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Journal articles on the topic 'OR with probabilistic transitions'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Khimenko, V. I. "Random processes with random transitions between stable states." Information and Control Systems, no. 3 (June 21, 2019): 82–93. http://dx.doi.org/10.31799/1684-8853-2019-3-82-93.

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Introduction: Studying random processes with several stable states and random transitions between them is important because it opens a wide range of practical problems. The detailed information structure is not studied well enough, and there is no unified approach to the description and probabilistic analysis of such processes.Purpose: Studying the main probabilistic characteristics of random processes with two stable states, and probabilistic analysis of control over chaotic transitions under various control actions.Results: We show the ways to represent and preliminarily analyze random processes with two stable states on the phase plane and in the pseudophase space. A general probabilistic model for the processes in question is proposed in the form of a two-component probabilistic «mixture» of distributions. A probabilistic analysis was carried out for the principles of control over random transitions between different states. We have defined the basic probabilistic characteristics for the processes in a management action with a variety of spectral-correlation properties and a changeable threshold for random transitions. The Poisson model of a random transition flow is analyzed with an example of «high» threshold levels.Practical relevance: The methods of visual, qualitative and analytical research in studying dynamic systems with several stable states can be combined. The proposed probabilistic models, regardless of the physical nature of the processes under consideration, can be used in problems of probabilistic analysis, control over probabilistic structure of random transitions, and simulation of physical, technical or biological systems with random switching.

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2

Groote, J. F., H. J. Rivera Verduzco, and E. P. de Vink. "An efficient algorithm to determine probabilistic bisimulation." Algorithms 11, no. 9 (2018): 131. http://dx.doi.org/10.3390/a11090131.

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We provide an algorithm to efficiently compute bisimulation for probabilistic labeled transition systems, featuring non-deterministic choice as well as discrete probabilistic choice. The algorithm is linear in the number of transitions and logarithmic in the number of states, distinguishing both action states and probabilistic states, and the transitions between them. The algorithm improves upon the proposed complexity bounds of the best algorithm addressing the same purpose so far by Baier, Engelen and Majster-Cederbaum (Journal of Computer and System Sciences 60:187–231, 2000). In addition, experimentally, on various benchmarks, our algorithm performs rather well; even on relatively small transition systems, a performance gain of a factor 10,000 can be achieved.

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3

Ciobanu, Gabriel, and Laura Cornacel. "Probabilistic transitions for P systems." Progress in Natural Science 17, no. 4 (2007): 432–41. http://dx.doi.org/10.1080/10020070708541020.

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4

Itoh, Sanae-I., Shinichiro Toda, Masatoshi Yagi, Kimitaka Itoh, and Atsushi Fukuyama. "Probabilistic Excitation of Plasma Transitions." Journal of the Physical Society of Japan 67, no. 12 (1998): 4080–83. http://dx.doi.org/10.1143/jpsj.67.4080.

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5

Jabarov, S. H., R. T. Aliyev, and N. A. Ismayilova. "Probabilistic model of structural phase transition in perovskites." Modern Physics Letters B 35, no. 12 (2021): 2150211. http://dx.doi.org/10.1142/s0217984921502110.

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In this work, the crystal structures and phase transitions of compounds with perovskite structure were investigated. The classification of structural phase transitions in perovskites was carried out, the most common crystal structures and structural phase transitions were shown. A mathematical model was constructed, a theorem was given and proved for the probability of a possible transition. The formulas [Formula: see text] and [Formula: see text] are given for the mathematical expectation and variance of random variable [Formula: see text], which is the moment when the stochastic process [Formula: see text] deviation from the boundary [0, [Formula: see text]] interval for the first time. According to the mathematical model, one of the trajectories of random processes corresponding to the phase transitions that occur in perovskites is constructed.

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6

Huang, Yi Sheng, and Ho Shan Chiang. "Enhancement of a Fault Measure for AMSs Using Probabilistic Timed Automata." Advanced Materials Research 317-319 (August 2011): 681–84. http://dx.doi.org/10.4028/www.scientific.net/amr.317-319.681.

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A novel approach for probabilistic timed structure that is based on combining the formalisms of timed automata and probabilistic automata representation of the system is proposed. Due to their real-valued clocks can measure the passage of time and transitions can be probabilistic such that it can be expressed as a discrete probability distribution on the set of target states. The usage of clock variables and the specification of state space are illustrated with real value time applications. The transitions between states are probabilistic by events which describe either the occurrence of faults or normal working conditions. Additionally, the passage of discrete time and transitions can be probabilistic by mean of the theory of expectation sets to obtain a unified measure reasoning strategy.

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7

FRANK, T. D. "A SYNERGETIC GAIT TRANSITION MODEL FOR HYSTERETIC GAIT TRANSITIONS FROM WALKING TO RUNNING." Journal of Biological Systems 24, no. 01 (2016): 51–61. http://dx.doi.org/10.1142/s0218339016500030.

