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Relevant bibliographies by topics / Combinatorial set theory

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Academic literature on the topic 'Combinatorial set theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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Journal articles on the topic "Combinatorial set theory"

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Todorcevic, Stevo. "Combinatorial Dichotomies in Set Theory." Bulletin of Symbolic Logic 17, no. 1 (2011): 1–72. http://dx.doi.org/10.2178/bsl/1294186662.

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AbstractWe give an overview of a research line concentrated on finding to which extent compactness fails at the level of first uncountable cardinal and to which extent it could be recovered on some other perhaps not so large cardinal. While this is of great interest to set theorists, one of the main motivations behind this line of research is in its applicability to other areas of mathematics. We give some details about this and we expose some possible directions for further research.

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Schindler, Ralf. "Lorenz J. Halbeisen: “Combinatorial Set Theory”." Jahresbericht der Deutschen Mathematiker-Vereinigung 115, no. 2 (2013): 119–21. http://dx.doi.org/10.1365/s13291-013-0063-5.

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Mileti, Joseph R. "Partition Theorems and Computability Theory." Bulletin of Symbolic Logic 11, no. 3 (2005): 411–27. http://dx.doi.org/10.2178/bsl/1122038995.

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The connections between mathematical logic and combinatorics have a rich history. This paper focuses on one aspect of this relationship: understanding the strength, measured using the tools of computability theory and reverse mathematics, of various partition theorems. To set the stage, recall two of the most fundamental combinatorial principles, König's Lemma and Ramsey's Theorem. We denote the set of natural numbers by ω and the set of finite sequences of natural numbers by ω<ω. We also identify each n ∈ ω with its set of predecessors, so n = {0, 1, 2, …, n − 1}.

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Williams, Neil H., Paul Erdos, Andras Hajnal, Attila Mate, and Richard Rado. "Combinatorial Set Theory: Partition Relations for Cardinals." Journal of Symbolic Logic 53, no. 1 (1988): 310. http://dx.doi.org/10.2307/2274453.

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Hodel, R. E. "Combinatorial set theory and cardinal function inequalities." Proceedings of the American Mathematical Society 111, no. 2 (1991): 567. http://dx.doi.org/10.1090/s0002-9939-1991-1039531-7.

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Hajnal, A., and P. Komjáth. "Some higher-gap examples in combinatorial set theory." Annals of Pure and Applied Logic 33 (1987): 283–96. http://dx.doi.org/10.1016/0168-0072(87)90084-4.

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Shablya, Yuriy, Dmitry Kruchinin, and Vladimir Kruchinin. "Method for Developing Combinatorial Generation Algorithms Based on AND/OR Trees and Its Application." Mathematics 8, no. 6 (2020): 962. http://dx.doi.org/10.3390/math8060962.

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In this paper, we study the problem of developing new combinatorial generation algorithms. The main purpose of our research is to derive and improve general methods for developing combinatorial generation algorithms. We present basic general methods for solving this task and consider one of these methods, which is based on AND/OR trees. This method is extended by using the mathematical apparatus of the theory of generating functions since it is one of the basic approaches in combinatorics (we propose to use the method of compositae for obtaining explicit expression of the coefficients of gener

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BUCCI, MICHELANGELO, SVETLANA PUZYNINA, and LUCA Q. ZAMBONI. "Central sets generated by uniformly recurrent words." Ergodic Theory and Dynamical Systems 35, no. 3 (2013): 714–36. http://dx.doi.org/10.1017/etds.2013.69.

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AbstractA subset $A$ of $ \mathbb{N} $ is called an IP-set if $A$ contains all finite sums of distinct terms of some infinite sequence $\mathop{({x}_{n} )}\nolimits_{n\in \mathbb{N} } $ of natural numbers. Central sets, first introduced by Furstenberg using notions from topological dynamics, constitute a special class of IP-sets possessing rich combinatorial properties: each central set contains arbitrarily long arithmetic progressions and solutions to all partition regular systems of homogeneous linear equations. In this paper we investigate central sets in the framework of combinatorics on w

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Chen, Herman Z. Q., and Sergey Kitaev. "On universal partial words for word-patterns and set partitions." RAIRO - Theoretical Informatics and Applications 54 (2020): 5. http://dx.doi.org/10.1051/ita/2020004.

