Results for 'Random graphs'

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  1. The Strange Logic of Random Graphs.Joel Spencer - 2001 - Springer Verlag.
    The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.
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  2.  34
    Random Graphs in the Monadic Theory of Order.Shmuel Lifsches & Saharon Shelah - 1999 - Archive for Mathematical Logic 38 (4-5):273-312.
    We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the monadic theory of all chains. It is provable from ZFC that the theory of random graphs is not interpretable in the monadic second order theory of short chains (hence, in the monadic theory of the real line).
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  3.  32
    The Cofinality of the Random Graph.Steve Warner - 2001 - Journal of Symbolic Logic 66 (3):1439-1446.
    We show that under Martin's Axiom, the cofinality cf(Aut(Γ)) of the automorphism group of the random graph Γ is 2 ω.
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  4.  28
    Reducts of the Random Graph.Simon Thomas - 1991 - Journal of Symbolic Logic 56 (1):176-181.
  5.  6
    Saturating the Random Graph with an Independent Family of Small Range. [REVIEW]Saharon Shelah & Maryanthe Malliaris - 2015 - In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. pp. 319-338.
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  6.  4
    In the Random Graph G(N, P), P = N−A: If Ψ has Probability O(N−Ε) for Every Ε > 0 Then It has Probability O(E−Nε) for Some Ε > 0. [REVIEW]Saharon Shelah - 1996 - Annals of Pure and Applied Logic 82 (1):97-102.
  7.  10
    In the Random Graph G(N, P), P = N−A: If Ψ has Probability O(N−Ε) for Every Ε > 0 Then It has Probability O(E−Nε) for Some Ε > 0.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 82 (1):97-102.
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  8.  19
    In the Random Graph< I> G(< I> N_,< I> P_),< I> P_=< I> N_< Sup>− a: If Ψ has Probability< I> O_(< I> N_< Sup>− Ε) for Every< I> Ε_> 0 Then It has Probability< I> O_(< I> E_< Sup>− Nε) for Some< I> Ε> 0. [REVIEW]Saharon Shelah - 1996 - Annals of Pure and Applied Logic 82 (1):97-102.
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  9.  13
    The Metamathematics of Random Graphs.John T. Baldwin - 2006 - Annals of Pure and Applied Logic 143 (1-3):20-28.
    We explain and summarize the use of logic to provide a uniform perspective for studying limit laws on finite probability spaces. This work connects developments in stability theory, finite model theory, abstract model theory, and probability. We conclude by linking this context with work on the Urysohn space.
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  10.  43
    The Conjugacy Problem for the Automorphism Group of the Random Graph.Samuel Coskey, Paul Ellis & Scott Schneider - 2011 - Archive for Mathematical Logic 50 (1-2):215-221.
    We prove that the conjugacy problem for the automorphism group of the random graph is Borel complete, and discuss the analogous problem for some other countably categorical structures.
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  11.  12
    Monadic Second-Order Properties of Very Sparse Random Graphs.L. B. Ostrovsky & M. E. Zhukovskii - 2017 - Annals of Pure and Applied Logic 168 (11):2087-2101.
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  12.  50
    Infinitary Logics and Very Sparse Random Graphs.James F. Lynch - 1997 - Journal of Symbolic Logic 62 (2):609-623.
    Let L ω ∞ω be the infinitary language obtained from the first-order language of graphs by closure under conjunctions and disjunctions of arbitrary sets of formulas, provided only finitely many distinct variables occur among the formulas. Let p(n) be the edge probability of the random graph on n vertices. It is shown that if p(n) ≪ n -1 satisfies certain simple conditions on its growth rate, then for every σ∈ L ω ∞ω , the probability that σ holds (...)
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  13.  19
    The Cofinality of the Saturated Uncountable Random Graph.Steve Warner - 2004 - Archive for Mathematical Logic 43 (5):665-679.
