Academic literature on the topic 'Sets of points of a given property'
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Journal articles on the topic "Sets of points of a given property"
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BARRAL, JULIEN, and STÉPHANE SEURET. "Ubiquity and large intersections properties under digit frequencies constraints." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 3 (November 2008): 527–48. http://dx.doi.org/10.1017/s030500410800159x.
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AbstractWe are interested in two properties of real numbers: the first one is the property of being well-approximated by some dense family of real numbers {xn}n≥1, such as rational numbers and more generally algebraic numbers, and the second one is the property of having given digit frequencies in some b-adic expansion.We combine these two ways of classifying the real numbers, in order to provide a finer classification. We exhibit sets S of points x which are approximated at a given rate by some of the {xn}n, those xn being selected according to their digit frequencies. We compute the Hausdorff dimension of any countable intersection of such sets S, and prove that these sets enjoy the so-called large intersection property.
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Yurkov, V. "Images of Linear Conditions on a Manhattan Plane." Geometry & Graphics 8, no. 1 (April 20, 2020): 3–14. http://dx.doi.org/10.12737/2308-4898-2020-3-14.
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In this paper are considered planar point sets generated by linear conditions, which are realized in rectangular or Manhattan metric. Linear conditions are those expressed by the finite sum of the products of distances by numerical coefficients. Finite sets of points and lines are considered as figures defining linear conditions. It has been shown that linear conditions can be defined relative to other planar figures: lines, polygons, etc. The design solutions of the following general geometric problem are considered: for a finite set of figures (points, line segments, polygons...) specified on a plane with a rectangular metric, which are in a common position, it is necessary to construct sets that satisfy any linear condition. The problems in which the given sets are point and segment ones have been considered in detail, and linear conditions are represented as a sum or as relations of distances. It is proved that solution result can be isolated points, broken lines, and areas on the plane. Sets of broken lines satisfying the given conditions form families of isolines for the given condition. An algorithm for building isoline families is presented. The algorithm is based on the Hanan lattice construction and the isolines behavior in each node and each sub-region of the lattice. For isoline families defined by conditions for relation of distances, some of their properties allowing accelerate their construction process are proved. As an example for application of the described theory, the problem of plane partition into regions corresponding to a given set of points, lines and other figures is considered. The problem is generalized problem of Voronoi diagram construction, and considered in general formulation. It means the next: 1) the problem is considered in rectangular metric; 2) all given points may be integrated in various figures – separate points, line segments, triangles, quadrangles etc.; 3) the Voronoi diagram’s property of proximity is changed for property of proportionality. Have been represented examples for plane partition into regions, determined by two-point sets.
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BOMFIM, THIAGO, and PAULO VARANDAS. "Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets." Ergodic Theory and Dynamical Systems 37, no. 1 (October 12, 2015): 79–102. http://dx.doi.org/10.1017/etds.2015.46.
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In this article we prove estimates for the topological pressure of the set of points whose Birkhoff time averages are far from the space averages corresponding to the unique equilibrium state that has a weak Gibbs property. In particular, if$f$has an expanding repeller and$\unicode[STIX]{x1D719}$is a Hölder continuous potential, we prove that the topological pressure of the set of points whose accumulation values of Birkhoff averages belong to some interval$I\subset \mathbb{R}$can be expressed in terms of the topological pressure of the whole system and the large deviations rate function. As a byproduct we deduce that most irregular sets for maps with the specification property have topological pressure strictly smaller than the whole system. Some extensions to a non-uniformly hyperbolic setting, level-2 irregular sets and hyperbolic flows are also given.
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Sun, Chia-Liang. "Weak Approximation for Points with Coordinates in Rank-one Subgroups of Global Function Fields." Canadian Mathematical Bulletin 61, no. 4 (November 20, 2018): 878–90. http://dx.doi.org/10.4153/cmb-2018-008-3.
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AbstractFor every affine variety over a global function field, we show that the set of its points with coordinates in an arbitrary rank-one multiplicative subgroup of this function field satisfies the required property of weak approximation for finite sets of places of this function field avoiding arbitrarily given finitely many places.
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Polyrakis, Ioannis A. "Strongly exposed points in bases for the positive cone of ordered Banach spaces and characterizations of l1(Г)." Proceedings of the Edinburgh Mathematical Society 29, no. 2 (June 1986): 271–82. http://dx.doi.org/10.1017/s0013091500017648.
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The study of extreme, strongly exposed points of closed, convex and bounded sets in Banach spaces has been developed especially by the interconnection of the Radon–Nikodým property with the geometry of closed, convex and bounded subsets of Banach spaces [5],[2] . In the theory of ordered Banach spaces as well as in the Choquet theory, [4], we are interested in the study of a special type of convex sets, not necessarily bounded, namely the bases for the positive cone. In [7] the geometry (extreme points, dentability) of closed and convex subsets K of a Banach space X with the Radon-Nikodým property is studied and special emphasis has been given to the case where K is a base for acone P of X. In [6, Theorem 1], it is proved that an infinite-dimensional, separable, locally solid lattice Banach space is order-isomorphic to l1 if, and only if, X has the Krein–Milman property and its positive cone has a bounded base.
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Kent, Steven L., Roy A. Mimna, and Jamal K. Tartir. "A Note on Topological Properties of Non-Hausdorff Manifolds." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–4. http://dx.doi.org/10.1155/2009/891785.
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The notion of compatible apparition points is introduced for non-Hausdorff manifolds, and properties of these points are studied. It is well known that the Hausdorff property is independent of the other conditions given in the standard definition of a topological manifold. In much of literature, a topological manifold of dimension is a Hausdorff topological space which has a countable base of open sets and is locally Euclidean of dimension . We begin with the definition of a non-Hausdorff topological manifold.
