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Journal articles on the topic 'Bernoulli systems'

Author: Grafiati

Published: 14 December 2024

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1

GERBER, MARLIES, and PHILIPP KUNDE. "Loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli." Ergodic Theory and Dynamical Systems 42, no. 3 (October 1, 2021): 917–73. http://dx.doi.org/10.1017/etds.2021.73.

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AbstractForeman and Weiss [Measure preserving diffeomorphisms of the torus are unclassifiable. Preprint, 2020, arXiv:1705.04414] obtained an anti-classification result for smooth ergodic diffeomorphisms, up to measure isomorphism, by using a functor $\mathcal {F}$ (see [Foreman and Weiss, From odometers to circular systems: a global structure theorem. J. Mod. Dyn.15 (2019), 345–423]) mapping odometer-based systems, $\mathcal {OB}$ , to circular systems, $\mathcal {CB}$ . This functor transfers the classification problem from $\mathcal {OB}$ to $\mathcal {CB}$ , and it preserves weakly mixing extensions, compact extensions, factor maps, the rank-one property, and certain types of isomorphisms. Thus it is natural to ask whether $\mathcal {F}$ preserves other dynamical properties. We show that $\mathcal {F}$ does not preserve the loosely Bernoulli property by providing positive and zero-entropy examples of loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli. We also construct a loosely Bernoulli circular system whose corresponding odometer-based system has zero entropy and is not loosely Bernoulli.

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2

Chernov, N. I., and C. Haskell. "Nonuniformly hyperbolic K-systems are Bernoulli." Ergodic Theory and Dynamical Systems 16, no. 1 (February 1996): 19–44. http://dx.doi.org/10.1017/s0143385700008695.

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AbstractWe prove that those non-uniformly hyperbolic maps and flows (with singularities) that enjoy the K-property are also Bernoulli. In particular, many billiard systems, including those systems of hard balls and stadia that have the K-property, and hyperbolic billiards, such as the Lorentz gas in any dimension, are Bernoulli. We obtain the Bernoulli property for both the billiard flows and the associated maps on the boundary of the phase space.

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3

Filipovic, Mirjana. "New form of the Euler-Bernoulli rod equation applied to robotic systems." Theoretical and Applied Mechanics 35, no. 4 (2008): 381–406. http://dx.doi.org/10.2298/tam0804381f.

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This paper presents a theoretical background and an example of extending the Euler-Bernoulli equation from several aspects. Euler-Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. The stiffness matrix is a full matrix. Damping is an omnipresent elasticity characteristic of real systems, so that it is naturally included in the Euler-Bernoulli equation. It is shown that Daniel Bernoulli's particular integral is just one component of the total elastic deformation of the tip of any mode to which we have to add a component of the elastic deformation of a stationary regime in accordance with the complexity requirements of motion of an elastic robot system. The elastic line equation mode of link of a complex elastic robot system is defined based on the so-called 'Euler-Bernoulli Approach' (EBA). It is shown that the equation of equilibrium of all forces present at mode tip point ('Lumped-mass approach' (LMA)) follows directly from the elastic line equation for specified boundary conditions. This, in turn, proves the essential relationship between LMA and EBA approaches. In the defined mathematical model of a robotic system with multiple DOF (degree of freedom) in the presence of the second mode, the phenomenon of elasticity of both links and joints are considered simultaneously with the presence of the environment dynamics - all based on the previously presented theoretical premises. Simulation results are presented. .

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4

ORNSTEIN, DONALD, and BENJAMIN WEISS. "On the Bernoulli nature of systems with some hyperbolic structure." Ergodic Theory and Dynamical Systems 18, no. 2 (April 1998): 441–56. http://dx.doi.org/10.1017/s0143385798100354.

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It is shown that systems with hyperbolic structure have the Bernoulli property. Some new results on smooth cross-sections of hyperbolic Bernoulli flows are also derived. The proofs involve an abstract version of our original methods for showing that the geodesic flow on surfaces of negative curvature are Bernoulli.