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A model for gait transitions from walking to running is proposed. The model is based on the theory of pattern formation and synergetics. Walking and running are considered as spatiotemporal patterns, while walk-to-run and run-to-walk transitions are regarded as bifurcations. Consequently, the model is cast in the form of coupled amplitude equations as known in the literature on pattern formation. It is shown that the model can reproduce hysteretic gait transitions that have been observed in experimental studies with humans walking on treadmills when locomotion speed is gradually increased and decreased. The control parameter is an appropriately rescaled velocity measure, the so-called Froude number, which is a body-scaled parameter that takes leg length into account. It is shown that the model can reproduce observed gait transitions for individuals and populations. In particular, probabilistic functions describing gait transitions on the population level can be defined that resemble the experimentally determined probabilistic function.

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8

Alves, S. G., and J. G. Moreira. "Transitions in a probabilistic interface growth model." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 04 (2011): P04022. http://dx.doi.org/10.1088/1742-5468/2011/04/p04022.

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9

Andova, S., and T. A. C. Willemse. "Equivalences for Silent Transitions in Probabilistic Systems." Electronic Notes in Theoretical Computer Science 128, no. 2 (2005): 53–66. http://dx.doi.org/10.1016/j.entcs.2004.11.028.

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10

Troyer, Todd W., Michael S. Brainard, and Kristofer E. Bouchard. "Timing during transitions in Bengalese finch song: implications for motor sequencing." Journal of Neurophysiology 118, no. 3 (2017): 1556–66. http://dx.doi.org/10.1152/jn.00296.2017.

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To investigate mechanisms of action sequencing, we examined the relationship between timing and sequencing of syllables in Bengalese finch song. An individual’s song comprises acoustically distinct syllables organized into probabilistic sequences: a given syllable potentially can transition to several different syllables (divergence points), and several different syllables can transition to a given syllable (convergence points). In agreement with previous studies, we found that more probable transitions at divergence points occur with shorter intersyllable gaps. One intuition for this relationship is that selection between syllables reflects a competitive branching process, in which stronger links to one syllable lead to both higher probabilities and shorter latencies for transitions to that syllable vs. competing alternatives. However, we found that simulations of competitive race models result in overlapping winning-time distributions for competing outcomes and fail to replicate the strong negative correlation between probability and gap duration found in song data. Further investigation of song structure revealed strong positive correlation between gap durations for transitions that share a common convergent point. Such transitions are not related by a common competitive process, but instead reflect a common terminal syllable. In contrast to gap durations, transition probabilities were not correlated at convergence points. Together, our data suggest that syllable selection happens early during the gap, with gap timing determined chiefly by the latency to syllable initiation. This may result from a process in which probabilistic sequencing is first stabilized, followed by a shortening of the latency to syllables that are sung more often. NEW & NOTEWORTHY Bengalese finch songs consist of probabilistic sequences of syllables. Previous studies revealed a strong negative correlation between transition probability and the duration of intersyllable gaps. We show here that the negative correlation is inconsistent with previous suggestions that timing at syllable transitions is governed by a race between competing alternatives. Rather, the data suggest that syllable selection happens early during the gap, with gap timing determined chiefly by the latency to syllable initiation.

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11

Mills, Caitlin, Andre Zamani, Rebecca White, and Kalina Christoff. "Out of the blue: understanding abrupt and wayward transitions in thought using probability and predictive processing." Philosophical Transactions of the Royal Society B: Biological Sciences 376, no. 1817 (2020): 20190692. http://dx.doi.org/10.1098/rstb.2019.0692.

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Thoughts that appear to come to us ‘out of the blue’ or ‘out of nowhere’ are a familiar aspect of mental experience. Such thoughts tend to elicit feelings of surprise and spontaneity. Although we are beginning to understand the neural processes that underlie the arising of such thoughts, little is known about what accounts for their peculiar phenomenology. Here, we focus on one central aspect of this phenomenology—the experience of surprise at their occurrence, as it relates to internal probabilistic predictions regarding mental states. We introduce a distinction between two phenomenologically different types of transitions in thought content: (i) abrupt transitions , which occur at surprising times but lead to unsurprising thought content, and (ii) wayward transitions , which occur at surprising times and also lead to surprising thought content. We examine these two types of transitions using a novel approach that combines probabilistic and predictive processing concepts and principles. We employ two different probability metrics—transition and occurrence probability—to characterize and differentiate between abrupt and wayward transitions. We close by discussing some potentially beneficial ways in which these two kinds of transitions in thought content may contribute to mental function, and how they may be implemented at the neural level. This article is part of the theme issue ‘Offline perception: voluntary and spontaneous perceptual experiences without matching external stimulation’.

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12

MEYER, HARTMUT. "SIMULATIONS OF THE IMMUNOLOGICAL SHAPE SPACE: INFLUENCE OF THE INTERACTION RANGE IN AN ISING-LIKE MODEL." International Journal of Modern Physics C 06, no. 06 (1996): 765–72. http://dx.doi.org/10.1142/s0129183195000629.

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Stauffer7 has replaced the window automata rules — applied by de Boer, Segel and Perelson2 for simulating the immunological shape space — by probabilistic rules, very similar to the ones of the ferromagnetic Ising Model. Based on this model, we extend the interaction range to more than nearest neighbors and find phase transitions not only in higher dimensions, but also in two dimensions, Biologically these phase transitions correspond to a transition from a reasonable to a non-reasonable behavior of the whole immune network.

