Relevant bibliographies by topics / Computation Theory and Mathematics

Contents

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

Academic literature on the topic 'Computation Theory and Mathematics'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 January 2023

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Journal articles on the topic "Computation Theory and Mathematics"

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Dean, Walter. "Computational Complexity Theory and the Philosophy of Mathematics†." Philosophia Mathematica 27, no. 3 (October 1, 2019): 381–439. http://dx.doi.org/10.1093/philmat/nkz021.

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Abstract Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof.
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Maley, Carlo C. "DNA Computation: Theory, Practice, and Prospects." Evolutionary Computation 6, no. 3 (September 1998): 201–29. http://dx.doi.org/10.1162/evco.1998.6.3.201.

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L. M. Adleman launched the field of DNA computing with a demonstration in 1994 that strands of DNA could be used to solve the Hamiltonian path problem for a simple graph. He also identified three broad categories of open questions for the field. First, is DNA capable of universal computation? Second, what kinds of algorithms can DNA implement? Third, can the error rates in the manipulations of the DNA be controlled enough to allow for useful computation? In the two years that have followed, theoretical work has shown that DNA is in fact capable of universal computation. Furthermore, algorithms for solving interesting questions, like breaking the Data Encryption Standard, have been described using currently available technology and methods. Finally, a few algorithms have been proposed to handle some of the apparently crippling error rates in a few of the common processes used to manipulate DNA. It is thus unlikely that DNA computation is doomed to be only a passing curiosity. However, much work remains to be done on the containment and correction of errors. It is far from clear if the problems in the error rates can be solved sufficiently to ever allow for general-purpose computation that will challenge the more popular substrates for computation. Unfortunately, biological demonstrations of the theoretical results have been sadly lacking. To date, only the simplest of computations have been carried out in DNA. To make significant progress, the field will require both the assessment of the practicality of the different manipulations of DNA and the implementation of algorithms for realistic problems. Theoreticians, in collaboration with experimentalists, can contribute to this research program by settling on a small set of practical and efficient models for DNA computation.
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Yamada, Shinichi. "A mathematical theory of randomized computation, I." Proceedings of the Japan Academy, Series A, Mathematical Sciences 64, no. 4 (1988): 115–18. http://dx.doi.org/10.3792/pjaa.64.115.

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Yamada, Shinichi. "A mathematical theory of randomized computation, II." Proceedings of the Japan Academy, Series A, Mathematical Sciences 64, no. 5 (1988): 155–58. http://dx.doi.org/10.3792/pjaa.64.155.

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Yamada, Shinichi. "A mathematical theory of randomized computation, III." Proceedings of the Japan Academy, Series A, Mathematical Sciences 64, no. 6 (1988): 201–4. http://dx.doi.org/10.3792/pjaa.64.201.

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Duhr, Claude. "Function Theory for Multiloop Feynman Integrals." Annual Review of Nuclear and Particle Science 69, no. 1 (October 19, 2019): 15–39. http://dx.doi.org/10.1146/annurev-nucl-101918-023551.

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Precise predictions for collider observables require the computation of higher orders in perturbation theory. This task usually involves the evaluation of complicated multiloop integrals, which typically give rise to complicated special functions. This article discusses recent progress in understanding the mathematics underlying multiloop Feynman integrals and discusses a class of functions that generalizes the logarithm and that often appears in multiloop computations. The same class of functions is an active area of research in modern mathematics, which has led to the development of new powerful tools to compute Feynman integrals. These tools are at the heart of some of the most complicated computations ever performed for a hadron collider.
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Lenstra Jr., H. W., Steven M. Serbin, Stig Larsson, Ohannes Karakashian, J. Thomas King, and Ewald Quak. "Book Review: Mathematics of Computation 1943--1993: A half-century of computational mathematics." Mathematics of Computation 66, no. 219 (July 1, 1997): 1367–75. http://dx.doi.org/10.1090/s0025-5718-97-00877-6.

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Conceição, Ana C., and Jéssica C. Pires. "Symbolic Computation Applied to Cauchy Type Singular Integrals." Mathematical and Computational Applications 27, no. 1 (December 31, 2021): 3. http://dx.doi.org/10.3390/mca27010003.

