A Calculus of Evolving Objects

The demands of developing modern, highly dynamic applications have led to an increasing interest in dynamic programming languages and mechanisms. Not only applications must evolve over time, but the object models themselves may need to be adapted to the requirements of different run-time contexts. Class-based models and prototype-based models, for example, may need to co-exist to meet the demands of dynamically evolving applications. Multi-dimensional dispatch, fine-grained and dynamic software composition, and run-time evolution of behaviour are further examples of diverse mechanisms which may need to co-exist in a dynamically evolving run-time environment How can we model the semantics of these highly dynamic features, yet still offer some reasonable safety guarantees? To this end we present an original calculus in which objects can adapt their behaviour at run-time to changing contexts. Both objects and environments are represented by first-class mappings between variables and values. Message sends are dynamically resolved to method calls. Variables may be dynamically bound, making it possible to model a variety of dynamic mechanisms within the same calculus. Despite the highly dynamic nature of the calculus, safety properties are assured by a type assignment system.

A Calculus of Evolving Objects

The demands of developing modern, highly dynamic applications have led to an increasing interest in dynamic programming languages and mechanisms. Not only must applications evolve over time, but the object models themselves may need to be adapted to the requirements of different run-time contexts. Class-based models and prototype-based models, for example, may need to co-exist to meet the demands of dynamically evolving applications. Multi-dimensional dispatch, fine-grained and dynamic software composition, and run-time evolution of behaviour are further examples of diverse mechanisms which may need to co-exist in a dynamically evolving run-time environment. How can we model the semantics of these highly dynamic features, yet still offer some reasonable safety guarantees? To this end we present an original calculus in which objects can adapt their behaviour at run-time. Both objects and environments are represented by first-class mappings between variables and values. Message sends are dynamically resolved to method calls. Variables may be dynamically bound, making it possible to model a variety of dynamic mechanisms within the same calculus. Despite the highly dynamic nature of the calculus, safety properties are assured by a type assignment system.

Local Stereology of Tensors of Convex Bodies

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.

Granular computing as a tool of human data interaction - a cognitive cities use case

The article proposes granular computing as a theoretical, formal and methodological basis for the newly emerging research field of human–data interaction (HDI). We argue that the ability to represent and reason with information granules is a prerequisite for data legibility. As such, it allows for extending the research agenda of HDI to encompass the topic of collective intelligence amplification, which is seen as an opportunity of today’s increasingly pervasive computing environments. As an example of collective intelligence amplification in HDI, we introduce a collaborative urban planning use case in a cognitive city environment and show how an iterative process of user input and human-oriented automated data processing can support collective decision making. As a basis for automated human-oriented data processing, we use the spatial granular calculus of granular geometry.

Granular computing as a basis of human–data interaction: a cognitive cities use case

The article proposes granular computing as a theoretical, formal and methodological basis for the newly emerging research field of human–data interaction (HDI). We argue that the ability to represent and reason with information granules is a prerequisite for data legibility. As such, it allows for extending the research agenda of HDI to encompass the topic of collective intelligence amplification, which is seen as an opportunity of today’s increasingly pervasive computing environments. As an example of collective intelligence amplification in HDI, we introduce a collaborative urban planning use case in a cognitive city environment and show how an iterative process of user input and human-oriented automated data processing can support collective decision making. As a basis for automated human-oriented data processing, we use the spatial granular calculus of granular geometry.

Lions-type compactness and Rubik actions on the Heisenberg group

In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group TeX is provided by the unitary group U(n) × {1} and its appropriate subgroups, which will be used to construct subspaces with specific symmetry and compactness properties in the Folland-Stein’s horizontal Sobolev space TeX. As an application, we study the multiplicity of solutions for a singular subelliptic problem by exploiting a technique of solving the Rubik-cube applied to subgroups of U(n) × {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods.

Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Self-disclosure and privacy calculus on social networking sites: the role of culture

Social Networking Sites (SNSs) have become extremely popular around the world. They rely on user-generated content to offer engaging experience to its members. Cultural differences may influence the motivation of users to create and share content on SNS. This study adopts the privacy calculus perspective to examine the role of culture in individual self-disclosure decisions. The authors use structural equation modeling and multi-group analysis to investigate this dynamics. The findings reveal the importance of cultural dimensions of individualism and uncertainty avoidance in the cognitive processes of SNS users.

Behind the curtains of privacy calculus on social networking sites: the study of Germany and the USA

As social networking sites (SNSs) become increasingly global, the issues of cultural differences in participation patterns become acute. However, current research offers only limited insights into the role of culture behind SNS usage. Aiming to fill this gap, this study adopts a ‘privacy calculus’ perspective to study the differences between German and American SNS users. Results of structural equation modeling and multi-group analysis reveal distinct variability in the cognitive patterns of American and German subjects. We contribute to the theory by rejecting the universal nature of privacy-calculus processes. From a practical standpoint, our results signal that SNS providers cannot rely on the “proven” means in ensuring user participation when crossing geographic boundaries. When financial means are limited, SNS providers should direct their investments into enhancing platform enjoyment and granting users with more control and, paradoxically, lobbying for more legalistic safeguards of user privacy.

Stereological estimation of particle shape and orientation from volume tensors

In the present paper, we describe new robust methods of estimating cell shape and orientation in 3D from sections. The descriptors of 3D cell shape and orientation are based on volume tensors which are used to construct an ellipsoid, the Miles ellipsoid, approximating the average cell shape and orientation in 3D. The estimators of volume tensors are based on observations in several optical planes through sampled cells. This type of geometric sampling design is known as the optical rotator. The statistical behaviour of the estimator of the Miles ellipsoid is studied under a flexible model for 3D cell shape and orientation. In a simulation study, the lengths of the axes of the Miles ellipsoid can be estimated with CVs of about 2% if 100 cells are sampled. Finally, we illustrate the use of the developed methods in an example, involving neurons in the medial prefrontal cortex of rat.