On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Effect of surface conditions on flow of a micropolar fluid driven by a porous stretching sheet

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Exploring the effectiveness of virtual product placement on recall and recognition of new brands

This paper investigates the effectiveness of virtual product placement as a marketing tool by examining the relationship between brand recall and recognition and virtual product placement. It also aims to address a gap in the existing academic literature by focusing on the impact of product placement on recall and recognition of new brands. The growing importance of product placement is discussed and a review of previous research on product placement and virtual product placement is provided. The research methodology used to study the recall and recognition effects of virtual product placement are described and key findings presented. Finally, implications are discussed and recommendations for future research provided.

Polymer nanocomposites based on P3OT, TPU and SWNT: preparation and characterization

Single walled carbon nanotubes (SWNTs) were incorporated in polymer nanocomposites based on poly(3-octylthiophene) (P3OT), thermoplastic polyurethane (TPU) or a blend of them. Thermogravimetry demonstrated the success of the purification procedure employed in the chemical treatment of SWNTs prior to composite preparation. Stable dispersions of SWNTs in chloroform were obtained by non-covalent interactions with the dissolved polymers. Composites exhibited glass transitions, melting temperatures and heat of fusion which changed in relation to pure polymers. This behavior is discussed as associated to interactions between nanotubes and polymers. The conductivity at room temperature of the blend (TPU-P3OT) with SWNT is higher than the P3OT/SWNT composite.

A Multiplicative Homomorphic Sealed-Bid Auction-Based on Goldwasser-Micali Encryption

Instead of the costly encryption algorithms traditionally employed in auction schemes, efficient Goldwasser-Micali encryption is used to design a new sealed-bid auction. Multiplicative homomorphism instead of the traditional additive homomorphism is exploited to achieve security and high efficiency in the auction. The new scheme is the currently known most efficient non-interactive sealed-bid auction with bid privacy.