Relevant bibliographies by topics / Graphical calculus

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Graphical calculus'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 April 2022

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Journal articles on the topic "Graphical calculus"

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Lanese, Ivan, and Ugo Montanari. "A Graphical Fusion Calculus." Electronic Notes in Theoretical Computer Science 104 (November 2004): 199–215. http://dx.doi.org/10.1016/j.entcs.2004.08.026.

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BIAN, Xiaoning, and Quanlong WANG. "Graphical Calculus for Qutrit Systems." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E98.A, no. 1 (2015): 391–99. http://dx.doi.org/10.1587/transfun.e98.a.391.

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FIORENZA, DOMENICO, and RICCARDO MURRI. "FEYNMAN DIAGRAMS VIA GRAPHICAL CALCULUS." Journal of Knot Theory and Its Ramifications 11, no. 07 (November 2002): 1095–131. http://dx.doi.org/10.1142/s0218216502002165.

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We use Reshetikhin-Turaev graphical calculus to define Feynman diagrams and prove that asymptotic expansions of Gaussian integrals can be written as a sum over a suitable family of graphs. We discuss how different kinds of interactions give rise to different families of graphs. In particular, we show how symmetric and cyclic interactions lead to "ordinary" and "ribbon" graphs respectively. As an example, the 't Hooft-Kontsevich model for 2D quantum gravity is treated in some detail.
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Khovanov, Mikhail. "Heisenberg algebra and a graphical calculus." Fundamenta Mathematicae 225, no. 1 (2014): 169–210. http://dx.doi.org/10.4064/fm225-1-8.

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Alves, Sandra, Maribel Fernández, and Ian Mackie. "A new graphical calculus of proofs." Electronic Proceedings in Theoretical Computer Science 48 (February 11, 2011): 69–84. http://dx.doi.org/10.4204/eptcs.48.8.

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KAUFFMAN, LOUIS H., and PIERRE VOGEL. "LINK POLYNOMIALS AND A GRAPHICAL CALCULUS." Journal of Knot Theory and Its Ramifications 01, no. 01 (March 1992): 59–104. http://dx.doi.org/10.1142/s0218216592000069.

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This paper constructs invariants of rigid vertex isotopy for graphs embedded in three dimensional space. For the Homfly and Dubrovnik polynomials, the skein formalism for these invariants is as shown below. Homfly. [Formula: see text] Dubrovnik. [Formula: see text]
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Gowrisankar, Arulprakash, Alireza Khalili Golmankhaneh, and Cristina Serpa. "Fractal Calculus on Fractal Interpolation Functions." Fractal and Fractional 5, no. 4 (October 8, 2021): 157. http://dx.doi.org/10.3390/fractalfract5040157.

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In this paper, fractal calculus, which is called Fα-calculus, is reviewed. Fractal calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non-differentiable and non-integrable in the sense of ordinary calculus. Graphical representations of fractal calculus of fractal interpolation functions and Weierstrass functions are presented.
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Berry, John S., and Melvin A. Nyman. "Promoting students’ graphical understanding of the calculus." Journal of Mathematical Behavior 22, no. 4 (January 2003): 479–95. http://dx.doi.org/10.1016/j.jmathb.2003.09.006.

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Lu, Xuexing, Yu Ye, and Sen Hu. "A Graphical Calculus for Semi-Groupal Categories." Applied Categorical Structures 27, no. 2 (November 19, 2018): 163–97. http://dx.doi.org/10.1007/s10485-018-9549-8.

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Kim, Joon-Hwi, Maverick S. H. Oh, and Keun-Young Kim. "Boosting vector calculus with the graphical notation." American Journal of Physics 89, no. 2 (February 2021): 200–209. http://dx.doi.org/10.1119/10.0002142.

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Dissertations / Theses on the topic "Graphical calculus"

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Zhou, Y. "A graphical calculus : extension, implication and application." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365370.

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Kim, Dongseok. "Graphical calculus on representations of quantum Lie algebras /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2003. http://uclibs.org/PID/11984.

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Hagge, Tobias J. "Graphical calculus for fusion categories and quantum invariants for 3-manifolds." [Bloomington, Ind.] : Indiana University, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3334995.

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Backens, Miriam K. "Completeness and the ZX-calculus." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:0120239e-b504-4376-973d-d720a095f02e.

