Recently, the theory of dense graph limits has received attention from multiple disciplines including graph theory, computer science, statistical physics, probability, statistics, and group theory. In this paper we initiate the study of the general structure of differentiable graphon parameters F . We derive consistency conditions among the higher Gâteaux derivatives of F when restricted to the...

The shapes of a cryptographic protocol are its minimal, essentially different executions. In previous work, we have described a search algorithm to discover the shapes of a protocol, and implemented the algorithm in a Cryptographic Protocol Shape Analyzer cpsa. In this paper, we show its completeness, i.e. that every shape can in fact be found in a finite number of steps. The steps in question ...

Solution: For the action mentioned in the hint, the stabilizer of the coset eH (e is the identity) is H since gH = H implies that g ∈ H. The kernel K of the homomorphism of G into the permutation group of the cosets is a normal subgroup of G which is the intersection of stabilizers of all cosets. In particular the kernel K of the above homomorphism is a subgroup of H. Its index in G is equal to...

We give explicit formulas for maps in a long exact sequence connecting bialgebra cohomology to Hochschild cohomology. We give a sufficient condition for the connecting homomorphism to be surjective. We apply these results to compute all bialgebra two-cocycles of certain Radford biproducts (bosonizations). These two-cocycles are precisely those associated to the finite dimensional pointed Hopf a...

It is proved that a homomorphism h preserves the class of languages recognized by trellis automata augmented with the capacity of handling the empty string (or, equivalently, generated by linear conjunctive grammars) if and only if either h is injective, or h maps every symbol to the empty string. The transformation is effective in the former case and cannot be effectively done in the latter.

Variable threshold concept lattice (VTCL) was proposed by Ma et al.(2006), which provide a new parameterized way to obtain formal concepts from data with fuzzy attributes. Axiomatic Fuzzy Set (AFS) algebras were proposed by Liu (1998), which are new semantic methodology relating to the fuzzy theory. In this paper, in order to explore the relationship between the AFS algebras and VTCL, three alg...

A signed graph is a simple with two types of edges. Switching vertex v corresponds to changing the type each edge incident v. homomorphism from G another H mapping φ:V(G)→V(H) such that, after switching any number vertices G, φ maps every an same in H. The chromatic χs(G) order smallest that there We show triangular grids at most 10 and hexagonal 4.

Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from affine super Yangian [Formula: see text] to universal enveloping algebra of rectangular W-superalgebra for all m ≠ n, m, n ≥ 2 or 3, = 0. Furthermore, show that image this is dense, provided k + ( − n)( l 1)

208 NOTICES OF THE AMS VOLUME 51, NUMBER 2 As far as I know, the notion of a quasi-morphism does not have much to do with category theory. This very natural idea underlies several interesting recent developments at the crossroads of algebra, topology, geometry, and dynamics. Other, perhaps better, names currently in use for the same concept are quasi-homomorphism and pseudo-character. Let G be ...

(a) Prove that [G,G]CG. (b) Prove that the quotient Gab := G/[G,G] (called the abelianization of G) is abelian. (c) If N CG is any normal subgroup such that G/N is abelian, prove that [G,G] ≤ N . (d) Put everything together to prove the universal property of abelianization: Given a homomorphism φ : G→ A to an abelian group A, there exists a unique homomorphism φ̄ := Gab → A such that φ = φ̄ ◦ π, ...