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Relevant bibliographies by topics / Farey tree

Academic literature on the topic 'Farey tree'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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Dissertations / Theses
Books
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Journal articles on the topic "Farey tree"

1

Goldberg, Lisa, and Charles Tresser. "Rotation orbits and the Farey tree." Ergodic Theory and Dynamical Systems 16, no. 5 (October 1996): 1011–29. http://dx.doi.org/10.1017/s0143385700010154.

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AbstractAn α-rotation orbit for a self-map of the circle is an orbit whose cyclic order on the circle is the same as for any orbit of rotation by a. In this paper, we classify sets which are minimal sets comprised of a-rotation orbits for degree d αself-coverings of the circle.

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Mosko, Marc, and J. J. Garcia-Luna-Aceves. "Fraction interpolation walking a Farey tree." Information Processing Letters 98, no. 1 (April 2006): 19–23. http://dx.doi.org/10.1016/j.ipl.2005.11.014.

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Golubeva, E. P. "Random variables associated with the Farey tree." Journal of Mathematical Sciences 193, no. 1 (July 24, 2013): 32–39. http://dx.doi.org/10.1007/s10958-013-1430-6.

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Kim, Dong Han, Seonhee Lim, Hitoshi Nakada, and Rie Natsui. "Farey maps, Diophantine approximation and Bruhat–Tits tree." Finite Fields and Their Applications 30 (November 2014): 14–32. http://dx.doi.org/10.1016/j.ffa.2014.05.007.

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PIACQUADIO, M., and E. CESARATTO. "MULTIFRACTAL SPECTRUM AND THERMODYNAMICAL FORMALISM OF THE FAREY TREE." International Journal of Bifurcation and Chaos 11, no. 05 (May 2001): 1331–58. http://dx.doi.org/10.1142/s0218127401002754.

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Let (Ω, μ) be a set of real numbers to which we associate a measure μ. Let α≥0, let Ωα={x∈Ω/α(x)=α}, where α is the concentration index defined by Halsey et al. [1986]. Let fH(α) be the Hausdorff dimension of Ωα. Let fL(α) be the Legendre spectrum of Ω, as defined in [Riedi & Mandelbrot, 1998]; and fC(α) the classical computational spectrum of Ω, defined in [Halsey et al., 1986]. The task of comparing fH, fC and fL for different measures μ was tackled by several authors [Cawley & Mauldin, 1992; Mandelbrot & Riedi, 1997; Riedi & Mandelbrot, 1998] working, mainly, on self-similar measures μ. The Farey tree partition in the unit segment induces a probability measure μ on an universal class of fractal sets Ω that occur in physics and other disciplines. This measure μ is the Hyperbolic measure μℍ, fundamentally different from any self-similar one. In this paper we compare fH, fC and fL for μℍ.

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Piacquadio, M., and M. Rosen. "Multifractal Spectrum of an Experimental (Video Feedback) Farey Tree." Journal of Statistical Physics 127, no. 4 (March 7, 2007): 783–804. http://dx.doi.org/10.1007/s10955-006-9217-5.

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Devaney, Robert L. "The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence." American Mathematical Monthly 106, no. 4 (April 1999): 289. http://dx.doi.org/10.2307/2589552.

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Lagarias, J. C., and C. P. Tresser. "A walk along the branches of the extended Farey Tree." IBM Journal of Research and Development 39, no. 3 (May 1995): 283–94. http://dx.doi.org/10.1147/rd.393.0283.

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Devaney, Robert L. "The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence." American Mathematical Monthly 106, no. 4 (April 1999): 289–302. http://dx.doi.org/10.1080/00029890.1999.12005046.

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Ringland, John, and Mark Schell. "The Farey tree embodied — In bimodal maps of the interval." Physics Letters A 136, no. 7-8 (April 1989): 379–86. http://dx.doi.org/10.1016/0375-9601(89)90419-2.

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Dissertations / Theses on the topic "Farey tree"

1

Howell, Gareth. "Normalised distance function considered over the partition of the unit interval generated by the points of the Farey tree." Thesis, Cardiff University, 2010. http://orca.cf.ac.uk/55096/.

