, hold promise to be more performant solutions. Our motivation is to improve the performance of the tranSMART data warehouse with a view to supporting Next Generation Sequencing data. Results In this paper we introduce a new data model better suited for high-dimensional data storage and querying, optimized for database scalability and performance. We have designed a key-value pair data model to support faster queries over large-scale microarray data and implemented the model using HBase, an implementation of Google's BigTable storage system. An experimental performance comparison was carried out against the traditional relational data model implemented in both MySQL Cluster and MongoDB, using a large publicly available transcriptomic data set taken from NCBI GEO concerning Multiple Myeloma. Our new key-value data model implemented on HBase exhibits an average 5.24-fold increase in high-dimensional biological data query performance compared to the relational model implemented on MySQL Cluster, and an average 6.47-fold increase on query performance on MongoDB. Conclusions The performance evaluation found that the new key-value data model, in particular its implementation in HBase, outperforms the relational model currently implemented in tranSMART. We propose that NoSQL technology holds great promise for large-scale data management, in particular for high-dimensional biological data such as that demonstrated in the performance evaluation described in this paper. We aim to use this new data
Taşkin Kaya, Gülşen
2013-10-01
-output relationships in high-dimensional systems for many problems in science and engineering. The HDMR method is developed to improve the efficiency of the deducing high dimensional behaviors. The method is formed by a particular organization of low dimensional component functions, in which each function is the contribution of one or more input variables to the output variables.
High dimensional biological data retrieval optimization with NoSQL technology.
Wang, Shicai; Pandis, Ioannis; Wu, Chao; He, Sijin; Johnson, David; Emam, Ibrahim; Guitton, Florian; Guo, Yike
2014-01-01
High-throughput transcriptomic data generated by microarray experiments is the most abundant and frequently stored kind of data currently used in translational medicine studies. Although microarray data is supported in data warehouses such as tranSMART, when querying relational databases for hundreds of different patient gene expression records queries are slow due to poor performance. Non-relational data models, such as the key-value model implemented in NoSQL databases, hold promise to be more performant solutions. Our motivation is to improve the performance of the tranSMART data warehouse with a view to supporting Next Generation Sequencing data. In this paper we introduce a new data model better suited for high-dimensional data storage and querying, optimized for database scalability and performance. We have designed a key-value pair data model to support faster queries over large-scale microarray data and implemented the model using HBase, an implementation of Google's BigTable storage system. An experimental performance comparison was carried out against the traditional relational data model implemented in both MySQL Cluster and MongoDB, using a large publicly available transcriptomic data set taken from NCBI GEO concerning Multiple Myeloma. Our new key-value data model implemented on HBase exhibits an average 5.24-fold increase in high-dimensional biological data query performance compared to the relational model implemented on MySQL Cluster, and an average 6.47-fold increase on query performance on MongoDB. The performance evaluation found that the new key-value data model, in particular its implementation in HBase, outperforms the relational model currently implemented in tranSMART. We propose that NoSQL technology holds great promise for large-scale data management, in particular for high-dimensional biological data such as that demonstrated in the performance evaluation described in this paper. We aim to use this new data model as a basis for migrating
Dynamical real numbers and living systems
International Nuclear Information System (INIS)
Datta, Dhurjati Prasad
2004-01-01
Recently uncovered second derivative discontinuous solutions of the simplest linear ordinary differential equation define not only an nonstandard extension of the framework of the ordinary calculus, but also provide a dynamical representation of the ordinary real number system. Every real number can be visualized as a living cell-like structure, endowed with a definite evolutionary arrow. We discuss the relevance of this extended calculus in the study of living systems. We also present an intelligent version of the Newton's first law of motion
Dynamical properties of unconventional magnetic systems
International Nuclear Information System (INIS)
Helgesen, G.
1997-05-01
The Advanced Study Institute addressed the current experimental and theoretical knowledge of the dynamical properties of unconventional magnetic systems including low-dimensional and mesoscopic magnetism, unconventional ground state, quantum magnets and soft matter. The main approach in this Advanced Study Institute was to obtain basic understanding of co-operative phenomena, fluctuations and excitations in the wide range unconventional magnetic systems now being fabricated or envisioned. The report contains abstracts for lectures, invited seminars and posters, together with a list of the 95 participants from 24 countries with e-mail addresses
Vertebrate gravity sensors as dynamic systems
Ross, M. D.
1985-01-01
This paper considers verterbrate gravity receptors as dynamic sensors. That is, it is hypothesized that gravity is a constant force to which an acceleration-sensing system would readily adapt. Premises are considered in light of the presence of kinocilia on hair cells of vertebrate gravity sensors; differences in loading of the sensors among species; and of possible reduction in loading by inclusion of much organic material in otoconia. Moreover, organic-inorganic interfaces may confer a piezoelectric property upon otoconia, which increase the sensitivity of the sensory system to small accelerations. Comparisons with man-made accelerometers are briefly taken up.
Reconstruction of dynamical systems from interspike intervals
International Nuclear Information System (INIS)
Sauer, T.
1994-01-01
Attractor reconstruction from interspike interval (ISI) data is described, in rough analogy with Taken's theorem for attractor reconstruction from time series. Assuming a generic integrate-and-fire model coupling the dynamical system to the spike train, there is a one-to-one correspondence between the system states and interspike interval vectors of sufficiently large dimension. The correspondence has an important implication: interspike intervals can be forecast from past history. We show that deterministically driven ISI series can be distinguished from stochastically driven ISI series on the basis of prediction error
Testing relativity with solar system dynamics
Hellings, R. W.
1984-01-01
A major breakthrough is described in the accuracy of Solar System dynamical tests of relativistic gravity. The breakthrough was achieved by factoring in ranging data from Viking Landers 1 and 2 from the surface of Mars. Other key data sources included optical transit circle observations, lunar laser ranging, planetary radar, and spacecraft (Mariner 9 to Mars and Mariner 10 to Mercury). The Solar System model which is used to fit the data and the process by which such fits are performed are explained and results are discussed. The results are fully consistent with the predictions of General Relativity.
Shaffer, Patrick; Valsson, Omar; Parrinello, Michele
2016-02-02
The capabilities of molecular simulations have been greatly extended by a number of widely used enhanced sampling methods that facilitate escaping from metastable states and crossing large barriers. Despite these developments there are still many problems which remain out of reach for these methods which has led to a vigorous effort in this area. One of the most important problems that remains unsolved is sampling high-dimensional free-energy landscapes and systems that are not easily described by a small number of collective variables. In this work we demonstrate a new way to compute free-energy landscapes of high dimensionality based on the previously introduced variationally enhanced sampling, and we apply it to the miniprotein chignolin.
Shaffer, Patrick; Valsson, Omar; Parrinello, Michele
2016-01-01
The capabilities of molecular simulations have been greatly extended by a number of widely used enhanced sampling methods that facilitate escaping from metastable states and crossing large barriers. Despite these developments there are still many problems which remain out of reach for these methods which has led to a vigorous effort in this area. One of the most important problems that remains unsolved is sampling high-dimensional free-energy landscapes and systems that are not easily described by a small number of collective variables. In this work we demonstrate a new way to compute free-energy landscapes of high dimensionality based on the previously introduced variationally enhanced sampling, and we apply it to the miniprotein chignolin. PMID:26787868
Robustness of dynamic systems with parameter uncertainties
Balemi, S; Truöl, W
1992-01-01
Robust Control is one of the fastest growing and promising areas of research today. In many practical systems there exist uncertainties which have to be considered in the analysis and design of control systems. In the last decade methods were developed for dealing with dynamic systems with unstructured uncertainties such as HOO_ and £I-optimal control. For systems with parameter uncertainties, the seminal paper of V. L. Kharitonov has triggered a large amount of very promising research. An international workshop dealing with all aspects of robust control was successfully organized by S. P. Bhattacharyya and L. H. Keel in San Antonio, Texas, USA in March 1991. We organized the second international workshop in this area in Ascona, Switzer land in April 1992. However, this second workshop was restricted to robust control of dynamic systems with parameter uncertainties with the objective to concentrate on some aspects of robust control. This book contains a collection of papers presented at the International W...
Literature Review on Dynamic Cellular Manufacturing System
Nouri Houshyar, A.; Leman, Z.; Pakzad Moghadam, H.; Ariffin, M. K. A. M.; Ismail, N.; Iranmanesh, H.
2014-06-01
In previous decades, manufacturers faced a lot of challenges because of globalization and high competition in markets. These problems arise from shortening product life cycle, rapid variation in demand of products, and also rapid changes in manufcaturing technologies. Nowadays most manufacturing companies expend considerable attention for improving flexibility and responsiveness in order to overcome these kinds of problems and also meet customer's needs. By considering the trend toward the shorter product life cycle, the manufacturing environment is towards manufacturing a wide variety of parts in small batches [1]. One of the major techniques which are applied for improving manufacturing competitiveness is Cellular Manufacturing System (CMS). CMS is type of manufacturing system which tries to combine flexibility of job shop and also productivity of flow shop. In addition, Dynamic cellular manufacturing system which considers different time periods for the manufacturing system becomes an important topic and attracts a lot of attention to itself. Therefore, this paper made attempt to have a brief review on this issue and focused on all published paper on this subject. Although, this topic gains a lot of attention to itself during these years, none of previous researchers focused on reviewing the literature of that which can be helpful and useful for other researchers who intend to do the research on this topic. Therefore, this paper is the first study which has focused and reviewed the literature of dynamic cellular manufacturing system.