    Assuming CH, let be the saturated random graph of cardinality ω1. In this paper we prove that it is consistent that and can be any two prescribed regular cardinals subject only to the requirement.
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  14.  3
    Which Subsets of an Infinite Random Graph Look Random?Will Brian - 2018 - Mathematical Logic Quarterly 64 (6):478-486.
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  15.  2
    The Structure of Random Automorphisms of the Random Graph.Udayan B. Darji, Márton Elekes, Kende Kalina, Viktor Kiss & Zoltán Vidnyánszky - 2022 - Annals of Pure and Applied Logic 173 (9):103152.
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  16.  6
    Dilution of Ferromagnets Via a Random Graph-Based Strategy.Marco Alberto Javarone & Daniele Marinazzo - 2018 - Complexity 2018:1-11.
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  17.  12
    The Poset of All Copies of the Random Graph has the 2-Localization Property.Miloš S. Kurilić & Stevo Todorčević - 2016 - Annals of Pure and Applied Logic 167 (8):649-662.
  18.  10
    Reducts of the Random Bipartite Graph.Yun Lu - 2013 - Notre Dame Journal of Formal Logic 54 (1):33-46.
    Let $\Gamma$ be the random bipartite graph, a countable graph with two infinite sides, edges randomly distributed between the sides, but no edges within a side. In this paper, we investigate the reducts of $\Gamma$ that preserve sides. We classify the closed permutation subgroups containing the group $\operatorname {Aut}(\Gamma)^{\ast}$ , where $\operatorname {Aut}(\Gamma)^{\ast}$ is the group of all isomorphisms and anti-isomorphisms of $\Gamma$ preserving the two sides. Our results rely on a combinatorial theorem of Nešetřil and Rödl and a (...)
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  19.  29
    Erdős Graphs Resolve Fine's Canonicity Problem.Robert Goldblatt, Ian Hodkinson & Yde Venema - 2004 - Bulletin of Symbolic Logic 10 (2):186-208.
    We show that there exist 2 ℵ 0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames (a monomodal example can then be obtained using simulation results of (...)
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  20.  8
    The Complexity of Random Ordered Structures.Joel Spencer & Katherine St John - 2008 - Annals of Pure and Applied Logic 152 (1-3):174-179.
    We show that for random bit strings, Up, with probability, image, the first order quantifier depth D) needed to distinguish non-isomorphic structures is Θ, with high probability. Further, we show that, with high probability, for random ordered graphs, G≤,p with edge probability image, D)=Θ, contrasting with the results for random graphs, Gp, given by Kim et al. [J.H. Kim, O. Pikhurko, J. Spencer, O. Verbitsky, How complex are random graphs in first order logic? (...)
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  21.  12
    The Complexity of Random Ordered Structures.Joel H. Spencer & Katherine St John - 2008 - Annals of Pure and Applied Logic 152 (1):174-179.
    We show that for random bit strings, Up, with probability, image, the first order quantifier depth D) needed to distinguish non-isomorphic structures is Θ, with high probability. Further, we show that, with high probability, for random ordered graphs, G≤,p with edge probability image, D)=Θ, contrasting with the results for random graphs, Gp, given by Kim et al. [J.H. Kim, O. Pikhurko, J. Spencer, O. Verbitsky, How complex are random graphs in first order logic? (...)
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  22.  17
    Ramsey-Type Graph Coloring and Diagonal Non-Computability.Ludovic Patey - 2015 - Archive for Mathematical Logic 54 (7-8):899-914.
    A function is diagonally non-computable if it diagonalizes against the universal partial computable function. D.n.c. functions play a central role in algorithmic randomness and reverse mathematics. Flood and Towsner asked for which functions h, the principle stating the existence of an h-bounded d.n.c. function implies Ramsey-type weak König’s lemma. In this paper, we prove that for every computable order h, there exists an ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega}$$\end{document} -model of h-DNR which is not a not (...)