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The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At the present time, this theory has wide applications in the study of non-linear differential equations, in linear transport theory, in the theory of diffraction of acoustic and electromagnetic waves, in the theory of scattering and of inverse scattering, among others. In our work, we use the computer algebra system Mathematica to implement, for the first time on a computer, analytical algorithms developed by us and others within operator theory. The main goal of this paper is to present new operator theory algorithms related to Cauchy type singular integrals, defined in the unit circle. The design of these algorithms was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. Several nontrivial examples computed with the algorithms are presented. The corresponding source code of the algorithms has been made available as a supplement to the online edition of this article.
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Edalat, Abbas. "Domains for Computation in Mathematics, Physics and Exact Real Arithmetic." Bulletin of Symbolic Logic 3, no. 4 (December 1997): 401–52. http://dx.doi.org/10.2307/421098.

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AbstractWe present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they are used to give a computational framework in several areas in mathematics and physics. These include fractal geometry, where new results on existence and uniqueness of attractors and invariant distributions have been obtained, measure and integration theory, where a generalization of the Riemann theory of integration has been developed, and real arithmetic, where a feasible setting for exact computer arithmetic has been formulated. We give a number of algorithms for computation in the theory of iterated function systems with applications in statistical physics and in period doubling route to chaos; we also show how efficient algorithms have been obtained for computing elementary functions in exact real arithmetic.
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Doerr, Benjamin, and Thomas Jansen. "Theory of Evolutionary Computation." Algorithmica 59, no. 3 (November 9, 2010): 299–300. http://dx.doi.org/10.1007/s00453-010-9472-3.

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Dissertations / Theses on the topic "Computation Theory and Mathematics"

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Bryant, Ross. "A Computation of Partial Isomorphism Rank on Ordinal Structures." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5387/.

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We compute the partial isomorphism rank, in the sense Scott and Karp, of a pair of ordinal structures using an Ehrenfeucht-Fraisse game. A complete formula is proven by induction given any two arbitrary ordinals written in Cantor normal form.
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Zhang, Yue. "Sparsity in Image Processing and Machine Learning: Modeling, Computation and Theory." Case Western Reserve University School of Graduate Studies / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=case1523017795312546.

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Semegni, Jean Yves. "On the computation of freely generated modular lattices." Thesis, Stellenbosch : Stellenbosch University, 2008. http://hdl.handle.net/10019.1/1207.

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Khafizov, Farid T. "Descriptions and Computation of Ultrapowers in L(R)." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc277867/.

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The results from this dissertation are an exact computation of ultrapowers by measures on cardinals $\aleph\sb{n},\ n\in w$, in $L(\IR$), and a proof that ordinals in $L(\IR$) below $\delta\sbsp{5}{1}$ represented by descriptions and the identity function with respect to sequences of measures are cardinals. An introduction to the subject with the basic definitions and well known facts is presented in chapter I. In chapter II, we define a class of measures on the $\aleph\sb{n},\ n\in\omega$, in $L(\IR$) and derive a formula for an exact computation of the ultrapowers of cardinals by these measures. In chapter III, we give the definitions of descriptions and the lowering operator. Then we prove that ordinals represented by descriptions and the identity function are cardinals. This result combined with the fact that every cardinal $<\delta\sbsp{5}{1}$ in $L(\IR$) is represented by a description (J1), gives a characterization of cardinals in $L(\IR$) below $\delta\sbsp{5}{1}. Concrete examples of formal computations are shown in chapter IV.
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Theeranaew, Wanchat. "STUDY ON INFORMATION THEORY: CONNECTION TO CONTROL THEORY, APPROACH AND ANALYSIS FOR COMPUTATION." Case Western Reserve University School of Graduate Studies / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=case1416847576.

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Marsden, Daniel. "Logical aspects of quantum computation." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:e99331a3-9d93-4381-8075-ad843fb9b77c.