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Tolmie, Julie, and julie tolmie@techbc ca. "Visualisation, navigation and mathematical perception: a visual notation for rational numbers mod1." The Australian National University. School of Mathematical Sciences, 2000. http://thesis.anu.edu.au./public/adt-ANU20020313.101505.

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There are three main results in this dissertation. The first result is the construction of an abstract visual space for rational numbers mod1, based on the visual primitives, colour, and rational radial direction. Mathematics is performed in this visual notation by defining increasingly refined visual objects from these primitives. In particular, the existence of the Farey tree enumeration of rational numbers mod1 is identified in the texture of a two-dimensional animation. ¶ The second result is a new enumeration of the rational numbers mod1, obtained, and expressed, in abstract visual space, as the visual object coset waves of coset fans on the torus. Its geometry is shown to encode a countably infinite tree structure, whose branches are cosets, nZ+m, where n, m (and k) are integers. These cosets are in geometrical 1-1 correspondence with sequences kn+m, (of denominators) of rational numbers, and with visual subobjects of the torus called coset fans. ¶ The third result is an enumeration in time of the visual hierarchy of the discrete buds of the Mandelbrot boundary by coset waves of coset fans. It is constructed by embedding the circular Farey tree geometrically into the empty internal region of the Mandelbrot set. In particular, coset fans attached to points of the (internal) binary tree index countably infinite sequences of buds on the (external) Mandelbrot boundary.

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Mugnaini, Silvia. "Il libro di testo nell'Italia post-unitaria : “Fatta l’Italia bisogna fare gli italiani! (Massimo D’Azeglio). Tre esempi: Collodi, Baccini, De Amicis." Thesis, Högskolan Dalarna, Italienska, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:du-11793.

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Tolmie, Julie. "Visualisation, navigation and mathematical perception: a visual notation for rational numbers mod1." Phd thesis, 2000. http://hdl.handle.net/1885/6969.

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There are three main results in this dissertation. The first result is the construction of an abstract visual space for rational numbers mod1, based on the visual primitives, colour, and rational radial direction. Mathematics is performed in this visual notation by defining increasingly refined visual objects from these primitives. In particular, the existence of the Farey tree enumeration of rational numbers mod1 is identified in the texture of a two-dimensional animation. The second result is a new enumeration of the rational numbers mod1, obtained, and expressed, in abstract visual space, as the visual object coset waves of coset fans on the torus. Its geometry is shown to encode a countably infinite tree structure, whose branches are cosets, nZ+m, where n, m (and k) are integers. These cosets are in geometrical 1-1 correspondence with sequences kn+m, (of denominators) of rational numbers, and with visual subobjects of the torus called coset fans. The third result is an enumeration in time of the visual hierarchy of the discrete buds of the Mandelbrot boundary by coset waves of coset fans. It is constructed by embedding the circular Farey tree geometrically into the empty internal region of the Mandelbrot set. In particular, coset fans attached to points of the (internal) binary tree index countably infinite sequences of buds on the (external) Mandelbrot boundary.

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Books on the topic "Farey tree"

1

Farney, Charles Edward. The revised Farney family tree. Gilbert, AZ (708 Cullumber Ave., Gilbert 85234-6405): Hampton and Associates Research and Pub., 1995.

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Foxwood, Orion. Tree of enchantment: Ancient wisdom of magical practices of the faery tradition. San Francisco, CA: Weiser Books, 2008.

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1950-, Meyer Peter, ed. Fatal embrace. New York, N.Y: St. Martin's Paperbacks, 1999.

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Ceschin, Arianna, Ilaria Crotti, and Alessandra Trevisan. Venezia Novecento. Venice: Fondazione Università Ca’ Foscari, 2020. http://dx.doi.org/10.30687/978-88-6969-422-5.

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In questi Atti di Convegno, Paola Masino, Milena Milani e Venezia si propongono come tre poli di un dialogo a più voci. Alcuni dei volti e delle trame della vita in città, negli anni Trenta e Quaranta e nei decenni successivi, sono infatti riuniti attorno a due autrici che hanno saputo fare della scrittura un mestiere fecondo. Il loro contributo, evidenziato nel volume da nove relatrici, ridisegna il volto della laguna con particolare attenzione ai luoghi e ai tempi, cogliendo, di decennio in decennio, peculiarità e variazioni. Un profilo, quello di Venezia Novecento, poco o per nulla narrato dalle donne, che trova in questi saggi un timbro di autenticità.