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Universal words are words containing exactly once each element from a given set of combinatorial structures admitting encoding by words. Universal partial words (u-p-words) contain, in addition to the letters from the alphabet in question, any number of occurrences of a special “joker” symbol. We initiate the study of u-p-words for word-patterns (essentially, surjective functions) and (2-)set partitions by proving a number of existence/non-existence results and thus extending the results in the literature on u-p-words and u-p-cycles for words and permutations. We apply methods of graph theory

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Akihiro Kanamori. "Zermelo and Set Theory." Bulletin of Symbolic Logic 10, no. 4 (2004): 487–553. http://dx.doi.org/10.2178/bsl/1102083759.

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Ernst Friedrich Ferdinand Zermelo (1871–1953) transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set theory. Two decades later Zermelo promoted a distin

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Dissertations / Theses on the topic "Combinatorial set theory"

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Ahmed, Shehzad. "Progressive Ideals in Combinatorial Set Theory." Ohio University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1554379497651916.

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Walker, D. J. "Combinatorial applications of the core model." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355807.

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Gutekunst, Todd M. "Subsets of finite groups exhibiting additive regularity." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 128 p, 2008. http://proquest.umi.com/pqdweb?did=1605136271&sid=5&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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Choi, Sul-young. "Maximal (0,1,2,...t)-cliques of some association schemes /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487261553059595.

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Phillips, Linzy. "Erasure-correcting codes derived from Sudoku & related combinatorial structures." Thesis, University of South Wales, 2013. https://pure.southwales.ac.uk/en/studentthesis/erasurecorrecting-codes-derived-from-sudoku--related-combinatorial-structures(b359130e-bfc2-4df0-a6f5-55879212010d).html.

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This thesis presents the results of an investigation into the use of puzzle-based combinatorial structures for erasure correction purposes. The research encompasses two main combinatorial structures: the well-known number placement puzzle Sudoku and a novel three component construction designed specifically with puzzle-based erasure correction in mind. The thesis describes the construction of outline erasure correction schemes incorporating each of the two structures. The research identifies that both of the structures contain a number of smaller sub-structures, the removal of which results in

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Miller, Sam. "Combinatorial Polynomial Hirsch Conjecture." Scholarship @ Claremont, 2017. https://scholarship.claremont.edu/hmc_theses/109.

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The Hirsch Conjecture states that for a d-dimensional polytope with n facets, the diameter of the graph of the polytope is at most n-d. This conjecture was disproven in 2010 by Francisco Santos Leal. However, a polynomial bound in n and d on the diameter of a polytope may still exist. Finding a polynomial bound would provide a worst-case scenario runtime for the Simplex Method of Linear Programming. However working only with polytopes in higher dimensions can prove challenging, so other approaches are welcome. There are many equivalent formulations of the Hirsch Conjecture, one of which is the

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Lambie-Hanson, Christopher. "Covering Matrices, Squares, Scales, and Stationary Reflection." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/368.

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In this thesis, we present a number of results in set theory, particularly in the areas of forcing, large cardinals, and combinatorial set theory. Chapter 2 concerns covering matrices, combinatorial structures introduced by Viale in his proof that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. In the course of this proof and subsequent work with Sharon, Viale isolated two reflection principles, CP and S, which can hold of covering matrices. We investigate covering matrices for which CP and S fail and prove some results about the connections between such covering matri

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Wang, Ruidong. "Combinatorial problems for graphs and partially ordered sets." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54483.

