Relevant bibliographies by topics / Arrow Calculus

Academic literature on the topic 'Arrow Calculus'

Author: Grafiati
Published: 7 July 2024
Last updated: 7 July 2024

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Journal articles on the topic "Arrow Calculus":

1

LINDLEY, SAM, PHILIP WADLER, and JEREMY YALLOP. "The arrow calculus." Journal of Functional Programming 20, no. 1 (January 2010): 51–69. http://dx.doi.org/10.1017/s095679680999027x.

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AbstractWe introduce the arrow calculus, a metalanguage for manipulating Hughes's arrows with close relations both to Moggi's metalanguage for monads and to Paterson's arrow notation. Arrows are classically defined by extending lambda calculus with three constructs satisfying nine (somewhat idiosyncratic) laws; in contrast, the arrow calculus adds four constructs satisfying five laws (which fit two well-known patterns). The five laws were previously known to be sound; we show that they are also complete, and hence that the five laws may replace the nine.
2

Reeder, Patrick. "Zeno’s arrow and the infinitesimal calculus." Synthese 192, no. 5 (January 10, 2015): 1315–35. http://dx.doi.org/10.1007/s11229-014-0620-1.

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Meilhan, Jean-Baptiste, and Akira Yasuhara. "Arrow calculus for welded and classical links." Algebraic & Geometric Topology 19, no. 1 (February 6, 2019): 397–456. http://dx.doi.org/10.2140/agt.2019.19.397.

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Mărășoiu, Andrei. "Is the Arrow’s Flight a Process?" Studii de istorie a filosofiei universale 31 (December 30, 2023): 113–21. http://dx.doi.org/10.59277/sifu.2023.09.

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Zeno’s famous arrow’s paradox has troubled philosophers for a long time. In the aftermath of Russell’s discussion of the paradox in terms of the calculus, I argue that the paradox leaves a lingering question as to how our everyday, pre-theoretical notions of the motion of objects (such as arrows) intermesh with the mathematical physics thought to fully account for them. Starting from Russell and Salmon’s reformulations of the arrow paradox in terms of ‘at-at’ theories of motion, I argue that such solutions can only account for our pre-theoretical intuitions if supplemented ontologically, by something in the vein of (though perhaps not necessarily identical with) Whitehedian processes. I then explore the suitability of this approach to the arrow paradox, and end by exploring ontological and metaontological concerns one might raise about whether this is a viable way out of paradox.
5

Östlund, Olof-Petter. "A diagrammatic approach to link invariants of finite degree." MATHEMATICA SCANDINAVICA 94, no. 2 (June 1, 2004): 295. http://dx.doi.org/10.7146/math.scand.a-14444.

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In [5] M. Polyak and O. Viro developed a graphical calculus of diagrammatic formulas for Vassiliev link invariants, and presented several explicit formulas for low degree invariants. M. Goussarov [2] proved that this arrow diagram calculus provides formulas for all Vassiliev knot invariants. The original note [5] contained no proofs, and it also contained some minor inaccuracies. This paper fills the gap in literature by presenting the material of [5] with all proofs and details, in a self-contained form. Furthermore, a compatible coalgebra structure, related to the connected sum of knots, is introduced on the algebra of based arrow diagrams with one circle.
6

Thomas, Sebastian. "On the 3-arrow calculus for homotopy categories." Homology, Homotopy and Applications 13, no. 1 (2011): 89–119. http://dx.doi.org/10.4310/hha.2011.v13.n1.a5.

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Tymofieiev, Oleksii, and Olha Cherniak. "Ultrasound in the Detection of Floating Sialoliths." Journal of Diagnostics and Treatment of Oral and Maxillofacial Pathology 3, no. 8 (August 31, 2019): 196–97. http://dx.doi.org/10.23999/j.dtomp.2019.8.2.

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A 36-year-old man with a 3-year history of recurrent salivary colic was referred to a maxillofacial surgery department. Gray scale ultrasound (US) showed enlarged right submandibular gland, significantly dilated intraglandular duct with two sialoliths (with an artifact of acoustic shadowing) inside, one – floating (Video-Panel A and B, arrow) and another – nonmovable (arrowhead). Left nonsymptomatic normal in size gland (asterisk) is showed at Panel C. The affected gland was excised under general anesthesia due to the diagnosis of chronic submandibular obstructive sialolithiasis. Intraglandular duct contained two yellowish stones, first was an oval form with a pellet surface (Panel D, arrow), second – a round shaped with a smooth surface (Panel D, asterisk) and it was presented at US as a floating sialolith; both are easily crumbled on palpation. As the specimen and intraglandular duct were dissected longitudinally, that`s why dissected intraglandular duct (Panel D, arrowheads) is visible in both parts of the gland. Also, a 1 small calculus (Panel D, curved arrow) was found in the parenchymal ducts. Postoperative period was smooth, and 1-year follow-up after surgery, the patient has no complaints.
8

PEARCE, DAVID W. "Benefit-cost analysis, environment, and health in the developed and developing world." Environment and Development Economics 2, no. 2 (May 1997): 195–221. http://dx.doi.org/10.1017/s1355770x97250163.