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Martínez, Teresa, and José L. Torrea. "Boundedness of vector-valued martingale transforms on extreme points and applciations." Journal of the Australian Mathematical Society 76, no. 2 (April 2004): 207–22. http://dx.doi.org/10.1017/s1446788700008909.
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AbstractLet Β1, Β2be a pair of Banach spaces andTbe a vector valued martingale transform (with respect to general filtration) which maps Β1-valued martingales into Β2-valued martingales. Then, the following statements are equivalent:Tis bounded fromintofor somep(or equivalently for everyp) in the range 1 <p< ∞;Tis bounded fromintoBMOB2;Tis bounded fromBMOB1intoBMOB2;Tis bounded frominto. Applications toUMDand martingale cotype properties are given. We also prove that the Hardy spacedefined in the case of a general filtration has nice dense sets and nice atomic decompositions if and only if Β has the Radon-Nikodým property.
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Palmer, T. N. "Discretization of the Bloch sphere, fractal invariant sets and Bell’s theorem." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2236 (April 2020): 20190350. http://dx.doi.org/10.1098/rspa.2019.0350.
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An arbitrarily dense discretization of the Bloch sphere of complex Hilbert states is constructed, where points correspond to bit strings of fixed finite length. Number-theoretic properties of trigonometric functions (not part of the quantum-theoretic canon) are used to show that this constructive discretized representation incorporates many of the defining characteristics of quantum systems: completementarity, uncertainty relationships and (with a simple Cartesian product of discretized spheres) entanglement. Unlike Meyer’s earlier discretization of the Bloch Sphere, there are no orthonormal triples, hence the Kocken–Specker theorem is not nullified. A physical interpretation of points on the discretized Bloch sphere is given in terms of ensembles of trajectories on a dynamically invariant fractal set in state space, where states of physical reality correspond to points on the invariant set. This deterministic construction provides a new way to understand the violation of the Bell inequality without violating statistical independence or factorization, where these conditions are defined solely from states on the invariant set. In this finite representation, there is an upper limit to the number of qubits that can be entangled, a property with potential experimental consequences.
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Uehara, Kiyohiko, and Kaoru Hirota. "Multi-Level Interpolation for Inference with Sparse Fuzzy Rules: An Extended Way of Generating Multi-Level Points." Journal of Advanced Computational Intelligence and Intelligent Informatics 17, no. 2 (March 20, 2013): 127–48. http://dx.doi.org/10.20965/jaciii.2013.p0127.
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As an extended way for inference based on multi-level interpolation, the number of multi-level points, generated with the α-cuts of given facts, is increased by making larger the number of levels of α. The conventional way uses the number of the levels adopted to define each given fact by α-cuts. A basic study is performed with triangular membership functions, where it is examined how the accuracy of mapping with fuzzy rules changes in increasing the number of the levels. It is also examined how deduced consequences behave when the number is increased. Moreover, convergent core sets of consequences are theoretically derived in the increase by the effective use of non-adaptive inference operations for core sets. They are used as references in simulation studies. Increasing the number of the levels provides nonlinear mapping with more precise reflection of distribution forms of sparse fuzzy rules to consequences. The basic study here contributes to improving the reflection accuracy. In simulations for the basic study, it is found that the mapping accuracy improves when the number of levels of α is increased. It is also confirmed that deduced core sets converge to those theoretically derived. Support sets are also found to converge in increasing the number of the levels. The core sets and support sets of deduced consequences do not, however, monotonically converge. This property causes difficulty in determining the optimized number of the levels so as to satisfy required mapping accuracy. In order to solve this problem, further discussions may be possible to theoretically derive convergent consequences and to use them in practical fields, in accordance with the theoretically derived core sets mentioned above.
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Lasserre, Jean B. "Level Sets and NonGaussian Integrals of Positively Homogeneous Functions." International Game Theory Review 17, no. 01 (March 2015): 1540001. http://dx.doi.org/10.1142/s0219198915400010.
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We investigate various properties of the sublevel set G = {x : g(x) ≤ 1} and the integration of h on this sublevel set when g and h are positively homogeneous functions (and in particular homogeneous polynomials). For instance, the latter integral reduces to integrating h exp (-g) on the whole space ℝn (a nonGaussian integral) and when g is a polynomial, then the volume of G is a convex function of the coefficients of g. We also provide a numerical approximation scheme to compute the volume of G or integrate h on G (or, equivalently to approximate the associated nonGaussian integral). We also show that finding the sublevel set {x : g(x) ≤ 1} of minimum volume that contains some given subset K is a (hard) convex optimization problem for which we also propose two convergent numerical schemes. Finally, we provide a Gaussian-like property of nonGaussian integrals for homogeneous polynomials that are sums of squares and critical points of a specific function.
Dissertations / Theses on the topic "Sets of points of a given property"
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Dyntarová, Miroslava. "Problémy žáků střední školy při řešení konstrukčních úloh." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-446397.
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Title: Problems of pupils of high school in solving geometric construction exercises Author: Miroslava Dyntarová Department: Department of Mathematics and Mathematical Education Supervisor: Mgr. Michal Zamboj, Ph.D., Department of Mathematics and Mathema- tical Education Abstract: The aim of this thesis is to reveal various errors and issues that high school students face in triangle construction problems. The thesis is divided into two parts for clarity. In the theoretical part we deal with construction problems in general and look into their various solution methods and formal procedures recommended by high school textbooks. Next, we focus on sets of points of a given property (that are part of the high school curriculum), give related denitions, basic properties and use cases. For better understanding of the demonstrated problems the thesis is lled with au- xiliary graphs made in the program GeoGebra. In the last chapter of the theoretical part, we introduce various problems that are expected to occur during geometry con- struction problem solving by students themselves. Those were the main focus of the following study. The preparation of the study, its implementation and subsequent ana- lysis of collected data is described in the practical part of the thesis. The study was conducted with 10 students....