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  23.  6
    On countably saturated linear orders and certain class of countably saturated graphs.Ziemowit Kostana - 2021 - Archive for Mathematical Logic 60 (1):189-209.
    The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality \. We provide some examples of pairwise non-isomorphic countably saturated linear orders of cardinality \, under different set-theoretic assumptions. We give a new proof of the old theorem of Harzheim, that the class of countably saturated linear orders has a uniquely determined one-element basis. From (...)
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  24.  56
    Adding One Random Real.Tomek Bartoszyński, Andrzej Rosłanowski & Saharon Shelah - 1996 - Journal of Symbolic Logic 61 (1):80-90.
    We study the cardinal invariants of measure and category after adding one random real. In particular, we show that the number of measure zero subsets of the plane which are necessary to cover graphs of all continuous functions may be large while the covering for measure is small.
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  25.  21
    Automatic Semantic Edge Labeling Over Legal Citation Graphs.Ali Sadeghian, Laksshman Sundaram, Daisy Zhe Wang, William F. Hamilton, Karl Branting & Craig Pfeifer - 2018 - Artificial Intelligence and Law 26 (2):127-144.
    A large number of cross-references to various bodies of text are used in legal texts, each serving a different purpose. It is often necessary for authorities and companies to look into certain types of these citations. Yet, there is a lack of automatic tools to aid in this process. Recently, citation graphs have been used to improve the intelligibility of complex rule frameworks. We propose an algorithm that builds the citation graph from a document and automatically labels each edge (...)
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  26. Classification of Drug-Naive Children with Attention-Deficit/Hyperactivity Disorder From Typical Development Controls Using Resting-State fMRI and Graph Theoretical Approach.Masoud Rezaei, Hoda Zare, Hamidreza Hakimdavoodi, Shahrokh Nasseri & Paria Hebrani - 2022 - Frontiers in Human Neuroscience 16.
    Background and objectivesThe study of brain functional connectivity alterations in children with Attention-Deficit/Hyperactivity Disorder has been the subject of considerable investigation, but the biological mechanisms underlying these changes remain poorly understood. Here, we aim to investigate the brain alterations in patients with ADHD and Typical Development children and accurately classify ADHD children from TD controls using the graph-theoretical measures obtained from resting-state fMRI.Materials and methodsWe investigated the performances of rs-fMRI data for classifying drug-naive children with ADHD from TD controls. Fifty (...)
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  27.  1
    Children ASD Evaluation Through Joint Analysis of EEG and Eye-Tracking Recordings With Graph Convolution Network.Shasha Zhang, Dan Chen, Yunbo Tang & Lei Zhang - 2021 - Frontiers in Human Neuroscience 15.
    Recent advances in neuroscience indicate that analysis of bio-signals such as rest state electroencephalogram and eye-tracking data can provide more reliable evaluation of children autism spectrum disorder than traditional methods of behavior measurement relying on scales do. However, the effectiveness of the new approaches still lags behind the increasing requirement in clinical or educational practices as the “bio-marker” information carried by the bio-signal of a single-modality is likely insufficient or distorted. This study proposes an approach to joint analysis of EEG (...)
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  28.  7
    Monitoring Effective Connectivity in the Preterm Brain: A Graph Approach to Study Maturation.M. Lavanga, O. De Wel, A. Caicedo, K. Jansen, A. Dereymaeker, G. Naulaers & S. Van Huffel - 2017 - Complexity:1-13.
    In recent years, functional connectivity in the developmental science received increasing attention. Although it has been reported that the anatomical connectivity in the preterm brain develops dramatically during the last months of pregnancy, little is known about how functional and effective connectivity change with maturation. The present study investigated how effective connectivity in premature infants evolves. To assess it, we use EEG measurements and graph-theory methodologies. We recorded data from 25 preterm babies, who underwent long-EEG monitoring at least twice during (...)