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13

Habeck, Michael, and Thach Nguyen. "A probabilistic network model for structural transitions in biomolecules." Proteins: Structure, Function, and Bioinformatics 86, no. 6 (2018): 634–43. http://dx.doi.org/10.1002/prot.25490.

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14

Khrennikov, Andrei. "Linear representations of probabilistic transformations induced by context transitions." Journal of Physics A: Mathematical and General 34, no. 47 (2001): 9965–81. http://dx.doi.org/10.1088/0305-4470/34/47/304.

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15

Nicolis, Grégoire, and Stamatios C. Nicolis. "Probabilistic Network Approach to Decision-Making." Open Systems & Information Dynamics 22, no. 02 (2015): 1550012. http://dx.doi.org/10.1142/s1230161215500122.

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A probabilistic approach to decision-making is developed in which the states of the underlying stochastic process, assumed to be of the Markov type, represent the competing options. The principal parameters determining the dominance of a particular option versus the others are identified and the transduction of information associated to the transitions between states is quantified using a set of entropy-like quantities.

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16

Alonso-Sanz, Ramón. "Phase transitions in an elementary probabilistic cellular automaton with memory." Physica A: Statistical Mechanics and its Applications 347 (March 2005): 383–401. http://dx.doi.org/10.1016/j.physa.2004.08.082.

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17

Berlin, Y. A., D. O. Drobnitsky, and V. V. Kuz'min. "General probabilistic approach to the problem of irreversible stochastic transitions." Journal of Physics A: Mathematical and General 26, no. 21 (1993): 5973–84. http://dx.doi.org/10.1088/0305-4470/26/21/034.

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18

Stoop, R., and J. Parisi. "Phase Transitions of Scaling Functions Derived from Experimental Time Series." Zeitschrift für Naturforschung A 47, no. 7-8 (1992): 819–25. http://dx.doi.org/10.1515/zna-1992-7-805.

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Abstract The occurrence of phase transitions in dynamical systems is intimately related to the analyticity properties of the thermodynamical functions. Such effects are believed to be of generic nature (for example, homoclinic tangency points). For one-dimensional maps, their existence has been proven for both the probabilistic and the dynamical scaling functions (that is, the / (a) and <P (A) spectra, respectively). With the help of simple model systems, we elucidate the different combinations in which the two types of phase transitions (namely, in the f(x) and <ϕ(λ) spectra) can appear. Moreover, we demonstrate the numerical evidence of phase-transition-like behavior in both spectra derived from experimental time series of laser and semiconductor systems. Finally, we discuss new aspects for the evaluation of the thermodynamic functions from time series

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19

Skobelev, V. V., V. P. Krasin, and S. V. Kopylov. "On spatial transitions in a system of atoms." Izvestiya vysshikh uchebnykh zavedenii. Fizika 64, no. 1 (2021): 16–20. http://dx.doi.org/10.17223/00213411/64/1/16.

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This work is a generalization of our two previous ones wherein, alter alia, a version with the minimum and maximum number of atoms in spatial configurations 1 + 2 + 3 was considered. Some of the results of these works relating to probabilistic transitions of atoms from one configuration to another are obtained from the results of this work as a special case.

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20

MÜHLENBEIN, HEINZ, and THOMAS AUS DER FÜNTEN. "AN INVESTIGATION OF THE PHASE TRANSITIONS OF A FAMILY OF PROBABILISTIC AUTOMATA." Advances in Complex Systems 07, no. 01 (2004): 93–123. http://dx.doi.org/10.1142/s0219525904000081.

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We investigate a family of totalistic probabilistic cellular automata (PCA) which depend on three parameters. For the uniform random neighborhood and for the symmetric 1D PCA the exact stationary distribution is computed for all finite n. This result is used to evaluate approximations (uni-variate and bi-variate marginals). It is proven that the uni-variate approximation (also called mean-field) is exact for the uniform random neighborhood PCA. The exact results and the approximations are used to investigate phase transitions. We compare the results of two order parameters, the uni-variate marginal and the normalized entropy. Sometimes different transitions are indicated by the Ehrenfest classification scheme. This result shows the limitations of using just one or two order parameters for detecting and classifying major transitions of the stationary distribution. Furthermore, finite size scaling is investigated. We show that extrapolations to n=∞ from numerical calculations of finite n can be misleading in difficult parameter regions. Here, exact analytical estimates are necessary.

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21

German, Paul W., and Howard L. Fields. "How Prior Reward Experience Biases Exploratory Movements: A Probabilistic Model." Journal of Neurophysiology 97, no. 3 (2007): 2083–93. http://dx.doi.org/10.1152/jn.00303.2006.

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Animals return to rewarded locations. An example of this is conditioned place preference (CPP), which is widely used in studies of drug reward. Although CPP is expressed as increased time spent in a previously rewarded location, the behavioral strategy underlying this change is unknown. We continuously monitored rats ( n = 22) in a three-room in-line configuration, before and after morphine conditioning in one end room. Although sequential room visit durations were variable, their probability distribution was exponential, indicating that the processes controlling visit durations can be modeled by instantaneous room exit probabilities. Further analysis of room transitions and computer simulations of probabilistic models revealed that the exploratory bias toward the morphine room is best explained by an increase in the probability of a subset of rapid, direct transitions from the saline- to the morphine-paired room by the central room. This finding sharply delineates and constrains possible neural mechanisms for a class of self-initiated, goal-directed behaviors toward previously rewarded locations.