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5

LIAO, GANG, WENXIANG SUN, EDSON VARGAS, and SHIROU WANG. "Approximation of Bernoulli measures for non-uniformly hyperbolic systems." Ergodic Theory and Dynamical Systems 40, no. 1 (May 11, 2018): 233–47. http://dx.doi.org/10.1017/etds.2018.33.

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An invariant measure is called a Bernoulli measure if the corresponding dynamics is isomorphic to a Bernoulli shift. We prove that for$C^{1+\unicode[STIX]{x1D6FC}}$diffeomorphisms any weak mixing hyperbolic measure could be approximated by Bernoulli measures. This also holds true for$C^{1}$diffeomorphisms preserving a weak mixing hyperbolic measure with respect to which the Oseledets decomposition is dominated.

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6

DOOLEY, A. H., V. YA GOLODETS, D. J. RUDOLPH, and S. D. SINEL’SHCHIKOV. "Non-Bernoulli systems with completely positive entropy." Ergodic Theory and Dynamical Systems 28, no. 1 (February 2008): 87–124. http://dx.doi.org/10.1017/s014338570700034x.

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AbstractA new approach to actions of countable amenable groups with completely positive entropy (cpe), allowing one to answer some basic questions in this field, was recently developed. The question of the existence of cpe actions which are not Bernoulli was raised. In this paper, we prove that every countable amenable groupG, which contains an element of infinite order, has non-Bernoulli cpe actions. In fact we can produce, for any$h \in (0, \infty ]$, an uncountable family of cpe actions of entropyh, which are pairwise automorphically non-isomorphic. These actions are given by a construction which we call co-induction. This construction is related to, but different from the standard induced action. We study the entropic properties of co-induction, proving that ifαGis co-induced from an actionαΓof a subgroup Γ, thenh(αG)=h(αΓ). We also prove that ifαΓis a non-Bernoulli cpe action of Γ, thenαGis also non-Bernoulli and cpe. Hence the problem of finding an uncountable family of pairwise non-isomorphic cpe actions of the same entropy is reduced to one of finding an uncountable family of non-Bernoulli cpe actions of$\mathbb Z$, which pairwise satisfy a property we call ‘uniform somewhat disjointness’. We construct such a family using refinements of the classical cutting and stacking methods.

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7

Barbieri, Giuseppina, and Giacomo Lenzi. "Entropy of MV-algebraic dynamical systems: An example." Mathematica Slovaca 69, no. 2 (April 24, 2019): 267–74. http://dx.doi.org/10.1515/ms-2017-0221.

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Abstract We give examples showing that the Kolmogorov-Sinai entropy generator theorem is false for both upper and lower Riesz entropy of MV-algebraic dynamical systems, both two sided (i.e., analogous to two sided Bernoulli shifts) and one sided (i.e., analogous to one sided Bernoulli shifts).

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8

Nicol, Matthew. "Induced maps of hyperbolic Bernoulli systems." Discrete & Continuous Dynamical Systems - A 7, no. 1 (2001): 147–54. http://dx.doi.org/10.3934/dcds.2001.7.147.

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9

Beebee, John. "Bernoulli Numbers and Exact Covering Systems." American Mathematical Monthly 99, no. 10 (December 1992): 946. http://dx.doi.org/10.2307/2324488.

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10

Akaishi, A., M. Hirata, K. Yamamoto, and A. Shudo. "Meeting time distributions in Bernoulli systems." Journal of Physics A: Mathematical and Theoretical 44, no. 37 (August 26, 2011): 375101. http://dx.doi.org/10.1088/1751-8113/44/37/375101.

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11

Beebee, John. "Bernoulli Numbers and Exact Covering Systems." American Mathematical Monthly 99, no. 10 (December 1992): 946–48. http://dx.doi.org/10.1080/00029890.1992.11995959.

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12

Kanamori, Takafumi, and Naoya Osugi. "Model Description of Similarity-Based Recommendation Systems." Entropy 21, no. 7 (July 17, 2019): 702. http://dx.doi.org/10.3390/e21070702.