Books on the topic "Sets of points of a given property"
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Logachev, Vladimir, Aleksandr Pastukhov, Viktor Korneev, Igor Kravchenko, Mikhail Erofeev, Aleksandr Kolomeychenko, and Dmitriy Petrovskiy. Basics of patent. ru: INFRA-M Academic Publishing LLC., 2017. http://dx.doi.org/10.12737/21945.
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The textbook sets out the basics of invention, patenting, rationalization, legal protection and methods of protection of intellectual and industrial property. The structure, rules of registration, procedure for filing and examination of applications for inventions, utility models, industrial designs and software products are given. Special attention is paid to the content and use of patent information, as well as to the economic aspects of inventive and rationalization activities. The issues of legal regulation of the sphere of intellectual activity and patent research are considered.
Meets the requirements of the Federal state educational standard of higher education of the latest generation.
For master's students studying in the field of training 35.04.06 "Agroengineering" and related specialties, as well as bachelors, graduate students, teachers, engineers and scientists who create innovative products and high technologies in research and production organizations.
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Hrushovski, Ehud, and François Loeser. Strongly stably dominated points. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0008.
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This chapter focuses on the properties of strongly stably dominated types over valued fields bases. In this setting, strong stability corresponds to a strong form of the Abhyankar property for valuations: the transcendence degrees of the extension coincide with those of the residue field extension. The chapter proves a Bertini type result and shows that the strongly stable points form a strict ind-definable subset Vsuperscript Number Sign of unit vector V. It then proves a rigidity statement for iso-definable Γ-internal subsets of maximal o-minimal dimension of unit vector V, namely that they cannot be deformed by any homotopy leaving appropriate functions invariant. The chapter also describes the closure of iso-definable Γ-internal sets in Vsuperscript Number Sign and proves that Vsuperscript Number Sign is exactly the union of all skeleta.
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Salverda, Wiemer, and Stefan Thewissen. How Has the Middle Fared in the Netherlands? A Tale of Stagnation and Population Shifts. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198807032.003.0009.
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This chapter sets out how inequality and real incomes across the distribution evolved in the Netherlands from the late 1970s through the economic Crisis. Inequality grew, though not dramatically, while wages showed remarkably little real increase. This meant that real income increases for households relied for the most part on the growth in female labour-force participation and in dual-income couples. The chapter highlights the major changes in population and household structures that underpinned the observed changes in household incomes at different points in the distribution. It also sets out key features of the institutional structures in the labour market and broader welfare state, and the centrality of the priority given to wage moderation and the maintenance of competitiveness in the growth model adopted throughout the period.
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Wüstholz, Gisbert, and Clemens Fuchs, eds. Arithmetic and Geometry. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691193779.001.0001.
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This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria—provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course contains recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces. The second course addresses the famous Pell equation—not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course originates in the Chowla–Selberg formula and relates values of the L-function for elliptic curves with the height of Heegner points on the curves. It proves the Gross–Zagier formula on Shimura curves and verifies the Colmez conjecture on average.
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Filppula, Markku, Juhani Klemola, and Devyani Sharma, eds. The Oxford Handbook of World Englishes. Oxford University Press, 2013. http://dx.doi.org/10.1093/oxfordhb/9780199777716.001.0001.
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As the most documented language in human history, English holds a unique key to unlocking some of the mysteries of that uniquely human endowment: language. Yet the field of World Englishes has remained somewhat marginal in linguistic theory and vice versa. This collection calls for more direct and mutually constructive engagement with current linguistic theories, questions, and methodologies. It aims to achieve this through a design that combines areal overviews, theoretical chapters, and case studies. The thirty-six chapters are divided into four thematic parts: Foundations, World Englishes and Linguistic Theory, Areal Profiles, and Case Studies. Part I sets out the complex history of the global spread of English, which has given rise to the extraordinary regional variation we see today. This is followed, in Part II, by chapters addressing the mutual relevance and importance of World Englishes and numerous theoretical subfields of Linguistics, ranging from phonology and syntax to sociolinguistics and language contact. Part III offers detailed accounts of the structure and social histories of specific varieties of English spoken across the globe, highlighting points of theoretical interest. The collection closes with a set of case studies that exemplify the type of analysis encouraged by the volume. As attention is focused on innovative work at the interface of dialect description and theoretical explanation, the book is more succinct in its treatment of applied themes, which are given complementary coverage in other works.
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Gamer, Michael. Oeuvre-Making and Canon-Formation. Edited by David Duff. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199660896.013.29.
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During the eighteenth century, the activities of oeuvre-making and canon-formation unquestionably—and increasingly—fed off one another. Much of the reason had to do with changing intellectual property regimes, which made the Statute of Anne law in Scotland by 1751 and in England by 1774. After these dates, publishers in each country could reprint the works of given authors both as stand-alone sets (oeuvres) and as parts of larger, national collections (canons). Between 1774 and 1824, enterprising booksellers did just that, with sales registering in the millions of copies. These publishers’ canons shaped how writers of the Romantic period thought about canonicity. In addition, their publications verify fundamental assumptions about the relative prestige of genres and the rivalries that exist between them, with poetry garnering the most cultural status, followed by drama, and then prose fiction.
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Cameron, Charles M., and Lewis A. Kornhauser. Theorizing the U.S. Supreme Court. Oxford University Press, 2017. http://dx.doi.org/10.1093/acrefore/9780190228637.013.264.