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22

Alexander, F. J., I. Edrei, P. L. Garrido, and J. L. Lebowitz. "Phase transitions in a probabilistic cellular automaton: Growth kinetics and critical properties." Journal of Statistical Physics 68, no. 3-4 (1992): 497–514. http://dx.doi.org/10.1007/bf01341759.

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23

Krishnan, Sanjay, Animesh Garg, Sachin Patil, et al. "Transition state clustering: Unsupervised surgical trajectory segmentation for robot learning." International Journal of Robotics Research 36, no. 13-14 (2017): 1595–618. http://dx.doi.org/10.1177/0278364917743319.

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Demonstration trajectories collected from a supervisor in teleoperation are widely used for robot learning, and temporally segmenting the trajectories into shorter, less-variable segments can improve the efficiency and reliability of learning algorithms. Trajectory segmentation algorithms can be sensitive to noise, spurious motions, and temporal variation. We present a new unsupervised segmentation algorithm, transition state clustering (TSC), which leverages repeated demonstrations of a task by clustering segment endpoints across demonstrations. TSC complements any motion-based segmentation algorithm by identifying candidate transitions, clustering them by kinematic similarity, and then correlating the kinematic clusters with available sensory and temporal features. TSC uses a hierarchical Dirichlet process Gaussian mixture model to avoid selecting the number of segments a priori. We present simulated results to suggest that TSC significantly reduces the number of false-positive segments in dynamical systems observed with noise as compared with seven probabilistic and non-probabilistic segmentation algorithms. We additionally compare algorithms that use piecewise linear segment models, and find that TSC recovers segments of a generated piecewise linear trajectory with greater accuracy in the presence of process and observation noise. At the maximum noise level, TSC recovers the ground truth 49% more accurately than alternatives. Furthermore, TSC runs 100× faster than the next most accurate alternative autoregressive models, which require expensive Markov chain Monte Carlo (MCMC)-based inference. We also evaluated TSC on 67 recordings of surgical needle passing and suturing. We supplemented the kinematic recordings with manually annotated visual features that denote grasp and penetration conditions. On this dataset, TSC finds 83% of needle passing transitions and 73% of the suturing transitions annotated by human experts.

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24

Hansen, Wolfhard. "Modification of balayage spaces by transitions with application to coupling of PDE’s." Nagoya Mathematical Journal 169 (2003): 77–118. http://dx.doi.org/10.1017/s002776300000845x.

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AbstractModifications of balayage spaces are studied which, in probabilistic terms, correspond to killing and transitions (creation of mass combined with jumps). This is achieved by a modification of harmonic kernels for sufficiently small open sets. Applications to coupling of elliptic and parabolic partial differential equations of second order are discussed.

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25

Huillet, Thierry, and Martin Möhle. "Duality and Asymptotics for a Class of Nonneutral Discrete Moran Models." Journal of Applied Probability 46, no. 03 (2009): 866–93. http://dx.doi.org/10.1017/s0021900200005921.

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A Markov chainXwith finite state space {0,…,N} and tridiagonal transition matrix is considered, where transitions fromitoi-1 occur with probability (i/N)(1-p(i/N)) and transitions fromitoi+1 occur with probability (1-i/N)p(i/N). Herep:[0,1]→[0,1] is a given function. It is shown that ifpis continuous withp(x)≤p(1) for allx∈[0,1] then, for eachN, a dual processYtoX(with respect to a specific duality function) exists if and only if 1-pis completely monotone withp(0)=0. A probabilistic interpretation ofYin terms of an ancestral process of a mixed multitype Moran model with a random number of types is presented. It is shown that, under weak conditions onp, the processY, properly time and space scaled, converges to an Ornstein–Uhlenbeck process asNtends to ∞. The asymptotics of the stationary distribution ofYis studied asNtends to ∞. Examples are presented involving selection mechanisms. results.

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26

Mali, Amol D. "Probabilistic Roadmaps with Higher Expressive Power." International Journal on Artificial Intelligence Tools 25, no. 04 (2016): 1650027. http://dx.doi.org/10.1142/s0218213016500275.

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Sampling-based motion planning had an enormous impact on robot motion planning because of its efficiency and scalability. Many sampling-based motion planners construct a probabilistic roadmap (PRM) that captures the connectivity of the robot's free configuration space. A valid node of a PRM contains a collision-free robot configuration (also known as a sample) and a valid edge of a PRM connects two valid nodes with a collision-free path. Nodes connected by an edge are usually also required to satisfy additional requirements based on the distance between them. PRM planners use PRMs. Increasing the expressive power will allow PRMs to be used for a wider set of motion planning problems. In this paper we report on increasing the expressive power of PRMs by including the following five features in PRMs-nodes with multiple samples that need not be organized as a graph, temporal intervals of validity of nodes and edges, nodes with samples of multiple robots, special edges for the state transitions performed by humans sharing a workspace with robots, and conditional validity of samples and edges. We report on motion planning problems solvable using these new features.

