“…The proposed strategy for estimating missing nucleotides is based on probabilistic formulae developed in the framework of the Jukes-Cantor [10] and Kimura 2-parameter [11] models. The relative performances of the new method were assessed through simulations carried out with the SeqGen program [20], for data generation, and the Bio NJ method [7], for inferring phylogenies. …”
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“…Over the past few decades, various conjectures were advanced that Saturn’s rings are Cantor-like sets, although no convincing fractal analysis of actual images has ever appeared. …”
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“…In this study, the microstructure and mechanical properties of the so-called Cantor alloy composed of Co, Cr, Fe, Mn, and Ni in equiatomic ratios prepared by various techniques (casting, melt-spinning, spark plasma sintering) were examined. …”
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“…Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecker and Zermelo are here translated for the first time. …”
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“…The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. …”
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“…The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two proofs), the No Retraction Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem, the Open Mapping Theorem, the Riemann-Hurwitz Theorem, and the Classification Theorem for Compact 2-manifolds. …”
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“…The first half of the book introduces some of the key ideas in fractal geometry and dimension theory--Cantor sets, Hausdorff dimension, box dimension--using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. …”
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“…The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. …”
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“…In this paper, a particular geometric model of point clustering approaching the Cantor shape in 2D, with a symmetry scale θ being an intermittency parameter, is proposed. …”
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“…However, most of the existing methods for identifying polarity of sentiment words only consider the positive and negative polarity by the Cantor set, and no attention is paid to the fuzziness of the polarity intensity of sentiment words. …”
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“…The theory presented generalizes one due to David Cantor for the projective line. As with most adelic theories, it has a local and a global part. …”
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“…Key features of this text include: • Applications from several parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; • A heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; • Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; • A self-contained treatment of the fundamental theorems of calculus in the general case using the Sunrise Lemma; • The integral is defined as the area under the graph, while the area is defined for every subset of the plane; • 450 problems with all the solutions presented at the back of the text. …”
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“…Differential Equations Linear Maps/Difference Equations Fixed (Equilibrium) Points Graphical Iteration and Stability Criteria for Stability Periodic Points and Their Stability The Period-Doubling Route to Chaos Applications Attraction and Bifurcation Introduction Basin of Attraction of Fixed Points Basin of Attraction of Periodic Orbits Singer's Theorem Bifurcation Sharkovsky's Theorem The Lorenz Map Period-Doubling in the Real World Poincaré Section/Map Appendix Chaos in One Dimension Introduction Density of the Set of Periodic Points Transitivity Sensitive Dependence Definition of Chaos Cantor Sets Symbolic Dynamics Conjugacy Other Notions of Chaos Rössler's Attractor Saturn's Rings Stability of Two-Dimensional Maps Linear Maps vs. …”
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“…Deciding whether a transition matrix is embeddable or not enables us to know if the observed substitution probabilities are consistent with a homogeneous continuous time substitution model, such as the Kimura models, the Jukes-Cantor model or the general time-reversible model. …”
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“…The patient underwent surgery 3 years ago in which hemimandibulectomy was performed due to oral squamous cell carcinoma. The patient had a Cantor and Curtis Type II defect. The mandible was resected distally from canine region on the right side of the arch. …”
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“…While minor differences exist and are herein described, our overall results strongly suggest that in our experiments with synergy in MLR, we may be dealing with the same T(1)- and T(2)-cell subpopulations described by Cantor and Asofsky and coworkers (1, 2, 4, 5, 14) as displaying synergy in the graft-vs.…”
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“…We apply our results to a two-dimensional fat Cantor-like fractal, calculating analytic expressions for the scattering intensities and structure factors. …”
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“…3 NAP Theory:   3.1 First four axioms of NAP;   3.2 Continuity and conditional probability;   3.3 The final axiom of NAP;   3.4 Infinite sums;   3.5 Definition of NAP functions via infinite sums;   3.6 Relation to numerosity theory; 4 Objections and Replies:   4.1 Cantor and the Archimedean property;   4.2 Ticket missing from an infinite lottery;   4.3 Williamson’s infinite sequence of coin tosses;   4.4 Point sets on a circle;   4.5 Easwaran and Pruss; 5 Dividends:   5.1 Measure and utility;   5.2 Regularity and uniformity;   5.3 Credence and chance;   5.4 Conditional probability; 6 General Considerations:   6.1 Non-uniqueness;   6.2 Invariance. …”
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