Tournament Sequences and Meeussen Sequences

A "tournament sequence" is an increasing sequence of positive integers (t_1,t_2,...) such that t_1=1 and t_{i+1} <= 2 t_i. A "Meeussen sequence" is an increasing sequence of positive integers (m_1,m_2,...) such that m_1=1, every nonnegative integer is the sum of a subset of the {m_i}, and each integer m_i-1 is the sum of a unique such subset. We show that these two properties are isomorphic. That is, we present a bijection between tournament and Meeussen sequences which respects the natural tree structure on each set. We also present an efficient technique for counting the number of tournament sequences of length n, and discuss the asymptotic growth of this number. The counting technique we introduce is suitable for application to other well-behaved counting problems of the same sort where a closed form or generating function cannot be found.Comment: 16 pages, 1 figure. Minor changes only; final version as published in EJ

Implementability Among Predicates

Much work has been done to understand when given predicates (relations) on discrete variables can be conjoined to implement other predicates. Indeed, the lattice of "co-clones" (sets of predicates closed under conjunction, variable renaming, and existential quantification of variables) has been investigated steadily from the 1960's to the present. Here, we investigate a more general model, where duplicatability of values is not taken for granted. This model is motivated in part by large scale neural models, where duplicating a value is similar in cost to computing a function, and by quantum mechanics, where values cannot be duplicated. Implementations in this case are naturally given by a graph fragment in which vertices are predicates, internal edges are existentially quantified variables, and "dangling edges" (edges emanating from a vertex but not yet connected to another vertex) are the free variables of the implemented predicate. We examine questions of implementability among predicates in this scenario, and we present the solution to all implementability problems for single predicates on up to three boolean values. However, we find that a variety of proof methods are required, and the question of implementability indeed becomes undecidable for larger predicates, although this is tricky to prove. We find that most predicates cannot implement the 3-way equality predicate, which reaffirms the view that duplicatability of values should not be assumed a priori

Networks of Relations for Representation, Learning, and Generalization

We propose representing knowledge as a network of relations. Each relation relates only a few continuous or discrete variables, so that any overall relationship among the many variables treated by the network winds up being distributed throughout the network. Each relation encodes which combinations of values correspond to past experience for the variables related by the relation. Variables may or may not correspond to understandable aspects of the situation being modeled by the network. A distributed calculational process can be used to access the information stored in such a network, allowing the network to function as an associative memory. This process in its simplest form is purely inhibitory, narrowing down the space of possibilities as much as possible given the data to be matched. In contrast with methods that always retrieve a best fit for all variables, this method can return values for inferred variables while leaving non-inferable variables in an unknown or partially known state. In contrast with belief propagation methods, this method can be proven to converge quickly and uniformly for any network topology, allowing networks to be as interconnected as the relationships warrant, with no independence assumptions required. The generalization properties of such a memory are aligned with the network's relational representation of how the various aspects of the modeled situation are related

Mapping Transitions towards Sustainable Consumption : Latitudes, Legends and Declinations in the Interaction between Consumers Culture and Sustainable Business Models

This paper seeks to chart “a navigation route“ towards sustainable consumption. We draw on data collected in research on consumers’ response to integrated products and services bundles conceptualized in design literature as Product Service Systems (PSS). PSS is of interest as it offers potential social and environmental benefits. Such services- based sustainable consumption practices have been neglected by consumer researchers. Methodological approaches to sustainable consumption favoured by policy makers focus research and interventions on individual consumer behaviour, but these have very limited success. Consumer practices, and the role that Government and other institutions play, are a more appropriate conceptual framework to explicate sustainable consumption. However, this Practice Theory approach is not sufficient either; the best solution might be a combination of this with an understanding of the individual value pursued by consumers. We extend Shove (2010)’s contention that adoption of sustainable consumption practices can only be explained with socio-cultural approaches; we propose that a combination of this perspective with an understanding of the value expected by individual consumers, is a more suitable approach than either behavioural paradigms or practices on their own to map these adoption mechanisms.Non peer reviewe

A Geometric Theorem for Network Design

Consider an infinite square grid G. How many discs of given radius r, centered at the vertices of G, are required, in the worst case, to completely cover an arbitrary disc of radius r placed on the plane? We show that this number is an integer in the set {3,4,5,6} whose value depends on the ratio of r to the grid spacing. One application of this result is to design facility location algorithms with constant approximation factors. Another application is to determine if a grid network design, where facilities are placed on a regular grid in a way that each potential customer is within a reasonably small radius around the facility, is cost effective in comparison to a nongrid design. This can be relevant to determine a cost effective design for base station placement in a wireless network

What value do consumers really expect from Product Service Systems? : Reflections on how a different conception of value could facilitate the implementation of PSS in consumer markets

Purpose – This paper explores how PSS may create value in consumer markets in urban environment and how consumers value PSS beyond a narrow focus on functionality. Design/ methodology/approach – Within a case study of a use orientated PSS based on baby products, we conducted ten ethnographic interviews of current users of the scheme. Findings – Our data gives evidence that some of these products are important possessions for consumers’ identity construction. In contrast with highly visible products such as push-chairs, however, baby cots and car seats are seen by consumers from a more utilitarian perspective. Practical implications – The design of a PSS provision around products which are highly symbolic is problematic because of a need to fully understand the complex symbolism and hedonic value consumers attribute to these products. Originality /value – We fill a gap in PSS research by adopting a constructivist perspective to explore the multidimensional value consumers co-create around a baby products PSS.Non peer reviewedFinal Accepted Versio

Consuming use orientated product service systems: A consumer culture theory perspective

Research suggests that product service systems (PSS) may usefully form part of the mix of innovations necessary to move society toward more sustainable futures. However, PSS implementation rates are disappointingly low and an implementation gap has emerged. Drawing on consumer culture theory (CCT), this paper provides insights to help resolve this issue in business to consumer markets. Since consumption of use orientated PSS is analogous to access based consumption, six dimensions of access are set out to analyse a case study of infant car seat provision. Five outcomes are derived from the analysis and these include partial identification with accessed product and interplay of use and symbolic value. This analysis questions the view that PSS do not create sufficient value to overcome a preference for ownership in western societies. Rather, PSS consumption is likely to arise when both functional and symbolic value are extracted by consumers and when PSS are promoted to appropriate consumer groups such as ‘nomads’. Further research is needed to explore these phenomena and address the issues they raise in PSS design processes

Product Service Systems Users and Harley Davidson Riders: the importance of consumer identity in the diffusion of sustainable consumption solutions

This paper sets out an approach to researching socio-cultural aspects of Product Service Systems (PSS) consumption in consumer markets. PSS are relevant to Industrial Ecology as they may form part of the mix of innovations that move society toward more sustainable material and energy flows. The paper uses two contrasting case studies drawing on ethnographic analysis, Harley Davidson motorcycles and Zip Car Car Club, one a case of consumption involving ownership, the other without. The analysis draws on Consumer Culture Theory to explicate the socio-cultural, experiential, symbolic and ideological aspects of these case studies, focusing on product ownership. The paper shows that ownership of Harley Davidson motorcycles enables riders to identify with a brand community and to define themselves. Owners appropriate their motorcycles through customization. In contrast, Zip Car users resist the company’s attempts to involve them in a brand community, see use of car sharing as a temporary fix and even fear contamination from shared use of cars. We conclude that iconic products such as Harley Davidson motorcycles create emotional attachment and can challenge PSS propositions. But we also suggest that somewhat standardized products may present similar difficulties. Knowing more about socio-cultural aspects of PSS may help designers overcome these difficulties