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27

Zaffaroni, Gaia, Satoshi Okawa, Manuel Morales-Ruiz, and Antonio del Sol. "An integrative method to predict signalling perturbations for cellular transitions." Nucleic Acids Research 47, no. 12 (2019): e72-e72. http://dx.doi.org/10.1093/nar/gkz232.

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Abstract Induction of specific cellular transitions is of clinical importance, as it allows to revert disease cellular phenotype, or induce cellular reprogramming and differentiation for regenerative medicine. Signalling is a convenient way to accomplish such transitions without transfer of genetic material. Here we present the first general computational method that systematically predicts signalling molecules, whose perturbations induce desired cellular transitions. This probabilistic method integrates gene regulatory networks (GRNs) with manually-curated signalling pathways obtained from MetaCore from Clarivate Analytics, to model how signalling cues are received and processed in the GRN. The method was applied to 219 cellular transition examples, including cell type transitions, and overall correctly predicted experimentally validated signalling molecules, consistently outperforming other well-established approaches, such as differential gene expression and pathway enrichment analyses. Further, we validated our method predictions in the case of rat cirrhotic liver, and identified the activation of angiopoietins receptor Tie2 as a potential target for reverting the disease phenotype. Experimental results indicated that this perturbation induced desired changes in the gene expression of key TFs involved in fibrosis and angiogenesis. Importantly, this method only requires gene expression data of the initial and desired cell states, and therefore is suited for the discovery of signalling interventions for disease treatments and cellular therapies.

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28

Maity, R., and D. Prasad. "Technical note on probabilistic assessment of one-step-ahead rainfall variation by Split Markov Process." Hydrology and Earth System Sciences Discussions 8, no. 1 (2011): 189–206. http://dx.doi.org/10.5194/hessd-8-189-2011.

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Abstract. In this paper, Split Markov Process (SMP) is developed to assess one-step-ahead variation of daily rainfall at a rain gauge station. SMP is an advancement of general Markov Process (MP) and specially developed for probabilistic assessment of change in daily rainfall magnitude. The approach is based on a first-order Markov chain to simulate daily rainfall variation at a point through state/sub-state Transitional Probability Matrix (TPM). The state/sub-state TPM is based on the historical transitions from a particular state to a particular sub-state, which is the basic difference between SMP and general MP. In MP, the transition from a particular state to another state is investigated. However, in SMP, the daily rainfall magnitude is categorized into different states and change in magnitude from one temporal step to another is categorized into different sub-states for the probabilistic assessment of rainfall variation. The cumulative state/sub-state TPM is represented in a contour plot at different probability levels. The developed cumulative state/sub-state TPM is used to assess the possible range of rainfall in next time step, in a probabilistic sense. Application of SMP is investigated for daily rainfall at Khandwa station in the Nimar district of Madhya Pradesh, India. Eighty years of daily monsoon rainfall is used to develop the state/sub-state TPM and twenty years data is used to investigate its performance. It is observed that the predicted range of daily rainfall captures the actual observed rainfall with few exceptions. Overall, the assessed range, particularly the upper limit, provides a quantification possible extreme value in the next time step, which is very useful information to tackle the extreme events, such flooding, water logging etc.

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Tomé, T., and J. R. Drugowich de Fel Icio. "Short Time Dynamics of an Irreversible Probabilistic Cellular Automaton." Modern Physics Letters B 12, no. 21 (1998): 873–79. http://dx.doi.org/10.1142/s0217984998001001.

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We study the short-time dynamics of a three-state probabilistic cellular automaton. This automaton, termed TD model, possess "up-down" symmetry similar to Ising models, and displays continuous kinetic phase transitions belonging to the Ising model universality class. We perform Monte Carlo simulations on the early time regime of the two-dimensional TD model at criticality and obtain the dynamic exponent θ associated to this regime, and the exponents β/ν and z. Our results indicate that, although the model do not possess microscopic reversibility, it presents short-time universality which is consistent with the one of the kinetic Ising model.

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30

Bartels, Falk. "GSOS for probabilistic transition systems." Electronic Notes in Theoretical Computer Science 65, no. 1 (2002): 29–53. http://dx.doi.org/10.1016/s1571-0661(04)80358-x.

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31

Menyhard, N. "Inhomogeneous mean-field approximation for phase transitions in probabilistic cellular automata: an example." Journal of Physics A: Mathematical and General 21, no. 5 (1988): 1283–92. http://dx.doi.org/10.1088/0305-4470/21/5/022.

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32

Hsu, J. P. "Fuzzy Transitions from Quantum to Classical Mechanics and New Phenomena of Mesoscopic Objects." Zeitschrift für Naturforschung A 52, no. 1-2 (1997): 25–30. http://dx.doi.org/10.1515/zna-1997-1-209.

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Abstract A new "phase invariant" equation of motion for both microscopic and macroscopic objects is proposed. It reduces to the probabilistic wave equation for small masses and the deterministic classical equation for large masses. The motions of mesoscopic objects and fuzzy transitions between quantum and classical mechanics are discussed on the basis of the generalized equation. Experimental tests of new predictions are discussed.

