Examinando por Materia "Computation theory"
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Ítem Combining interactive and automatic reasoning in first order theories of functional programs(SPRINGER, 2012-01-01) Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónWe propose a new approach to the computer-assisted verification of functional programs. We work in first order theories of functional programs which are obtained by extending Aczel's first order theory of combinatory formal arithmetic with positive inductive and coinductive predicates. Rather than building a special purpose system we implement our theories in Agda, a proof assistant for dependent type theory which can be used as a generic theorem prover. Agda provides support for interactive reasoning by encoding first order theories using the formulae-as-types principle. Further support is provided by off-the-shelf automatic theorem provers for first order logic which can be called by a program which translates Agda representations of first order formulae into the TPTP language understood by the provers. We show some examples where we combine interactive and automatic reasoning, covering both proof by induction and coinduction. © 2012 Springer-Verlag Berlin Heidelberg.Ítem Efficient solution for the diffraction of elastic SH waves by a wedge: Performance of various exact, asymptotic and simplified solutions(Elsevier Ltd, 2017-04-01) Aristizabal, V.H.; Velez, F.J.; Jaramillo, J.D.; Mecánica AplicadaThe diffraction of horizontally polarized shear waves by a semi-infinite wedge in frequency and time domains is studied. In particular, this work focus on the performance of different solutions, including the classical contributions from Macdonald, Sommerfeld and Kouyoumjian & Pathak. In addition, two fully analytical, simplified solutions are proposed using arguments from the so-called geometrical theory of diffraction. The main advantage of the two proposed solutions is the fact that the resulting solutions can be scaled to problems with arbitrary and complex geometries. Moreover, it is found that one of the proposed new solutions is highly efficient in terms of accuracy and computational speed as compared to alternative formulations (approximately 1000 times faster than the Macdonald and Kouyoumjian & Pathak solutions), thus, this important characteristic renders this solution ideal for implementation in GPUs (Graphics Processor Units) for multiscale modeling applications. © 2017 Elsevier LtdÍtem Exploring Undergraduate Students' Computational Modeling Abilities and Conceptual Understanding of Electric Circuits(Institute of Electrical and Electronics Engineers Inc., 2018-08-01) Ortega-Alvarez J.D.; Sanchez W.; Magana A.J.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de ProcesosContribution: This paper adds to existing literature on teaching basic concepts of electricity using computer-based instruction; findings suggest that students can develop an accurate understanding of electric circuits when they generate multiple and complementary representations that build toward computational models. Background: Several studies have explored the efficacy of computer-based, multi-representational teaching of electric circuits for novice learners. Existing research has found that instructional use of computational models that move from abstract to concrete representations can foster students' comprehension of electric circuit concepts, but other features of effective instruction using computational models need further investigation. Research Questions: 1) Is there a correlation between students' representational fluency and their ability to reason qualitatively on electric circuits? and 2) Is the quality of student-generated computational representations correlated to their conceptual understanding of electric circuits? Methodology: The study comprised two cases in which 51 sophomore-engineering students completed a voluntary assignment designed to assess their representational fluency and conceptual understanding of electric circuits. Qualitative insights from the first case informed the design of a scoring rubric that served as both the assessment and the data collection instrument. Findings: The results suggest that a multi-representational approach aimed at the construction of computational models can foster conceptual understanding of electric circuits. The number and quality of students' representations showed a positive correlation with their conceptual understanding. In particular, the quality of the computational representations was found to be highly, and significantly, correlated with the correctness of students' answers to qualitative reasoning questions. © 1963-2012 IEEE.Ítem Implementing an active learning platform to support student learning in a numerical analysis course(Institute of Electrical and Electronics Engineers Inc., 2017-01-01) Zabala F.J.C.; Parker H.E.; Vieira C.; Zabala F.J.C.; Parker H.E.; Vieira C.