201 research outputs found
Lawrence Grossberg and Cultural Studies Today
No full textLawrence Grossberg is a scholar at the University of North Carolina (USA) and one of the most prominent exponents of American Cultural Studies, having worked with Stuart Hall, Richard Hoggart and James W. Carey. Author of Mediamaking: mass media and popular culture (with Charles Whitney and Ellen Wartella, Sage Publishers, 1998) and Caught in the Crossfire: Kids, Politics, and America’s Future (Paradigm Publishers, 2005), in June, 2013, professor Grossberg has been the Keynote Speaker of the 22nd Annual Meeting of Compós, in Salvador, Brazil. In this interview, Lawrence Grossberg speaks of his influences and of contemporary challenges for a cultural studies perspective.

Keywords
Cultural Studies. Communication Theory.</jats:p
Grossberg-Karshon twisted cubes and hesitant jumping walk avoidance
No full textⓒ The author. Let G be a complex simply-laced semisimple algebraic group of rank r and B a Borel subgroup. Let i is an element of [r](n) be a word and let l = (l(1), ...,l(n)) be a sequence of non-negative integers. Grossberg and Karshon introduced a virtual lattice polytope associated to i and l called a twisted cube, whose lattice points encode the character of a B-representation. More precisely, lattice points in the twisted cube, counted with sign according to a certain density function, yield the character of the generalized Dernazure module determined by i and l. In a recent work, the author and Harada described precisely when the Grossberg-Karshon twisted cube is untwisted, i.e., the twisted cube is a closed convex polytope, in the situation when the integer sequence l comes from a weight lambda for G. However, not every integer sequence l comes from a weight for G. In the present paper, we interpret the untwistedness of Grossberg Karshon twisted cubes associated with any word i and any integer sequence t using the combinatorics of i and l. Indeed, we prove that the Grossberg-Karshon twisted cube is untwisted precisely when i is hesitant-jumping-l-walk-avoiding11sci
Abstract decomposition theorem and applications
No full textelementary classes K with the amalgamation property, under the assumption that certain axioms regarding independence, existence of some prime models, and regular types are satisfied. This context encompasses the following: (1) K is the class of models of an ℵ0-stable first order theory. (2) K is the class of F a ℵ0-saturated models of a superstable first order theory. (3) K is the class of models of an excellent Scott sentence ψ ∈ Lω1,ω. (4) K the class of locally saturated models of a superstable good diagram D. (5) K is the class of (D, ℵ0)-homogeneous models of a totally transcendental good diagram D. We also prove the nonstructure part necessary to obtain a Main Gap theorem for (5), which appears in the second author’s Ph.D. thesis [Le]. The main gap in the contexts (1) and (2) are theorems of Shelah [Sh a]; (3) is by Grossberg and Hart [GrHa]; (4) by Hyttinen and Shelah [HySh2]
Global asymptotic stability of nonautonomous Cohen-Grossberg neural network models with infinite delays
No full textFor a general Cohen-Grossberg neural network model with potentially unbounded time-varying
coeffi cients and infi nite distributed delays, we give su fficient conditions for its global asymptotic
stability. The model studied is general enough to include, as subclass, the most of famous
neural network models such as Cohen-Grossberg, Hopfi eld, and bidirectional associative memory.
Contrary to usual in the literature, in the proofs we do not use Lyapunov functionals. As
illustrated, the results are applied to several concrete models studied in the literature and a
comparison of results shows that our results give new global stability criteria for several neural
network models and improve some earlier publications.The second author research was suported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the "Fundacao para a Ciencia e a Tecnologia", through the project PEstOE/MAT/UI0013/2014. The authors thank the referee for valuable comments
CANONICAL FORKING IN AECS
No full textAbstract. Boney and Grossberg [BG] proved that every nice AEC has an independence relation. We prove that this relation is unique: In any given AEC, there can exist at most one independence relation that satisfies existence, extension, uniqueness and local character. While doing this, we study more generally properties of independence relations for AECs and also prove a canonicity result for Shelah’s good frames. The usual tools of first-order logic (like the finite equivalence relation theorem or the type amalgamation theorem in simple theories) are not available in this context. In addition to the loss of the compactness theorem, we have the added difficulty of not being able to assume that types are sets of formulas. We work axiomatically and develop new tools to understand this general framework. Content
UNIQUENESS OF LIMIT MODELS IN CLASSES WITH AMALGAMATION
No full textAbstract. We prove: Theorem 0.1 (Main Theorem). Let K be an AEC and µ> LS(K). Suppose K satisfies the disjoint amalgamation property for models of cardinality µ. If K is µ-Galois-stable, does not have long splitting chains, and satisfies locality of splitting 1, then any two (µ, σℓ)-limits over M for (ℓ ∈ {1, 2}) are isomorphic over M. This result extends results of Shelah from [Sh 394], [Sh 576], [Sh 600], Kolman and Shelah in [KoSh] and Shelah & Villaveces from [ShVi]. Our uniqueness theorem was used by Grossberg and VanDieren to prove a case of Shelah’s categoricity conjecture for tame AEC in [GrVa2]. 1. introduction In 1977, Shelah, building on the work of Jónsson and Fraïssé, identified a non-elementary context in which a model theoretic analysis could be carried out. Shelah began to study classes of models equipped with a partial order which exhibit many of the properties that the models of a first order theory have with respect to the elementary submodel relation. Such classes were named abstract elementary classes. They are broad enough to generalize Lω1,ω(Q). We reproduce the definition here. Definition 1.1. Let K be a class of structures all in the same similarity type L(K), and let ≺K be a partial order on K. The ordered pair 〈K, ≺K 〉 is an abstract elementary class, AEC for short iff A0 (Closure under isomorphism) (a) For every M ∈ K and every L(K)-structure N if M ∼ = N then N ∈ K. (b) Let N1, N2 ∈ K and M1, M2 ∈ K such that there exist fl: Nl ∼ = Ml (for l = 1, 2) satisfying f1 ⊆ f2 then N1 ≺K N2 implies tha
Classification Theory for Abstract Elementary Classes
No full textIn this paper some of the basics of classification theory for abstract elementary classes are discussed. Instead of working with types which are sets of formulas (in the first-order case) we deal instead with Galois types which are essentially orbits of automorphism groups acting on the structure. Some of the most basic results in classification theory for non elementary classes are presented. The motivating point of view is Shelah's categoricity conjecture for L# 1 ,# . While only very basic theorems are proved, an effort is made to present number of different technologies: Flavors of weak diamond, models of weak set theories, and commutative diagrams. We focus in issues involving existence of Galois types, extensions of types and Galois-stability
Canonical forking in AECs
No full textBoney and Grossberg [BG] proved that every nice AEC has an independence relation. We prove that this relation is unique: In any given AEC, there can exist at most one independence relation that satisfies existence, extension, uniqueness and local character. While doing this, we study more generally properties of independence relations for AECs and also prove a canonicity result for Shelah’s good frames. The usual tools of first-order logic (like the finite equivalence relation theorem or the type amalgamation theorem in simple theories) are not available in this context. In addition to the loss of the compactness theorem, we have the added difficulty of not being able to assume that types are sets of formulas. We work axiomatically and develop new tools to understand this general framework.</p
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