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We summarize the formal theoretical literature on Supreme Court decision-making. We focus on two core questions: What does the Supreme Court of the United States do, and how can one model those actions; and, what do the justices of the Supreme Court want, and how can one model those preferences? Given the current state of play in judicial studies, these questions then direct this survey mostly to so-called separation of powers (SOP) models, and to studies of a multi-member (“collegial”) court employing the Supreme Court’s very distinctive and highly unusual voting rule.The survey makes four main points. First, it sets out a new taxonomy that unifies much of the literature by linking judicial actions, modeling conventions, and the treatment of the status quo. In addition, the taxonomy identifies some models that employ inconsistent assumptions about Supreme Court actions and consequences. Second, the discussion of judicial preferences clarifies the links between judicial actions and judicial preferences. It highlights the relationships between preferences over dispositions, preferences over rules, and preferences over social outcomes. And, it explicates the difference between consequential and expressive preferences. Third, the survey delineates the separate strands of SOP models. It suggests new possibilities for this seemingly well-explored line of inquiry. Fourth, the discussion of voting emphasizes the peculiar characteristics of the Supreme Court’s voting rule. The survey maps the movement from early models that ignored the special features of this rule, to more recent ones that embrace its features and explore the resulting (and unusual) incentive effects.
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Streiner, David L., Geoffrey R. Norman, and John Cairney. Validity. Oxford University Press, 2015. http://dx.doi.org/10.1093/med/9780199685219.003.0010.
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In order for a scale to be useful, the user must be able to draw accurate conclusions about the presence or absence of the attribute being measured. This is the domain of validity. What validity is and how it is assessed has changed greatly over the past 40 years, although many who develop or validate scales are unaware of this. This chapter discusses what is meant by validity and how it is assessed. The major points are that: (1) validity is not a property of the test, but may change depending on the sample and the conditions under which the test is given, and (2) there are not different ‘types’ of validity—they are all various aspects of construct validity. The chapter also describes different types of studies that can establish construct validity.
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Sime, Stuart. A Practical Approach to Civil Procedure. Oxford University Press, 2019. http://dx.doi.org/10.1093/he/9780198838593.001.0001.
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A Practical Approach to Civil Procedure guides the reader through the procedural requirements employed in the civil courts. The volume provides an overview of the key statutory provisions, rules, practice directions, and case law which govern the various stages of a civil litigation claim. Providing practical guidance, the text charts the progress of a typical civil litigation claim, from funding litigation and issuing and serving proceedings, through to trial, enforcement, and appeal. Full coverage of alternative dispute resolution is also included. Relevant sample documentation is featured throughout and introduces the forms and documents which will be encountered in practice, while key points summaries featured at the end of chapters highlight the essential points covered. This edition has been revised to incorporate rule changes up to the Civil Procedure (Amendment) Rules 2019 and the 105th Update. Changes incorporated into the new edition include the pilot scheme for disclosure of documents in the Business and Property Courts. Among the many recent cases incorporated into the text are MacDonald v D & F Contracts Ltd which marks a departure from the traditional approach on whether it is possible to enter a default judgment after late filing of the defence; a number of cases on enforcing the undertakings in damages given in interim injunction applications, costs management and qualified one-way costs shifting, and Supreme Court decision on service against unnamed defendants in Cameron v Liverpool Insurance.
Book chapters on the topic "Sets of points of a given property"
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Fryszkowski, Andrzej. "Fixed points property." In Fixed Point Theory for Decomposable Sets, 139–40. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-2499-1_10.
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Fryszkowski, Andrzej. "Fixed points property for convex-valued mappings." In Fixed Point Theory for Decomposable Sets, 107–11. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-2499-1_7.
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Abate, Carmine, Roberto Blanco, Ștefan Ciobâcă, Adrien Durier, Deepak Garg, Cătălin Hrițcu, Marco Patrignani, Éric Tanter, and Jérémy Thibault. "Trace-Relating Compiler Correctness and Secure Compilation." In Programming Languages and Systems, 1–28. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44914-8_1.
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AbstractCompiler correctness is, in its simplest form, defined as the inclusion of the set of traces of the compiled program into the set of traces of the original program, which is equivalent to the preservation of all trace properties. Here traces collect, for instance, the externally observable events of each execution. This definition requires, however, the set of traces of the source and target languages to be exactly the same, which is not the case when the languages are far apart or when observations are fine-grained. To overcome this issue, we study a generalized compiler correctness definition, which uses source and target traces drawn from potentially different sets and connected by an arbitrary relation. We set out to understand what guarantees this generalized compiler correctness definition gives us when instantiated with a non-trivial relation on traces. When this trace relation is not equality, it is no longer possible to preserve the trace properties of the source program unchanged. Instead, we provide a generic characterization of the target trace property ensured by correctly compiling a program that satisfies a given source property, and dually, of the source trace property one is required to show in order to obtain a certain target property for the compiled code. We show that this view on compiler correctness can naturally account for undefined behavior, resource exhaustion, different source and target values, side-channels, and various abstraction mismatches. Finally, we show that the same generalization also applies to many secure compilation definitions, which characterize the protection of a compiled program against linked adversarial code.
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"Hierarchical Order II." In Boundedness and Self-Organized Semantics: Theory and Applications, 70–87. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-2202-9.ch004.
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The self-organization under boundedness is considered as an operational protocol, which describes the highly non-trivial interplay between the inter-level feedback and the spatio-temporal pattern that describes the corresponding homeostasis. A generic property of the feedback is that it sets metrics in the state space and defines the admissible transitions from any given state. Further, the state space is partitioned into basins-of-attraction so that each of them is tangent to the point called accumulation point. A distinctive property of the basins-of-attraction is that the discrete band of the power spectrum appears as intra-basin invariant and thus turns as appropriate candidate for a “letter.” The accumulation point is associated with the notion of a “space bar.” Then, since the motion in a bounded attractor is orbital, it is appropriate to associate a “word” with an orbit. The latter open the door for assigning a specific non-mechanical engine to each and every orbit. In turn the functional irreversibility of any engine substantiates the sensitivity to permutations of every semantic unit.