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The quality of online services highly depends on the accuracy of the recommendations they can provide to users. Researchers have proposed various similarity measures based on the assumption that similar people like or dislike similar items or people, in order to improve the accuracy of their services. Additionally, statistical models, such as the stochastic block models, have been used to understand network structures. In this paper, we discuss the relationship between similarity-based methods and statistical models using the Bernoulli mixture models and the expectation-maximization (EM) algorithm. The Bernoulli mixture model naturally leads to a completely positive matrix as the similarity matrix. We prove that most of the commonly used similarity measures yield completely positive matrices as the similarity matrix. Based on this relationship, we propose an algorithm to transform the similarity matrix to the Bernoulli mixture model. Such a correspondence provides a statistical interpretation to similarity-based methods. Using this algorithm, we conduct numerical experiments using synthetic data and real-world data provided from an online dating site, and report the efficiency of the recommendation system based on the Bernoulli mixture models.

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13

Sahu, P. K., and S. Saha Ray. "A New Bernoulli Wavelet Method for Numerical Solutions of Nonlinear Weakly Singular Volterra Integro-Differential Equations." International Journal of Computational Methods 14, no. 03 (April 13, 2017): 1750022. http://dx.doi.org/10.1142/s0219876217500220.

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In this paper, Bernoulli wavelet method has been developed to solve nonlinear weakly singular Volterra integro-differential equations. Bernoulli wavelets are generated by dilation and translation of Bernoulli polynomials. The properties of Bernoulli wavelets and Bernoulli polynomials are first presented. The present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by Newton’s method. Convergence analysis of the present method has been discussed in this paper. Some illustrative examples have been demonstrated to show the applicability and accuracy of the present method.

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14

Arbieto, Alexander, Carlos Matheus, and Maria José Pacifico. "The Bernoulli Property for Weakly Hyperbolic Systems." Journal of Statistical Physics 117, no. 1/2 (October 2004): 243–60. http://dx.doi.org/10.1023/b:joss.0000044058.99450.c9.

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15

Qu, Changzheng, and Liu Chao. "Heterotic Liouville systems from the Bernoulli equation." Physics Letters A 199, no. 5-6 (April 1995): 349–52. http://dx.doi.org/10.1016/0375-9601(95)00147-u.

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16

Blanc, J. P. C., and R. D. van der Mei. "Optimization of polling systems with Bernoulli schedules." Performance Evaluation 22, no. 2 (April 1995): 139–58. http://dx.doi.org/10.1016/0166-5316(93)e0045-7.

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17

Ju, Feng, and Jingshan Li. "A Bernoulli Model of Selective Assembly Systems." IFAC Proceedings Volumes 47, no. 3 (2014): 1692–97. http://dx.doi.org/10.3182/20140824-6-za-1003.00525.

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18

Bershadskii, A. "Multifractal Bernoulli fluctuations in disordered mesoscopic systems." Journal of Physics A: Mathematical and General 31, no. 41 (October 16, 1998): L707—L711. http://dx.doi.org/10.1088/0305-4470/31/41/001.

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19

Elishakoff, Isaac, Menahem Baruch, Liping Zhu, and Raoul Caimi. "Random Vibration of Space Shuttle Weather Protection Systems." Shock and Vibration 2, no. 2 (1995): 111–18. http://dx.doi.org/10.1155/1995/562346.

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The article deals with random vibrations of the space shuttle weather protection systems. The excitation model represents a fit to the measured experimental data. The cross-spectral density is given as a convex combination of three exponential functions. It is shown that for the type of loading considered, the Bernoulli-Euler theory cannot be used as a simplified approach, and the structure will be more properly modeled as a Timoshenko beam. Use of the simple Bernoulli-Euler theory may result in an error of about 50% in determining the mean-square value of the bending moment in the weather protection system.

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20

Katok, Anatole, and Keith Burns. "Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems." Ergodic Theory and Dynamical Systems 14, no. 4 (December 1994): 757–85. http://dx.doi.org/10.1017/s0143385700008142.

