Set Matching: An Enhancement of the Hales-Jewett Pairing Strategy

When solving k-in-a-Row games, the Hales-Jewett pairing strategy [4] is a well-known strategy to prove that specific positions are (at most) a draw. It requires two empty squares per possible winning line (group) to be marked, i.e., with a coverage ratio of 2.0. In this paper we present a new strategy, called Set Matching. A matching set consists of a set of nodes (the markers), a set of possible winning lines (the groups), and a coverage set indicating how all groups are covered after every first initial move. This strategy needs less than two markers per group. As such it is able to prove positions in k-in-a-Row games to be draws, which cannot be proven using the Hales-Jewett pairing strategy. We show several efficient configurations with their matching sets. These include Cycle Configurations, BiCycle Configurations, and PolyCycle Configurations involving more than two cycles. Depending on configuration, the coverage ratio can be reduced to 1.14. Many examples in the domain of solving k-in-a-Row games are given, including the direct proof (without further investigation) that the empty 4 x 4 board is a draw for 4-in-a-Row

On Competition and the Strategic Management of Intellectual Property in Oligopoly

An innovative firm with private information about its indivisible process innovation chooses strategically whether to apply for a patent with probabilistic validity or rely on secrecy. By doing so, the firm manages its rivals’ beliefs about the size of the innovation, and affects the incentives in the product market. A Cournot competitor tends to patent big innovations, and keep small innovations secret, while a Bertrand competitor adopts the reverse strategy. Increasing the number of firms gives a greater (smaller) patenting incentive for Cournot (Bertrand) competitors. Increasing the degree of product substitutability increases the incentives to patent the innovation

The EU Strategy for Central Asia says 'security'. Does this include Security Sector Reform? EUCAM Policy Brief No. 10, 12 November 2009

Central Asia faces a broad range of security challenges. Due to the region's position at the crossroads between Russia, China and Afghanistan, Pakistan, Iran and the Caspian Sea it is confronted with a range of trans-national issues such as drug trafficking, human trafficking, organised crime and terrorism. Central Asia also encounters specific regional threats including scarcity of water resources for generating power and irrigation purposes, which is currently causing tension. On a national level the five Central Asian republics face the threat of instability due to bad governance and the harsh impact of the economic crisis. The European Union regards itself as a security actor and takes a keen interest in working with Central Asian states on the basis of joint security interests. This EUCAM policy brief assesses in what aspects of Security Sector Reform the EU is engaged in with Central Asia and in what context these possible activities should be viewed

Study of Fish Weight Loss in Solar Dryer Across Different Agro-Ecological Zones of Nigeria

Drying sessions were conducted across Nigeria to study the interaction between fish weight loss and the meteorological parameters. Correlation analyses using weight loss values show that latitude is strongly related (r =+0.96) to weight loss of fish inside the dryer while altitude had a weak relationship (r = +0.24) with weight loss. The results show that New Bussa recorded more weight loss of fish than Jos, despite their uniform latitude. Weight loss records in Jos, was however better than those of Warri and Ibadan

The Effects of Disclosure Regulation on Innovative Firms: Common Values

Firms in an R&D race actively manage rivals’ beliefs by disclosing and concealinginformation on their cost of investment. The firms’ disclosure strategies affect theirincentives to invest in R&D, and to acquire information. We compare equilibria undervoluntary disclosure with those under mandatory disclosure in a model where the firms’cost of investment are identically independently distributed. Under voluntary disclosurefirms conceal bad news, and disclose good news only if little knowledge spills over toheir rival. Under mandatory disclosure firms expect higher profits for giveninformation acquisition investments, but they acquire less information. ZUSAMMENFASSUNG - (Die Wirkung von Offenlegungsvorschriften auf innovative Firmen: Perfekt korrelierte Werte) Unternehmen, welche an einem F&E -Wettbewerb teilnehmen, managen aktiv die Erwartungen ihrer Konkurrenten, indem sie gezielt entscheiden, ob sie Informationen über ihre Investitionskosten veröffentlichen oder geheim halten. Durch ihre Offenlegungsstrategien beeinflussen sie sowohl die Anreize Ihrer Konkurrenten, Informationen zu sammeln, wie auch deren Anreize, F&E zu betreiben. Anhand eines Modells mit vollständig positiver Korrelation zwischen den Investitionskosten der Unternehmen vergleicht der Beitrag Gleichgewichte in denen die Unternehmen freiwillig wählen, ob sie ihre Informationen offen legen wollen, mit den Gleichgewichten, bei denen Unternehmen ihre Information offen legen müssen. Bei freiwilliger Offenlegung veröffentlichen Unternehmen schlechte Nachrichten und behalten gute für sich, um Mitbewerber zu entmutigen. Bei Offenlegungspflicht erwarten Unternehmen typischerweise höhere Gewinne für vorgegebene Investitionen in Informationskosten, aber sie beschaffen sich weniger Information.R&D Competition, Information Acquisition, Disclosure Regulation

The e-revolution and post-compulsory education: using e-business models to deliver quality education

The best practices of e-business are revolutionising not just technology itself but the whole process through which services are provided; and from which important lessons can be learnt by post-compulsory educational institutions. This book aims to move debates about ICT and higher education beyond a simple focus on e-learning by considering the provision of post-compulsory education as a whole. It considers what we mean by e-business, why e-business approaches are relevant to universities and colleges and the key issues this raises for post-secondary education

Between unsafe spaces and the comfort zone? Exploring the impact of learning environments on ‘doing’ learning

This paper explores how learning can be understood as a liminal space or transitional journey from one way of knowing to another; and where ‘doing’ learning is as much about being inculcated into the un-noticed rules and conventions of education itself as it is about developing understanding of the content of a subject discipline. By starting from Meyer and Land’s notion of threshold concepts and from ethnomethodological approaches which explore the ‘problematic accomplishment’ of everyday social and spatial practices, this paper considers how both new e-learning environments and more traditional face-to-face settings intersect with, and impact on, our conventional routines for producing and recognizing learning. Through a case study of a design project with interior architecture students, it explores what happened when attempts were made to inculcate a complex threshold concept - offering an alternative understanding of the relationship between disability and architecture to ‘standard’ conventions of accessibility – in both the ‘normal’ studio environment and online, via a blog. The paper concludes by suggesting we need to understand much more about what kinds of unspoken social and spatial practices frame the learning process in different disciplines in order to explore how we can create effective liminal spaces for both teachers and learners