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  29.  34
    Novel Method of Identifying Time Series Based on Network Graphs.Ying Li, Hongduo Caö & Yong Tan - 2011 - Complexity 17 (1):13-34.
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  30.  35
    Phase Transitions in Associative Memory Networks.Ben Goertzel - 1993 - Minds and Machines 3 (3):313-317.
    Ideas from random graph theory are used to give an heuristic argument that associative memory structure depends discontinuously on pattern recognition ability. This argument suggests that there may be a certain minimal size for intelligent systems.
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  31.  12
    Food-Sharing Networks in Lamalera, Indonesia.David A. Nolin - 2010 - Human Nature 21 (3):243-268.
    Exponential random graph modeling (ERGM) is used here to test hypotheses derived from human behavioral ecology about the adaptive nature of human food sharing. Respondents in all (n = 317) households in the fishing and sea-hunting village of Lamalera, Indonesia, were asked to name those households to whom they had more frequently given (and from whom they had more frequently received) food during the preceding sea-hunting season. The responses were used to construct a social network of between-household food-sharing relationships (...)
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  32.  3
    Exact Saturation in Pseudo-Elementary Classes for Simple and Stable Theories.Itay Kaplan, Nicholas Ramsey & Saharon Shelah - forthcoming - Journal of Mathematical Logic.
    We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class -exact saturation meaningfully reflects combinatorial dividing lines. We study PC-exact saturation for stable and simple theories. Among other results, we show that PC-exact saturation characterizes the stability cardinals of size at least continuum of a countable stable theory and, additionally, that simple unstable theories have PC-exact saturation at singular cardinals satisfying mild set-theoretic hypotheses. This had previously been open even (...)
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  33. Spatial Embedding and the Structure of Complex Networks.S. Bullock, L. Barnett & E. A. Di Paolo - 2010 - Complexity 16 (2):20-28.
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  34.  8
    The theories of Baldwin–Shi hypergraphs and their atomic models.Danul K. Gunatilleka - 2021 - Archive for Mathematical Logic 60 (7):879-908.
    We show that the quantifier elimination result for the Shelah-Spencer almost sure theories of sparse random graphs \\) given by Laskowski extends to their various analogues. The analogues will be obtained as theories of generic structures of certain classes of finite structures with a notion of strong substructure induced by rank functions and we will call the generics Baldwin–Shi hypergraphs. In the process we give a method of constructing extensions whose ‘relative rank’ is negative but arbitrarily small in (...)
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  35.  13
    On Some Dynamical Aspects of NIP Theories.Alireza Mofidi - 2018 - Archive for Mathematical Logic 57 (1-2):37-71.
    We investigate some dynamical features of the actions of automorphisms in the context of model theory. We interpret a few notions such as compact systems, entropy and symbolic representations from the theory of dynamical systems in the realm of model theory. In this direction, we settle a number of characterizations of NIP theories in terms of dynamics of automorphisms and invariant measures. For example, it is shown that the property of NIP corresponds to the compactness property of some associated systems (...)
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  36.  3
    Personality Traits, Self-Efficacy, and Friendship Establishment: Group Characteristics and Network Clustering of College Students’ Friendships.Dongdong Yan, Xi Yang & Huanzhe Zhang - 2022 - Frontiers in Psychology 13.
    Friendship establishment was analyzed using constructs from social cognitive theory and social network theory. In further studies, we investigated the effect of personality traits, interpersonal self-efficacy, and network structure on the establishment of friendships. In this study, we used social network analysis method and exponential random graph model. The following findings are reported. First, the friendship network of college students had small group characteristics, and the formation of this small group was more based on personality complementarity than similarity. The (...)
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  37.  10
    The Finite Submodel Property and Ω-Categorical Expansions of Pregeometries.Marko Djordjević - 2006 - Annals of Pure and Applied Logic 139 (1):201-229.