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Arrow et al. revisit the case for using benefit-cost analysis in a developed country, the USA, where markets work reasonably efficiently and where the capacity to implement such studies is undoubted. Their recommendations deserve wholehearted support in that context, particularly their recommendation 1 calling for a comparison of gains and losses from regulatory actions. Those who have not worked in government will recognise that most decisions are not in fact made with any form of calculus that we might describe as 'cost benefit thinking'. Indeed, the whole process of policy priority setting is all too often ad hoc, reactive, crisis-based and over-responsive to often ill-informed pressure groups (of all kinds).
9

Nguyen, Manh-Hung, and Phu Nguyen-Van. "OPTIMAL ENDOGENOUS GROWTH WITH NATURAL RESOURCES: THEORY AND EVIDENCE." Macroeconomic Dynamics 20, no. 8 (April 8, 2016): 2173–209. http://dx.doi.org/10.1017/s1365100515000061.

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This paper considers an optimal endogenous growth model where the production function is assumed to exhibit increasing returns to scale and two types of resource (renewable and nonrenewable) are imperfect substitutes. Natural resources, labor, and physical capital are used in the final goods sector and in the accumulation of knowledge. Based on results in the calculus of variations, a direct proof of the existence of an optimal solution is provided. Analytical solutions for the planner case, balanced growth paths, and steady states are found for a specific CRRA utility and Cobb–Douglas production function. It is possible to have long-run growth where both energy resources are used simultaneously along the equilibrium path. As the law of motion of the technological change is not concave, reflecting the increasing returns to scale, so that the Arrow–Mangasarian sufficiency conditions do not apply, we provide a sufficient condition directly. Transitional dynamics to the steady state from the theoretical model are used to derive three convergence equations of output intensity growth rate, exhaustible resource growth rate, and renewable resource growth rate, which are tested based on OECD data on production and energy consumption.
10

Bodie, Zvi. "Robert C. Merton and the Science of Finance." Annual Review of Financial Economics 11, no. 1 (December 26, 2019): 1–20. http://dx.doi.org/10.1146/annurev-financial-011019-040506.

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Starting with his 1970 doctoral dissertation and continuing to today, Robert C. Merton has revolutionized the theory and practice of finance. In 1997, Merton shared a Nobel Prize in Economics “for a new method to determine the value of derivatives.” His contributions to the science of finance, however, go far beyond that. In this article I describe Merton's main contributions. They include the following: 1. The introduction of continuous-time stochastic models (the Ito calculus) to the theory of household consumption and investment decisions. Merton's technique of dynamic hedging in continuous time provided a bridge between the theoretical complete-markets equilibrium model of Kenneth Arrow and the real world of personal financial planning and management. 2. The derivation of the multifactor Intertemporal Capital Asset Pricing Model (ICAPM). The ICAPM generalizes the single-factor CAPM and explains why that model might fail to properly account for observed market excess returns. It also provides a theory to identify potential forward-looking risk premia for use in factor-based investment strategies. It is therefore both a positive and normative theory. 3. The invention of Contingent Claims Analysis (CCA) as a generalization of option pricing theory. CCA applies the technique of dynamic replication to the valuation and risk management of a wide range of corporate and government liabilities. Merton's CCA model for the valuation and analysis of risky debt is known among scholars and practitioners alike as the Merton Model. 4. The development of financial engineering, which employs CCA to design and produce new financial products. Merton was the first to apply CCA to analyze government guaranty programs such as deposit insurance, and to suggest improvements in the way those programs are managed. He and his students have applied his insights at both the micro and macro policy levels. 5. And finally, the development of a theory of financial intermediation that explains and predicts how financial systems differ across countries and change over time. Merton has applied that theory, called functional and structural finance, to guide the design and regulation of financial systems at the levels of the firm, the industry, and the nation. He has also used it to propose reforms in pensions, sovereign wealth funds, and macrostabilization policy.
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You might also be interested in the extended bibliographies on the topic 'Arrow Calculus' for particular source types:
Journal articles

Dissertations / Theses on the topic "Arrow Calculus":

1

Graff, Emmanuel. ""Link-homotopy" in low dimensional topology." Electronic Thesis or Diss., Normandie, 2023. http://www.theses.fr/2023NORMC244.