International Nuclear Information System (INIS)
Shin, Seung Ki; Seong, Poong Hyun
2008-01-01
Conventional static reliability analysis methods are inadequate for modeling dynamic interactions between components of a system. Various techniques such as dynamic fault tree, dynamic Bayesian networks, and dynamic reliability block diagrams have been proposed for modeling dynamic systems based on improvement of the conventional modeling methods. In this paper, we review these methods briefly and introduce dynamic nodes to the existing Reliability Graph with General Gates (RGGG) as an intuitive modeling method to model dynamic systems. For a quantitative analysis, we use a discrete-time method to convert an RGGG to an equivalent Bayesian network and develop a software tool for generation of probability tables
Complex and adaptive dynamical systems a primer
Gros, Claudius
2015-01-01
This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are presented step by step and are easy to follow. This new fourth edition has been fully reorganized and includes new chapters, figures and exercises. The core aspects of modern complex system sciences are presented in the first chapters, covering network theory, dynamical systems, bifurcation and catastrophe theory, chaos and adaptive processes, together with the principle of self-organization in reaction-diffusion systems and social animals. Modern information theoretical principles are treated in further chapters, together with the concept of self-organized criticality, gene regulation networks, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase transitions and the cognitive system approach to the brain. Technical course prerequisites are the standard ...
Vlasov dynamics of periodically driven systems
Banerjee, Soumyadip; Shah, Kushal
2018-04-01
Analytical solutions of the Vlasov equation for periodically driven systems are of importance in several areas of plasma physics and dynamical systems and are usually approximated using ponderomotive theory. In this paper, we derive the plasma distribution function predicted by ponderomotive theory using Hamiltonian averaging theory and compare it with solutions obtained by the method of characteristics. Our results show that though ponderomotive theory is relatively much easier to use, its predictions are very restrictive and are likely to be very different from the actual distribution function of the system. We also analyse all possible initial conditions which lead to periodic solutions of the Vlasov equation for periodically driven systems and conjecture that the irreducible polynomial corresponding to the initial condition must only have squares of the spatial and momentum coordinate. The resulting distribution function for other initial conditions is aperiodic and can lead to complex relaxation processes within the plasma.
Dynamical Systems Theory: Application to Pedagogy
Abraham, Jane L.
Theories of learning affect how cognition is viewed, and this subsequently leads to the style of pedagogical practice that is used in education. Traditionally, educators have relied on a variety of theories on which to base pedagogy. Behavioral learning theories influenced the teaching/learning process for over 50 years. In the 1960s, the information processing approach brought the mind back into the learning process. The current emphasis on constructivism integrates the views of Piaget, Vygotsky, and cognitive psychology. Additionally, recent scientific advances have allowed researchers to shift attention to biological processes in cognition. The problem is that these theories do not provide an integrated approach to understanding principles responsible for differences among students in cognitive development and learning ability. Dynamical systems theory offers a unifying theoretical framework to explain the wider context in which learning takes place and the processes involved in individual learning. This paper describes how principles of Dynamic Systems Theory can be applied to cognitive processes of students, the classroom community, motivation to learn, and the teaching/learning dynamic giving educational psychologists a framework for research and pedagogy.
Persistent topological features of dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Maletić, Slobodan, E-mail: slobodan@hitsz.edu.cn [Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen (China); Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade (Serbia); Zhao, Yi, E-mail: zhao.yi@hitsz.edu.cn [Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen (China); Rajković, Milan, E-mail: milanr@vinca.rs [Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade (Serbia)
2016-05-15
Inspired by an early work of Muldoon et al., Physica D 65, 1–16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network.
Geometric methods for discrete dynamical systems
Easton, Robert W
1998-01-01
This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from round-off in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of external controls. The author provides an introduction accessible to beginning graduate students and emphasizing geometric aspects of the theory. Conley''s ideas about rough orbits and chain-recurrence play a central role in the treatment. The book will be a useful reference for mathematicians, scientists, and engineers studying this field, and an ideal text for graduate courses in dynamical systems.
Resetting dynamic behaviour of pipework systems
International Nuclear Information System (INIS)
Gaudin, M.
1997-01-01
Resetting models is applied to electricity generating plant pipework systems. A frequency approach to the problem is made in an original way thanks to the use of precise dynamic rigidity matrices. The method assumes two kinds of unknown: the usually processed mechanical characteristics (Young's Modulus, density etc.) and new resetting parameters acting on the dynamic behaviour of unknown connections. As the latter have a very wide range of possible variation, they benefit from a change of variable which allows the assumptions formulated to be complied with. The minimized cost function is based on a error in load. The frequencies required for building it are automatically selected thanks to different tests on measurements. Minimization uses a sensitivity technique linked with a method of least standard squares. The method has been programmed in Fortran 90 within the CIRCUS code and tried out on various examples which were simulated and sound effects cases as well as an actual case. (author)
Dynamical systems with applications using Mathematica
Lynch, Stephen
2017-01-01
This textbook, now in its second edition, provides a broad introduction to the theory and practice of both continuous and discrete dynamical systems with the aid of the Mathematica software suite. Taking a hands-on approach, the reader is guided from basic concepts to modern research topics. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. The book begins with an efficient tutorial introduction to Mathematica, enabling new users to become familiar with the program, while providing a good reference source for experts. Working Mathematica notebooks will be available at: http://library.wolfram.com/infocenter/Books/9563/ The author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum, though references are included for the inquisitive reader. The book is intended for senior undergraduate and graduate students as well as w...
Modeling the Dynamic Digestive System Microbiome
Directory of Open Access Journals (Sweden)
Anne M. Estes
2015-08-01
Full Text Available “Modeling the Dynamic Digestive System Microbiome” is a hands-on activity designed to demonstrate the dynamics of microbiome ecology using dried pasta and beans to model disturbance events in the human digestive system microbiome. This exercise demonstrates how microbiome diversity is influenced by: 1 niche availability and habitat space and 2 a major disturbance event, such as antibiotic use. Students use a pictorial key to examine prepared models of digestive system microbiomes to determine what the person with the microbiome “ate.” Students then model the effect of taking antibiotics by removing certain “antibiotic sensitive” pasta. Finally, they add in “environmental microbes” or “native microbes” to recolonize the digestive system, determine how resilient their model microbome community is to disturbance, and discuss the implications. Throughout the exercise, students discuss differences in the habitat space available and microbiome community diversity. This exercise can be modified to discuss changes in the microbiome due to diet shifts and the emergence of antibiotic resistance in more depth.
Crossed product algebras associated with topological dynamical systems
Svensson, Pär Christian
2009-01-01
We study connections between topological dynamical systems and associated algebras of crossed product type. We derive equivalences between structural properties of a crossed product and dynamical properties of the associated system and furthermore derive qualitative results concerning the crossed
Dynamic loads on the primary system
International Nuclear Information System (INIS)
Rohde, J.
1980-01-01
As a result of pipe breaks f.ex. in the primary system of a PWR-plant dynamic forces act on the components of the system as well as on their support-structures and internals. The design basis must guarantee that LOCA or system-transient generated loads cannot produce deformations or fractures that endanger the coolability of the reactor, the emergency feedwater supply to the core-region and a safe shut-down of the reactor. In this lecture the first part of a LOCA will be discussed, where the highest dynamic loads on the primary system are expected. In this connection comments are given on the main assumptions and boundary conditions, the related regulations and guide-lines, as well as the possible consequences of an accident. Next, a review is presented of the analytical methods being used for the determination of thermohydraulic generated loads. The stress-calculations on the basis of these load-functions are discussed in the following lectures. The application of the analytical methods, i.e. the different computer codes, and the verification on the basis of the experimental results are described together with a discussion of the theoretical results. In addition a survey will be given of the research work done in connection with the problems of the dynamic loads under accident conditions. Finally, the problems of the fluid-structure interaction will be explained and comments made on computer code development now under way regarding this problem. A short film will be presented to provide a better understanding of fast transient phenomena. (orig./RW)
Modelling the crop: from system dynamics to systems biology
Yin, X.; Struik, P.C.
2010-01-01
There is strong interplant competition in a crop stand for various limiting resources, resulting in complex compensation and regulation mechanisms along the developmental cascade of the whole crop. Despite decades-long use of principles in system dynamics (e.g. feedback control), current crop models
Description of the grout system dynamic simulation
International Nuclear Information System (INIS)
Zimmerman, B.D.