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This dissertation has three principal components. The first component is about the connections between the dimension of posets and the size of matchings in comparability and incomparability graphs. In 1951, Hiraguchi proved that for any finite poset P, the dimension of P is at most half of the number of points in P. We develop some new inequalities for the dimension of finite posets. These inequalities are then used to bound dimension in terms of the maximum size of matchings. We prove that if the dimension of P is d and d is at least 3, then there is a matching of size d in the comparability

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Williams, Elizabeth C. "A study of Polya's enumeration theorem." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Summer/master's/WILLIAMS_ELIZABETH_6.pdf.

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Krohne, Edward. "Continuous Combinatorics of a Lattice Graph in the Cantor Space." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc849680/.

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We present a novel theorem of Borel Combinatorics that sheds light on the types of continuous functions that can be defined on the Cantor space. We specifically consider the part X=F(2ᴳ) from the Cantor space, where the group G is the additive group of integer pairs ℤ². That is, X is the set of aperiodic {0,1} labelings of the two-dimensional infinite lattice graph. We give X the Bernoulli shift action, and this action induces a graph on X in which each connected component is again a two-dimensional lattice graph. It is folklore that no continuous (indeed, Borel) function provides a two-color

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Books on the topic "Combinatorial set theory"

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Halbeisen, Lorenz J. Combinatorial Set Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-60231-8.

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Halbeisen, Lorenz J. Combinatorial Set Theory. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2173-2.

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Farah, Ilijas. Combinatorial Set Theory of C*-algebras. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-27093-3.

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Anderson, Ian. Combinatorics of finite sets. Clarendon, 1987.

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Richard, Warren. The structure of k-CS-transitive cycle-free partial orders. American Mathematical Society, 1997.

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Sargsyan, Grigor. Hod mice and the mouse set conjecture. American Mathematical Society, 2015.

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service), SpringerLink (Online, ed. Combinatorial Set Theory: With a Gentle Introduction to Forcing. Springer-Verlag London Limited, 2012.

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Ian, Anderson. Combinatorics of finite sets. Clarendon Press, 1987.

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Ian, Anderson. Combinatorics of finite sets. Dover Publications, 2002.

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Trotter, William T. Combinatorics And Partially Ordered Sets: Dimension Theory. The Johns Hopkins University Press, 1992.

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Book chapters on the topic "Combinatorial set theory"

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Schimmerling, E. "Combinatorial Set Theory and Inner Models." In Set Theory. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-015-8988-8_14.

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Baumgartner, James. "Hajnal’s contributions to combinatorial set theory and the partition calculus." In Set Theory. American Mathematical Society, 2002. http://dx.doi.org/10.1090/dimacs/058/02.

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Blass, Andreas. "Combinatorial Cardinal Characteristics of the Continuum." In Handbook of Set Theory. Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-1-4020-5764-9_7.

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Hosono, Kiyoshi, Ferran Hurtado, Masatsugu Urabe, and Jorge Urrutia. "On a Triangle with the Maximum Area in a Planar Point Set." In Combinatorial Geometry and Graph Theory. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-30540-8_11.

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Dasgupta, Anirban, Ravi Kumar, and D. Sivakumar. "Sparse and Lopsided Set Disjointness via Information Theory." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32512-0_44.

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Uiterwijk, Jos W. H. M., and Lianne V. Hufkens. "Solving Impartial SET Using Knowledge and Combinatorial Game Theory." In Computers and Games. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-34017-8_9.

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Cervante, Liam, Bing Xue, Lin Shang, and Mengjie Zhang. "A Multi-objective Feature Selection Approach Based on Binary PSO and Rough Set Theory." In Evolutionary Computation in Combinatorial Optimization. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-37198-1_3.

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Harzheim, E. "A Combinatorial Theorem Which is Related to the Invariance of the Separating Set for the Plane." In Topics in Combinatorics and Graph Theory. Physica-Verlag HD, 1990. http://dx.doi.org/10.1007/978-3-642-46908-4_39.