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Graphical languages offer intuitive and rigorous formalisms for quantum physics. They can be used to simplify expressions, derive equalities, and do computations. Yet in order to replace conventional formalisms, rigour alone is not sufficient: the new formalisms also need to have equivalent deductive power. This requirement is captured by the property of completeness, which means that any equality that can be derived using some standard formalism can also be derived graphically. In this thesis, I consider the ZX-calculus, a graphical language for pure state qubit quantum mechanics. I show that it is complete for pure state stabilizer quantum mechanics, so any problem within this fragment of quantum theory can be fully analysed using graphical methods. This includes questions of central importance in areas such as error-correcting codes or measurement-based quantum computation. Furthermore, I show that the ZX-calculus is complete for the single-qubit Clifford+T group, which is approximately universal: any single-qubit unitary can be approximated to arbitrary accuracy using only Clifford gates and the T-gate. In experimental realisations of quantum computers, operations have to be approximated using some such finite gate set. Therefore this result implies that a wide range of realistic scenarios in quantum computation can be analysed graphically without loss of deductive power. Lastly, I extend the use of rigorous graphical languages outside quantum theory to Spekkens' toy theory, a local hidden variable model that nevertheless exhibits some features commonly associated with quantum mechanics. The toy theory for the simplest possible underlying system closely resembles stabilizer quantum mechanics, which is non-local; it thus offers insights into the similarities and differences between classical and quantum theories. I develop a graphical calculus similar to the ZX-calculus that fully describes Spekkens' toy theory, and show that it is complete. Hence, stabilizer quantum mechanics and Spekkens' toy theory can be fully analysed and compared using graphical formalisms. Intuitive graphical languages can replace conventional formalisms for the analysis of many questions in quantum computation and foundations without loss of mathematical rigour or deductive power.
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Stiles, Nancy L. Hathway Robert G. "Graphing calculators and calculus." Normal, Ill. Illinois State University, 1994. http://wwwlib.umi.com/cr/ilstu/fullcit?p9510432.

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Thesis (D.A.)--Illinois State University, 1994.
Title from title page screen, viewed March 31, 2006. Dissertation Committee: Robert G. Hathway (chair), Lynn H. Brown, John A. Dossey, Arnold J. Insel, Patricia H. Klass. Includes bibliographical references (leaves 33-34) and abstract. Also available in print.
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Prokopová, Dagmar. "Vizualizace výrazů procesní algebry pi-kalkul." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2017. http://www.nusl.cz/ntk/nusl-363857.

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This work deals with the problem of visual representation of Pi-calculus expressions. The theoretical part of this paper discusses general principles of process algebras as well as specific properties of individual models, with a focus on Pi-calculus. Also included is the comparison of several text and graphical representations of expressions. The main part of the thesis deals with the design and implementation of an application for converting text representation of expressions into graphical representation. In addition to the text and graphical representation, an internal tree representation designed to work with expressions within the application is also proposed. The thesis also describes algorithms for finding feasible reductions, performing reductions and expression simplification that operate with the proposed tree representation.
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Maldonado, Aldo Rene. "Conversations with Hypatia : the use of computers and graphing calculators in the formulation of mathematical arguments in college calculus /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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Tall, David Orme. "Building and testing a cognitive approach to the calculus using interactive computer graphics." Thesis, University of Warwick, 1986. http://wrap.warwick.ac.uk/2409/.

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This thesis consists of a theoretical building of a cognitive approach to the calculus and an empirical testing of the theory in the classroom. A cognitive approach to the teaching of a knowledge domain is defined to be one that aims to make the material potentially meaningful at every stage (in the sense of Ausubel). As a resource in such an approach, the notion of a generic organiser is introduced (after Dienes), which is an environment enabling the learner to explore examples of mathematical processes and concepts, providing cognitive experience to assist in the abstraction of higher order concepts embodied by the organiser. This allows the learner to build and test concepts in a mode 1 environment (in the sense of Skemp) rather than the more abstract modes of thinking typical in higher mathematics. The major hypothesis of the thesis is that appropriately designed generic organisers, supported by an appropriate learning environment, are able to provide students with global gestalts for mathematical processes and concepts at an earlier stage than occurs with current teaching methods. The building of the theory involves an in-depth study of cognitive development, of the cultural growth and theoretical content of the mathematics, followed by the design and programming of appropriate organisers for the teaching of the calculus. Generic organisers were designed for differentiation (gradient of a graph), integration (area), and differential equations, to be coherent ends in themselves as well as laying foundations for the formal theories of both standard and non-standard analysis. The testing is concerned with the program GRADIENT, which is designed to give a global gestalt of the dynamic concept of the gradient of a graph. Three experimental classes (one taught by the researcher in conjunction with the regular class teacher) used the software as an adjunct to the normal study of the calculus and five other classes acted as controls. Matched pairs were selected on a pre-test for the purpose of statistical comparison of performance on the post-test. Data was also collected from a third school where the organisers functioned less well, and from university mathematics students who had not used a computer. The generic organiser GRADIENT, supported by appropriate teaching, enabled the experimental students to gain a global gestalt of the gradient concept. They were able to sketch derivatives. for given graphs significantly better than the controls on the post-test, at a level comparable with more able students reading mathematics at university. Their conceptualizations of gradient and tangent transferred to a new situation involving functions given by different formulae on either side of the point in question, performing significantly better than the control students and at least as well, or better, than those at university.
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Brumberg, Marsha. "A study of the impact graphing calculators have on the achievement in high school pre calculus /." Full text available online, 2007. http://www.lib.rowan.edu/find/theses.