1993-07-01
The grout system dynamic computer simulation was created to allow investigation of the ability of the grouting system to meet established milestones, for various assumed system configurations and parameters. The simulation simulates the movement of tank waste through the system versus time, from initial storage tanks, through feed tanks and the grout plant, then finally to a grout vault. The simulation properly accounts for the following (1) time required to perform various actions or processes, (2) delays involved in gaining regulatory approval, (3) random system component failures, (4) limitations on equipment capacities, (5) available parallel components, and (6) different possible strategies for vault filling. The user is allowed to set a variety of system parameters for each simulation run. Currently, the output of a run primarily consists of a plot of projected grouting campaigns completed versus time, for comparison with milestones. Other outputs involving any model component can also be quickly created or deleted as desired. In particular, sensitivity runs where the effect of varying a model parameter (flow rates, delay times, number of feed tanks available, etc.) on the ability of the system to meet milestones can be made easily. The grout system simulation was implemented using the ITHINK* simulation language for Macintosh** computers
Data based identification and prediction of nonlinear and complex dynamical systems
Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso
2016-07-01
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical
Data based identification and prediction of nonlinear and complex dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Wang, Wen-Xu [School of Systems Science, Beijing Normal University, Beijing, 100875 (China); Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Lai, Ying-Cheng, E-mail: Ying-Cheng.Lai@asu.edu [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States); Department of Physics, Arizona State University, Tempe, AZ 85287 (United States); Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom); Grebogi, Celso [Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom)
2016-07-12
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear
Data based identification and prediction of nonlinear and complex dynamical systems
International Nuclear Information System (INIS)
Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso
2016-01-01
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear
Large-scale Machine Learning in High-dimensional Datasets
DEFF Research Database (Denmark)
Hansen, Toke Jansen
Over the last few decades computers have gotten to play an essential role in our daily life, and data is now being collected in various domains at a faster pace than ever before. This dissertation presents research advances in four machine learning fields that all relate to the challenges imposed...... are better at modeling local heterogeneities. In the field of machine learning for neuroimaging, we introduce learning protocols for real-time functional Magnetic Resonance Imaging (fMRI) that allow for dynamic intervention in the human decision process. Specifically, the model exploits the structure of f...
Intrinsic information carriers in combinatorial dynamical systems
Harmer, Russ; Danos, Vincent; Feret, Jérôme; Krivine, Jean; Fontana, Walter
2010-09-01
Many proteins are composed of structural and chemical features—"sites" for short—characterized by definite interaction capabilities, such as noncovalent binding or covalent modification of other proteins. This modularity allows for varying degrees of independence, as the behavior of a site might be controlled by the state of some but not all sites of the ambient protein. Independence quickly generates a startling combinatorial complexity that shapes most biological networks, such as mammalian signaling systems, and effectively prevents their study in terms of kinetic equations—unless the complexity is radically trimmed. Yet, if combinatorial complexity is key to the system's behavior, eliminating it will prevent, not facilitate, understanding. A more adequate representation of a combinatorial system is provided by a graph-based framework of rewrite rules where each rule specifies only the information that an interaction mechanism depends on. Unlike reactions, which deal with molecular species, rules deal with patterns, i.e., multisets of molecular species. Although the stochastic dynamics induced by a collection of rules on a mixture of molecules can be simulated, it appears useful to capture the system's average or deterministic behavior by means of differential equations. However, expansion of the rules into kinetic equations at the level of molecular species is not only impractical, but conceptually indefensible. If rules describe bona fide patterns of interaction, molecular species are unlikely to constitute appropriate units of dynamics. Rather, we must seek aggregate variables reflective of the causal structure laid down by the rules. We call these variables "fragments" and the process of identifying them "fragmentation." Ideally, fragments are aspects of the system's microscopic population that the set of rules can actually distinguish on average; in practice, it may only be feasible to identify an approximation to this. Most importantly, fragments are
Intrinsic information carriers in combinatorial dynamical systems.
Harmer, Russ; Danos, Vincent; Feret, Jérôme; Krivine, Jean; Fontana, Walter
2010-09-01
Many proteins are composed of structural and chemical features--"sites" for short--characterized by definite interaction capabilities, such as noncovalent binding or covalent modification of other proteins. This modularity allows for varying degrees of independence, as the behavior of a site might be controlled by the state of some but not all sites of the ambient protein. Independence quickly generates a startling combinatorial complexity that shapes most biological networks, such as mammalian signaling systems, and effectively prevents their study in terms of kinetic equations-unless the complexity is radically trimmed. Yet, if combinatorial complexity is key to the system's behavior, eliminating it will prevent, not facilitate, understanding. A more adequate representation of a combinatorial system is provided by a graph-based framework of rewrite rules where each rule specifies only the information that an interaction mechanism depends on. Unlike reactions, which deal with molecular species, rules deal with patterns, i.e., multisets of molecular species. Although the stochastic dynamics induced by a collection of rules on a mixture of molecules can be simulated, it appears useful to capture the system's average or deterministic behavior by means of differential equations. However, expansion of the rules into kinetic equations at the level of molecular species is not only impractical, but conceptually indefensible. If rules describe bona fide patterns of interaction, molecular species are unlikely to constitute appropriate units of dynamics. Rather, we must seek aggregate variables reflective of the causal structure laid down by the rules. We call these variables "fragments" and the process of identifying them "fragmentation." Ideally, fragments are aspects of the system's microscopic population that the set of rules can actually distinguish on average; in practice, it may only be feasible to identify an approximation to this. Most importantly, fragments are
Dynamic Systems Analysis for Turbine Based Aero Propulsion Systems
Csank, Jeffrey T.
2016-01-01
The aircraft engine design process seeks to optimize the overall system-level performance, weight, and cost for a given concept. Steady-state simulations and data are used to identify trade-offs that should be balanced to optimize the system in a process known as systems analysis. These systems analysis simulations and data may not adequately capture the true performance trade-offs that exist during transient operation. Dynamic systems analysis provides the capability for assessing the dynamic tradeoffs at an earlier stage of the engine design process. The dynamic systems analysis concept, developed tools, and potential benefit are presented in this paper. To provide this capability, the Tool for Turbine Engine Closed-loop Transient Analysis (TTECTrA) was developed to provide the user with an estimate of the closed-loop performance (response time) and operability (high pressure compressor surge margin) for a given engine design and set of control design requirements. TTECTrA along with engine deterioration information, can be used to develop a more generic relationship between performance and operability that can impact the engine design constraints and potentially lead to a more efficient engine.
Nam, Julia EunJu; Mueller, Klaus
2013-02-01
Gaining a true appreciation of high-dimensional space remains difficult since all of the existing high-dimensional space exploration techniques serialize the space travel in some way. This is not so foreign to us since we, when traveling, also experience the world in a serial fashion. But we typically have access to a map to help with positioning, orientation, navigation, and trip planning. Here, we propose a multivariate data exploration tool that compares high-dimensional space navigation with a sightseeing trip. It decomposes this activity into five major tasks: 1) Identify the sights: use a map to identify the sights of interest and their location; 2) Plan the trip: connect the sights of interest along a specifyable path; 3) Go on the trip: travel along the route; 4) Hop off the bus: experience the location, look around, zoom into detail; and 5) Orient and localize: regain bearings in the map. We describe intuitive and interactive tools for all of these tasks, both global navigation within the map and local exploration of the data distributions. For the latter, we describe a polygonal touchpad interface which enables users to smoothly tilt the projection plane in high-dimensional space to produce multivariate scatterplots that best convey the data relationships under investigation. Motion parallax and illustrative motion trails aid in the perception of these transient patterns. We describe the use of our system within two applications: 1) the exploratory discovery of data configurations that best fit a personal preference in the presence of tradeoffs and 2) interactive cluster analysis via cluster sculpting in N-D.
Chaotic Behavior in a Switched Dynamical System
Directory of Open Access Journals (Sweden)
Fatima El Guezar
2008-01-01
Full Text Available We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator which is a Scilab (scientific laboratory package. The followed approach takes into account the hybrid nature of the circuit.
Structural system identification: Structural dynamics model validation
Energy Technology Data Exchange (ETDEWEB)
Red-Horse, J.R.
1997-04-01
Structural system identification is concerned with the development of systematic procedures and tools for developing predictive analytical models based on a physical structure`s dynamic response characteristics. It is a multidisciplinary process that involves the ability (1) to define high fidelity physics-based analysis models, (2) to acquire accurate test-derived information for physical specimens using diagnostic experiments, (3) to validate the numerical simulation model by reconciling differences that inevitably exist between the analysis model and the experimental data, and (4) to quantify uncertainties in the final system models and subsequent numerical simulations. The goal of this project was to develop structural system identification techniques and software suitable for both research and production applications in code and model validation.
Systems approaches to study root architecture dynamics
Directory of Open Access Journals (Sweden)
Candela eCuesta
2013-12-01
Full Text Available The plant root system is essential for providing anchorage to the soil, supplying minerals and water, and synthesizing metabolites. It is a dynamic organ modulated by external cues such as environmental signals, water and nutrients availability, salinity and others. Lateral roots are initiated from the primary root post-embryonically, after which they progress through discrete developmental stages which can be independently controlled, providing a high level of plasticity during root system formation.Within this review, main contributions are presented, from the classical forward genetic screens to the more recent high-throughput approaches, combined with computer model predictions, dissecting how lateral roots and thereby root system architecture is established and developed.
