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We bound the error for the normal approximation of the number of triangles in the Erdős–Rényi random graph with respect to the Kolmogorov metric. Our bounds match the best available Wasserstein bounds obtained by Barbour et al. [(1989). A central limit theorem for decomposable random variables with applications to random graphs. Journal of Combinatorial Theory, Series B 47: 125–145], resolving a long-standing open problem. The proofs are based on a new variant of the Stein–Tikhomirov method—a combination of Stein's method and characteristic functions introduced by Tikhomirov [(1976). The rate of convergence in the central limit theorem for weakly dependent variables. Vestnik Leningradskogo Universiteta 158–159, 166].
We take Carnap’s problem to be to what extent standard consequence relations in various formal languages fix the meaning of their logical vocabulary, alone or together with additional constraints on the form of the semantics. This paper studies Carnap’s problem for basic modal logic. Setting the stage, we show that neighborhood semantics is the most general form of compositional possible worlds semantics, and proceed to ask which standard modal logics (if any) constrain the box operator to be interpreted as in relational Kripke semantics. Except when restricted to finite domains, no modal logic characterizes exactly the Kripkean interpretations of $\Box $. Moreover, we show that, in contrast with the case of first-order logic, the obvious requirement of permutation invariance is not adequate in the modal case. After pointing out some known facts about modal logics that nevertheless force the Kripkean interpretation, we focus on another feature often taken to embody the gist of modal logic: locality. We show that invariance under point-generated subframes (properly defined) does single out the Kripkean interpretations, but only among topological interpretations, not in general. Finally, we define a notion of bisimulation invariance—another aspect of locality—that, together with a reasonable closure condition, gives the desired general result. Along the way, we propose a new perspective on normal neighborhood frames as filter frames, consisting of a set of worlds equipped with an accessibility relation, and a free filter at every world.
In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
This paper aims at developing a novel method to assess the kinematic reliability of robotic manipulators based on the fuzzy theory. The kinematic reliability quantifies the probability of obtaining positioning errors within acceptable limits. For this purpose, the fuzzy reliability evaluates the effect of the joint clearances on the end-effector position to compute a failure possibility index. As an alternative to the conventional methods reported in the literature, this failure possibility index conveys a novel assessment of the kinematic performance. The numerical results are compared with the well-known probabilistic approach based on the Monte Carlo simulation.
The General Framework requires case studies to progress its development. Case studies of HCI design knowledge can be successful or unsuccessful. Successful case-studies are considered to fall within the scope of the design knowledge being applied. Unsuccessful case studies are considered not to fall within its scope. Thus, successful and unsuccessful case studies together define the scope of the application of HCI design knowledge.Case studies are of two types: of the framework itself and of the HCI knowledge, acquired with its support by means of HCI research. In turn, these two types of case study can be divided into acquisition and validation case studies. The latter types of case study have yet to be carried out for the General Framework, comprising concepts of discipline, general as common, general problem, particular scope, general research, general knowledge and general practices. However, on the basis of case studies reported in the literature, and the validation proposal made here, suggestions are made as to the research needed to conduct such case studies.
The chapter presents the specific art approach to HCI research, including an illustration from the literature. The latter claims that empirical investigations of videogame play and videogame engagement are often delimited along demographic or genre lines. In contrast, the illustration proposes a theory of players engaging with games, if they can find a sense of net personal cultural value.The chapter then presents the specific art framework for HCI research, comprising art as discipline, general problem, particular scope, research, knowledge and practices. The specific art framework is followed by the art design research exemplar, as the art design cycle and the art design research cycle. The lower-level art framework comprises the art application, the art interactive system, and the art interactive system performance. Both the exemplar and the lower-level framework are applied to the same illustration of the art approach taken from the literature, which proposes a theory of players engaging with games, if they can find a sense of net personal cultural value.
The chapter presents the specific engineering approach to HCI research, including an illustration from the literature. The latter advances contrasting views of engineering as the servant of design, which identifies user needs outside its process and as HCI comprising iterative software development life cycles.The chapter then presents the specific engineering framework for HCI research comprising engineering as discipline, general problem, particular scope, research, knowledge and practices. The specific engineering framework is followed by the engineering design research exemplar as the engineering design cycle and the engineering design research cycle. The lower-level engineering framework comprises the engineering application, the engineering interactive system, and the engineering interactive system performance. Both the exemplar and the lower-level framework are applied to the same illustration of the engineering approach taken from the literature, which contrasts engineering as the servant of design and as HCI comprising iterative software development life cycles.
What about the future? Some researchers may be more engaged in finding specific solutions to specific problems, concerning interactive systems or their parts, as they relate to one or more user requirements. These researchers might be considered to be more research practice researchers to whom the greater rigour of a framework is more appropriate. Other researchers may be more engaged in designing interactive systems or their parts, as they relate to one or more user requirements. These researchers might be considered to be more design practice researchers to whom the lesser rigour of an approach may be more appropriate.
The main thrust of the book is that the General Framework and the general and specific design research exemplars require both types of research and specify the relations between them, in addition to the relations between approaches and frameworks.