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A fundamental component of theoretical computer science is the application of logic. Logic provides the formalisms by which we can model and reason about computational questions, and novel computational features provide new directions for the development of logic. From this perspective, the unusual features of quantum computation present both challenges and opportunities for computer science. Our existing logical techniques must be extended and adapted to appropriately model quantum phenomena, stimulating many new theoretical developments. At the same time, tools developed with quantum applications in mind often prove effective in other areas of logic and computer science. In this thesis we explore logical aspects of this fruitful source of ideas, with category theory as our unifying framework. Inspired by the success of diagrammatic techniques in quantum foundations, we begin by demonstrating the effectiveness of string diagrams for practical calculations in category theory. We proceed by example, developing graphical formulations of the definitions and proofs of many topics in elementary category theory, such as adjunctions, monads, distributive laws, representable functors and limits and colimits. We contend that these tools are particularly suitable for calculations in the field of coalgebra, and continue to demonstrate the use of string diagrams in the remainder of the thesis. Our coalgebraic studies commence in chapter 3, in which we present an elementary formulation of a representation result for the unitary transformations, following work developed in a fibrational setting in [Abramsky, 2010]. That paper raises the question of what a suitable "fibred coalgebraic logic" would be. This question is the starting point for our work in chapter 5, in which we introduce a parameterized, duality based frame- work for coalgebraic logic. We show sufficient conditions under which dual adjunctions and equivalences can be lifted to fibrations of (co)algebras. We also prove that the semantics of these logics satisfy certain "institution conditions" providing harmony between syntactic and semantic transformations. We conclude by studying the impact of parameterization on another logical aspect of coalgebras, in which certain fibrations of predicates can be seen as generalized invariants. Our focus is on the lifting of coalgebra structure along a fibration from the base category to an associated total category of predicates. We show that given a suitable parameterized generalization of the usual liftings of signature functors, this induces a "fibration of fibrations" capturing the relationship between the two different axes of variation.
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Kirk, Neil Patrick. "Computational aspects of singularity theory." Thesis, University of Liverpool, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359187.

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In this thesis we develop computational methods suitable for performing the symbolic calculations common to local singularity theory. For classification theory we employ the unipotent determinacy techniques of Bruce, du Plessis, Wall and complete transversal theorems of Bruce, du Plessis. The latter results are, as yet, unpublished and we spend some time reviewing these results, extending them to filtrations of the module m,,,.E (n, p) other than the standard filtration by degree. Weighted filtrations and filtrations induced by the action of a nilpotent Lie algebra are considered. A computer package called Transversal is developed. This is written in the mathematical language Maple and performs calculations such as those mentioned above and those central to unfolding theory. We discuss the package in detail and give examples of calculations performed in this thesis. Several classifications are obtained. The first is an extensive classification of map-germs (R2,0) -p (R4,0) under A-equivalence. We also consider the classification of function-germs (CP, O) -f (C, 0) under R(D)-equivalence: the restriction of R-equivalence to source coordinate changes which preserve a discriminant variety, D. We consider the cases where D is the discriminant of the A2 and A3 singularities, extending the results of Arnol'd. Several other simple singularities are discussed briefly; in particular, we consider the cases where D is the discriminant of the A4, D4, D5, D6, and Ek singularities. The geometry of the singularities (R2,0) -f (R4,0) is investigated by calculating the adjacencies and several geometrical invariants. For the given source and target dimensions, the invariants associated to the double point schemes and L-codimension of the germs are particularly significant. Finally we give an application of computer graphics to singularity theory. A program is written (in C) which calculates and draws the family of profiles of a surface rotating about a fixed axis in R3, the resulting envelope of profiles, and several other geometrical features. The program was used in recent research by Rycroft. We review some of the results and conclude with computer produced images which demonstrate certain transitions of the singularities on the envelope.
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Fatouros, Stavros. "Approximate algebraic computations in control theory." Thesis, City University London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274524.

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Heyman, Joseph Lee. "On the Computation of Strategically Equivalent Games." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1561984858706805.

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Fukasawa, Ricardo. "Single-row mixed-integer programs : theory and computations /." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24660.

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Thesis (Ph.D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Chair: William J. Cook; Committee Member: Ellis Johnson; Committee Member: George Nemhauser; Committee Member: Robin Thomas; Committee Member: Zonghao Gu
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Books on the topic "Computation Theory and Mathematics"

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Tourlakis, George J. Theory of computation. Hoboken, N.J: Wiley, 2012.