Synchronization of hypernetworks of coupled dynamical systems
International Nuclear Information System (INIS)
Sorrentino, Francesco
2012-01-01
We consider the synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems is coupled through the connections of two or more distinct networks (each of which corresponds to a distinct type of interaction), and we refer to such a system as a dynamical hypernetwork. Applications include neural networks made up of both electrical gap junctions and chemical synapses, the coordinated motion of shoals of fish communicating through both vision and flow sensing, and hypernetworks of coupled chaotic oscillators. We first analyze the case of a hypernetwork made up of m = 2 networks. We look for the necessary and sufficient conditions for synchronization. We attempt to reduce the linear stability problem to a master stability function (MSF) form, i.e. decoupling the effects of the coupling functions from the structure of the networks. Unfortunately, we are unable to obtain a reduction in an MSF form for the general case. However, we show that such a reduction is possible in three cases of interest: (i) the Laplacian matrices associated with the two networks commute; (ii) one of the two networks is unweighted and fully connected; and (iii) one of the two networks is such that the coupling strength from node i to node j is a function of j but not of i. Furthermore, we define a class of networks such that if either one of the two coupling networks belongs to this class, the reduction can be obtained independently of the other network. As an example of interest, we study synchronization of a neural hypernetwork for which the connections can be either chemical synapses or electrical gap junctions. We propose a generalization of our stability results to the case of hypernetworks formed of m ⩾ 2 networks. (paper)
Delay differential systems for tick population dynamics.
Fan, Guihong; Thieme, Horst R; Zhu, Huaiping
2015-11-01
Ticks play a critical role as vectors in the transmission and spread of Lyme disease, an emerging infectious disease which can cause severe illness in humans or animals. To understand the transmission dynamics of Lyme disease and other tick-borne diseases, it is necessary to investigate the population dynamics of ticks. Here, we formulate a system of delay differential equations which models the stage structure of the tick population. Temperature can alter the length of time delays in each developmental stage, and so the time delays can vary geographically (and seasonally which we do not consider). We define the basic reproduction number [Formula: see text] of stage structured tick populations. The tick population is uniformly persistent if [Formula: see text] and dies out if [Formula: see text]. We present sufficient conditions under which the unique positive equilibrium point is globally asymptotically stable. In general, the positive equilibrium can be unstable and the system show oscillatory behavior. These oscillations are primarily due to negative feedback within the tick system, but can be enhanced by the time delays of the different developmental stages.
Reliability of dynamic systems under limited information.
Energy Technology Data Exchange (ETDEWEB)
Field, Richard V., Jr. (.,; .); Grigoriu, Mircea
2006-09-01
A method is developed for reliability analysis of dynamic systems under limited information. The available information includes one or more samples of the system output; any known information on features of the output can be used if available. The method is based on the theory of non-Gaussian translation processes and is shown to be particularly suitable for problems of practical interest. For illustration, we apply the proposed method to a series of simple example problems and compare with results given by traditional statistical estimators in order to establish the accuracy of the method. It is demonstrated that the method delivers accurate results for the case of linear and nonlinear dynamic systems, and can be applied to analyze experimental data and/or mathematical model outputs. Two complex applications of direct interest to Sandia are also considered. First, we apply the proposed method to assess design reliability of a MEMS inertial switch. Second, we consider re-entry body (RB) component vibration response during normal re-entry, where the objective is to estimate the time-dependent probability of component failure. This last application is directly relevant to re-entry random vibration analysis at Sandia, and may provide insights on test-based and/or model-based qualification of weapon components for random vibration environments.
Indirect learning control for nonlinear dynamical systems
Ryu, Yeong Soon; Longman, Richard W.
1993-01-01
In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.
Dynamic data filtering system and method
Bickford, Randall L; Palnitkar, Rahul M
2014-04-29
A computer-implemented dynamic data filtering system and method for selectively choosing operating data of a monitored asset that modifies or expands a learned scope of an empirical model of normal operation of the monitored asset while simultaneously rejecting operating data of the monitored asset that is indicative of excessive degradation or impending failure of the monitored asset, and utilizing the selectively chosen data for adaptively recalibrating the empirical model to more accurately monitor asset aging changes or operating condition changes of the monitored asset.
The self as a complex dynamic system
Directory of Open Access Journals (Sweden)
Sarah Mercer
2011-04-01
Full Text Available This article explores the potential offered by complexity theories for understanding language learners’ sense of self and attempts to show how the self might usefully be conceived of as a complex dynamic system. Rather than presenting empirical findings, the article discusses existent research on the self and aims at outlining a conceptual perspective that may inform future studies into the self and possibly other individual learner differences. The article concludes by critically considering the merits of a complexity perspective but also reflecting on the challenges it poses for research.
Advances in dynamical systems and control
Zgurovsky, Mikhail
2016-01-01
Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields. .
A dynamical systems approach to motor development.
Kamm, K; Thelen, E; Jensen, J L
1990-12-01
The study of motor development has long influenced the clinical practice of physical therapy. We first review the contributions and deficiencies of two traditional maturational and reflex-based models of motor development. Second, we describe basic principles of kinematic and kinetic analyses of movement and show how we have applied these techniques to understand infant stepping and kicking. Third, we propose a theory of motor development based on a dynamical systems perspective that is consistent with our infant studies. Finally, we explore the implications of the model for physical therapists.
Electron dynamics inside short-coherence systems
International Nuclear Information System (INIS)
Ferrari, Giulio; Bordone, Paolo; Jacoboni, Carlo
2006-01-01
We present theoretical results on electron dynamics inside nanometric systems, where the coherence of the electron ensemble is maintained in a very short region. The contacts are supposed to spoil such a coherence, therefore the interference processes between the carrier wavefunction and the internal potential profile can be affected by the proximity of the contacts. The problem has been analysed by using the Wigner-function formalism. For very short devices, transport properties, such as tunnelling through potential barriers, are significantly influenced by the distance between the contacts
The Matrix exponential, Dynamic Systems and Control
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
The matrix exponential can be found in various connections in analysis and control of dynamic systems. In this short note we are going to list a few examples. The matrix exponential usably pops up in connection to the sampling process, whatever it is in a deterministic or a stochastic setting...... or it is a tool for determining a Gramian matrix. This note is intended to be used in connection to the teaching post the course in Stochastic Adaptive Control (02421) given at Informatics and Mathematical Modelling (IMM), The Technical University of Denmark. This work is a result of a study of the litterature....
Architectural Analysis of Dynamically Reconfigurable Systems
Lindvall, Mikael; Godfrey, Sally; Ackermann, Chris; Ray, Arnab; Yonkwa, Lyly
2010-01-01
oTpics include: the problem (increased flexibility of architectural styles decrease analyzability, behavior emerges and varies depending on the configuration, does the resulting system run according to the intended design, and architectural decisions can impede or facilitate testing); top down approach to architecture analysis, detection of defects and deviations, and architecture and its testability; currently targeted projects GMSEC and CFS; analyzing software architectures; analyzing runtime events; actual architecture recognition; GMPUB in Dynamic SAVE; sample output from new approach; taking message timing delays into account; CFS examples of architecture and testability; some recommendations for improved testablity; and CFS examples of abstract interfaces and testability; CFS example of opening some internal details.
Correlated Levy Noise in Linear Dynamical Systems
International Nuclear Information System (INIS)
Srokowski, T.
2011-01-01
Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed symmetric white noise. Correlation properties of the process are discussed. The Fokker-Planck equation driven by that noise is solved. Distributions have the Levy shape and their width, for a given time, is smaller than for processes in the white noise limit. Applicability of the adiabatic approximation in the case of the linear force is discussed. (author)
Self-dissimilarity as a High Dimensional Complexity Measure
Wolpert, David H.; Macready, William
2005-01-01
For many systems characterized as "complex" the patterns exhibited on different scales differ markedly from one another. For example the biomass distribution in a human body "looks very different" depending on the scale at which one examines it. Conversely, the patterns at different scales in "simple" systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self-dissimilarity between the patterns of a system at various scales constitute a complexity "signature" of that system. Here we present a novel quantification of self-dissimilarity. This signature can, if desired, incorporate a novel information-theoretic measure of the distance between probability distributions that we derive here. Whatever distance measure is chosen, our quantification of self-dissimilarity can be measured for many kinds of real-world data. This allows comparisons of the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. species densities in a rain-forest vs. capital density in an economy, etc.). Moreover, in contrast to many other suggested complexity measures, evaluating the self-dissimilarity of a system does not require one to already have a model of the system. These facts may allow self-dissimilarity signatures to be used a s the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self-dissimilarity we present several numerical experiments. In particular, we show that underlying structure of the logistic map is picked out by the self-dissimilarity signature of time series produced by that map
Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems
Lucarini, Valerio; Faranda, Davide; Wouters, Jeroen; Kuna, Tobias
2014-02-01
In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan-Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.
Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems.
Lucarini, Valerio; Faranda, Davide; Wouters, Jeroen; Kuna, Tobias
2014-01-01
In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan-Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.