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AbstractWe establish general criteria for ergodicity and Bernoulliness for volume preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold a C∞ Riemannian metric whose geodesic flow is Bernoulli.

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21

Hicks, J. W., and H. S. Badeer. "Gravity and the circulation: "open" vs. "closed" systems." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 262, no. 5 (May 1, 1992): R725—R732. http://dx.doi.org/10.1152/ajpregu.1992.262.5.r725.

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The elementary principles of liquid dynamics are described by the equations of Bernoulli and Poiseuille. Bernoulli's equation deals with nonviscous liquids under steady streamline flow. Pressures in such flows are related to gravity and/or acceleration. Changes in elevation affect the gravitational potential energy of the liquid and the velocity of flow determines the kinetic energy. The sum of these three factors represented in the Bernoulli equation remains constant, but the variables are interconvertible. In contrast, the Poiseuille equation describes the pressures related to viscous resistance only, and the energy of flow is dissipated as heat. A combination of the two equations describes the flow in tubes more realistically than either equation alone. In "open" systems gravity hinders uphill flow and causes downhill flow, in which the liquid acts as a falling body. In contrast, in "closed" systems, like the circulation, gravity does not hinder uphill flow nor does it cause downhill flow, because gravity acts equally on the ascending and descending limbs of the circuit. Furthermore, in closed systems, the liquid cannot "fall" by gravity from higher levels of gravitational potential to lower levels of potential. Flow, up or down, must be induced by some source of energy against the resistance of the circuit. In the case of the circulation, the pumping action of the heart supplies the needed energy gradients. Flow in collapsible tubes, like veins, obeys the same basic laws of liquid dynamics except that transmural pressures near zero or below zero reduce markedly the cross-sectional area of the tube, which increases the viscous resistance to flow.(ABSTRACT TRUNCATED AT 250 WORDS)

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22

Wang, Guoliang. "Control of Multiagent Systems: A Stochastic Pinning Viewpoint." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/985356.

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A stochastic pinning approach for multiagent systems is developed, which guarantees such systems being almost surely stable. It is seen that the pinning is closely related to being a Bernoulli variable. It has been proved for the first time that a series of systems can be stabilized by a Brownian noise perturbation in terms of a pinning scheme. A new terminology named “stochastic pinning control” is introduced to describe the given pinning algorithm. Additionally, two general cases that the expectation of the Bernoulli variable with bounded uncertainty or being unknown are studied. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed methods.

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23

Pei, Yangjun, Qi Han, Chao Liu, Dedong Tang, and Junjian Huang. "Chaotic Behaviors of Symbolic Dynamics about Rule 58 in Cellular Automata." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/834268.

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The complex dynamical behaviors of rule 58 in cellular automata are investigated from the viewpoint of symbolic dynamics. The rule is Bernoulliστ-shift rule, which is members of Wolfram’s class II, and it was said to be simple as periodic before. It is worthwhile to study dynamical behaviors of rule 58 and whether it possesses chaotic attractors or not. It is shown that there exist two Bernoulli-measure attractors of rule 58. The dynamical properties of topological entropy and topological mixing of rule 58 are exploited on these two subsystems. According to corresponding strongly connected graph of transition matrices of determinative block systems, we divide determinative block systems into two subsets. In addition, it is shown that rule 58 possesses rich and complicated dynamical behaviors in the space of bi-infinite sequences. Furthermore, we prove that four rules of global equivalence classε43of CA are topologically conjugate. We use diagrams to explain the attractors of rule 58, where characteristic function is used to describe that some points fall into Bernoulli-shift map after several times iterations, and we find that these attractors are not global attractors. The Lameray diagram is used to show clearly the iterative process of an attractor.

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24

Zhao, Cong, and Jingshan Li. "A Bernoulli Model of Multi-Product Manufacturing Systems." IFAC Proceedings Volumes 46, no. 9 (2013): 1268–73. http://dx.doi.org/10.3182/20130619-3-ru-3018.00235.