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Faery Tree: Earth Queen of Faery. Independently Published, 2020.

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Foxwood, Orion. Tree of Enchantment: Ancient Wisdom and Magic Practices of the Faery Tradition. Red Wheel/Weiser, 2008.

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Farry, Kim, and Katherine Jackson. My Money Tree: The Life of Kim Farry, the 'Million Pound Shoplifter'. Independently Published, 2019.

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Barrish, Cris, and Meyer Peter. Fatal Embrace: The Inside Story of the Thomas Capano/Anne Marie Fahey Murder Case. St. Martin's Press, 2014.

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Barrish, Cris, and Peter Meyer. Fatal Embrace: The Inside Story Of The Thomas Capano/Anne Marie Fahey Murder Case (St. Martin's True Crime Library.). St. Martin's True Crime, 2007.

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Grosse Ruse-Khan, Henning. The Perspective of World Trade Law on IP Rights. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199663392.003.0010.

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This chapter takes the perspective of international trade law, as embodied in the General Agreement on Tariffs and Trade (GATT), and examines how the rules on trade in goods address intellectual property (IP) protection and enforcement measures. It first looks at IP protection and enforcement as a potential barrier to and facilitator of global trade. Next, early GATT cases are discussed as examples for how national IP rights fared under multilateral trade rules in a pre-Trade Related Aspects of International Property Rights (TRIPS) era. The chapter then scrutinizes whether the same holds true in a post-TRIPS environment that is commonly characterized by TRIPS-plus protection and enforcement measures. Hereafter, certain provisions from the GATT are discussed as the central conflict norm in the trade–IP relationship. Finally, the chapter returns to the role of TRIPS in assessing IP protection and enforcement measures as potential breaches of GATT.

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Book chapters on the topic "Farey tree"

1

Kocić, Ljubiša, and Liljana Stefanovska. "A Property of Farey Tree." In Lecture Notes in Computer Science, 345–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-31852-1_41.

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Dana, I., and W. P. Reinhardt. "Intrinsic nonadiabaticities on the Farey tree." In The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function, 146–50. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-17894-5_339.

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Fang, Jin-Qing, and Yong Li. "Generalized Farey Tree Network with Small-World." In Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 1678–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02469-6_46.

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Short, Ian, and Mairi Walker. "Even-Integer Continued Fractions and the Farey Tree." In Symmetries in Graphs, Maps, and Polytopes, 287–300. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30451-9_15.

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Margalit, Dan. "Groups Acting on Trees." In Office Hours with a Geometric Group Theorist. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691158662.003.0003.

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This chapter considers groups acting on trees. It examines which groups act on which spaces and, if a group does act on a space, what it says about the group. These spaces are called trees—that is, connected graphs without cycles. A group action on a tree is free if no nontrivial element of the group preserves any vertex or any edge of the tree. The chapter first presents the theorem stating that: If a group G acts freely on a tree, then G is a free group. The condition that G is free is equivalent to the condition that G acts freely on a tree. The discussion then turns to the Farey tree and shows how to construct the Farey complex using the Farey graph. The chapter concludes by describing free and non-free actions on trees. Exercises and research projects are included.

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Griffiths, Owen, and A. C. Paseau. "The Heterogeneity Objection." In One True Logic, 157–72. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780198829713.003.0008.

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Abstract In this chapter, there begins a defence of isomorphism invariance against its most forceful criticisms. The chapter opens with the heterogeneity objection that no natural explanation is given by the account of what constitutes the same logical operation. This leads on to a discussion of other forms of invariantism offered in the literature, which the authors argue fare worse. The first to be considered is Feferman’s invariantism, which is found to be flawed. Second, Bonnay’s invariantism is examined and again found to be less successful than the version of isomorphism invariance outlined in this book. In both cases, the authors criticise some of the judgements about particular expressions, such as identity, as well as the motivation for those views.

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Ahluwalia, Madhu V., Aryya Gangopadhyay, and Zhiyuan Chen. "Preserving Privacy in Mining Quantitative Associations Rules." In Security and Privacy Assurance in Advancing Technologies, 310–26. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-60960-200-0.ch019.