Disease processes as hybrid dynamical systems
Directory of Open Access Journals (Sweden)
Pietro Liò
2012-08-01
Full Text Available We investigate the use of hybrid techniques in complex processes of infectious diseases. Since predictive disease models in biomedicine require a multiscale approach for understanding the molecule-cell-tissue-organ-body interactions, heterogeneous methodologies are often employed for describing the different biological scales. Hybrid models provide effective means for complex disease modelling where the action and dosage of a drug or a therapy could be meaningfully investigated: the infection dynamics can be classically described in a continuous fashion, while the scheduling of multiple treatment discretely. We define an algebraic language for specifying general disease processes and multiple treatments, from which a semantics in terms of hybrid dynamical system can be derived. Then, the application of control-theoretic tools is proposed in order to compute the optimal scheduling of multiple therapies. The potentialities of our approach are shown in the case study of the SIR epidemic model and we discuss its applicability on osteomyelitis, a bacterial infection affecting the bone remodelling system in a specific and multiscale manner. We report that formal languages are helpful in giving a general homogeneous formulation for the different scales involved in a multiscale disease process; and that the combination of hybrid modelling and control theory provides solid grounds for computational medicine.
Dynamics of Shape Memory Alloy Systems, Phase 2
2015-12-22
Nonlinear Dynamics and Chaos in Systems with Discontinuous Support Using a Switch Model”, DINAME 2005 - XI International Conference on Dynamic Problems in...AFRL-AFOSR-CL-TR-2016-0003 Dynamics of Shape Memory Alloy Systems , Phase 2 Marcelo Savi FUNDACAO COORDENACAO DE PROJETOS PESQUISAS E EEUDOS TECNOL...release. 2 AFOSR FINAL REPORT Grant Title: Nonlinear Dynamics of Shape Memory Alloy Systems , Phase 2 Grant #: FA9550-11-1-0284 Reporting Period
Adding Dynamic Innovation to Environmental Management Systems
DEFF Research Database (Denmark)
Schmidt, Kirsten
Over the last two decades, a number of organizations have implemented Environmental Management Systems (EMS) to assure a systematic approach and continuous improvements. Such systems include a number of “rules” for specific actions to be taken by members of the organization in given situations....... While such procedures may ensure a certain level of environmental effort they also tend to favor a learning style in the organization based on optimization of already known actions. This is among other things due to the fact that a certified EMS should include regular audits, and to the people...... in the organization it may become a purpose in itself to avoid failures that may lead to a nonconformity remark in the audit report. How then encourage a more dynamic and experimenting learning style that may support the requirements for continuous improvements, enhance cooperation with stakeholders and add...
Cosmic infinity: a dynamical system approach
Energy Technology Data Exchange (ETDEWEB)
Bouhmadi-López, Mariam; Marto, João [Departamento de Física, Universidade da Beira Interior, Rua Marquês D' Ávila e Bolama, 6201-001 Covilhã (Portugal); Morais, João [Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, 48080 Bilbao (Spain); Silva, César M., E-mail: mbl@ubi.pt, E-mail: jmarto@ubi.pt, E-mail: jviegas001@ikasle.ehu.eus, E-mail: csilva@ubi.pt [Centro de Matemática e Aplicações da Universidade da Beira Interior (CMA-UBI), Rua Marquês D' Ávila e Bolama, 6201-001 Covilhã (Portugal)
2017-03-01
Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse the asymptotic behaviour of the universe. On this paper, we show how this can be carried out for 3-form models. In fact, we show that there are fixed points at infinity mainly by introducing appropriate compactifications and defining a new time variable that washes away any potential divergence of the system. The richness of 3-form models allows us as well to identify normally hyperbolic non-isolated fixed points. We apply this analysis to three physically interesting situations: (i) a pre-inflationary era; (ii) an inflationary era; (iii) the late-time dark matter/dark energy epoch.
Nonlinear dynamic analysis of flexible multibody systems
Bauchau, Olivier A.; Kang, Nam Kook
1991-01-01
Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.
Regularized forecasting of chaotic dynamical systems
International Nuclear Information System (INIS)
Bollt, Erik M.
2017-01-01
While local models of dynamical systems have been highly successful in terms of using extensive data sets observing even a chaotic dynamical system to produce useful forecasts, there is a typical problem as follows. Specifically, with k-near neighbors, kNN method, local observations occur due to recurrences in a chaotic system, and this allows for local models to be built by regression to low dimensional polynomial approximations of the underlying system estimating a Taylor series. This has been a popular approach, particularly in context of scalar data observations which have been represented by time-delay embedding methods. However such local models can generally allow for spatial discontinuities of forecasts when considered globally, meaning jumps in predictions because the collected near neighbors vary from point to point. The source of these discontinuities is generally that the set of near neighbors varies discontinuously with respect to the position of the sample point, and so therefore does the model built from the near neighbors. It is possible to utilize local information inferred from near neighbors as usual but at the same time to impose a degree of regularity on a global scale. We present here a new global perspective extending the general local modeling concept. In so doing, then we proceed to show how this perspective allows us to impose prior presumed regularity into the model, by involving the Tikhonov regularity theory, since this classic perspective of optimization in ill-posed problems naturally balances fitting an objective with some prior assumed form of the result, such as continuity or derivative regularity for example. This all reduces to matrix manipulations which we demonstrate on a simple data set, with the implication that it may find much broader context.
Dynamics of human respiratory system mycoflora
Directory of Open Access Journals (Sweden)
Anna Biedunkiewicz
2014-08-01
Full Text Available The study aimed at determing the prevalence of individual species of fungi in the respiratory systems of women and men, analysis of the dynamics of the fungi in individual sections of the respiratory system as concerns their quantity and identification of phenology of the isolated fungi coupled with an attempt at identifying their possible preferences for appearing during specific seasons of thc year. During 10 years of studies (1989- 1998. 29 species of fungi belonging: Candida, Geolrichum, Saccharomyces, Saccharomycopsis, Schizosaccharomyces, Torulopsis, Trichosporon and Aspergillus were isolated from the ontocenoses of the respiratory systems of patients at the Independent Public Center for Pulmonology and Oncology in Olsztyn. Candida albicans was a clearly dominating fungus. Individual species appeared individually, in twos or threes in a single patient, they were isolated more frequently in the spring and autumn, less frequently during the winter and summer. The largest number of fungi species were isolated from sputum (29 species, bronchoscopic material (23 species and pharyngeal swabs (15 species. Sacchoromycopsis capsularis and Trichosporon beigelii should be treated as new for the respiratory system. Biodiversity of fungi, their numbers and continous fluctuations in frequency indicate that the respiratory system ontocenose offers the optimum conditions for growth and development of the majority of the majority of yeasts - like fungi.
Dissipative dynamics of superconducting hybrid qubit systems
Energy Technology Data Exchange (ETDEWEB)
Montes, Enrique; Calero, Jesus M; Reina, John H, E-mail: enriquem@univalle.edu.c, E-mail: j.reina-estupinan@physics.ox.ac.u [Departamento de Fisica, Universidad del Valle, A.A. 25360, Cali (Colombia)
2009-05-01
We perform a theoretical study of composed superconducting qubit systems for the case of a coupled qubit configuration based on a hybrid qubit circuit made of both charge and phase qubits, which are coupled via a sigma{sub x} x sigma{sub z} interaction. We compute the system's eigen-energies in terms of the qubit transition frequencies and the strength of the inter-qubit coupling, and describe the sensitivity of the energy crossing/anti-crossing features to such coupling. We compute the hybrid system's dissipative dynamics for the cases of i) collective and ii) independent decoherence, whereby the system interacts with one common and two different baths of harmonic oscillators, respectively. The calculations have been performed within the Bloch-Redfield formalism and we report the solutions for the populations and the coherences of the system's reduced density matrix. The dephasing and relaxation rates are explicitly calculated as a function of the heat bath temperature.
Efficient and accurate nearest neighbor and closest pair search in high-dimensional space
Tao, Yufei; Yi, Ke; Sheng, Cheng; Kalnis, Panos
2010-01-01
Nearest Neighbor (NN) search in high-dimensional space is an important problem in many applications. From the database perspective, a good solution needs to have two properties: (i) it can be easily incorporated in a relational database, and (ii
Dynamically allocated virtual clustering management system
Marcus, Kelvin; Cannata, Jess
2013-05-01
The U.S Army Research Laboratory (ARL) has built a "Wireless Emulation Lab" to support research in wireless mobile networks. In our current experimentation environment, our researchers need the capability to run clusters of heterogeneous nodes to model emulated wireless tactical networks where each node could contain a different operating system, application set, and physical hardware. To complicate matters, most experiments require the researcher to have root privileges. Our previous solution of using a single shared cluster of statically deployed virtual machines did not sufficiently separate each user's experiment due to undesirable network crosstalk, thus only one experiment could be run at a time. In addition, the cluster did not make efficient use of our servers and physical networks. To address these concerns, we created the Dynamically Allocated Virtual Clustering management system (DAVC). This system leverages existing open-source software to create private clusters of nodes that are either virtual or physical machines. These clusters can be utilized for software development, experimentation, and integration with existing hardware and software. The system uses the Grid Engine job scheduler to efficiently allocate virtual machines to idle systems and networks. The system deploys stateless nodes via network booting. The system uses 802.1Q Virtual LANs (VLANs) to prevent experimentation crosstalk and to allow for complex, private networks eliminating the need to map each virtual machine to a specific switch port. The system monitors the health of the clusters and the underlying physical servers and it maintains cluster usage statistics for historical trends. Users can start private clusters of heterogeneous nodes with root privileges for the duration of the experiment. Users also control when to shutdown their clusters.