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Ng, Ho Lun. "ROD-TV : surface reconstruction on demand by tensor voting /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?COMP%202003%20NG.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003.
Includes bibliographical references (leaves 123-127). Also available in electronic version. Access restricted to campus users.
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Books on the topic "Graphical calculus"

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Finney, Ross L. Calculus: Graphical, Numerical, Algebraic. Menlo Park, Calif: Scott Foresman/Addison-Wesley, 1999.

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Ostebee, Arnold. Calculus: From graphical, numerical and symbolic points of view. Fort Worth, TX: Saunders College Pub, 1997.

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1951-, Zorn Paul, ed. Calculus: From graphical, numerical and symbolic points of view. Fort Worth, TX: Saunders College Pub, 1997.

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Extended graphical calculus for categorified quantum sl(2). Providence, R.I: American Mathematical Society, 2011.

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Ostebee, Arnold. Instructor's resource manual Calculus from graphical, numerical, and symbolic points of view. Fort Worth: Saunders College Pub., 1996.

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Ostebee, Arnold. Calculus from graphical, numerical, and symbolic points of view. Fort Worth, TX: Harcourt College Pub., 1997.

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1951-, Zorn Paul, ed. Calculus from graphical, numerical, and symbolic points of view. Fort Worth: Saunders College Pub., 1997.

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Paul, Zorn, ed. Calculus from graphical, numerical, and symbolic points of view. Fort Worth: Saunders College Publishing, 1994.

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1951-, Zorn Paul, ed. Calculus from graphical, numerical, and symbolic points of view. 2nd ed. Fort Worth: Harcourt College Publishers, 2002.

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1951-, Zorn Paul, ed. Calculus from graphical, numerical, and symbolic points of view. Fort Worth: Saunders College Pub., 1997.

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Book chapters on the topic "Graphical calculus"

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Curtis, Sharon, and Gavin Lowe. "A graphical calculus." In Lecture Notes in Computer Science, 214–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60117-1_12.

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Turaev, Vladimir, and Alexis Virelizier. "The graphical calculus." In Monoidal Categories and Topological Field Theory, 31–51. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_2.

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Coecke, Bob, and Ross Duncan. "Tutorial: Graphical Calculus for Quantum Circuits." In Reversible Computation, 1–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36315-3_1.

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Milner, Robin. "Pi-nets: A graphical form of π-calculus." In Programming Languages and Systems — ESOP '94, 26–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-57880-3_2.

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Phillips, Andrew, Luca Cardelli, and Giuseppe Castagna. "A Graphical Representation for Biological Processes in the Stochastic pi-Calculus." In Lecture Notes in Computer Science, 123–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11905455_7.

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Vilmart, Renaud. "The Structure of Sum-Over-Paths, its Consequences, and Completeness for Clifford." In Lecture Notes in Computer Science, 531–50. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71995-1_27.

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AbstractWe show that the formalism of “Sum-Over-Path” (SOP), used for symbolically representing linear maps or quantum operators, together with a proper rewrite system, has the structure of a dagger-compact PROP. Several consequences arise from this observation:– Morphisms of SOP are very close to the diagrams of the graphical calculus called ZH-Calculus, so we give a system of interpretation between the two– A construction, called the discard construction, can be applied to enrich the formalism so that, in particular, it can represent the quantum measurement.We also enrich the rewrite system so as to get the completeness of the Clifford fragments of both the initial formalism and its enriched version.
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Ostebee, Arnold. "Symbolic Computation Systems and Algebraic, Graphical, and Numerical Viewpoints in Elementary Calculus." In Advanced Educational Technologies for Mathematics and Science, 565–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-02938-1_20.