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Association rule mining is an important data mining method that has been studied extensively by the academic community and has been applied in practice. In the context of association rule mining, the state-of-the-art in privacy preserving data mining provides solutions for categorical and Boolean association rules but not for quantitative association rules. This article fills this gap by describing a method based on discrete wavelet transform (DWT) to protect input data privacy while preserving data mining patterns for association rules. A comparison with an existing kd-tree based transform shows that the DWT-based method fares better in terms of efficiency, preserving patterns, and privacy.

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Vansteenkiste, Maarten, and Bart Soenens. "Less Is Sometimes More." In Motivation Science, 123—C3.3T1. Oxford University PressNew York, 2023. http://dx.doi.org/10.1093/oso/9780197662359.003.0021.

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Abstract Motivation plays a key role in individuals’ persistence, well-being, and performance. A common assumption is that everyone fares better when strongly motivated. Yet, as the authors of this essay point out, this is not always true. Although a lack of motivation is problematic, more motivation is not necessarily better. According to self-determination theory, autonomous motivation (“wantivation”) represents ideal motivation with a clear-cut pattern of desirable effects, while controlled motivation (“mustivation”) represents a mixed bag, yielding both desirable and undesirable outcomes. Extensive research now allows motivational researchers to safely conclude that “not all types of motivation are created equal.” Although a lack of motivation is problematic, for motivation to carry durable positive effects, it is strongly desirable that individuals display high wantivation instead of high mustivation.

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Strausfeld, Nicholas J. "The Insect Visual System: Correspondence with Vertebrates and with Olfactory Processing." In Handbook of Brain Microcircuits, edited by Gordon M. Shepherd and Sten Grillner, 293–306. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190636111.003.0024.

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A 1915 monograph by the Nobel Prize–winning neuroanatomist Santiago Ramón y Cajal and Domingo Sánchez y Sánchez, describing neurons and their organization in the optic lobes of insects, is now standard fare for those studying the microcircuitry of the insect visual system. The work contains prescient assumptions about possible functional arrangements, such as lateral interactions, centrifugal pathways, and the convergence of neurons onto wider dendritic trees, to provide central integration of information processed at peripheral levels of the system. This chapter will consider further indications of correspondence between the insect-crustacean and the vertebrate visual systems, with particular reference to the deep organization of the optic lobe’s third optic neuropil, the lobula, and part of the lateral forebrain (protocerebrum) that receives inputs from it. Together, the lobula and lateral protocerebrum suggest valid comparison with the visual cortex and olfactory centers.

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Dwyer, Jim. "33 Fare-Beater Inc. A Former Seminarian Found His True Calling in the Subtle Art of Sluggery." In New York Stories, 225–28. New York University Press, 2022. http://dx.doi.org/10.18574/nyu/9780814769355.003.0037.

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Conference papers on the topic "Farey tree"

1

Wu, X., Y. Zhang, J. Peng, S. Boscolo, C. Finot, and H. Zeng. "Farey Tree and Devil’s Staircase of a Breather Mode-Locked Fibre Laser." In Nonlinear Photonics. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/np.2022.npth3e.4.

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We demonstrate frequency locking at Farey fractions of breathing solitons in an ultrafast fibre laser. The ratios of the breathing frequency to the cavity-repetition frequency display the devil staircase’s structure with a 0.906 fractal dimension.

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Xiao, Yuzhi, and Haixing Zhao. "Counting the number of spanning trees of generalization Farey graph." In 2013 9th International Conference on Natural Computation (ICNC). IEEE, 2013. http://dx.doi.org/10.1109/icnc.2013.6818271.

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Everitt, Tom, Victoria Krakovna, Laurent Orseau, and Shane Legg. "Reinforcement Learning with a Corrupted Reward Channel." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/656.

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No real-world reward function is perfect. Sensory errors and software bugs may result in agents getting higher (or lower) rewards than they should. For example, a reinforcement learning agent may prefer states where a sensory error gives it the maximum reward, but where the true reward is actually small. We formalise this problem as a generalised Markov Decision Problem called Corrupt Reward MDP. Traditional RL methods fare poorly in CRMDPs, even under strong simplifying assumptions and when trying to compensate for the possibly corrupt rewards. Two ways around the problem are investigated. First, by giving the agent richer data, such as in inverse reinforcement learning and semi-supervised reinforcement learning, reward corruption stemming from systematic sensory errors may sometimes be completely managed. Second, by using randomisation to blunt the agent's optimisation, reward corruption can be partially managed under some assumptions.