On High Dimensional Searching Spaces and Learning Methods
DEFF Research Database (Denmark)
Yazdani, Hossein; Ortiz-Arroyo, Daniel; Choros, Kazimierz
2017-01-01
, and similarity functions and discuss the pros and cons of using each of them. Conventional similarity functions evaluate objects in the vector space. Contrarily, Weighted Feature Distance (WFD) functions compare data objects in both feature and vector spaces, preventing the system from being affected by some...
A Dynamic Systems Approach to Internationalization of Higher Education
Zhou, Jiangyuan
2016-01-01
Research shows that internationalization of higher education is a process rather than an end product. This paper applies the Dynamic Systems Theory to examine the nature and development of internationalization of higher education, and proposes that internationalization of higher education is a dynamic system. A dynamic framework of…
Range use and dynamics in the agropastoral system of ...
African Journals Online (AJOL)
Occurrence of equilibrium and non equilibrium system dynamics in semiarid environments present serious management challenges. In these areas, resource management strategies are increasingly based on equilibrium rather than non equilibrium dynamics that assume simple system dynamics and strong coupling of ...
Diffuse charge dynamics in ionic thermoelectrochemical systems
Stout, Robert F.; Khair, Aditya S.
2017-08-01
Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1 /D κ2 , where D is the Brownian diffusion coefficient of both ion species, and κ-1 is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L2/D , where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion
Diffuse charge dynamics in ionic thermoelectrochemical systems.
Stout, Robert F; Khair, Aditya S
2017-08-01
Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1/Dκ^{2}, where D is the Brownian diffusion coefficient of both ion species, and κ^{-1} is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L^{2}/D, where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion
Dynamics of the Yellowstone hydrothermal system
Hurwitz, Shaul; Lowenstern, Jacob B.
2014-01-01
The Yellowstone Plateau Volcanic Field is characterized by extensive seismicity, episodes of uplift and subsidence, and a hydrothermal system that comprises more than 10,000 thermal features, including geysers, fumaroles, mud pots, thermal springs, and hydrothermal explosion craters. The diverse chemical and isotopic compositions of waters and gases derive from mantle, crustal, and meteoric sources and extensive water-gas-rock interaction at variable pressures and temperatures. The thermal features are host to all domains of life that utilize diverse inorganic sources of energy for metabolism. The unique and exceptional features of the hydrothermal system have attracted numerous researchers to Yellowstone beginning with the Washburn and Hayden expeditions in the 1870s. Since a seminal review published a quarter of a century ago, research in many fields has greatly advanced our understanding of the many coupled processes operating in and on the hydrothermal system. Specific advances include more refined geophysical images of the magmatic system, better constraints on the time scale of magmatic processes, characterization of fluid sources and water-rock interactions, quantitative estimates of heat and magmatic volatile fluxes, discovering and quantifying the role of thermophile microorganisms in the geochemical cycle, defining the chronology of hydrothermal explosions and their relation to glacial cycles, defining possible links between hydrothermal activity, deformation, and seismicity; quantifying geyser dynamics; and the discovery of extensive hydrothermal activity in Yellowstone Lake. Discussion of these many advances forms the basis of this review.
Dynamic Causal Models and Autopoietic Systems
Directory of Open Access Journals (Sweden)
OLIVIER DAVID
2007-01-01
Full Text Available Dynamic Causal Modelling (DCM and the theory of autopoietic systems are two important conceptual frameworks. In this review, we suggest that they can be combined to answer important questions about self-organising systems like the brain. DCM has been developed recently by the neuroimaging community to explain, using biophysical models, the non-invasive brain imaging data are caused by neural processes. It allows one to ask mechanistic questions about the implementation of cerebral processes. In DCM the parameters of biophysical models are estimated from measured data and the evidence for each model is evaluated. This enables one to test different functional hypotheses (i.e., models for a given data set. Autopoiesis and related formal theories of biological systems as autonomous machines represent a body of concepts with many successful applications. However, autopoiesis has remained largely theoretical and has not penetrated the empiricism of cognitive neuroscience. In this review, we try to show the connections that exist between DCM and autopoiesis. In particular, we propose a simple modification to standard formulations of DCM that includes autonomous processes. The idea is to exploit the machinery of the system identification of DCMs in neuroimaging to test the face validity of the autopoietic theory applied to neural subsystems. We illustrate the theoretical concepts and their implications for interpreting electroencephalographic signals acquired during amygdala stimulation in an epileptic patient. The results suggest that DCM represents a relevant biophysical approach to brain functional organisation, with a potential that is yet to be fully evaluated
Analysis of biogas compression system dynamics
International Nuclear Information System (INIS)
Morini, Mirko; Pinelli, Michele; Venturini, Mauro
2009-01-01
The use of biogas for energy production has progressively increased in recent years, due to an increasing interest both in agricultural and energy policies of many industrialized countries. Biogas compression by means of natural gas infrastructure seems the most immediate solution, but could also lead to problems due to the different physical properties of the two gases. In this paper, a non-linear one-dimensional modular dynamic model is developed and used for the simulation of compression system transient behavior. The arrangement consists of a main line, where the compressor operates, and an anti-surge control, which consists of a recycle loop activated by a fast acting valve. Different maneuvers (start-up, normal operation, emergency shutdown and operating point variation) are simulated by using two different working fluids (methane and biogas). Simulations prove that the design of the surge protection system should consider the fluid to be elaborated. Moreover, system predisposition to surge increases as the ratio between system volumes and the inertia of the rotating masses increases.
Dynamic Parameter-Control Chaotic System.
Hua, Zhongyun; Zhou, Yicong
2016-12-01
This paper proposes a general framework of 1-D chaotic maps called the dynamic parameter-control chaotic system (DPCCS). It has a simple but effective structure that uses the outputs of a chaotic map (control map) to dynamically control the parameter of another chaotic map (seed map). Using any existing 1-D chaotic map as the control/seed map (or both), DPCCS is able to produce a huge number of new chaotic maps. Evaluations and comparisons show that chaotic maps generated by DPCCS are very sensitive to their initial states, and have wider chaotic ranges, better unpredictability and more complex chaotic behaviors than their seed maps. Using a chaotic map of DPCCS as an example, we provide a field-programmable gate array design of this chaotic map to show the simplicity of DPCCS in hardware implementation, and introduce a new pseudo-random number generator (PRNG) to investigate the applications of DPCCS. Analysis and testing results demonstrate the excellent randomness of the proposed PRNG.
Advances in dynamic network modeling in complex transportation systems
Ukkusuri, Satish V
2013-01-01
This book focuses on the latest in dynamic network modeling, including route guidance and traffic control in transportation systems and other complex infrastructure networks. Covers dynamic traffic assignment, flow modeling, mobile sensor deployment and more.
The nonlinear dynamics of a coupled fission system
International Nuclear Information System (INIS)
Bilanovic, Z.; Harms, A.A.
1993-01-01
The dynamic properties of a nonlinear and in situ vibrationally perturbed nuclear-to-thermal coupled neutron multiplying medium are examined. Some unique self-organizational temporal patterns appear in such fission systems and suggest a complex underlying dynamic. (Author)
Is DNA a nonlinear dynamical system where solitary conformational ...
Indian Academy of Sciences (India)
Unknown
DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The ... nonlinear differential equations and their soliton-like solu- .... structure and dynamics can be added till the most accurate.
Interactive Visualization of Large High-Dimensional Datasets
Ding, Wei; Chen, Ping
Nowadays many companies and public organizations use powerful database systems for collecting and managing information. Huge amount of data records are often accumulated within a short period of time. Valuable information is embedded in these data, which could help discover interesting knowledge and significantly assist in decision-making process. However, human beings are not capable of understanding so many data records which often have lots of attributes. The need for automated knowledge extraction is widely recognized, and leads to a rapidly developing market of data analysis and knowledge discovery tools.
Dynamical system analysis of interacting models
Carneiro, S.; Borges, H. A.
2018-01-01
We perform a dynamical system analysis of a cosmological model with linear dependence between the vacuum density and the Hubble parameter, with constant-rate creation of dark matter. We show that the de Sitter spacetime is an asymptotically stable critical point, future limit of any expanding solution. Our analysis also shows that the Minkowski spacetime is an unstable critical point, which eventually collapses to a singularity. In this way, such a prescription for the vacuum decay not only predicts the correct future de Sitter limit, but also forbids the existence of a stable Minkowski universe. We also study the effect of matter creation on the growth of structures and their peculiar velocities, showing that it is inside the current errors of redshift space distortions observations.