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónClassroom instruction in the 21st century needs to incorporate innovative, research-based pedagogies. The engineering classroom is currently experiencing a shift towards more active learning activities due to both advances in educational research, and advances in technologies that enable practices such as the flipped classroom model. Given that course transformation is a gradual process that begins at the level of the instructor, educators need access to the essential tools and training in order to introduce these changes into the curricula. This paper introduces a course re-design based on Self-Determination Theory and Constructivism; and outlines effectively implemented active learning strategies using the flipped classroom model. The data were collected from a Numerical Analysis course, which is an important course across several engineering disciplines at Universidad EAFIT. This course enables engineering students to solve complex problems using mathematical and computational methods. This paper describes the implementation of an online active learning platform called "Numérico Interactivo" for two related engineering courses: Numerical Analysis (NA) and Numerical Processes (NP). The platform was available to all students, but only NA implemented it using a flipped classroom model. NP made the platform available as an optional course tool. Informed by SDT principles, "Numérico Interactivo" includes a variety of instructional materials such as explanations, examples, frequently asked questions (FAQ), self-assessment tools, and evaluation. This study compares the two courses in terms of: (1) students' perceptions about the instructional materials of the course; (2) students' use of the platform; and (3) students' perceived usefulness of the different elements within the platform. Results suggest that students in the NA course found the classroom sessions and the homework assignments more useful as compared to the students enrolled in the NP course. In addition, in the NA course students used the platform more often for class preparation and to study before each module. The way in which the platform was implemented in NA also increased student motivation in the course. Overall, the results suggest that "Numérico Interactivo" is useful to implement course re-designs into engineering and computing education courses, but such tools need to be guided by active learning practices so that students can fully benefit from them. © 2017 IEEE.Ítem Limits of quotients of polynomial functions in three variables(ASSOC COMPUTING MACHINERY, 2017-06-01) Velez, Juan D.; Hernandez, Juan P.; Cadavid, Carlos A.; Velez, Juan D.; Hernandez, Juan P.; Cadavid, Carlos A.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y AplicacionesA method for computing limits of quotients of real analytic functions in two variables was developed in [4]. In this article we generalize the results obtained in that paper to the case of quotients q = f(x, y, z)/g(x, y, z) of polynomial functions in three variables with rational coefficients. The main idea consists in examining the behavior of the function q along certain real variety X(q) (the discriminant variety associated to q). The original problem is then solved by reducing to the case of functions of two variables. The inductive step is provided by the key fact that any algebraic curve is birationally equivalent to a plane curve. Our main result is summarized in Theorem 2. In Section 4 we describe an effective method for computing such limits. We provide a high level description of an algorithm that generalizes the one developed in [4], now available in Maple as the limit/multi command.Ítem Topological and geometrical quantum computation in cohesive Khovanov homotopy type theory(SPIE-INT SOC OPTICAL ENGINEERING, 2015-05-21) Ospina, Juan; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónThe recently proposed Cohesive Homotopy Type Theory is exploited as a formal foundation for central concepts in Topological and Geometrical Quantum Computation. Specifically the Cohesive Homotopy Type Theory provides a formal, logical approach to concepts like smoothness, cohomology and Khovanov homology; and such approach permits to clarify the quantum algorithms in the context of Topological and Geometrical Quantum Computation. In particular we consider the so-called a "open-closed stringy topological quantum computera" which is a theoretical topological quantum computer that employs a system of open-closed strings whose worldsheets are open-closed cobordisms. The open-closed stringy topological computer is able to compute the Khovanov homology for tangles and for hence it is a universal quantum computer given than any quantum computation is reduced to an instance of computation of the Khovanov homology for tangles. The universal algebra in this case is the Frobenius Algebra and the possible open-closed stringy topological quantum computers are forming a symmetric monoidal category which is equivalent to the category of knowledgeable Frobenius algebras. Then the mathematical design of an open-closed stringy topological quantum computer is involved with computations and theorem proving for generalized Frobenius algebras. Such computations and theorem proving can be performed automatically using the Automated Theorem Provers with the TPTP language and the SMT-solver Z3 with the SMT-LIB language. Some examples of application of ATPs and SMT-solvers in the mathematical setup of an open-closed stringy topological quantum computer will be provided. © 2015 SPIE.Ítem Using computer algebra for Yang-Baxterization applied to quantum computing(SPIE-INT SOC OPTICAL ENGINEERING, 2006-05-12) Velez, Mario; Ospina, Juan; Velez, Mario; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónUsing Computer Algebra Software (Mathematica and Maple), the recently introduced topic of Yang-Baxterization applied to quantum computing, is explored from the mathematical and computational views. Some algorithms of computer algebra were elaborated with the aim to make the calculations to obtain some of results that were originally presented in the paper by Shang-Kauffman-Ge. Also certain new results about computational Yang-baxterization are presented. We obtain some Hamiltonians for hypothetical physical systems which can be realized within the domain of spin chains and certain diffusion process. We conclude that it is possible to have real physical systems on which implement, via Yang-baxterization, the standard quantum gates with topological protection. Finally some lines for future research are deligned.