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25

Bershadskii, A. "Quasi Bernoulli fluctuations in random and disordered systems." European Physical Journal B 3, no. 2 (July 1998): 141–42. http://dx.doi.org/10.1007/s100510050293.

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26

Athorne, Chris. "Projective Lifts and Generalised Ermakov and Bernoulli Systems." Journal of Mathematical Analysis and Applications 233, no. 2 (May 1999): 552–63. http://dx.doi.org/10.1006/jmaa.1999.6305.

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27

Llibre, Jaume, Weber F. Pereira, and Claudio Pessoa. "Phase portraits of Bernoulli quadratic polynomial differential systems." Electronic Journal of Differential Equations 2020, no. 01-132 (May 22, 2020): 48. http://dx.doi.org/10.58997/ejde.2020.48.

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In this article we study a new class of quadratic polynomial differential systems. We classify all global phase portraits in the Poincare disk of Bernoulli quadratic polynomial differential systems in R^2. For more information see https://ejde.math.txstate.edu/Volumes/2020/48/abstr.html

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MUNTEANU, RADU B. "Entropy of systems." Ergodic Theory and Dynamical Systems 38, no. 3 (September 19, 2016): 1118–26. http://dx.doi.org/10.1017/etds.2016.52.

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In this paper we show that any ergodic measure preserving transformation of a standard probability space which is $\text{AT}(n)$ for some positive integer $n$ has zero entropy. We show that for every positive integer $n$ any Bernoulli shift is not $\text{AT}(n)$. We also give an example of a transformation which has zero entropy but does not have property $\text{AT}(n)$ for any integer $n\geq 1$.

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KÜMMERER, B., and H. MAASSEN. "A SCATTERING THEORY FOR MARKOV CHAINS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 03, no. 01 (March 2000): 161–76. http://dx.doi.org/10.1142/s0219025700000091.

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In the operator algebraic formulation of probability theory Markov processes typically appear as perturbations of Bernoulli processes. We develop a scattering theory for this situation. This theory applies to the isomorphism problem between Markov processes and Bernoulli shifts as well as to the description of open quantum systems.

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30

Micheal, Mathavavisakan, and Kandaiyan Indhira. "A literature review on retrial queueing system with Bernoulli vacation." Yugoslav Journal of Operations Research, no. 00 (2023): 20. http://dx.doi.org/10.2298/yjor230415020m.

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The retrial phenomenon occurs inherently in a wide range of queueing systems. The majority of retrial queueing models do not account for vacation. However, in practice, retrial queueing systems undergo vacations for maintenance or other reasons. In this study, we provide an in-depth analysis of the many possible retrial queueing systems when Bernoulli vacations are in effect. Moreover, this study outlines the key principles and reviews the relevant literature. The framework of a retrial queue with Bernoulli vacation has numerous applications in computer networking systems, manufacturing and production mechanisms, inventory systems, including network service, mail service and file transfer service, etc. Several retrial queueing systems have been investigated, notably M/M/1, M/M/C, M/G/1, M[X]/G/1, and Geo/G/1. Many other important situations, such as server interruption, feedback, G-queue, impatient customers, priority customers, etc., have been explored in relation to retrial queues with Bernoulli vacation and the results of these investigations are also highlighted. The foremost objective of this study is to help researchers, administrators and technical workers who want to use queuing theory to simulate congestion and need to know where to find details on the right models. Finally, some open problems and potential future lines of survey are also covered.

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31

Dingle, Kamal, Mohammad Alaskandarani, Boumediene Hamzi, and Ard A. Louis. "Exploring Simplicity Bias in 1D Dynamical Systems." Entropy 26, no. 5 (May 16, 2024): 426. http://dx.doi.org/10.3390/e26050426.

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Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input–output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability–complexity relationships may be a useful tool when studying patterns in dynamical systems.

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De La Rue, Thierry. "Systèmes dynamiques gaussiens d'entropie nulle, lâchement et non lâchement Bernoulli." Ergodic Theory and Dynamical Systems 16, no. 2 (April 1996): 379–404. http://dx.doi.org/10.1017/s0143385700008865.