Dynamics of asymmetric kinetic Ising systems revisited
International Nuclear Information System (INIS)
Huang, Haiping; Kabashima, Yoshiyuki
2014-01-01
The dynamics of an asymmetric kinetic Ising model is studied. Two schemes for improving the existing mean-field description are proposed. In the first scheme, we derive the formulas for instantaneous magnetization, equal-time correlation, and time-delayed correlation, considering the correlation between different local fields. To derive the time-delayed correlation, we emphasize that the small-correlation assumption adopted in previous work (Mézard and Sakellariou, 2011 J. Stat. Mech. L07001) is in fact not required. To confirm the prediction efficiency of our method, we perform extensive simulations on single instances with either temporally constant external driving fields or sinusoidal external fields. In the second scheme, we develop an improved mean-field theory for instantaneous magnetization prediction utilizing the notion of the cavity system in conjunction with a perturbative expansion approach. Its efficiency is numerically confirmed by comparison with the existing mean-field theory when partially asymmetric couplings are present. (paper)
Estimation and control of dynamical systems
Bensoussan, Alain
2018-01-01
This book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control. Many aspects which are not easily found in a single text are provided, such as connections between control theory and mathematical finance, as well as differential games. The book is self-contained and prioritizes concepts rather than full rigor, targeting scientists who want to use control theory in their research in applied mathematics, engineering, economics, and management science. Examples and exercises are included throughout, which will be useful for PhD courses and graduate courses in general. Dr. Alain Bensoussan is Lars Magnus Ericsson Chair at UT Dallas and Director of the International Center for Decision and Risk Analysis which develops risk management research as it pertains to large-investment industrial projects that involve new technologies, applications and markets. He is also Chair Professor at City University Hong Kong.
Problems of the dynamics of superradiant systems
International Nuclear Information System (INIS)
Bogolyubov, N.N.; Shumovskij, A.S.
1984-01-01
Consideration is being given to the problems of describing dynamics of superradiant systems related to determination of operation conditions, the choice of active media and evaluation of noncavity laser power. It is shown that coherent monochromatic electromagnetic radiation can be generated according to noncavity circuit in a wide frequency range (from optical up to far infrared one) in ordered polar media by means of disturbing their equilibrium state. The most suitable operation substances can be presented by pyroelectrics possessing high degree of dipole correlation, monodomain structure and characteristic temperature dependence of specific polarization, as well as by paramagnetics located in magnetic field. Rapid decrease of temperature can be used as the simplest pumping mechanism in the case of pyroelectrics
Transport and Dynamics in Toroidal Fusion Systems
International Nuclear Information System (INIS)
Sovinec, Carl
2016-01-01
The study entitled, 'Transport and Dynamics in Toroidal Fusion Systems,' (TDTFS) applied analytical theory and numerical computation to investigate topics of importance to confining plasma, the fourth state of matter, with magnetic fields. A central focus of the work is how non-thermal components of the ion particle distribution affect the 'sawtooth' collective oscillation in the core of the tokamak magnetic configuration. Previous experimental and analytical research had shown and described how the oscillation frequency decreases and amplitude increases, leading to 'monster' or 'giant' sawteeth, when the non-thermal component is increased by injecting particle beams or by exciting ions with imposed electromagnetic waves. The TDTFS study applied numerical computation to self-consistently simulate the interaction between macroscopic collective plasma dynamics and the non-thermal particles. The modeling used the NIMROD code [Sovinec, Glasser, Gianakon, et al., J. Comput. Phys. 195, 355 (2004)] with the energetic component represented by simulation particles [Kim, Parker, Sovinec, and the NIMROD Team, Comput. Phys. Commun. 164, 448 (2004)]. The computations found decreasing growth rates for the instability that drives the oscillations, but they were ultimately limited from achieving experimentally relevant parameters due to computational practicalities. Nonetheless, this effort provided valuable lessons for integrated simulation of macroscopic plasma dynamics. It also motivated an investigation of the applicability of fluid-based modeling to the ion temperature gradient instability, leading to the journal publication [Schnack, Cheng, Barnes, and Parker, Phys. Plasmas 20, 062106 (2013)]. Apart from the tokamak-specific topics, the TDTFS study also addressed topics in the basic physics of magnetized plasma and in the dynamics of the reversed-field pinch (RFP) configuration. The basic physics work contributed to a study of two
Transport and Dynamics in Toroidal Fusion Systems
Energy Technology Data Exchange (ETDEWEB)
Sovinec, Carl [Univ. of Wisconsin, Madison, WI (United States)
2016-09-07
The study entitled, "Transport and Dynamics in Toroidal Fusion Systems," (TDTFS) applied analytical theory and numerical computation to investigate topics of importance to confining plasma, the fourth state of matter, with magnetic fields. A central focus of the work is how non-thermal components of the ion particle distribution affect the "sawtooth" collective oscillation in the core of the tokamak magnetic configuration. Previous experimental and analytical research had shown and described how the oscillation frequency decreases and amplitude increases, leading to "monster" or "giant" sawteeth, when the non-thermal component is increased by injecting particle beams or by exciting ions with imposed electromagnetic waves. The TDTFS study applied numerical computation to self-consistently simulate the interaction between macroscopic collective plasma dynamics and the non-thermal particles. The modeling used the NIMROD code [Sovinec, Glasser, Gianakon, et al., J. Comput. Phys. 195, 355 (2004)] with the energetic component represented by simulation particles [Kim, Parker, Sovinec, and the NIMROD Team, Comput. Phys. Commun. 164, 448 (2004)]. The computations found decreasing growth rates for the instability that drives the oscillations, but they were ultimately limited from achieving experimentally relevant parameters due to computational practicalities. Nonetheless, this effort provided valuable lessons for integrated simulation of macroscopic plasma dynamics. It also motivated an investigation of the applicability of fluid-based modeling to the ion temperature gradient instability, leading to the journal publication [Schnack, Cheng, Barnes, and Parker, Phys. Plasmas 20, 062106 (2013)]. Apart from the tokamak-specific topics, the TDTFS study also addressed topics in the basic physics of magnetized plasma and in the dynamics of the reversed-field pinch (RFP) configuration. The basic physics work contributed to a study of two-fluid effects on interchange dynamics, where
Autonomous learning by simple dynamical systems with delayed feedback.
Kaluza, Pablo; Mikhailov, Alexander S
2014-09-01
A general scheme for the construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the dynamics towards the target performance. As an example, a system of coupled phase oscillators, which can, by changing the weights of connections between its elements, evolve to a dynamical state with the prescribed (low or high) synchronization level, is considered and investigated.
Feature selection for high-dimensional integrated data
Zheng, Charles; Schwartz, Scott; Chapkin, Robert S.; Carroll, Raymond J.; Ivanov, Ivan
2012-01-01
Motivated by the problem of identifying correlations between genes or features of two related biological systems, we propose a model of feature selection in which only a subset of the predictors Xt are dependent on the multidimensional variate Y, and the remainder of the predictors constitute a “noise set” Xu independent of Y. Using Monte Carlo simulations, we investigated the relative performance of two methods: thresholding and singular-value decomposition, in combination with stochastic optimization to determine “empirical bounds” on the small-sample accuracy of an asymptotic approximation. We demonstrate utility of the thresholding and SVD feature selection methods to with respect to a recent infant intestinal gene expression and metagenomics dataset.
Feature selection for high-dimensional integrated data
Zheng, Charles
2012-04-26
Motivated by the problem of identifying correlations between genes or features of two related biological systems, we propose a model of feature selection in which only a subset of the predictors Xt are dependent on the multidimensional variate Y, and the remainder of the predictors constitute a “noise set” Xu independent of Y. Using Monte Carlo simulations, we investigated the relative performance of two methods: thresholding and singular-value decomposition, in combination with stochastic optimization to determine “empirical bounds” on the small-sample accuracy of an asymptotic approximation. We demonstrate utility of the thresholding and SVD feature selection methods to with respect to a recent infant intestinal gene expression and metagenomics dataset.
RAPID DYNAMICAL CHAOS IN AN EXOPLANETARY SYSTEM
Energy Technology Data Exchange (ETDEWEB)
Deck, Katherine M.; Winn, Joshua N. [Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Holman, Matthew J.; Carter, Joshua A.; Ragozzine, Darin [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Agol, Eric [Department of Astronomy, Box 351580, University of Washington, Seattle, WA 98195 (United States); Lissauer, Jack J. [NASA Ames Research Center, Moffet Field, CA 94035 (United States)
2012-08-10
We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which consists of a super-Earth and a sub-Neptune in a tightly packed orbital configuration. The orbits of the planets, which we studied through numerical integrations of initial conditions that are consistent with observations of the system, are chaotic with a Lyapunov time of only {approx}10 years. The chaos is a consequence of a particular set of orbital resonances, with the inner planet orbiting 34 times for every 29 orbits of the outer planet. The rapidity of the chaos is due to the interaction of the 29:34 resonance with the nearby first-order 6:7 resonance, in contrast to the usual case in which secular terms in the Hamiltonian play a dominant role. Only one contiguous region of phase space, accounting for {approx}4.5% of the sample of initial conditions studied, corresponds to planetary orbits that do not show large-scale orbital instabilities on the timescale of our integrations ({approx}200 million years). Restricting the orbits to this long-lived region allows a refinement of estimates of the masses and radii of the planets. We find that the long-lived region consists of the initial conditions that satisfy the Hill stability criterion by the largest margin. Any successful theory for the formation of this system will need to account for why its current state is so close to unstable regions of phase space.
