In this work, we achieve gap amplification for the Small-Set Expansion problem. Specifically, we show that an instance of the Small-Set Expansion Problem with completeness ε and soundness 12 is at least as difficult as Small-Set Expansion with completeness ε and soundness f (ε), for any function f (ε) which grows faster than √ ε. We achieve this amplification via random walks – the output graph...

A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter ...

Servitization in the manufacturing industry implies a shift from an offer based mainly on standard goods, to a wider value proposition composed of solutions aimed at solving specific customers’ problems, obtained by integrating tangible and intangible elements. The purpose of this paper is to investigate the servitization strategies of manufacturing firms, more specifically about: (i) how manuf...

Let us consider the interval [0, 1) as a billiard table rectangle with perimeter 1 and a sequence F(m) ∈ [0, 1),m ∈ N ∪ {0}, of successive rebounds of a billiard ball against the sides of a billiard rectangle. We prove that if I is an open segment of a billiard rectangle, then the differences between the successive values of m for which the F(m) lies in I , take at most one even and at most fou...

Recent evidence suggests that electrical coupling plays a role in generating oscillatory behaviour in networks of neurons; however, the underlying mechanisms have not been identified. Using a cellular automata model proposed by Traub et al (Traub R D, Schmitz D, Jefferys J G and Draguhn A 1999 High-frequency population oscillations are predicted to occur in hippocampal pyramidal neural networks...

Purpose: The paper suggests a way to support work-integrated learning for knowledge work which poses a great challenge for current research and practice. Methodology/Approach: We first suggest a Workplace Learning Context Model which has been derived by analyzing knowledge work and the knowledge sources used by knowledge workers. We then focus on the part of the context which specifies competen...

This document briefly introduces the existing mechanisms that could be utilized for IPv6 site renumbering and tries to cover most of the explicit issues and requirements associated with IPv6 renumbering. The content is mainly a gap analysis that provides a basis for future works to identify and develop solutions or to stimulate such development as appropriate. The gap analysis is organized by t...

Current Status • In the last IETF meeting, there were two practice & gap analysis drafts presented. – draft-liu-dmm-of-deployment-00 – draft-zuniga-dmm-gap-analysis-03 • The authors decide to merge those two drafts according to the chairs suggestion. – draft-ietf-dmm-best-practices-gap-analysis-00 Progress • Progress: – Initial proposal for the structure of the draft. – WG draft has been submit...

In 1965 Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R3 is at least 2π2 and attains this minimal value if and only if the torus is a Möbius transform of the Clifford torus. This was recently proved by Marques and Neves in [13]. In this paper, we show for tori there is a gap to the next critical point of the Willmore energy and we discuss an a...