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Mkrtchian, Alexander. "MODELING PRESENT AND PROSPECTIVE DISTRIBUTION OF PHYTEUMA GENUS IN CARPATHIAN REGION WITH MACHINE LEARNING TECHNIQUES USING OPEN CLIMATIC AND SOIL DATA." In GEOLINKS Conference Proceedings. Saima Consult Ltd, 2021. http://dx.doi.org/10.32008/geolinks2021/b2/v3/17.

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"Species distribution modeling can be effectively carried out using open data and data analysis tools with machine learning techniques. Modeling of the distribution of Phyteuma genus in the Carpathian region has been carried out with data from the GBIF database, climatic data from the Worldclim database, and soil properties data from Soilgrids soil information system. Spatial distribution modeling was accomplished with machine learning techniques that have marked advantages over more traditional statistical methods, like the ability to fit complex nonlinear relationships common in ecology. Four methods have been examined: Maxent, Random Forest, Artificial Neural Networks (ANN), and Boosted Regression Trees. AUC and TSS criteria calculated for testing data with cross-validation have been applied for assessing the performance of the models and to tune their parameters. ANN with a reduced set of predictor variables (6 from initial 21) appeared to fare the best and was applied for predictive modeling. Prospective data based on future climate projections from Worldclim were input to the model to get the prospective distribution of the plant taxon considering expected climate changes under different RCPs"

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Thomas, Terry M., Micky C. Marine, Jeffrey L. Wirth, and Brian W. Peters. "Emergency-Locking Retractor Performance in Rollover Accidents." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-39101.

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Generally accepted accident statistical analyses indicate that seat belted occupants involved in automobile accidents fare far better than those that are not belted. This is especially true for rollover accidents, with the primary reason being that seat belts help prevent ejection of the occupant from the vehicle. Ejected occupants are far more likely to incur serious or fatal injuries than those that remain inside the vehicle occupant compartment. Nonetheless, even belted occupants can be seriously or fatally injured in rollovers. The excursion of belted occupants during rollover accidents has been a topic of research over the past several years. Much work has been reported on the effects of belt anchor geometry. More recently published analyses have looked at the performance of the seat belt retractor in rollover accidents as well as other accident scenarios. One theory, put forth by various analysts, is that the seat belt webbing can “spool-out” from vehicle-sensitive emergency-locking retractors (ELR’s). According to this theory, the “spool-out” mechanism occurs because the retractor may cycle between a locked condition to an unlocked condition as the vehicle is overturning. Seat belt webbing can then be spooled-out from the retractor if the occupant engages the seat belt at a time that the retractor is in an unlocked condition. The added webbing introduced into the seat belt system mitigates the effectiveness of the seat belt during the subsequent roll motion. In this paper, we specifically address the performance of ELR’s in rollover accidents. A detailed analysis of the various phases of a multiple-roll rollover sequence, with an emphasis on vehicle dynamics and occupant kinematics as they relate to the physics of the sensing mass and operation of the retractor spool and locking mechanism(s), is presented. Additionally, the results of full-scale rollover testing are analyzed. The conditions to effect a retractor “spool-out” require that the sensing mass of the ELR must move to a neutral position, and the occupant must move in such a way to release tension in the seat belt thereby allowing webbing to retract back onto the spool. This retraction motion is necessary to release the ELR lockup components from a locked position. After conditions have been achieved, the sensing mass must then remain in a neutral position while occupant moves sufficiently, relative to the vehicle, to withdraw seat belt webbing from the The analysis presented in this paper and the results of testing indicate that the circumstances necessary for retractor spool-out to occur are not present in rollover accidents. A condition where sensing mass of the ELR will remain in a neutral position long enough and coincident with the occupant moving relative to the vehicle in such a manner to withdraw appreciable webbing from the does not occur. The external inputs to the vehicle that induce occupant motion also induce mass motion. The sensing mass need only move fractions of an inch to activate the retractor mechanisms. As a result, the retractor will be locked before webbing can be extracted from webbing spool.

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