Dynamical chaos: systems of classical mechanics
International Nuclear Information System (INIS)
Loskutov, A Yu
2007-01-01
This article is a methodological manual for those who are interested in chaotic dynamics. An exposition is given on the foundations of the theory of deterministic chaos that originates in classical mechanics systems. Fundamental results obtained in this area are presented, such as elements of the theory of nonlinear resonance and the Kolmogorov-Arnol'd-Moser theory, the Poincare-Birkhoff fixed-point theorem, and the Mel'nikov method. Particular attention is given to the analysis of the phenomena underlying the self-similarity and nature of chaos: splitting of separatrices and homoclinic and heteroclinic tangles. Important properties of chaotic systems - unpredictability, irreversibility, and decay of temporal correlations - are described. Models of classical statistical mechanics with chaotic properties, which have become popular in recent years - billiards with oscillating boundaries - are considered. It is shown that if a billiard has the property of well-developed chaos, then perturbations of its boundaries result in Fermi acceleration. But in nearly-integrable billiard systems, excitations of the boundaries lead to a new phenomenon in the ensemble of particles, separation of particles in accordance their velocities. If the initial velocity of the particles exceeds a certain critical value characteristic of the given billiard geometry, the particles accelerate; otherwise, they decelerate. (methodological notes)
Coupled dynamic systems and Le Chatelier's principle in noise control
Maidanik, G.; Becker, K. J.
2004-05-01
Investigation of coupling an externally driven dynamic system-a master dynamic system-to a passive one-an adjunct dynamic system-reveals that the response of the adjunct dynamic system affects the precoupled response of the master dynamic system. The responses, in the two dynamic systems when coupled, are estimated by the stored energies (Es) and (E0), respectively. Since the adjunct dynamic system, prior to coupling, was with zero (0) stored energy, E0s=0, the precoupled stored energy (E00) in the master dynamic system is expected to be reduced to (E0) when coupling is instituted; i.e., one expects E0
Parametric Identification of Nonlinear Dynamical Systems
Feeny, Brian
2002-01-01
In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.
Fluid flow dynamics in MAS systems
Wilhelm, Dirk; Purea, Armin; Engelke, Frank
2015-08-01
The turbine system and the radial bearing of a high performance magic angle spinning (MAS) probe with 1.3 mm-rotor diameter has been analyzed for spinning rates up to 67 kHz. We focused mainly on the fluid flow properties of the MAS system. Therefore, computational fluid dynamics (CFD) simulations and fluid measurements of the turbine and the radial bearings have been performed. CFD simulation and measurement results of the 1.3 mm-MAS rotor system show relatively low efficiency (about 25%) compared to standard turbo machines outside the realm of MAS. However, in particular, MAS turbines are mainly optimized for speed and stability instead of efficiency. We have compared MAS systems for rotor diameter of 1.3-7 mm converted to dimensionless values with classical turbomachinery systems showing that the operation parameters (rotor diameter, inlet mass flow, spinning rate) are in the favorable range. This dimensionless analysis also supports radial turbines for low speed MAS probes and diagonal turbines for high speed MAS probes. Consequently, a change from Pelton type MAS turbines to diagonal turbines might be worth considering for high speed applications. CFD simulations of the radial bearings have been compared with basic theoretical values proposing considerably smaller frictional loss values. The discrepancies might be due to the simple linear flow profile employed for the theoretical model. Frictional losses generated inside the radial bearings result in undesired heat-up of the rotor. The rotor surface temperature distribution computed by CFD simulations show a large temperature gradient over the rotor.
Classification of Dynamic Vehicle Routing Systems
DEFF Research Database (Denmark)
Larsen, Allan; Madsen, Oli B.G.; Solomon, Marius M.
2007-01-01
This chapter discusses important characteristics seen within dynamic vehicle routing problems. We discuss the differences between the traditional static vehicle routing problems and its dynamic counterparts. We give an in-depth introduction to the degree of dynamism measure which can be used to c...
Energy Technology Data Exchange (ETDEWEB)
Zawadzka-Kazimierczuk, Anna; Kozminski, Wiktor [University of Warsaw, Faculty of Chemistry (Poland); Billeter, Martin, E-mail: martin.billeter@chem.gu.se [University of Gothenburg, Biophysics Group, Department of Chemistry and Molecular Biology (Sweden)
2012-09-15
While NMR studies of proteins typically aim at structure, dynamics or interactions, resonance assignments represent in almost all cases the initial step of the analysis. With increasing complexity of the NMR spectra, for example due to decreasing extent of ordered structure, this task often becomes both difficult and time-consuming, and the recording of high-dimensional data with high-resolution may be essential. Random sampling of the evolution time space, combined with sparse multidimensional Fourier transform (SMFT), allows for efficient recording of very high dimensional spectra ({>=}4 dimensions) while maintaining high resolution. However, the nature of this data demands for automation of the assignment process. Here we present the program TSAR (Tool for SMFT-based Assignment of Resonances), which exploits all advantages of SMFT input. Moreover, its flexibility allows to process data from any type of experiments that provide sequential connectivities. The algorithm was tested on several protein samples, including a disordered 81-residue fragment of the {delta} subunit of RNA polymerase from Bacillus subtilis containing various repetitive sequences. For our test examples, TSAR achieves a high percentage of assigned residues without any erroneous assignments.
Robust and sparse correlation matrix estimation for the analysis of high-dimensional genomics data.
Serra, Angela; Coretto, Pietro; Fratello, Michele; Tagliaferri, Roberto; Stegle, Oliver
2018-02-15
Microarray technology can be used to study the expression of thousands of genes across a number of different experimental conditions, usually hundreds. The underlying principle is that genes sharing similar expression patterns, across different samples, can be part of the same co-expression system, or they may share the same biological functions. Groups of genes are usually identified based on cluster analysis. Clustering methods rely on the similarity matrix between genes. A common choice to measure similarity is to compute the sample correlation matrix. Dimensionality reduction is another popular data analysis task which is also based on covariance/correlation matrix estimates. Unfortunately, covariance/correlation matrix estimation suffers from the intrinsic noise present in high-dimensional data. Sources of noise are: sampling variations, presents of outlying sample units, and the fact that in most cases the number of units is much larger than the number of genes. In this paper, we propose a robust correlation matrix estimator that is regularized based on adaptive thresholding. The resulting method jointly tames the effects of the high-dimensionality, and data contamination. Computations are easy to implement and do not require hand tunings. Both simulated and real data are analyzed. A Monte Carlo experiment shows that the proposed method is capable of remarkable performances. Our correlation metric is more robust to outliers compared with the existing alternatives in two gene expression datasets. It is also shown how the regularization allows to automatically detect and filter spurious correlations. The same regularization is also extended to other less robust correlation measures. Finally, we apply the ARACNE algorithm on the SyNTreN gene expression data. Sensitivity and specificity of the reconstructed network is compared with the gold standard. We show that ARACNE performs better when it takes the proposed correlation matrix estimator as input. The R
Celestial dynamics chaoticity and dynamics of celestial systems
Dvorak, Rudolf
2013-01-01
Written by an internationally renowned expert author and researcher, this monograph fills the need for a book conveying the sophisticated tools needed to calculate exo-planet motion and interplanetary space flight. It is unique in considering the critical problems of dynamics and stability, making use of the software Mathematica, including supplements for practical use of the formulae.A must-have for astronomers and applied mathematicians alike.
Dynamics of dissipative systems and computational physics
International Nuclear Information System (INIS)
Adam, Gh.; Scutaru, H.; Ixaru, L.; Adam, S.; Rizea, M.; Stefanescu, E.; Mihalache, D.; Mazilu, D.; Crasovan, L.
2002-01-01
During the first year of research activity in the frame of this project there have been investigated two main topics: I. Dynamics of systems of fermions in complex dissipative media; II. Solitons with topologic charge in dissipative systems. An essential problem of the quantum information systems is the controllability and observability of the quantum states, generally described by Lindblad's master equation with phenomenological coefficients. In its usual form, this equation describes a decay of the mean-values, but not necessarily the expected decaying transitions. The basic and very difficult problem of a dissipative quantum theory is to project the evolution of the total system (the system of interest + the environment) on the space of the system of interest. In this case, one obtains a quantum master equation where the system evolution is described by two terms: 1) a Hamiltonian term for the processes with energy conservation, and 2) a non-Hamiltonian term with coefficients depending on the dissipative coupling. That means that a master equation is based on some approximations enabling the replacement of the operators of the dissipative environment with average value coefficients. It is often assumed that the evolution operators of the dissipative system define a semigroup, not a group as in the case of an isolated system. In this framework, Lindblad obtained a quantum master equation in agreement with all the quantum-mechanical principles. However, the Lindblad master equation was unable to secure a correct description of the decaying states. To do that, one has to take into account the transition operators between the system eigenstates with appropriate coefficients. Within this investigation, we have obtained an equation obeying to this requirement, giving the ρ(t) time derivative in terms of creation-annihilation operators of the single-particle states |i>, and λ ij , representing the dissipative coefficients, the microscopic expressions of which are