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West-Eberhard, Mary Jane. "Modularity." In Developmental Plasticity and Evolution. Oxford University Press, 2003. http://dx.doi.org/10.1093/oso/9780195122343.003.0009.
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Modularity, like the responsiveness that gives rise to it during development and evolution, is a universal property of living things and a fundamental determinant of how they evolve. Modularity refers to the properties of discreteness and dissociability among parts and integration within parts. There are many other words for the same thing, such as atomization (Wagner, 1995), individualization (Larson and Losos, 1996), autonomy (Nijhout, 1991b), dislocation (Schwanwitsch, 1924), decomposability (Wimsatt, 1981), discontinuity (Alberch, 1982), gene nets (Bonner, 1988), subunit organization (West-Eberhard, 1992a, 1996), compartments or compartmentation (Garcia-Bellido et al., 1979; Zuckerkandl, 1994; Maynard-Smith and Szathmary, 1995; Kirschner and Gerhart, 1998), and compartmentalization (Gerhart and Kirschner, 1997). One purpose of this chapter is to give consistent operational meaning to the concept of modularity in organisms. Seger and Stubblefield (1996, p. 118) note that organisms show “natural planes of cleavage” among organ systems, biochemical pathways, life stages, and behaviors that allow independent selection of different ones. They ask, “What determines where these planes of cleavage are located” and suggest that a “theory of organic articulations” may give insight into the laws of correlation, without specifying what the laws of articulation may be. Wagner (1995, p. 282) recognizes the importance of modularity and proposes a “building block” concept of homology where structural units often correspond to units of function, but concludes (after Rosenberg, 1985) that “there exists no way to distinguish an adequate from an inadequate atomization of the organisms.” Here I propose that modularity has a specific developmental basis (see also West-Eberhard, 1989, 1992a, 1996; see also Larson and Losos, 1996). Modular traits are subunits of the phenotype that are determined by the switches or decision points that organize development, whether of morphology, physiology, or behavior. Development can be seen as a branching series of decision points, including those caused by physical borders such as membranes or contact zones of growing or diffusing parts (e.g., see Meinhardt, 1982; see also chapter 5, on development). Each decision point demarcates the expression or use of a trait—a modular set—and subordinate branches demarcate lower level modular subunits, producing modular sets within modular sets.
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Riggsby, Andrew M. "Representing Three Dimensions." In Mosaics of Knowledge, 130–53. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780190632502.003.0005.
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Ancient painting made little or no use of single-point perspective. Some modern scholars, however, have inferred from this that ancient artists and audiences lacked a sense of “space.” This chapter’s three case studies (two involving fresco painting and one low-relief stucco, all in the genre generally known as sacro-idyllic landscape) argue instead for the existence a diversity of ways of encoding spatial information. The approaches are distinct, but they show family resemblances by drawing differentially from more or less the same pool of strategies (involving color coding, scaling, and foreshortening of objects of predictable size and shape, physical overlap, narrative connection, and others). In combination, these do not determine a single spatial reading for any given work of art, but they constrain the range of plausible approximations. That several superficially diverse sets of works converge on this property shows that spatiality was important to all of them.
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Lovejoy, Shaun. "How big is a cloud?" In Weather, Macroweather, and the Climate. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780190864217.003.0007.
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We have discussed two extreme views of atmospheric variability: the scalebound view, in which every factor of 10 or so involves some new mechanism or law; and the opposing self- similar scaling view, in which zooming gives us something essentially the same— a single mechanism or law that could hold over ranges of thousands or more. By considering time series and spatial transects, we saw that, over various ranges of scale in space and in time, atmospheric scaling seemed to work quite well. We looked at a complication: Interesting geophysical quantities are not simply black or white (geometric sets of points), but have gray shades; they have numerical values everywhere. To deal with the associated extreme variability and intermittency, we saw that we had to go beyond fractal sets to multifractal fields (Box 2.2). Understanding multifractals turned out to be important. Failure to appreciate their importance led to numerous deleterious consequences.1 In this chapter, I want to consider something quite different: the morphologies of shapes in two or three dimensions. Up until now, we have identified scaling with self- similarity, the property that, following a usual isotropic zoom (one that is the same in all directions), small parts resemble the whole in some way. Yet in Chapter 1 (Fig. 1.8A, B), we saw that zooming into lidar vertical sections uncovered morphologies that changed with scale. As we zoomed into flat, stratified layers, structures became visibly more “roundish” (compare Fig. 1.8A with Fig. 1.8B). Vertical sections are thus not self- similar. Their degree of stratification— anisotropy— changes systematically with scale. But the vertical isn’t the only place where self- similarity is unrealistic. Although it is not as obvious, the same difficulty arises if we zoom into clouds in the horizontal. We criticized Orlanski’s powers of ten classification as being arbitrary and in contradiction with the scaling area– perimeter relation, but Orlanski was only trying to update an older phenomenological classification scheme, some of which predated the twentieth century.
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Hale, Bob. "Properties, Predication, and Arbitrary Sets." In Essence and Existence, edited by Jessica Leech and Kit Fine, 225–39. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198854296.003.0014.
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Shapiro and Hale disagree over the appropriate domain of quantification for second-order logic: Shapiro allows property variables to range over the full power set of the first-order domain, whereas Hale restricts the domain to only subsets which can be defined. Hale defends his view, via a discussion of Shapiro’s view that objects in a domain of quantification need not be able to be objects of singular reference (for example, geometrical points and electrons). Shapiro’s view is clearly at odds with Hale’s favoured broadly Fregean approach to ontology, according to which objects are simply those things to which reference may be made by means of actual or possible singular terms.
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Wickens, Christopher D., and Polly Baker. "Cognitive Issues in Virtual Reality." In Virtual Environments and Advanced Interface Design. Oxford University Press, 1995. http://dx.doi.org/10.1093/oso/9780195075557.003.0024.