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33

Bashkirtseva, Irina, and Lev Ryashko. "Analysis of Noise-Induced Chaos-Order Transitions in Rulkov Model Near Crisis Bifurcations." International Journal of Bifurcation and Chaos 27, no. 03 (2017): 1730014. http://dx.doi.org/10.1142/s0218127417300142.

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Noise-induced transitions from chaos to order in nonlinear systems with crisis bifurcations are studied. In this study, a discrete-time Rulkov system is used as a conceptual model of the neuronal activity. We investigate probabilistic mechanisms of noise-induced transitions from chaotic spiking to quiescence in zones of crisis bifurcations. To analyze these transitions parametrically, we apply a mathematical technique based on the stochastic sensitivity functions and confidence domains. A stochastic phenomenon of the shifts of crisis bifurcation points and the expansion of the order window under increasing noise is discussed and analyzed. Using our analytical approach, we construct a parametric description of chaotic and regular regimes for the randomly forced Rulkov model.

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34

Li, Xianneng, Shingo Mabu, Huiyu Zhou, Kaoru Shimada, and Kotaro Hirasawa. "Genetic Network Programming with Estimation of Distribution Algorithms for Class Association Rule Mining in Traffic Prediction." Journal of Advanced Computational Intelligence and Intelligent Informatics 14, no. 5 (2010): 497–509. http://dx.doi.org/10.20965/jaciii.2010.p0497.

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Genetic Network Programming (GNP) is one of the evolutionary optimization algorithms, which uses directed-graph structures to represent its solutions. It has been clarified that GNP works well to find class association rules in traffic prediction systems. In this paper, a novel evolutionary paradigm named GNP with Estimation of Distribution Algorithms (GNP-EDAs) is proposed and used to find important class association rules in traffic prediction systems. In GNP-EDAs, a probabilistic model replaces crossover and mutation to enhance the evolution. The new population of individuals is produced from the probabilistic distribution estimated from the selected elite individuals of the previous generation. The probabilistic information on the connections and transitions of GNP-EDAs is extracted from its population to construct the probabilistic model. In this paper, two methods are described to build the probabilistic model for producing the offspring. In addition, a classification mechanism is introduced to estimate the traffic prediction based on the extracted class association rules. We compared GNPEDAs with the conventional GNP and the simulation results showed that GNP-EDAs can extract the class association rules more effectively, when the number of the candidate class association rules increase. And the classification accuracy of the proposed method shows good results in traffic prediction systems.

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Huynh, Dung T., and Lu Tian. "On Some Equivalence Relations for Probabilistic Processes1." Fundamenta Informaticae 17, no. 3 (1992): 211–34. http://dx.doi.org/10.3233/fi-1992-17304.

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In this paper, we investigate several equivalence relations for probabilistic labeled transition systems: bisimulation equivalence, readiness equivalence, failure equivalence, trace equivalence, maximal trace equivalence and finite trace equivalence. We formally prove the inclusions (equalities) among these equivalences. We also show that readiness, failure, trace, maximum trace and finite trace equivalences for finite probabilistic labeled transition systems are decidable in polynomial time. This should be contrasted with the PSPACE completeness of the same equivalences for classical labeled transition systems. Moreover, we derive an efficient polynomial time algorithm for deciding bisimulation equivalence for finite probabilistic labeled transition systems. The special case of initiated probabilistic transition systems will be considered. We show that the isomorphism problem for finite initiated labeled probabilistic transition systems is NC(1) equivalent to graph isomorphism.

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Kuravsky, L. S., G. A. Yuryev, P. N. Dumin, and D. A. Pominov. "Comparative analysis of two new concepts of adaptive training." Experimental Psychology (Russia) 12, no. 2 (2019): 177–92. http://dx.doi.org/10.17759/exppsy.2019120213.

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Two new concepts of adaptive learning are presented. The first of them is based on a self-learning probabilistic model, the second one uses multivariate statistical analysis of wavelet representations for task execution trajectories as well as a matrix of recommended transitions. A comparative analysis of various aspects of their practical application has been carried out.

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BOXER, PAUL A. "LEARNING NAIVE PHYSICS BY VISUAL OBSERVATION: USING QUALITATIVE SPATIAL REPRESENTATIONS AND PROBABILISTIC REASONING." International Journal of Computational Intelligence and Applications 01, no. 03 (2001): 273–85. http://dx.doi.org/10.1142/s146902680100024x.

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Autonomous robots are unsuccessful at operating in complex, unconstrained environments. They lack the ability to learn about the physical behavior of different objects through the use of vision. We combine Bayesian networks and qualitative spatial representation to learn general physical behavior by visual observation. We input training scenarios that allow the system to observe and learn normal physical behavior. The position and velocity of the visible objects are represented as qualitative states. Transitions between these states over time are entered as evidence into a Bayesian network. The network provides probabilities of future transitions to produce predictions of future physical behavior. We use test scenarios to determine how well the approach discriminates between normal and abnormal physical behavior and actively predicts future behavior. We examine the ability of the system to learn three naive physical concepts, "no action at a distance", "solidity" and "movement on continuous paths". We conclude that the combination of qualitative spatial representations and Bayesian network techniques is capable of learning these three rules of naive physics.