The chapter presents the specific innovation approach to HCI research, including an illustration from the literature. The latter proposes how novel, emerging smell technology might be applied to develop smell-enhanced human–computer interactions. It then presents the specific innovation framework for HCI research, comprising innovation as discipline, general problem, particular scope, research, knowledge and practices. The specific innovation framework is followed by the innovation design research exemplar, as the innovation design cycle and the innovation design research cycle. The lower-level innovation framework comprises the innovation application, the innovation interactive system, and the innovation interactive system performance. Both the exemplar and the lower-level framework are applied to the same illustration of the innovation approach taken from the literature, which proposes how novel, emerging smell technology might be applied to develop smell-enhanced human–computer interactions.
The chapter introduces human–computer Interaction (HCI) and HCI research and describes their current states. Challenges to HCI research are identified as the need to address the growth and diversification of HCI and of the associated research, while decreasing the fragmentation of fields and theories.The aims of the book are presented as support for researchers to build on and to validate each other’s work and so to increase consensus, leading to increased HCI discipline progress. The concepts of approach and framework are outlined, together with their relations. The chapter sets the scene for the following two chapters, which address respectively approaches and frameworks separately and in greater depth.
The chapter proposes a general definition of the concept of framework, together with its derivation and exemplification. The definition and an existing conception are then applied to HCI research.The resulting core HCI research framework comprises discipline (as an academic field of study), general problem (as the design of human–computer interactions), particular scope (as the design of human–computer interactions to do something as desired), research (as the diagnosis of design problems and the prescription of design solutions, as they relate to performance, for the acquisition and for the validation of knowledge to support practices), knowledge (as acquired and validated, supporting practices) and practices (as supported by knowledge, acquired and validated by research). The core framework is sufficiently well specified for its application to approaches.
The chapter assesses the General Framework for HCI research for coherence against HCI theories. The General Framework comprises concepts of discipline, general as common, general problem, particular scope, general research, general knowledge and general practices. The theories comprise extended cognitive (as external cognition, distributed cognition and ecological cognition), social (as situated action and CSCW (computer-supported cooperative work)) and miscellaneous (as ethnography, grounded, design, human values, technology as experience, critical and in-the-wild).The assessment concerns the key concepts of the HCI theories, although other concepts are also referenced. The concepts of the General Framework are assessed as generally coherent. The assessment does not constitute a validation of the General Framework. However, it does show promise for such validation. The outcome is also indicative as to the potential of the General Framework to support research that aims to develop such theories.
By way of conclusion, the final chapter brings together the lessons learned and the lessons remaining concerning approaches and frameworks for HCI research. The scope of the lessons learned and the lessons remaining include approaches and frameworks for HCI research, approaches to HCI research, frameworks for HCI research, specific frameworks for HCI research, general approach and General Framework for HCI research, validating the general approach and the General Framework for HCI research, assessing the General Framework against other HCI frameworks, assessing the General Framework against HCI theories, methodological components for the General Framework, and case studies for the General Framework. The conclusion takes the form of a proposal for an HCI research programme, which builds on the lessons learned to formulate the lessons remaining. Together they constitute the research programme.
The chapter presents the specific craft approach to HCI research, including an illustration from the literature. The latter reports four phases of a design and research project to develop a location-mapping mobile application for breastfeeding women. It then presents the specific craft framework for HCI research, comprising craft as discipline, general problem, particular scope, research, knowledge and practices. The specific craft framework is followed by the craft design research exemplar, as the craft research and design cycle.The lower-level craft framework comprises the craft application, the craft interactive system, and the craft interactive system performance. Both the exemplar and the lower-level framework are applied to the same illustration of the craft approach taken from the literature reporting the development of a location-mapping mobile application for breastfeeding women.
The chapter first presents a general approach to HCI research. The general approach comprises addressing the topic or problem of designing human–computer interactions, performing of actions to progress that approach to designing human–computer interactions, evaluating of the success of the actions performed to progress that approach to designing human–computer interactions and cumulating of the successes as a way of establishing whether the topic or problem of designing human–computer interactions has been addressed or not. The chapter then proposes a General Framework for HCI research (including a core framework) comprising discipline, general as common, general problem, particular scope, general research, general knowledge and general practices. The General Framework is followed by a general design research exemplar as general design research cycles. The lower-level general framework comprises application, interactive system and performance.
HCI frameworks, including the General Framework, are largely substantive in nature at this time. This is in spite of some lesser reference to practices and methods. Knowledge, however, is both methodological and substantive. Hence the requirement for a greater methodological component for such frameworks. The research framework and theory elements, which reference practices and methods, are in many respects very different. However, they have common aspects. The latter, in some cases, may even be identical to the elements appearing in HCI design practices and methods. The latter, then, could form the starting point for meeting the methodological framework requirement identified here. The HCI design practices and methods include user-centred design methods, structured analysis and design methods and research structured analysis and design methods. Suggestions are made as to the research needed to develop a greater methodological component. The latter would be for the General Framework and for other such generic frameworks. In this way, the requirement could be met.