This paper illuminates the derivation, applicability, and efficiency of the multiplicative Runge–Kutta method, derived in the framework of geometric multiplicative calculus. The removal of the restrictions of geometric multiplicative calculus on positive-valued functions of real variables and the fact that the multiplicative derivative does not exist at the roots of the function are presented explicitly to ensure that the proposed method is universally applicable. The error and stability analyses are also carried out explicitly in the framework of geometric multiplicative calculus. The method presented is applied to various problems and the results are compared to those obtained from the ordinary Runge–Kutta method. Moreover, for one example, a comparison of the computation time against relative error is worked out to illustrate the general advantage of the proposed method.

Face-to-face social contacts are potentially important transmission routes for acute respiratory infections, and understanding the contact network can improve our ability to predict, contain, and control epidemics. Although workplaces are important settings for infectious disease transmission, few studies have collected workplace contact data and estimated workplace contact networks. We use contact diaries, architectural distance measures, and institutional structures to estimate social contact networks within a Swiss research institute. Some contact reports were inconsistent, indicating reporting errors. We adjust for this with a latent variable model, jointly estimating the true (unobserved) network of contacts and duration-specific reporting probabilities. We find that contact probability decreases with distance, and that research group membership, role, and shared projects are strongly predictive of contact patterns. Estimated reporting probabilities were low only for 0–5 min contacts. Adjusting for reporting error changed the estimate of the duration distribution, but did not change the estimates of covariate effects and had little effect on epidemic predictions. Our epidemic simulation study indicates that inclusion of network structure based on architectural and organizational structure data can improve the accuracy of epidemic forecasting models.

We consider ‘unconstrained’ random k-XORSAT, which is a uniformly random system of m linear non-homogeneous equations in $\mathbb{F}$ 2 over n variables, each equation containing k ⩾ 3 variables, and also consider a ‘constrained’ model where every variable appears in at least two equations. Dubois and Mandler proved that m/n = 1 is a sharp threshold for satisfiability of constrained 3-XORSAT, and analysed the 2-core of a random 3-uniform hypergraph to extend this result to find the threshold for unconstrained 3-XORSAT.

We show that m/n = 1 remains a sharp threshold for satisfiability of constrained k-XORSAT for every k ⩾ 3, and we use standard results on the 2-core of a random k-uniform hypergraph to extend this result to find the threshold for unconstrained k-XORSAT. For constrained k-XORSAT we narrow the phase transition window, showing that m − n → −∞ implies almost-sure satisfiability, while m − n → +∞ implies almost-sure unsatisfiability.

Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more. Modularity is a quality function that measures the difference between the number of edges found within clusters minus the number of edges one would statistically expect to find based on some equivalent random graph model. We explore a natural generalization of modularity based on the difference between the actual and expected number of walks within clusters, which we refer to as walk-modularity. Walk-modularity can be expressed in matrix form, and community detection can be performed by finding the leading eigenvector of the walk-modularity matrix. We demonstrate community detection on both synthetic and real-world networks and find that walk-modularity maximization returns significantly improved results compared to traditional modularity maximization.

A natural question in the λ-calculus asks what is the possible number of fixed points of a combinator (closed term). A complete answer to this question is still missing (Problem 25 of TLCA Open Problems List) and we investigate the related question about the number of fixed points of a combinator in λ-theories. We show the existence of a recursively enumerable lambda theory where the number is always one or infinite. We also show that there are λ-theories such that some terms have only two fixed points. In a first example, this is obtained by means of a non-constructive (more precisely non-r.e.) λ-theory where the range property is violated. A second, more complex example of a non-r.e. λ-theory (with a higher unsolvability degree) shows that some terms can have only two fixed points while the range property holds for every term.

We study 3-random-like graphs, that is, sequences of graphs in which the densities of triangles and anti-triangles converge to 1/8. Since the random graph $\mathcal{G}$ n,1/2 is, in particular, 3-random-like, this can be viewed as a weak version of quasi-randomness. We first show that 3-random-like graphs are 4-universal, that is, they contain induced copies of all 4-vertex graphs. This settles a question of Linial and Morgenstern [10]. We then show that for larger subgraphs, 3-random-like sequences demonstrate completely different behaviour. We prove that for every graph H on n ⩾ 13 vertices there exist 3-random-like graphs without an induced copy of H. Moreover, we prove that for every ℓ there are 3-random-like graphs which are ℓ-universal but not m-universal when m is sufficiently large compared to ℓ.

The objective of this research is to develop a computational representation of knowledge associated with affordance-based design (ABD). The ABD ontology formalizes the entities, properties, and relationships within the domains of ABD. The ontology enables designers to describe the affordances of existing products and specify the intended affordances of future products in line with ABD. The ontology consists of 14 concepts and 5 relationships. The ontology is developed using Protégé 4.3 and DL-query to query and reason with the ontology. The ontology is demonstrated using a consumer vacuum cleaner. The formal ontology serves as the basis for developing computer support for ABD applications. When implemented, these design tools will help designers manage the affordances of artifacts being designed, specifying the interacting entities of every affordance when a three-dimensional model of the artifact is available. Further, these software tools could be used to support ABD methods.