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Dasgupta, Abhijit. "Postscript II: Infinitary Combinatorics." In Set Theory. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8854-5_12.

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Hajnal, András. "Paul Erdős’ Set Theory." In Algorithms and Combinatorics. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60406-5_33.

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Conference papers on the topic "Combinatorial set theory"

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Shai, Offer, and Andreas Müller. "A Novel Combinatorial Algorithm for Determining the Generic/Topological Mobility of Planar and Spherical Mechanisms." 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/detc2013-13364.

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Structural mobility criteria, such as the well-known Chebychev-Kutzbach-Grübler (CKG) formula, give the correct generic mobility of a linkage (possibly of a certain class, e.g. planar, spherical, spatial) provided that it is not topologically overconstrained. As a matter of fact all known structural mobility criteria are prone to topological redundancies. In this paper a combinatorial algorithm is introduced that determines the correct generic/topological mobility of any planar and spherical mechanism. The algorithm also yields a set of independent links that can be used as input, as well as t

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Jurewicz, Mateusz, and Leon Derczynski. "Set Interdependence Transformer: Set-to-Sequence Neural Networks for Permutation Learning and Structure Prediction." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/434.

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The task of learning to map an input set onto a permuted sequence of its elements is challenging for neural networks. Set-to-sequence problems occur in natural language processing, computer vision and structure prediction, where interactions between elements of large sets define the optimal output. Models must exhibit relational reasoning, handle varying cardinalities and manage combinatorial complexity. Previous attention-based methods require n layers of their set transformations to explicitly represent n-th order relations. Our aim is to enhance their ability to efficiently model higher-ord

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Lima, Ana Y. F. de, Briza M. D. de Sousa, Daniel P. Cardeal, et al. "LUNCH: an Answer Set Programming System for Course Scheduling." In Encontro Nacional de Inteligência Artificial e Computacional. Sociedade Brasileira de Computação - SBC, 2023. http://dx.doi.org/10.5753/eniac.2023.234540.

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Timetable scheduling is a known NP-hard problem; despite this, there have been many efforts to enable fast and efficient algorithms and heuristics for such a challenging task. Within the realm of timetable scheduling lies the particularly complex problem of Course Scheduling (CS). The goal in CS is to find an optimal timetable configuration of courses within the constraints set by faculty, course requirements and departmental functions. Answer Set Programming (ASP) is a declarative logic programming paradigm for solving combinatorial search tasks; instead of explicitly writing the solution to

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Berg, Jeremias, Fahiem Bacchus, and Alex Poole. "Abstract Cores in Implicit Hitting Set MaxSat Solving (Extended Abstract)." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/643.

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Maximum satisfiability (MaxSat) solving is an active area of research motivated by numerous successful applications to solving NP-hard combinatorial optimization problems. One of the most successful approaches for solving MaxSat instances from real world domains are the so called implicit hitting set (IHS) solvers. IHS solvers decouple MaxSat solving into separate core-extraction (i.e. reasoning) and optimization steps which are tackled by a Boolean satisfiability (SAT) and an integer linear programming (IP) solver, respectively. While the approach shows state-of-the-art performance on many in

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I. Garmendia, Andoni, Quentin Cappart, Josu Ceberio, and Alexander Mendiburu. "MARCO: A Memory-Augmented Reinforcement Framework for Combinatorial Optimization." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/766.

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Neural Combinatorial Optimization (NCO) is an emerging domain where deep learning techniques are employed to address combinatorial optimization problems as a standalone solver. Despite their potential, existing NCO methods often suffer from inefficient search space exploration, frequently leading to local optima entrapment or redundant exploration of previously visited states. This paper introduces a versatile framework, referred to as Memory-Augmented Reinforcement for Combinatorial Optimization (MARCO), that can be used to enhance both constructive and improvement methods in NCO through an i

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Rosen, David W. "Design of Modular Product Architectures in Discrete Design Spaces Subject to Life Cycle Issues." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/dac-1485.