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AbstractWe construct two real Gaussian dynamical systems of zero entropy; the first one is not loosely Bernoulli, and the second is a loosely Bernoulli Gaussian-Kronecker system. To get loose-Bernoullicity for the second system, we prove and use a property of planar Brownian motion on [0, 1]: we can recover the whole trajectory knowing only some angles formed by the motion.

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33

Петров, Антон Олександрович. "Improvement test of critical systems survivability the Bernoulli scheme." Technology audit and production reserves 6, no. 3(8) (December 12, 2012): 35–36. http://dx.doi.org/10.15587/2312-8372.2012.5525.

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34

Ortega, Fernando, Raúl Lara-Cabrera, Ángel González-Prieto, and Jesús Bobadilla. "Providing reliability in recommender systems through Bernoulli Matrix Factorization." Information Sciences 553 (April 2021): 110–28. http://dx.doi.org/10.1016/j.ins.2020.12.001.

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35

Jia, Zhiyang, Liang Zhang, Jorge Arinez, and Guoxian Xiao. "Transient Performance Evaluation of Assembly Systems with Bernoulli MachinesÕ." IFAC-PapersOnLine 48, no. 3 (2015): 88–93. http://dx.doi.org/10.1016/j.ifacol.2015.06.063.

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36

Madine, K. H., and D. J. Colquitt. "Dynamic Green’s functions in discrete flexural systems." Quarterly Journal of Mechanics and Applied Mathematics 74, no. 3 (August 1, 2021): 323–50. http://dx.doi.org/10.1093/qjmam/hbab006.

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Summary The article presents an analysis of the dynamic behaviour of discrete flexural systems composed of Euler–Bernoulli beams. The canonical object of study is the discrete Green’s function, from which information regarding the dynamic response of the lattice under point loading by forces and moments can be obtained. Special attention is devoted to the interaction between flexural and torsional waves in a square lattice of Euler–Bernoulli beams, which is shown to yield a range of novel effects, including extreme dynamic anisotropy, asymmetric wave propagation, wave-guiding, filtering and the ability to create localised defect modes, all without the need for additional resonant elements or interfaces. The analytical study is complimented by numerical computations and finite element simulations, both of which are used to illustrate the effects predicted. A general algorithm is provided for constructing Green’s functions as well as defect modes. This algorithm allows the tuning of the lattice to produce pass bands, band gaps, resonant modes, wave-guides and defect modes, over any desired frequency range.

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37

Ban, Jung-Chao, Chih-Hung Chang, Ting-Ju Chen, and Mei-Shao Lin. "Dimension Spectrum for Sofic Systems." Advances in Mathematical Physics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/624523.

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We study the dimension spectrum of sofic system with the potential functions being matrix valued. For finite-coordinate dependent positive matrix potential, we set up the entropy spectrum by constructing the quasi-Bernoulli measure and the cut-off method is applied to deal with the infinite-coordinate dependent case. We extend this method to nonnegative matrix and give a series of examples of the sofic-affine set on which we can compute the spectrum concretely.

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38

Tohidi, Emran, M. M. Ezadkhah, and S. Shateyi. "Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/162896.

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This paper presents a computational approach for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on the Bernoulli polynomials approximation. Our method consists of reducing the main problems to the solution of algebraic equations systems by expanding the required approximate solutions as the linear combination of the Bernoulli polynomials. Several examples are given and the numerical results are shown to demonstrate the efficiency of the proposed method.

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RODRIGUEZ HERTZ, F., M. A. RODRIGUEZ HERTZ, A. TAHZIBI, and R. URES. "Maximizing measures for partially hyperbolic systems with compact center leaves." Ergodic Theory and Dynamical Systems 32, no. 2 (December 5, 2011): 825–39. http://dx.doi.org/10.1017/s0143385711000757.