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Vince, John. "Calculus: Derivatives." In Mathematics for Computer Graphics, 373–429. London: Springer London, 2017. http://dx.doi.org/10.1007/978-1-4471-7336-6_15.

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Vince, John. "Calculus: Integration." In Mathematics for Computer Graphics, 431–70. London: Springer London, 2017. http://dx.doi.org/10.1007/978-1-4471-7336-6_16.

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Vince, John. "Integral Calculus." In Calculus for Computer Graphics, 93–120. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11376-6_7.

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Conference papers on the topic "Graphical calculus"

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Santiago Acosta, Rubén Darío, Ernesto Manuel Hernández Cooper, Rafael Martínez Martínez, and Sergio Rogelio Morales Vargas. "COMPLEX VARIABLE CALCULUS THROUGH GRAPHICAL INTERACTIVE UNITS." In 12th annual International Conference of Education, Research and Innovation. IATED, 2019. http://dx.doi.org/10.21125/iceri.2019.2788.

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Garcia Zugasti, Pedro de Jesus, José de Jesús Navarro Delgado, Hugo I. Medellín Castillo, Carlos Valdez Dávila, and Juan Gabriel Sandoval Granja. "New Expression for a Blanking Force Calculus of a Cospel Using a Die Matrix Angled." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52215.

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Frequently it is desired to calculate the blanking shear force of a cospel using an angled matrix as main characteristics of the cutting die. There are two reasons that support the development of this calculation: the first is that the product may change its shape or material, which makes necessary to modify the operating parameters according to the geometric size and metal composition changes. The second is that the nominal capacity of the working press is established by the manufacturer and cannot be altered to adapt to a new product, this means that any new product parameters must be adapted to the capabilities of the machine. Also, the force equation must contain the main variables of the product and not just “proportions” or “factors”, allowing a better approximation of the cutting operation. In this work, a new expression for the blanking force calculus of a cospel is obtained, based on the geometric characteristics of the cutting die (punch and matrix). A matrix die angled is considered as a main characteristic of the sheet metal cutting die, maintaining the punch geometry without cut angles. Two formulas derived from analytical and graphical proposed methods are used and several blanking tests were conducted with a die designed and fabricated properly to run the laboratory tests. The graphical methods are based on a projected area of the metal cospel, obtained from the three dimensional cospel area to cut, this two dimensional projected area is utilized in the expression for the cutting force calculus. On the other hand, the analytical approach considers an area limited from a mathematical equation obtained from a model based on the geometry regions of the blanking die; this area has also utilized as the shear area in the cutting force calculus of a metal cospel. The experimental procedure consisted in reproduce the blanking operation of several metal cospels using the designed and fabricated die. The cutting force was measured using three different matrix die angles probed during the blanking tests, maintaining the same cut angle of the punch during the tests. The tests results were compared with both analytical and graphical methods showing good agreement. Similarly, the cutting force was calculated with analytical and experimental expressions obtained from the specialized literature in order to determine the degree of accuracy of the calculations.
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Ulazia, Alain, and Gabriel Ibarra-Berastegi. "Study of ocean and wind energy potential with R: an innovative experience in the classroom." In HEAd'16 - International Conference on Higher Education Advances. Valencia: Universitat Politècnica València, 2016. http://dx.doi.org/10.4995/head16.2016.2421.

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Abstract The Engineer School of Eibar initiated the Grade of Engineering in Renewable Energies four years ago. This pioneering educational project has shown many challenges to the teachers of the new grade. Among the different software skills used in this project, R programming language has been a very important one because of its capacity for spatio-temporal analysis and graphical visualization of wind energy and wave energy potential. A quarter of the subject's program in Wind Energy and Ocean Energy has been used via Problem Based Learning for the application of statistical calculus with R. The aim of this contribution is to show some paradigmatic problems solved by the students and the results obtained. Finally, the opinion of the students about the use of R and its learning potentiality have been gathered and analysed.
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Correa, Juan D., and Elias Bareinboim. "From Statistical Transportability to Estimating the Effect of Stochastic Interventions." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/230.