We describe three approaches to identify novel product affordances: affordance of absence; insights from lead users, specifically do-it-yourselfers (DIYers); and natural-language searches. While these approaches were separately pursued, we show their connection to each other in this paper. We begin by describing the affordance of absence, inspired by insights on affordances arising from a lack of resources. For example, in the absence of specialized tools, more general tools are used to accomplish similar tasks. Such absence clarifies how other tools could be modified to add relevant features and identifies critical features of the absent tool. In addition, the temporary removal of physical features and objects enables user interaction in ways that may not emerge in their presence. Affordance of absence has the potential to more fully specify affordances for a given object and to help overcome functional fixedness. For the second approach, we describe insights from DIYers obtained from the “IKEA hackers” online community. We consider DIYers lead users for seeking out and exploiting product affordances, often transforming product functions dramatically. We also discuss their projects through the lens of affordance of absence. For the third approach, we outline our natural-language approach to affordance extraction, beginning with consumer product reviews provided for Canadian Tire, a major Canadian retailer. We describe efforts toward automatically identifying less common affordances, and the use of cue phrases to highlight insightful DIY transformations from the IKEA hackers community. Finally, we comment on the potential value of this work for product design in general.

We consider a notion of approximation for terms of de Groote–Saurin Λμ-calculus. Then, we introduce an intersection type assignment system for that calculus which is invariant under subject conversion. The type assignment system also induces a filter model, which is an extensional Λμ-model in the sense of Nakazawa and Katsumata. We then establish the approximation theorem, stating that a type can be assigned to a term in the system if and only if it can be assigned to same of its approximations.

We introduce a new understanding of deontic modals that we call obligations as weakest permissions. We argue for its philosophical plausibility, study its expressive power in neighborhood models, provide a complete Hilbert-style axiom system for it and show that it can be extended and applied to practical norms in decision and game theory.

Function-based design approaches have been criticized for being too narrow to properly guide design. Specifically, they are said to be unable to cope with nonfunctional considerations, such as cost or maintenance issues without invoking other concepts, such as constraints. This paper investigates two alternative conceptualizations of the design process: the practical affordance-based design approach, as elaborated by Maier and Fadel, and the more theoretical use plan approach by Houkes and Vermaas. This paper compares function-, affordance-, and use plan-based design approaches. It highlights strengths and weaknesses of each approach and proposes a definition of the function of an artifact in terms of its affordances.

People interact with artifacts, either products or services, in their lives. These interactions are based on two-way communication between people and artifacts. The characteristics of artifacts that induce natural activities of people, affordances, play critical roles in making interactions successful and meaningful. The notion of affordance features, structural elements of artifacts that provide affordances, has been proposed earlier. In this paper, a methodological framework for design for affordances is proposed where repositories of affordance features are used. Affordances are identified through function–task interaction matrices or use activity observations. Using an affordance feature repository where many alternative structural elements for a specific affordance are stored together with corresponding design constraints and contexts, affordance features for those identified affordances are retrieved considering similarities between the target design constraints and those of the affordance features in the repositories. Using the clues given by such affordance features, a new affordance feature is to be designed through analogical reasoning. We present this design for affordance framework together with illustrative cases where various designers designed affordance features using affordance feature repositories.

One of the principal advantages of affordance-based design is that Gibson's theory of affordances is a relational theory, akin to other relational approaches such as relational biology and relational computer science. The relationships between artifacts and their designers and users are of such primary importance that only a theory that is able to deal with those relationships directly appears to be sufficient for describing the wide breadth of problems in engineering design. However, there is no precise definition for what qualifies as a relational theory. In mathematics, we do find something approaching a theory of relations, dating back at least to Charles Peirce's Logic of Relatives around 1870. While rather general, Peirce's ideas on the subject laid the foundation for advances in the 20th century, including the relational model of databases. This paper is a first attempt at applying the mathematics of relations to affordances, with the aim of more precisely characterizing affordances, which heretofore have been difficult to define and, lacking appropriate mathematics, nearly impossible to subject to computation. Meanwhile, the implicit computability of affordances as relations is demonstrated by examples drawn from engineering, physics, computer science, biology, and architecture.

The design community has growing familiarity with the concept of affordances and with the utility of this concept in many areas of design. Less emphasis has been placed on natural processes by which people acquire knowledge about affordances. Consequently, little is known about how design might be optimized to enable users to detect the actions that are available in a given human–machine system. We review scientific research about what people do to obtain information about affordances. We discuss implications of this research for design.

When developing an artifact, designers must first understand the problem. This includes the benefits that the artifact must deliver and the user variation that is present. Each user has a unique set of human factors, preferences, personal knowledge, and solution constraints that could potentially influence the characteristics of the artifact. Currently, there is little work supporting the process of how to formally generate user-specific design specifications, resulting in ad hoc or a priori decisions when generating design specifications. Further, because most design processes generate design specifications manually, the number of design specifications is not typically addressed at the user level. This research presents an affordance-based approach for use in the early stages of design to help designers establish user-specific design specifications. This information can then be used in the creation of a system or set of systems that meets the demands of both the user(s) and the organization that is developing the artifact. An affordance-based approach is leveraged because it maintains the relational field of view among the user, existing artifacts, and the artifact(s) being designed. Once individual design specifications are generated, designers can use this information in later stages of the design process.