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Huillet, Thierry, and Martin Möhle. "Duality and Asymptotics for a Class of Nonneutral Discrete Moran Models." Journal of Applied Probability 46, no. 3 (2009): 866–93. http://dx.doi.org/10.1239/jap/1253279856.

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A Markov chain X with finite state space {0,…,N} and tridiagonal transition matrix is considered, where transitions from i to i-1 occur with probability (i/N)(1-p(i/N)) and transitions from i to i+1 occur with probability (1-i/N)p(i/N). Here p:[0,1]→[0,1] is a given function. It is shown that if p is continuous with p(x)≤p(1) for all x∈[0,1] then, for each N, a dual process Y to X (with respect to a specific duality function) exists if and only if 1-p is completely monotone with p(0)=0. A probabilistic interpretation of Y in terms of an ancestral process of a mixed multitype Moran model with a random number of types is presented. It is shown that, under weak conditions on p, the process Y, properly time and space scaled, converges to an Ornstein–Uhlenbeck process as N tends to ∞. The asymptotics of the stationary distribution of Y is studied as N tends to ∞. Examples are presented involving selection mechanisms. results.

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39

Gill, Jeff, and George Casella. "Dynamic Tempered Transitions for Exploring Multimodal Posterior Distributions." Political Analysis 12, no. 4 (2004): 425–43. http://dx.doi.org/10.1093/pan/mph027.

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Multimodal, high-dimension posterior distributions are well known to cause mixing problems for standard Markov chain Monte Carlo (MCMC) procedures; unfortunately such functional forms readily occur in empirical political science. This is a particularly important problem in applied Bayesian work because inferences are made from finite intervals of the Markov chain path. To address this issue, we develop and apply a new MCMC algorithm based on tempered transitions of simulated annealing, adding a dynamic element that allows the chain to self-tune its annealing schedule in response to current posterior features. This important feature prevents the Markov chain from getting trapped in minor modal areas for long periods of time. The algorithm is applied to a probabilistic spatial model of voting in which the objective function of interest is the candidate's expected return. We first show that such models can lead to complex target forms and then demonstrate that the dynamic algorithm easily handles even large problems of this kind.

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LEE, JOOHYUNG, and YI WANG. "A Probabilistic Extension of Action Language." Theory and Practice of Logic Programming 18, no. 3-4 (2018): 607–22. http://dx.doi.org/10.1017/s1471068418000303.

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AbstractWe present a probabilistic extension of action language${\cal BC}$+$. Just like${\cal BC}$+$is defined as a high-level notation of answer set programs for describing transition systems, the proposed language, which we callp${\cal BC}$+$, is defined as a high-level notation of LPMLNprograms—a probabilistic extension of answer set programs. We show how probabilistic reasoning about transition systems, such as prediction, postdiction, and planning problems, as well as probabilistic diagnosis for dynamic domains, can be modeled inp${\cal BC}$+$and computed using an implementation of LPMLN.

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41

Bashkirtseva, Irina, Tatyana Ryazanova, and Lev Ryashko. "Confidence Domains in the Analysis of Noise-Induced Transition to Chaos for Goodwin Model of Business Cycles." International Journal of Bifurcation and Chaos 24, no. 08 (2014): 1440020. http://dx.doi.org/10.1142/s0218127414400203.

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Stochastically forced Goodwin model of business cycles is considered. In a multistable zone, we study the phenomena of noise-induced transitions and chaotization. To clarify a probabilistic mechanism of these phenomena found numerically, we apply a semi-analytical method based on the stochastic sensitivity function technique and confidence domains. Using elaborated method, we estimate a critical value of the noise intensity corresponding to the onset of chaos.

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Bitykov, V., F. Jablonski, and R. Kienzler. "Probabilistic modeling of hybrid transition structures." Materials & Design 82 (October 2015): 200–205. http://dx.doi.org/10.1016/j.matdes.2015.05.053.

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Toda, Shinichiro, Sanae-I. Itoh, Masatoshi Yagi, Kimitaka Itoh, and Atsushi Fukuyama. "Probabilistic Nature in L/H Transition." Journal of the Physical Society of Japan 68, no. 11 (1999): 3520–27. http://dx.doi.org/10.1143/jpsj.68.3520.

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44

Silva, A., L. C. Neves, P. L. Gaspar, and J. de Brito. "Probabilistic transition of condition: render facades." Building Research & Information 44, no. 3 (2015): 301–18. http://dx.doi.org/10.1080/09613218.2015.1023645.

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KOZMA, ROBERT, MARKO PULJIC, and LEONID PERLOVSKY. "MODELING GOAL-ORIENTED DECISION MAKING THROUGH COGNITIVE PHASE TRANSITIONS." New Mathematics and Natural Computation 05, no. 01 (2009): 143–57. http://dx.doi.org/10.1142/s1793005709001246.

