Worry, problem elaboration and suppression of imagery: the role of concreteness

Both lay concept and scientific theory claim that worry may be helpful for defining and analyzing problems. Recent studies, however, indicate that worrisome problem elaborations are less concrete than worry-free problem elaborations. This challenges the problem solving view of worry because abstract problem analyses are unlikely to lead to concrete problem solutions. Instead the findings support the avoidance theory of worry which claims that worry suppresses aversive imagery. Following research findings in the dual-coding framework [Paivio, A. (1971). Imagery and verbal processes. New York: Holt, Rhinehart and Winston; Paivio, A. (1986). Mental representations: a dual coding approach. New York: Oxford University Press.], the present article proposes that reduced concreteness may play a central role in the understanding of worry. First, reduced concreteness can explain how worry reduces imagery. Second, it offers an explanation why worrisome problem analyses are unlikely to arrive at solutions. Third, it provides a key for the understanding of worry maintenance

Kneser-Hecke-operators in coding theory

The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code $C$ over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect $C$ in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be described in terms of a coding-theory analogue of the Siegel $\Phi$-operator

Correcting Quantum Errors with Entanglement

We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error correcting codes, thus allowing us to ``quantize'' all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.Comment: 17 pages, no figure. To appear in Scienc

Successive Refinement with Decoder Cooperation and its Channel Coding Duals

We study cooperation in multi terminal source coding models involving successive refinement. Specifically, we study the case of a single encoder and two decoders, where the encoder provides a common description to both the decoders and a private description to only one of the decoders. The decoders cooperate via cribbing, i.e., the decoder with access only to the common description is allowed to observe, in addition, a deterministic function of the reconstruction symbols produced by the other. We characterize the fundamental performance limits in the respective settings of non-causal, strictly-causal and causal cribbing. We use a new coding scheme, referred to as Forward Encoding and Block Markov Decoding, which is a variant of one recently used by Cuff and Zhao for coordination via implicit communication. Finally, we use the insight gained to introduce and solve some dual channel coding scenarios involving Multiple Access Channels with cribbing.Comment: 55 pages, 15 figures, 8 tables, submitted to IEEE Transactions on Information Theory. A shorter version submitted to ISIT 201

A Dual Fano, and Dual Non-Fano Matroidal Network

Matroidal networks are useful tools in furthering research in network coding. They have been used to show the limitations of linear coding solutions. In this paper we examine the basic information on network coding and matroid theory. We then go over the method of creating matroidal networks. Finally we construct matroidal networks from the dual of the fano matroid and the dual of the non-fano matroid, and breifly discuss some coding solutions

What is Genselfdual?

This paper presents developed software in the area of Coding Theory. Using it, all binary self-dual codes with given properties can be classified. The programs have consequent and parallel implementations. ACM Computing Classification System (1998): G.4, E.4