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Virtual reality involves the creation of multisensory experience of an environment (its space and events) through artificial, electronic means; but that environment incorporates a sufficient number of features of the non-artificial world that it is experienced as “reality.” The cognitive issues of virtual reality are those that are involved in knowing and understanding about the virtual environment (cognitive: to perceive and to know). The knowledge we are concerned with in this chapter is both short term (Where am I in the environment? What do I see? Where do I go and how do I get there?), and long term (What can and do I learn about the environment as I see and explore it?). Given the recent interest in virtual reality as a concept (Rheingold, 1991; Wexelblat, 1993; Durlach and Mavor, 1994), it is important to consider that virtual reality is not, in fact, a unified thing, but can be broken down into a set of five features, any one of which can be present or absent to create a greater sense of reality. These features consist of the following five points. 1. Three-dimensional (perspective and/or stereoscopic) viewing vs. two-dimensional planar viewing. (Sedgwick, 1986; Wickens et al., 1989). Thus, the geography student who views a 3D representation of the environment has a more realistic view than one who views a 2D contour map. 2. Dynamic vs. static display. A video or movie is more real than a series of static images of the same material. 3. Closed-loop (interactive or learner-centered) vs. open-loop interaction. A more realistic closed-loop mode is one in which the learner has control over what aspect of the learning “world” is viewed or visited. That is, the learner is an active navigator as well as an observer. 4. Inside-out (ego-referenced) vs. outside-in (world-referenced) frame-of-reference. The more realistic inside-out frame-of-reference is one in which the image of the world on the display is viewed from the perspective of the point of ego-reference of the user (that point which is being manipulated by the control). This is often characterized as the property of “immersion.” Thus, the explorer of a virtual undersea environment will view that world from a perspective akin to that of a camera placed on the explorer’s head;
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Azevedo, Isabel, and Nuno Malheiro. "Teaching Property-Based Testing." In Software Engineering for Agile Application Development, 230–50. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-2531-9.ch010.
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Given the large dimensions of software algorithms, the creation of unit test sets is both very difficult to use as an assurance of software quality and also very resource consuming. Some of the industry has already focused on this issue, and several methods are being used to cope with traditional testing shortcomings. Property-based testing has been one of these techniques and has been gaining traction, mainly due to the shift to functional programming techniques which can be seen in most of the popular languages and platforms. To give students tools that can increase the quality of their production as software developers, property-based testing has been taught in the Advanced Programming Techniques course of the master's program in Informatics Engineering of the Instituto Superior de Engenharia do Porto.
Conference papers on the topic "Sets of points of a given property"
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O’Neal, Matthew J., and Cameron J. Turner. "Reducing the Size of NURBs Controls Nets Using Genetic Algorithms and CUDA." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63739.
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The typical goals for defining a control net for a Non-Uniform Rations B-spline (NURBs) based metamodel from a given set of data the desired result is the smallest set of control points in the least possible time while minimizing local and/or global error. Current metamodel fitting algorithms iteratively find and eliminate the largest sources of local error, thus creating a very accurate control net with sub-optimal size. Since, control net size is directly related to the speed the control net can be searched for global optima, the size must be reduced as much as possible without increasing local or global error. Current algorithms can model discontinuous portions of data by clustering numerous control points close together. This is both inefficient to search and may cause the search algorithm to become numerically unstable and crash because of control points placed too closely together. Furthermore, many current algorithms do not take advantage of the weight property of each control point. In this paper, a Genetic Algorithm (GA) is used to optimize existing control nets as well as create new control nets from data sets. In order to offer a comparable creation time for the control net, parallel programming techniques are used incorporating the CUDA GPU Architecture. CUDA was chosen because it is low cost, highly parallel architecture available on millions of computers. The code is intended for a single desktop computer, running a maximum of 4 CUDA devices, not a CUDA cluster. This approach may have fitting applications to both metamodels and geometric fitting of NURBs objects.
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Park, Jungseo, Seunghwan Mun, Chungmin Hyun, Byungkwon Kang, and Kwanghee Ko. "Similarity Assessment Method for Automated Curved Plate Forming." In SNAME 5th World Maritime Technology Conference. SNAME, 2015. http://dx.doi.org/10.5957/wmtc-2015-240.
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In this paper, a novel similarity estimation method for two shapes in the automated thermal forming is proposed. One shape is given as a CAD surface, and the other is given as a set of points measured points. These two shapes are registered with respect to a reference coordinate system so that they are aligned as closely as possible using the ICP based method. Three geometric properties are considered in the method. The first property is the distance between them. At each measured point, the closest distance to the CAD surface is computed, and the defined tolerance for the distances is used as a similarity measure. The second measure is the average distance of the minimum distances to the CAD surface at the measured points. The third one is the average of the bending strain values at the measured points and at the points on the CAD surface that are orthogonal projection points of the measured ones. The proposed similarity is computed as the linear combination of the three properties with weight values, which are determined empirically. Extensive experiments show that the proposed similarity method successfully computes the similarity of a plate to its CAD shape in the forming process.
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Malik, Arif, John Sanders, Ramana Grandhi, and Mark Zipf. "Reliability-Based Optimal Cluster Mill Pass Scheduling." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62565.