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Cognitive experiments indicate the presence of discontinuities in brain dynamics during high-level cognitive processing. Non-linear dynamic theory of brains pioneered by Freeman explains the experimental findings through the theory of metastability and edge-of-criticality in cognitive systems, which are key properties associated with robust operation and fast and reliable decision making. Recently, neuropercolation has been proposed to model such critical behavior. Neuropercolation is a family of probabilistic models based on the mathematical theory of bootstrap percolations on lattices and random graphs and motivated by structural and dynamical properties of neural populations in the cortex. Neuropercolation exhibits phase transitions and it provides a novel mathematical tool for studying spatio-temporal dynamics of multi-stable systems. The present work reviews the theory of cognitive phase transitions based on neuropercolation models and outlines the implications to decision making in brains and in artificial designs.

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46

Safina, G. L., A. G. Tashlinskii, and M. G. Tsaryov. "Adaptation of the mathematical apparatus of the Markov chain theory for the probabilistic analysis of recurrent estimation of image inter-frame geometric deformations." Information Technology and Nanotechnology, no. 2391 (2019): 103–8. http://dx.doi.org/10.18287/1613-0073-2019-2391-103-108.

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The paper is devoted to the analysis of the possibilities of using Markov chains for analyzing the accuracy of stochastic gradient relay estimation of image geometric deformations. One of the ways to reduce computational costs is to discretize the domain of studied parameters. This approach allows to choose the dimension of transition probabilities matrix a priori. However, such a matrix has a rather complicated structure. It does not significantly reduce the number of computations. A modification of the transition probabilities matrix is proposed, it’s dimension does not depend on the dimension of estimated parameters vector. In this case, the obtained relations determine a recurrent algorithm for calculating the matrix at the estimation iterations. For the one-step transitions matrix, the calculated expressions for the probabilities of image deformation parameters estimates drift are given.

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Karadoğan, Ernur. "Probabilistic evaluation of the one-dimensional Brinson model’s sensitivity to uncertainty in input parameters." Journal of Intelligent Material Systems and Structures 30, no. 7 (2019): 1070–83. http://dx.doi.org/10.1177/1045389x19828826.

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Brinson model is one of the most widely used shape memory alloy models due to its prediction power over a wide range of operating temperatures and inclusion of measurable engineering variables. The model involves parameters that are determined based on experimental data specific to a particular alloy. Therefore, it is subject to both experimental uncertainty and natural random variability in its parameters that propagate throughout the loading/unloading of the material. In this article, we analyse the sensitivity of the Brinson model to its parameters using a probabilistic approach, and present how the uncertainties in these parameters at different operating temperatures propagate as evidenced by the resulting stress–strain curves. The analyses were performed for isothermal loading/unloading and at various operating temperatures representing possible phase changes between martensite–austenite and martensite–martensite variants. The results show that the sensitivity of the model varies considerably based on the operating temperature and loading conditions. In addition, the variability in the model’s output is amplified after phase transitions during loading, and loading the material above the critical stress for martensite transition reduces variability during unloading. Based on the results of the sensitivity analysis, recommendations as to which parameters affect the variability of the model-predicted stress–strain curves are presented.

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Deale, O. C., R. C. Wesley, D. Morgan, and B. B. Lerman. "Nature of defibrillation: determinism versus probabilism." American Journal of Physiology-Heart and Circulatory Physiology 259, no. 5 (1990): H1544—H1550. http://dx.doi.org/10.1152/ajpheart.1990.259.5.h1544.

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The gradual transitions that are found between unsuccessful and successful shock strengths in percent success or dose-response curves suggest that defibrillation is a probabilistic phenomenon. This concept appears to be reinforced by the fact that a frequency distribution is observed in defibrillation threshold data and that a dose-response relationship is also obtained by integration of the frequency distribution. The purpose of this study was to investigate whether a deterministic threshold model (based on experimental results) could produce 1) gradual transitions in dose-response curves, and 2) a threshold frequency distribution for individual subjects. In the experimental phase of the study, a linear deterministic relationship was found between transthoracic threshold current and defibrillation episode number (other variables held constant) in pentobarbital-anesthetized dogs. The correlation coefficient for each dog was between 0.77 and 0.98 (P less than 0.01), and both positive and negative slopes were found. Based on these results, threshold current was modeled for computer simulation as a linear function of episode number. The model was thus purely deterministic with no random variability. For each simulated experiment, several parameters were varied: order of shocks (increment, decrement, random order), slope of threshold function, and percent error of the initial threshold. Several hundred computer simulations were performed to determine the effect of varying these parameters. In all cases, threshold-frequency distributions and sigmoidal dose-response curves with gradual transitions were produced. The results of this investigation demonstrate that the apparent probabilistic behavior of defibrillation can be produced by a deterministic relationship.

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Liu, Yi, Tao Chen, and Junghui Chen. "Auto-Switch Gaussian Process Regression-Based Probabilistic Soft Sensors for Industrial Multigrade Processes with Transitions." Industrial & Engineering Chemistry Research 54, no. 18 (2015): 5037–47. http://dx.doi.org/10.1021/ie504185j.

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Xu, Chaoqun. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model." Chaos, Solitons & Fractals 137 (August 2020): 109871. http://dx.doi.org/10.1016/j.chaos.2020.109871.

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