Displaying similar documents to “Antichains in the homomorphism order of graphs”

A strongly non-Ramsey uncountable graph

Péter Komjáth (1997)

Fundamenta Mathematicae

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It is consistent that there exists a graph X of cardinality ℵ 1 such that every graph has an edge coloring with ℵ 1 colors in which the induced copies of X (if there are any) are totally multicolored (get all possible colors).

The Farey graph.

Jones, Gareth A. (1987)

Séminaire Lotharingien de Combinatoire [electronic only]

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Discriminating between causal structures in Bayesian Networks given partial observations

Philipp Moritz, Jörg Reichardt, Nihat Ay (2014)

Kybernetika

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Given a fixed dependency graph G that describes a Bayesian network of binary variables X 1 , ⋯ , X n , our main result is a tight bound on the mutual information I c ( Y 1 , ⋯ , Y k ) = ∑ j = 1 k H ( Y j ) / c - H ( Y 1 , ⋯ , Y k ) of an observed subset Y 1 , ⋯ , Y k of the variables X 1 , ⋯ , X n . Our bound depends on certain quantities that can be computed from the connective structure of the nodes in G . Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.

Analytic determinacy and 0# A forcing-free proof of Harrington’s theorem

Ramez Sami (1999)

Fundamenta Mathematicae

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We prove the following theorem: Given a⊆ω and 1 ≤ α < ω 1 C K , if for some η < ℵ 1 and all u ∈ WO of length η, a is Σ α 0 ( u ) , then a is Σ α 0 . We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: Σ 1 1 -Turing-determinacy implies the existence of 0 .

A note on Tsirelson type ideals

Boban Veličković (1999)

Fundamenta Mathematicae

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Using Tsirelson’s well-known example of a Banach space which does not contain a copy of c 0 or l p , for p ≥ 1, we construct a simple Borel ideal I T such that the Borel cardinalities of the quotient spaces P ( ℕ ) / I T and P ( ℕ ) / I 0 are incomparable, where I 0 is the summable ideal of all sets A ⊆ ℕ such that ∑ n ∈ A 1 / ( n + 1 ) < ∞ . This disproves a “trichotomy” conjecture for Borel ideals proposed by Kechris and Mazur.

Entropy and growth of expanding periodic orbits for one-dimensional maps

A. Katok, A. Mezhirov (1998)

Fundamenta Mathematicae

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Let f be a continuous map of the circle S 1 or the interval I into itself, piecewise C 1 , piecewise monotone with finitely many intervals of monotonicity and having positive entropy h. For any ε > 0 we prove the existence of at least e ( h - ε ) n k periodic points of period n k with large derivative along the period, | ( f n k ) ' | > e ( h - ε ) n k for some subsequence n k of natural numbers. For a strictly monotone map f without critical points we show the existence of at least ( 1 - ε ) e h n such points.

Chaotic continua of (continuum-wise) expansive homeomorphisms and chaos in the sense of Li and Yorke

Hisao Kato (1994)

Fundamenta Mathematicae

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A homeomorphism f : X → X of a compactum X is expansive (resp. continuum-wise expansive) if there is c > 0 such that if x, y ∈ X and x ≠ y (resp. if A is a nondegenerate subcontinuum of X), then there is n ∈ ℤ such that d ( f n ( x ) , f n ( y ) ) > c (resp. d i a m f n ( A ) > c ). We prove the following theorem: If f is a continuum-wise expansive homeomorphism of a compactum X and the covering dimension of X is positive (dim X > 0), then there exists a σ-chaotic continuum Z = Z(σ) of f (σ = s or σ = u), i.e. Z is a nondegenerate...