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Learning systems often face a critical challenge when applied to settings that differ from those under which they were initially trained. In particular, the assumption that both the source/training and the target/deployment domains follow the same causal mechanisms and observed distributions is commonly violated. This implies that the robustness and convergence guarantees usually expected from these methods are no longer attainable. In this paper, we study these violations through causal lens using the formalism of statistical transportability [Pearl and Bareinboim, 2011] (PB, for short). We start by proving sufficient and necessary graphical conditions under which a probability distribution observed in the source domain can be extrapolated to the target one, where strictly less data is available. We develop the first sound and complete procedure for statistical transportability, which formally closes the problem introduced by PB. Further, we tackle the general challenge of identification of stochastic interventions from observational data [Sec.~4.4, Pearl, 2000]. This problem has been solved in the context of atomic interventions using Pearl's do-calculus, which lacks complete treatment in the stochastic case. We prove completeness of stochastic identification by constructing a reduction of any instance of this problem to an instance of statistical transportability, closing the problem.
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Konopatskiy, Evgeniy, and Andrey Bezditnyi. "Solid Modeling of Geometric Objects in Point Calculus." In 31th International Conference on Computer Graphics and Vision. Keldysh Institute of Applied Mathematics, 2021. http://dx.doi.org/10.20948/graphicon-2021-3027-666-672.

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The paper describes an approach to solid modeling of geometric objects in the form of an organized three-parameter set of points in three-dimensional space. The relevance of the research topic is due to the widespread use of solid-state models in various branches of science and technology, mechanical engineering, construction and medicine. Solid-state computer models are currently one of the basic computer graphics tools and an integral part of computer- aided design and calculation systems. It is widely used as one of the control elements of CNC machines and 3D printing, the development of information systems in the design and construction of buildings and structures, finite element calculations of deformed states in aircraft and mechanical engineering, their manufacture in medicine, etc. The choice of point calculus as a mathematical apparatus for the analytical description of solid models of geometric objects is substantiated. Examples of modeling sets of elliptical bodies and toroidal bodies in a simplex of three-dimensional space are given.
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Nuntawisuttiwong, Taweechai, and Natasha Dejdumrong. "An Educational Game for Learning Calculus." In 2011 Eighth International Conference on Computer Graphics, Imaging and Visualization (CGIV). IEEE, 2011. http://dx.doi.org/10.1109/cgiv.2011.34.

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Karimi, Amir. "A Freshman Engineering Education Experience." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43664.

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This paper describes a freshman engineering educational experience at The University of Texas at San Antonio (UTSA). It highlights the first year engineering curriculum and an academic support system that is designed for student success during the freshman year. Traditional course work in calculus, chemistry, calculus based physics, introductions to engineering, engineering graphics, and writing courses are a part of the freshman engineering curriculum. The university offers a number of academic support programs to help freshman students a smooth transition from high school to college life. A Freshmen Seminar course, which is designed to enhance students’ educational experiences during the freshman year, is an important element of the university’s academic support system. This paper briefly describes the content of an introductory course in engineering and the Freshman Seminar. It also describes some of the programs within the university that are implemented to improve student success during the freshman year.
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Bortolossi, Humberto, and David Pinho. "Obtaining the equation of the bivariate least squares regression line in high school using only quadratic functions." In Advances in Statistics Education: Developments, Experiences, and Assessments. International Association for Statistical Education, 2015. http://dx.doi.org/10.52041/srap.15114.

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In this paper, following and adapting the ideas of Casella & Berger (2002) and Niven (1981), we present, using only quadratic functions, a simple derivation of the formulas for the coefficients of the bivariate least squares regression line. Therefore, this approach is very suitable for High School students when Calculus and Linear Algebra are not available (as it is the case of Brazil and other countries). We also present an interactive companion GeoGebra applet to enhance graphically and algebraically the keys ideas.
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"PARALLEL SOLVERS COMPARISON FOR AN INVERSE PROBLEM IN FRACTIONAL CALCULUS." In 14th International Conference on Computer Graphics, Visualization, Computer Vision and Image Processing. IADIS Press, 2020. http://dx.doi.org/10.33965/tpmc2020_202011l024.

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Al-Haddad, Tristan, Keyan Rahimzadeh, and Jill Fredrickson. "Concrete Continuum: Concept, Calculus, Andamp; Construction Connected Through Parametric Representation." In XVII Conference of the Iberoamerican Society of Digital Graphics - SIGraDi: Knowledge-based Design. São Paulo: Editora Edgard Blücher, 2013. http://dx.doi.org/10.5151/despro-sigradi2013-0042.

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