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AbstractWe obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-dimensional manifolds having compact center leaves: either there is a unique entropy-maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0, or there are a finite number of entropy-maximizing measures, all of them with non-zero center Lyapunov exponents (at least one with a negative exponent and one with a positive exponent), that are finite extensions of a Bernoulli system. In the first case of the dichotomy, we obtain that the system is topologically conjugated to a rotation extension of a hyperbolic system. This implies that the second case of the dichotomy holds for an open and dense set of diffeomorphisms in the hypothesis of our result. As a consequence, we obtain an open set of topologically mixing diffeomorphisms having more than one entropy-maximizing measure.

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40

ZHENG, YONGAI, GUANRONG CHEN, and ZENGRONG LIU. "ON CHAOTIFICATION OF DISCRETE SYSTEMS." International Journal of Bifurcation and Chaos 13, no. 11 (November 2003): 3443–47. http://dx.doi.org/10.1142/s0218127403008661.

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In this paper, the problem of making a nonlinear system chaotic by using state-feedback control is studied. The feedback controller uses a simple sine function of the system state, but only one component in each dimension. It is proved, by using the anti-integrable limit method, that the designed control system generates chaos in the sense of Devaney. In fact, the controlled system so designed is a perturbation of the original system, which turns out to be a simple Bernoulli shift.

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41

Takine, T., H. Takagi, and T. Hasegawa. "Sojourn times in vacation and polling systems with Bernoulli feedback." Journal of Applied Probability 28, no. 2 (June 1991): 422–32. http://dx.doi.org/10.2307/3214877.

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We study sojourn times in M/G/1 multiple vacation systems and multiqueue cyclic-service (polling) systems with instantaneous Bernoulli feedback. Three service disciplines, exhaustive, gated, and 1-limited, are considered for both M/G/1 vacation and polling systems. The Laplace-Stieltjes transforms of the sojourn time distributions in the three vacation systems are derived. For polling systems, we provide explicit expressions for the mean sojourn times in symmetric cases. Furthermore a pseudo-conservation law with respect to the mean sojourn times is derived for a polling system with a mixture of the three service disciplines.

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42

Takine, T., H. Takagi, and T. Hasegawa. "Sojourn times in vacation and polling systems with Bernoulli feedback." Journal of Applied Probability 28, no. 02 (June 1991): 422–32. http://dx.doi.org/10.1017/s0021900200039796.

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Abstract:

We study sojourn times in M/G/1 multiple vacation systems and multiqueue cyclic-service (polling) systems with instantaneous Bernoulli feedback. Three service disciplines, exhaustive, gated, and 1-limited, are considered for both M/G/1 vacation and polling systems. The Laplace-Stieltjes transforms of the sojourn time distributions in the three vacation systems are derived. For polling systems, we provide explicit expressions for the mean sojourn times in symmetric cases. Furthermore a pseudo-conservation law with respect to the mean sojourn times is derived for a polling system with a mixture of the three service disciplines.

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43

Suresh Babu, Sumith Babu, and R. Kumar. "Multigroup Synchronization in 1D-Bernoulli Chaotic Collaborative CDMA." Wireless Communications and Mobile Computing 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/7561757.

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Code-division multiple access (CDMA) has played a remarkable role in the field of wireless communication systems, and its capacity and security requirements are still being addressed. Collaborative multiuser transmission and detection are a contemporary technique used in CDMA systems. The performance of these systems is governed by the proper accommodation of the users and by proper synchronization schemes. The major research concerns in the existing multiuser overloaded CDMA schemes are (i) statistically uncorrelated PN sequences that cause multiple-access interference (MAI) and (ii) the security of the user’s data. In this paper, a novel grouped CDMA scheme, the 1D-Bernoulli chaotic collaborative CDMA (BCC-CDMA), is introduced, in which mutually orthogonal chaotic sequences spread the users’ data within a group. The synchronization of multiple groups in this scheme has been analyzed under MAI limited environments and the results are presented. This increases the user capacity and also provides sufficient security as a result of the correlation properties possessed by the chaotic codes. Multigroup synchronization is achieved using a 1D chaotic pilot sequence generated by the Bernoulli Map. The mathematical model of the proposed system is described and compared with the theoretical model of the synchronization in CDMA, the simulation results of which are presented.