    We prove, by a probabilistic argument, that a class of ω-categorical structures, on which algebraic closure defines a pregeometry, has the finite submodel property. This class includes any expansion of a pure set or of a vector space, projective space or affine space over a finite field such that the new relations are sufficiently independent of each other and over the original structure. In particular, the random graph belongs to this class, since it is a sufficiently independent expansion of (...)
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  38.  17
    A Characterization of Retracts in Certain Fraïssé Limits.Igor Dolinka - 2012 - Mathematical Logic Quarterly 58 (1-2):46-54.
    Assuming certain conditions on a class equation image of finitely generated first-order structures admitting the model-theoretical construction of a Fraïssé limit, we characterize retracts of such limits as algebraically closed structures in a class naturally related to equation image. In this way we generalize an earlier description of retracts of the countably infinite random graph.
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  39.  77
    The Self-Organization of Time and Causality: Steps Towards Understanding the Ultimate Origin. [REVIEW]Francis Heylighen - 2010 - Foundations of Science 15 (4):345-356.
    Possibly the most fundamental scientific problem is the origin of time and causality. The inherent difficulty is that all scientific theories of origins and evolution consider the existence of time and causality as given. We tackle this problem by starting from the concept of self-organization, which is seen as the spontaneous emergence of order out of primordial chaos. Self-organization can be explained by the selective retention of invariant or consistent variations, implying a breaking of the initial symmetry exhibited by randomness. (...)
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  40.  17
    Information-Driven Network Analysis: Evolving the “Complex Networks” Paradigm.Remo Pareschi & Francesca Arcelli Fontana - 2016 - Mind and Society 15 (2):155-167.
    Network analysis views complex systems as networks with well-defined structural properties that account for their complexity. These characteristics, which include scale-free behavior, small worlds and communities, are not to be found in networks such as random graphs and lattices that do not correspond to complex systems. They provide therefore a robust ground for claiming the existence of “complex networks” as a non-trivial subset of networks. The theory of complex networks has thus been successful in making systematically explicit relevant (...)
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  41.  69
    Bare Canonicity of Representable Cylindric and Polyadic Algebras.Jannis Bulian & Ian Hodkinson - 2013 - Annals of Pure and Applied Logic 164 (9):884-906.
    We show that for finite n⩾3n⩾3, every first-order axiomatisation of the varieties of representable n-dimensional cylindric algebras, diagonal-free cylindric algebras, polyadic algebras, and polyadic equality algebras contains an infinite number of non-canonical formulas. We also show that the class of structures for each of these varieties is non-elementary. The proofs employ algebras derived from random graphs.
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  42. Strong Convergence in Finite Model Theory.Wafik Boulos Lotfallah - 2002 - Journal of Symbolic Logic 67 (3):1083-1092.
    In [9] we introduced a new framework for asymptotic probabilities, in which a $\sigma-additive$ measure is defined on the sample space of all sequences $A = $ of finite models, where the universe of An is {1, 2, .., n}. In this framework we investigated the strong 0-1 law for sentences, which states that each sentence either holds in An eventually almost surely or fails in An eventually almost surely. In this paper we define the strong convergence law for formulas, (...)
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  43.  1
    Partnering Strategies of Organizational Networks in Complex Environment of Disaster in the Centralized Political Context.Zhigang Tao & Haibo Zhang - 2020 - Complexity 2020:1-13.
    Organizational networks are a widely used approach to deal with the “wicked problems” of disasters. However, current studies are insufficient in examining what strategies organizations actually employ to select partners in a complex environment of disaster, particularly in the centralized administrative context. This case study uses exponential random graph models to explore different partnering strategies that organizations used to form organizational networks in response to the Tianjin Port blast, a well-known disaster in China. Results demonstrate that participating organizations prefer (...)
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  44.  24
    Spectra of Structures and Relations.Valentina S. Harizanov & Russel G. Miller - 2007 - Journal of Symbolic Logic 72 (1):324 - 348.