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Theory of computation. New York, NY: Wiley, 1987.

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Theory of computation. New York: Harper & Row, 1987.

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Linear dependence: Theory and computation. New York: Kluwer Academic/Plenum Publishers, 2000.

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Multiple criteria optimization: Theory, computation, and application. Malabar, Fla: Krieger, 1989.

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Steuer, Ralph E. Multiple criteria optimization: Theory, computation, and application. New York: Wiley, 1986.

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FCT '85 (1985 Cottbus, Germany). Fundamentals of computation theory. Berlin: Springer-Verlag, 1985.

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Electromagnetic field theory and computation. Hoboken, N.J: Wiley, 2010.

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Dasgupta, D. Immunological computation: Theory and applications. Boca Raton: Auerbach Publications, 2009.

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Dasgupta, D. Immunological computation: Theory and applications. Boca Raton: Auerbach Publications, 2009.

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Book chapters on the topic "Computation Theory and Mathematics"

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Sanders, Sam. "Reverse Mathematics and Computability Theory of Domain Theory." In Logic, Language, Information, and Computation, 550–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019. http://dx.doi.org/10.1007/978-3-662-59533-6_33.

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Kearfott, R. Baker. "Interval Mathematics Techniques for Control Theory Computations." In Computation and Control, 169–78. Boston, MA: Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4612-3704-4_12.

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Shparlinski, Igor E. "Finite Fields and Discrete Mathematics." In Finite Fields: Theory and Computation, 265–324. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9239-0_10.

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Stewart, Iain A. "On the Mathematics of Data Centre Network Topologies." In Fundamentals of Computation Theory, 283–95. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22177-9_22.

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Smale, Stephen. "Theory of computation." In Mathematical Research Today and Tomorrow, 59–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0089205.

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Friedman, Avner. "Computation of volume integrals in potential theory." In Mathematics in Industrial Problems, 122–30. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4615-7405-7_12.

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Kaltofen, Erich L. "Symbolic Computation and Complexity Theory Transcript of My Talk." In Computer Mathematics, 3–7. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-43799-5_1.

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Peck, Robert W. "Almost Difference Sets in Transformational Music Theory." In Mathematics and Computation in Music, 63–75. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71827-9_6.

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Mazzola, Guerino. "ComMute—Towards a Computational Musical Theory of Everything." In Mathematics and Computation in Music, 21–30. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21392-3_2.

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Freivalds, RŪsiņš. "Models of Computation, Riemann Hypothesis, and Classical Mathematics." In SOFSEM’ 98: Theory and Practice of Informatics, 89–106. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/3-540-49477-4_6.

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Conference papers on the topic "Computation Theory and Mathematics"

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Alozn, Ahmad E., and Abdulla Galadari. "Utility function under decision theory: A construction arbitration application." In INTERNATIONAL CONFERENCE ON MATHEMATICS: PURE, APPLIED AND COMPUTATION: Empowering Engineering using Mathematics. Author(s), 2017. http://dx.doi.org/10.1063/1.4994404.

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Setiawan, Ekky Kurnia, and I. Ketut Budayasa. "Application of graph theory concept for traffic light control at crossroad." In INTERNATIONAL CONFERENCE ON MATHEMATICS: PURE, APPLIED AND COMPUTATION: Empowering Engineering using Mathematics. Author(s), 2017. http://dx.doi.org/10.1063/1.4994457.

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Gibbs, Alison L., and Alex Stringer. "The Fundamental Role of Computation in Teaching Statistical Theory." In IASE 2021 Satellite Conference: Statistics Education in the Era of Data Science. International Association for Statistical Education, 2022. http://dx.doi.org/10.52041/iase.rmcxl.