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44

Komori, Yasushi, Kohji Matsumoto, and Hirofumi Tsumura. "Zeta and $L$-functions and Bernoulli polynomials of root systems." Proceedings of the Japan Academy, Series A, Mathematical Sciences 84, no. 5 (May 2008): 57–62. http://dx.doi.org/10.3792/pjaa.84.57.

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Zimmels, Y. "The Bernoulli equation for fluids in electromagnetic and interfacial systems." Journal of Colloid and Interface Science 125, no. 2 (October 1988): 399–419. http://dx.doi.org/10.1016/0021-9797(88)90004-5.

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46

Fioravanti, A. R., A. P. C. Gonçalves, and J. C. Geromel. "Optimal and mode-independent filters for generalised Bernoulli jump systems." International Journal of Systems Science 46, no. 3 (June 11, 2013): 405–17. http://dx.doi.org/10.1080/00207721.2013.784373.

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47

Toivanen, J. I., J. Haslinger, and R. A. E. Mäkinen. "Shape optimization of systems governed by Bernoulli free boundary problems." Computer Methods in Applied Mechanics and Engineering 197, no. 45-48 (August 2008): 3803–15. http://dx.doi.org/10.1016/j.cma.2008.03.002.

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48

Kosloff, Zemer, and Terry Soo. "Sinai factors of nonsingular systems: Bernoulli shifts and Anosov flows." Journal of Modern Dynamics 20 (2024): 597–634. http://dx.doi.org/10.3934/jmd.2024016.

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49

Hadžić, Neven, Viktor Ložar, Tihomir Opetuk, and Robert Keser. "Transient Response of Homogenous and Nonhomogenous Bernoulli Production Lines." Mathematics 11, no. 24 (December 13, 2023): 4945. http://dx.doi.org/10.3390/math11244945.

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The transient response of production systems is of significant importance especially if present advancements in Digital Twinning technology are taken into account. While the steady-state response enables long-term strategic decision making, the transient response enables more detailed simulation concerning aspects like production losses and preventive maintenance. This is especially relevant if nonhomogenous aspects of production systems are taken into account. An analytical and approximative solution to the problem of the transient response of homogenous and nonhomogenous Bernoulli production systems is developed in this paper based on the eigendecomposition of transition matrices, the eigenvalue problem, and the finite-state method. In particular, sub-resonant and resonant nonhomogeneous production lines are introduced for the first time. Also, the most significant key performance indicators are developed as functions of the time elapsed from the first cycle. Finally, the relationship between the number of eigenvalues and the accuracy of the results is inspected by employing a sensitivity analysis. The presented theoretical framework was employed in the case of a wood processing facility to present the potential application of the theory in the case of long- and short-term management of production systems.

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Liu, Xikui, Xinye Guo, Wencheng Liu, and Yan Li. "Finite-Time H∞ Control for Time-Delay Markovian Jump Systems with Partially Unknown Transition Rate via General Controllers." Entropy 25, no. 3 (February 22, 2023): 402. http://dx.doi.org/10.3390/e25030402.

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This paper deals with the problems of finite-time boundedness (FTB) and H∞ FTB for time-delay Markovian jump systems with a partially unknown transition rate. First of all, sufficient conditions are provided, ensuring the FTB and H∞ FTB of systems given by linear matrix inequalities (LMIs). A new type of partially delay-dependent controller (PDDC) is designed so that the resulting closed-loop systems are finite-time bounded and satisfy a given H∞ disturbance attenuation level. The PDDC contains both non-time-delay and time-delay states, though not happening at the same time, which is related to the probability distribution of the Bernoulli variable. Furthermore, the PDDC is extended to two other cases; one does not contain the Bernoulli variable, and the other experiences a disordering phenomenon. Finally, three numerical examples are used to show the effectiveness of the proposed approaches.

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