    We consider embeddings of structures which preserve spectra: if g: M → S with S computable, then M should have the same Turing degree spectrum (as a structure) that g(M) has (as a relation on S). We show that the computable dense linear order L is universal for all countable linear orders under this notion of embedding, and we establish a similar result for the computable random graph G. Such structures are said to be spectrally universal. We use our (...)
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  45.  1
    A Weighted Statistical Network Modeling Approach to Product Competition Analysis.Yaxin Cui, Faez Ahmed, Zhenghui Sha, Lijun Wang, Yan Fu, Noshir Contractor & Wei Chen - 2022 - Complexity 2022:1-16.
    Statistical network models have been used to study the competition among different products and how product attributes influence customer decisions. However, in existing research using network-based approaches, product competition has been viewed as binary, while in reality, the competition strength may vary among products. In this paper, we model the strength of the product competition by employing a statistical network model, with an emphasis on how product attributes affect which products are considered together and which products are ultimately purchased by (...)
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  46. Exploring the Role of Interpersonal Contexts in Peer Relationships Among Autistic and Non-Autistic Youth in Integrated Education.Yu-Lun Chen, Maxwell Schneider & Kristie Patten - 2022 - Frontiers in Psychology 13.
    The double empathy problem theory posits that autistic social difficulties emerge from an interpersonal misalignment in social experiences and expectations between autistic and non-autistic people. Supporting this, emerging research reveals better social outcomes in interactions within than across neurotypes among autistic and non-autistic people, emphasizing the need to examine the role of the interpersonal context in autistic social outcomes. However, research on peer relationships among autistic youth primarily focuses on individual characteristics in isolation from the interpersonal context. To address this, (...)
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  47.  7
    Solving Highly Cyclic Distributed Optimization Problems Without Busting the Bank: A Decimation-Based Approach.Jesús Cerquides, Juan Antonio Rodríguez-Aguilar, Rémi Emonet & Gauthier Picard - 2021 - Logic Journal of the IGPL 29 (1):72-95.
    In the context of solving large distributed constraint optimization problems, belief-propagation and incomplete inference algorithms are candidates of choice. However, in general, when the problem structure is very cyclic, these solution methods suffer from bad performance, due to non-convergence and many exchanged messages. As to improve performances of the MaxSum inference algorithm when solving cyclic constraint optimization problems, we propose here to take inspiration from the belief-propagation-guided decimation used to solve sparse random graphs. We propose the novel DeciMaxSum (...)
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  48.  22
    On $N$ -Dependence.Artem Chernikov, Daniel Palacin & Kota Takeuchi - 2019 - Notre Dame Journal of Formal Logic 60 (2):195-214.
    In this article, we develop and clarify some of the basic combinatorial properties of the new notion of n-dependence recently introduced by Shelah. In the same way as dependence of a theory means its inability to encode a bipartite random graph with a definable edge relation, n-dependence corresponds to the inability to encode a random -partite -hypergraph with a definable edge relation. We characterize n-dependence by counting φ-types over finite sets, and in terms of the collapse of (...) ordered -hypergraph indiscernibles down to order-indiscernibles. (shrink)
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  49.  20
    On Notions of Genericity and Mutual Genericity.J. K. Truss - 2007 - Journal of Symbolic Logic 72 (3):755 - 766.
    Generic automorphisms of certain homogeneous structures are considered, for instance, the rationals as an ordered set, the countable universal homogeneous partial order, and the random graph. Two of these cases were discussed in [7], where it was shown that there is a generic automorphism of the second in the sense introduced in [10]. In this paper. I study various possible definitions of 'generic' and 'mutually generic', and discuss the existence of mutually generic automorphisms in some cases. In addition, generics (...)
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  50.  2
    Coxeter Groups and Abstract Elementary Classes: The Right-Angled Case.Tapani Hyttinen & Gianluca Paolini - 2019 - Notre Dame Journal of Formal Logic 60 (4):707-731.
    We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes, for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of these results translates into (...)
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