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What skills, knowledge and habits of mind does a statistician require in order to contribute effectively as an inhabitant of the data science ecosystem? We describe a new course in statistical theory that was developed as part of our consideration of this question. The course is a core requirement in a new curriculum for undergraduate students enrolled in statistics programs of study. Problem solving and critical thinking are developed through both mathematical and computational thinking and all ideas are motivated through questions to be answered from large, open and messy data. Central to the development of the course is the tenet that the use of computation is as fundamental to statistical thinking as the use of mathematics. We describe the course, including its connection to the learning outcomes of our new statistics program of study, and the multiple ways we use and integrate computation.
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Milasi, Monica, Annamaria Barbagallo, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Preface of Minisymposium “Variational Inequalities and Equilibrium Problems: Existence and Duality Theory and Computation”." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241373.

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M. Bouniaev, Mikhail, and Nikolai P. Dolbilin. "Local Theory of Crystals: Development and Current Status." In Annual International Conference on Computational Mathematics, Computational Geometry & Statistics. Global Science and Technology Forum (GSTF), 2015. http://dx.doi.org/10.5176/2251-1911_cmcgs15.42.

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Bethune, Iain. "PrimeGrid: a Volunteer Computing Platform for Number Theory." In Annual International Conference on Computational Mathematics, Computational Geometry & Statistics. Global Science and Technology Forum (GSTF), 2015. http://dx.doi.org/10.5176/2251-1911_cmcgs15.43.

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Gale, Ella, Ben De Lacy Costello, and Andrew Adamatzky. "Observation and characterization of memristor current spikes and their application to neuromorphic computation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756553.

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Zhigljavsky, Anatoly, and Vladimir Kornikov. "Classical areas of mathematics where the concept of grossone could be useful." In NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”. Author(s), 2016. http://dx.doi.org/10.1063/1.4965310.

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Khimich, Alexander, Volodymyr Sydoruk, and Pavlo Yershov. "Intellectualization Of Computation Based On Neural Networks For Mathematical Modeling." In 2019 IEEE International Conference on Advanced Trends in Information Theory (ATIT). IEEE, 2019. http://dx.doi.org/10.1109/atit49449.2019.9030444.

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"A Non-lineal Mathematical Model for Annealing Stainless Steel Coils." In International Conference on Neural Computation Theory and Applications. SciTePress - Science and and Technology Publications, 2012. http://dx.doi.org/10.5220/0004112206070610.

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Reports on the topic "Computation Theory and Mathematics"

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McCarthy, John. Mathematical Theory of Computation. Fort Belvoir, VA: Defense Technical Information Center, August 1991. http://dx.doi.org/10.21236/ada239419.

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Yau, Shing-Tung. Mathematics and string theory. Office of Scientific and Technical Information (OSTI), November 2002. http://dx.doi.org/10.2172/809056.

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Jaffe, A., and Shing-Tung Yau. [Mathematics and string theory]. Office of Scientific and Technical Information (OSTI), January 1993. http://dx.doi.org/10.2172/6327345.

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Jaffe, A., S. Klimek, B. Greene, and S.-T. Yau. (Mathematics and string theory). Office of Scientific and Technical Information (OSTI), January 1989. http://dx.doi.org/10.2172/5148870.

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Greenberg, W., and P. Zweifel. Applied mathematics of transport theory. Office of Scientific and Technical Information (OSTI), May 1990. http://dx.doi.org/10.2172/6703991.

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Schreiber, Robert, and Beresford Parlett. Block Reflectors: Theory and Computation. Fort Belvoir, VA: Defense Technical Information Center, May 1987. http://dx.doi.org/10.21236/ada206861.

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Gidaspow, D. Computation of hydrodynamics using kinetic theory. Office of Scientific and Technical Information (OSTI), December 1991. http://dx.doi.org/10.2172/5686161.

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Robinson, Stephen M. Computation and Theory in Nonlinear Optimization. Fort Belvoir, VA: Defense Technical Information Center, April 1996. http://dx.doi.org/10.21236/ada311415.

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Hoffman, D. [Geometry, analysis, and computation in mathematics and applied science]. Progress report. Office of Scientific and Technical Information (OSTI), February 1994. http://dx.doi.org/10.2172/218245.

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Kusner, R. B., D. A. Hoffman, P. Norman, F. Pedit, N. Whitaker, and D. Oliver. Geometry, analysis, and computation in mathematics and applied sciences. Final report. Office of Scientific and Technical Information (OSTI), December 1995. http://dx.doi.org/10.2172/171332.

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