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Abstract A product’s architecture affects the ability of a company to customize, assemble, service, and recycle the product. Much of the flexibility to address these issues is locked into the product’s design during the configuration design stage when the architecture is determined. The concepts of modules and modularity are central to the description of an architecture, where a module is a set of components that share some characteristic. Modularity is a measure of the correspondence between the modules of a product from different viewpoints, such as functionality and physical structure. The

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Meel, Kuldeep S. "Counting, Sampling, and Synthesis: The Quest for Scalability." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/817.

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The current generation of symbolic reasoning techniques excel at the qualitative tasks (i.e., when the answer is Yes or No); such techniques sufficed for traditional systems whose design sought to achieve deterministic behavior. In contrast, modern computing systems crucially rely on the statistical methods to account for the uncertainty in the environment, and to reason about behavior of these systems, there is need to look beyond qualitative symbolic reasoning techniques. We will discuss our work focused on the development of the next generation of automated reasoning techniques that can per

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Souza, Uéverton, Fábio Protti, Maise Da Silva, and Dieter Rautenbach. "Multivariate Investigation of NP-Hard Problems: Boundaries Between Parameterized Tractability and Intractability." In XXVIII Concurso de Teses e Dissertações da SBC. Sociedade Brasileira de Computação - SBC, 2020. http://dx.doi.org/10.5753/ctd.2015.9996.

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In this thesis we present a multivariate investigation of the complexity of some NP-hard problems, i.e., we first develop a systematic complexity analysis of these problems, defining its subproblems and mapping which one belongs to each side of an “imaginary boundary” between polynomial time solvability and intractability. After that, we analyze which sets of aspects of these problems are sources of their intractability, that is, subsets of aspects for which there exists an algorithm to solve the associated problem, whose non-polynomial time complexity is purely a function of those sets. Thus,

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Shakarji, Craig M., and Vijay Srinivasan. "Convexity and Optimality Conditions for Constrained Least-Squares Fitting of Planes and Parallel Planes to Establish Datums." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70899.

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This paper addresses some important theoretical issues for constrained least-squares fitting of planes and parallel planes to a set of input points. In particular, it addresses the convexity of the objective function and the combinatorial characterizations of the optimality conditions. These problems arise in establishing planar datums and systems of planar datums in digital manufacturing. It is shown that even when the input points are in general position: (1) a primary planar datum can contact 1, 2, or 3 input points, (2) a secondary planar datum can contact 1 or 2 input points, and (3) two

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Corbett, Brian P., and David W. Rosen. "Platform Commonization With Discrete Design Spaces: Introduction of the Flow Design Space." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/dtm-48678.

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Many companies have adopted the usage of common platforms to support the development of product families. The problem addressed in this paper deals with the development of a common platform for an existing set of products that may or may not already form a product family. The common platform embodies the core function, form, and technology base shared across the product family. In this work, we focus on configuration aspects of the platform commonization problem to determine which components are in the platform and the relationships among these components. Configuration design spaces are discr

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Reports on the topic "Combinatorial set theory"

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Altstein, Miriam, and Ronald J. Nachman. Rational Design of Insect Control Agent Prototypes Based on Pyrokinin/PBAN Neuropeptide Antagonists. United States Department of Agriculture, 2013. http://dx.doi.org/10.32747/2013.7593398.bard.

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The general objective of this study was to develop rationally designed mimetic antagonists (and agonists) of the PK/PBAN Np class with enhanced bio-stability and bioavailability as prototypes for effective and environmentally friendly pest insect management agents. The PK/PBAN family is a multifunctional group of Nps that mediates key functions in insects (sex pheromone biosynthesis, cuticular melanization, myotropic activity, diapause and pupal development) and is, therefore, of high scientific and applied interest. The objectives of the current study were: (i) to identify an antagonist bioph

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