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Optimal pass-scheduling on cluster-type cold rolling mills, use to process flat metals, presents added challenges over conventional (vertical-stack) mills due to the complexity of roll arrangements. Cluster-type rolling mills not only pose difficulties in modeling deflections occurring in the multi-roll stack, they also impose the burden of modeling more sophisticated mechanisms used to adjust rolling force distribution and achieve desired strip flatness. In a competitive global market for very thin gauge strip, an advantage is gained through use of efficient mathematical set-up models that can adequately optimize the flatness actuators according to the target gauge reductions for each rolling pass. The mill’s process control computer should therefore determine a gauge reduction schedule leading to minimum number of passes, while simultaneously assigning nominal flatness control actuator set-points. Although recent developments in roll-stack deflection modeling using simplified, mixed finite element techniques have enabled more efficient roll-stack deflection modeling in 20-high and other cluster mills, the optimal pass-schedule problem is still complicated by the abundance of geometric and mechanical property variations in the strip or sheet to be processed. Furthermore, problems with strip flatness frequently arise because of uncertainties in roll diameter profiles resulting from variations in the roll grinding and roll wear patterns. In this paper, we extend recent work in pass schedule optimization (through improved rollstack deflection) by applying First Order Reliability Methods to rigorously account for various rolling process uncertainties. The results allow predictive probability constraints for strip flatness to be included in the optimization problem, thus enabling mill operators some insight and control into the likelihood of achieving desired strip flatness for a given rolling pass schedule.
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Schutte, Jeffrey, Jimmy Tai, Jonathan Sands, and Dimitri Mavris. "Cycle Design Exploration Using Multi-Design Point Approach." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-69334.
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The focus of this study is to compare the aerothermodynamic cycle design space of a gas turbine engine generated using two on-design approaches. The traditional approach uses a single design point (SDP) for on-design cycle analysis, where off-design cycle analysis must be performed at other operating conditions of interest. A multi-design point (MDP) method performs on-design cycle analysis at all operating conditions where performance requirements are specified. Effects on the topography of the cycle design space as well as the feasibility of the space are examined. The impacts that performance requirements and cycle assumptions have on the bounds and topography of the feasible space are investigated. The deficiencies of a SDP method in determining an optimum gas turbine engine will be shown for a given set of requirements. Analysis will demonstrate that the MDP method, unlike the SDP method, always obtains a properly sized engine for a set of given requirements and cycle design variables, resulting in an increased feasible region of the aerothermodynamic cycle design space from which the optimum performance engine can be obtained.
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Aras, Eyyup. "From Discrete Vectors to Point Sets in Machining Simulations With High-Order Tool Surfaces." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13260.
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In vector based machining simulations sampling only along one direction misses surface portions, such as sharp edges and vertical walls. This drawback can be removed when sampling along multiple directions, even without increasing the number of vectors. Therefore, given the same total number of vectors, vector hits are likely to be better distributed over the surface in a multiple-rayrep model than in a single one. But in this case, although we have a better in-process workpiece representation, we face with another problem: computational expense in the vector/envelope intersections. Computations are easy when the workpiece is represented by unidirectional vectors and when the tool axis is positioned along these vectors. On the other hand, a more complicated situation occurs when the machining simulations are performed in the multiple-reyrep based environments with tools having high-order geometries. In this case, the extensive usage of nonlinear root finding algorithms makes machining simulations impractical. One solution might be to eliminate the variable representing a vector from calculations. This leads to a union of 3D-points (i.e. polyhedral, voxel and Octree representations), at the loss of accuracy. Therefore, from a geometric viewpoint we can consider the aggregate of 3D-points as a special version of the multiple-rayrep model, in which the orthogonal vectors are discretized. In this paper, first the above mentioned drawbacks are presented for the triple-vector model based environments with arbitrarily oriented tool surfaces. Later, since each NC sequence is described by using the toolpath parameter, the above problems are reduced to a single equation with collection of toolpath parameters for the given 3D-points. Since its geometric complexity is highest among other APT-type cutter surfaces, the toroidal surface is chosen for the analysis.
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Yue, Kai, Xinxin Zhang, and Fan Yu. "Noninvasive Measurement of Thermal Property Parameters of Cylindrical Living Tissues." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72592.
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A new noninvasive measurement method is proposed to simultaneously determine the thermal parameters of cylindrical living tissues. The corresponding two-dimensional mathematic model is established based on the Pennes’ bioheat transfer equation. With respect to the measuring points on the surface of the given living tissue, the effects of thermal parameters on the temperature variations, the sensitivity coefficients of the key thermal parameters to the model temperatures and the relativities of these sensitivity coefficients are analyzed and calculated. The results show that the thermal parameters concerned can be estimated with high measuring precision and can be simultaneously estimated. The experimental system of the dynamic tissue phantom is established to validate the presented method. A number of experiments are carried out under different conditions and the experimental results indicate that the measured parameters are in good agreement with the reference values.
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Vance, Judy M., and Denis Dorozhkin. "Constraint-Based Synthesis of Shape-Morphing Structures in Virtual Reality." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29017.
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This manuscript outlines a novel approach to the design of compliant shape-morphing structures using constraint-based design method. Development of robust methods for designing shape-morphing structures is the focus of multiple current research projects, since the ability to modify geometric shapes of the individual system components, such as aircraft wings and antenna reflectors, provides the means to affect the performance of the corresponding mechanical systems. Of particular interest is the utilization of compliant mechanisms to achieve the desired adaptive shape change characteristics. Compliant mechanisms, as opposed to the traditional rigid link mechanisms, achieve motion guidance via the compliance and deformation of the mechanism’s members. The goal is to design a single-piece flexible structure capable of morphing a given curve or profile into a target curve or profile while utilizing the minimum number of actuators. The two primary methods prevalent in the design community at this time are the pseudo-rigid body method (PRBM) and the topological synthesis. Unfortunately these methods either tend to suffer from a poor ability to generate potential solutions (being more suitable for the analysis of existing structures) or are susceptible to overly-complex solutions. By utilizing the constraint-based design method (CBDM) we aim to address those shortcomings. The concept of CBDM has generally been confined to the Precision Engineering community and is based on the fundamental premise that all motions of a rigid body are determined by the position and orientation of the constraints (constraint topology) which are placed upon the body. Any mechanism motion path may then be defined by the proper combination of constraints. In order to apply the CBDM concepts to the design and analysis of shape-morphing compliant structures we propose a tiered design method that relies on kinematics, finite element analysis, and optimization. By discretizing the flexible element that comprises the active shape surface at multiple points in both the initial and the target configurations and treating the resulting individual elements as rigid bodies that undergo a planar or general spatial displacement we are able to apply the traditional kinematics theory to rapidly generate sets of potential solutions. The final design is then established via an FEA-augmented optimization sequence. Coupled with a virtual reality interface and a force-feedback device this approach provides the ability to quickly specify and evaluate multiple design problems in order to arrive at the desired solution.