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Ce mémoire explore la topologie de basse dimension, en mettant l'accent sur la théorie des nœuds. Une théorie consacrée à l'étude des nœuds tels qu'ils sont communément compris : des morceaux de ficelle enroulés dans l'espace ou, de manière plus générale, des entrelacs formés en prenant plusieurs bouts de ficelle. Les nœuds et les entrelacs sont étudiés à déformation près, par exemple, à isotopie près, ce qui implique des manipulations sans couper ni faire passer la ficelle à travers elle-même. Cette thèse explore la link-homotopie, une relation d'équivalence plus souple où des composantes distinctes demeurent séparées, mais où une composante donnée peut s'auto-intersecter. La théorie des claspers, des puissants outils de chirurgie, est développée à link-homotopie près. Leur utilisation permet une démonstration géométrique de la classification des entrelacs avec 4 composantes ou moins à link-homotopie près. Une attention particulière est ensuite accordée aux tresses, des objets mathématiques apparentés aux nœuds et aux entrelacs. Il est montré que le groupe de tresses homotopiques est linéaire, c'est-à-dire isomorphe à un sous-groupe de matrices. De nouvelles présentations de ce groupe sont également proposées. Enfin, il est établi que le groupe de tresse homotopique est sans torsion, quel que soit le nombre de composantes. Ce dernier résultat s'appuie sur le contexte plus large de la théorie des nœuds soudés
This thesis explores low-dimensional topology, with a focus on knot theory. Knot theory is dedicated to the study of knots as commonly understood: a piece of string tied in space or, more generally, links formed by taking several pieces of string. Knots and links are studied up to deformation, for example, up to isotopy, which involves manipulations that do not require cutting or passing the string through itself. This thesis explores link-homotopy, a more flexible equivalence relation where distinct components remain disjoint, but a single component can self-intersect. The theory of claspers, powerful tools of surgery, is developed up to link-homotopy. Their use allows for a geometric proof of the classification of links with 4 components or less up to link-homotopy. Special attention is then given to braids, mathematical objects related to knots and links. It is shown that the homotopy braid group is linear, meaning it is faithfully represented by a subgroup of matrices. New group presentations are also proposed. Finally, it is established that the homotopy braid group is torsion-free for any number of components. This last result draws upon the broader context of welded knot theory

Book chapters on the topic "Arrow Calculus":

1

Vizzotto, Juliana Kaizer, André Rauber Du Bois, and Amr Sabry. "The Arrow Calculus as a Quantum Programming Language." In Logic, Language, Information and Computation, 379–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02261-6_30.

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Leydesdorff, Loet. "Towards a Calculus of Redundancy." In Qualitative and Quantitative Analysis of Scientific and Scholarly Communication, 67–86. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-59951-5_4.

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AbstractIn this chapter, I extend Shannon’s linear model of communication into a model in which communication is differentiated both vertically and horizontally (Simon, 1973). Following Weaver (1949), three layers are distinguished operating in relation to one another: (i) at level A, the events are sequenced historically along the arrow of time, generating Shannon-type information (that is, uncertainty); (ii) the incursion of meanings at level B is referential to (iii) horizons of meaning spanned by codes in the communication at level C. In other words, relations at level A are first distinguished from correlations among patterns of relations and non-relations at level B. The correlations span a vector space on top of the network of relations. Relations are positioned in this vector space and can then be provided with meaning. Different positions provide other perspectives and horizons of meaning. Perspectives can overlap, for example, in Triple-Helix relations. Overlapping perspectives can generate redundancies—that is, new options—as a result of synergies.
3

Mancosu, Paolo, Sergio Galvan, and Richard Zach. "The sequent calculus." In An Introduction to Proof Theory, 167–201. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895936.003.0005.

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In addition to natural deduction, Gentzen developed a different calculus, called the sequent calculus. A sequent is a configuration presenting an arrow symbol (⇒) flanked on the left and on the right by finite sequences of formulas, possibly empty. The sequent calculus is developed, with examples of how to prove statements in the calculus, and a few results about transforming proofs through variable replacements are proved. Proofs in the intuitionistic sequent calculus can be translated into natural deductions, and vice versa (this system is obtained by restricting sequents to those that have at most one formula on the right hand side of the arrow).
4

McLarty, Colin. "Synthetic differential geometry." In Elementary Categories, Elementary Toposes, 219–28. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198533924.003.0024.

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Abstract The synthetic differential geometry axioms (SDG) describe a topos in which each object has a differentiable structure, each arrow has a derivative, and the basic rules of calculus are simple calculations with infinitesimals. For this chapter we assume that we have a particular topos Spaces that satisfies the axioms. We refer to objects of Spaces as spaces, to its arrows as maps, and to global elements p: 1→.M aspoints of the space M.

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