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Shibakov, Alexander, Stephen L. Canfield, and Patrick V. Hull. "Multivariate Parameter Sets for Optimal Synthesis of Compliant Mechanisms." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85379.
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This paper will propose the use of control maps along with discretized elements or meshes in the design parameter set for optimizing compliant mechanisms. The use of control maps will be demonstrated to encode the motion of groups of nodes or control points defining the mesh with simple mapping rules. The technique will serve as an alternative to increased mesh size or node wandering techniques that have been proposed to increase the number of alternative design shapes that may be considered. As an alternative approach, the proposed control map parameterization has the significant benefit that it minimizes the number of design parameters necessary (parameters increase linearly with the mesh size) in describing a given design making it computationally efficient. A limited number of tiles can produce a map that has a significant effect on the final shape. If the tiles are chosen appropriately, the problems such as material overlap and non-convex mesh elements are avoided automatically. This paper will describe the implementation of these control maps and provide several examples showing their implementation in the compliant mechanism topology synthesis process.
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Brown, Travis L., Tariq D. Aslam, and James P. Schmiedeler. "Determination of Minimum Time Rendezvous Points for Multiple Mobile Robots via Level Set Methods." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48282.
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This paper addresses the problem of finding the minimum time rendezvous point for a geographically distributed group of heterogeneous mobile robots. In contrast to the traditional treatment of the multi-agent rendezvous problem, focus is given mainly to the identification of the globally optimal solution rather than the behavior of the system based on a given control policy. Level sets are introduced as a tool to solve this problem by first computing an arrival time map for each robot, subject to speed, terrain, and dynamic constraints. The computation is parallelizable by requiring each agent to generate its own arrival time map. The arrival time maps can be easily combined to give the overall minimum time rendezvous point. Despite the apparent simplicity of this approach, it is capable of accommodating numerous complicating factors with minimal modification while simultaneously generating a target path trajectory for each robot through the state-space. Examples involving ground, sea, and air robots are used to illustrate the power of this technique.
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Schäfer, Felicitas, Shuai Guo, and Wolfgang Polifke. "The Impact of Exceptional Points on the Reliability of Thermoacoustic Stability Analysis." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-15496.
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Abstract Exceptional points can be found for specific sets of parameters in thermoacoustic systems. At an exceptional point, two eigenvalues and their corresponding eigenfunctions coalesce. Given that the sensitivity of these eigenvalues to parameter changes becomes infinite at the exceptional point, their occurrence may greatly affect the outcome and reliability of numerical stability analysis. We propose a new method to identify exceptional points in thermoacoustic systems. By iteratively updating the system parameters, two initially selected eigenvalues are shifted towards each other, ultimately colliding and generating the exceptional point. Using this algorithm, we were able to identify for the first time a physically meaningful exceptional point with positive growth rate in a thermoacoustic model. Furthermore, our analysis goes beyond previous studies inasmuch as we employ a more realistic flame transfer function to model flame dynamics. Building on these results, we analyze the effect of exceptional points on the reliability of thermoacoustic stability analysis. In the context of uncertainty quantification, we show that surrogate modeling is not reliable in the vicinity of an exceptional point, even when large sets of training samples are provided. The impact of exceptional points on the propagation of input uncertainties is demonstrated via Monte Carlo computations. The increased sensitivity associated with the exceptional point results in large variances for eigenvalue predictions, which needs to be taken into account for reliable stability analysis.
Reports on the topic "Sets of points of a given property"
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Kaffenberger, Michelle, and Lant Pritchett. Women’s Education May Be Even Better Than We Thought: Estimating the Gains from Education When Schooling Ain’t Learning. Research on Improving Systems of Education (RISE), September 2020. http://dx.doi.org/10.35489/bsg-rise-wp_2020/049.
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Women’s schooling has long been regarded as one of the best investments in development. Using two different cross-nationally comparable data sets which both contain measures of schooling, assessments of literacy, and life outcomes for more than 50 countries, we show the association of women’s education (defined as schooling and the acquisition of literacy) with four life outcomes (fertility, child mortality, empowerment, and financial practices) is much larger than the standard estimates of the gains from schooling alone. First, estimates of the association of outcomes with schooling alone cannot distinguish between the association of outcomes with schooling that actually produces increased learning and schooling that does not. Second, typical estimates do not address attenuation bias from measurement error. Using the new data on literacy to partially address these deficiencies, we find that the associations of women’s basic education (completing primary schooling and attaining literacy) with child mortality, fertility, women’s empowerment and the associations of men’s and women’s basic education with positive financial practices are three to five times larger than standard estimates. For instance, our country aggregated OLS estimate of the association of women’s empowerment with primary schooling versus no schooling is 0.15 of a standard deviation of the index, but the estimated association for women with primary schooling and literacy, using IV to correct for attenuation bias, is 0.68, 4.6 times bigger. Our findings raise two conceptual points. First, if the causal pathway through which schooling affects life outcomes is, even partially, through learning then estimates of the impact of schooling will underestimate the impact of education. Second, decisions about how to invest to improve life outcomes necessarily depend on estimates of the relative impacts and relative costs of schooling (e.g., grade completion) versus learning (e.g., literacy) on life outcomes. Our results do share the limitation of all previous observational results that the associations cannot be given causal interpretation and much more work will be needed to be able to make reliable claims about causal pathways.