6,770 research outputs found

    Functional Dynamics I : Articulation Process

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    The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function ff, not of variables, having a self-reference term f∘ff \circ f, introduced by recalling that operation in a biological system is often applied to itself, as is typically seen in rules in the natural language or genes. Starting from an inarticulate network, two types of fixed points are formed as an invariant structure with iterations. The function is folded with time, until it has finite or infinite piecewise-flat segments of fixed points, regarded as articulation. For an initial logistic map, attracted functions are classified into step, folded step, fractal, and random phases, according to the degree of folding. Oscillatory dynamics are also found, where function values are mapped to several fixed points periodically. The significance of our results to prototype categorization in language is discussed.Comment: 48 pages, 15 figeres (5 gif files

    Using Fuzzy Cognitive Maps (FCMs) to Evaluate the Vulnerabilities with ICT Assets Disposal Policies

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    Abstract-- This paper evaluates the possible vulnerabilities of ICT assets disposal policies and the associated impact that can affect the SMEs. A poorly implemented policy or unenforced policy is “potentially the weakest link ” in the cyber-security chain. Do SMEs have an idea of vulnerabilities or threats due to assets disposal? In the event of breaches, the SMEs pay for the cost of notifying the concerned stakeholders, compensate affected parties, invest in improved mitigation technologies and also may be subjected to unwarranted public scrutiny. ICT assets at the end-of-useful life span usually have data left on the hard disk drives or storage media, which is a source of data confidentiality vulnerability. SMEs were surveyed in developing economies on their assets disposal policies. The perceived correlations were analyzed using fuzzy cognitive maps (FCMs) to ascertain if any cyber-security vulnerabilities inherent in a particular policy have implications on others. The study endeavored to show that, SMEs ought to have appropriate assets disposal policies in place. Then, these policies ought to be signed off by all stakeholders as a matter of responsibility. By employing the FCM approach with fuzzy matrix operations, the results indicate positive correlations exist amongst the policy constructs. Thus, vulnerabilities with one policy have implications on others

    The Hyperdimensional Transform: a Holographic Representation of Functions

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    Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable functions into noise-robust, holographic, high-dimensional representations called hyperdimensional vectors. The central idea is to approximate a function by a linear combination of random functions. We formally introduce a set of stochastic, orthogonal basis functions and define the hyperdimensional transform and its inverse. We discuss general transform-related properties such as its uniqueness, approximation properties of the inverse transform, and the representation of integrals and derivatives. The hyperdimensional transform offers a powerful, flexible framework that connects closely with other integral transforms, such as the Fourier, Laplace, and fuzzy transforms. Moreover, it provides theoretical foundations and new insights for the field of hyperdimensional computing, a computing paradigm that is rapidly gaining attention for efficient and explainable machine learning algorithms, with potential applications in statistical modelling and machine learning. In addition, we provide straightforward and easily understandable code, which can function as a tutorial and allows for the reproduction of the demonstrated examples, from computing the transform to solving differential equations

    What are natural concepts? A design perspective

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    Conceptual spaces have become an increasingly popular modeling tool in cognitive psychology. The core idea of the conceptual spaces approach is that concepts can be represented as regions in similarity spaces. While it is generally acknowledged that not every region in such a space represents a natural concept, it is still an open question what distinguishes those regions that represent natural concepts from those that do not. The central claim of this paper is that natural concepts are represented by the cells of an optimally designed similarity space

    Anticipation and Risk – From the inverse problem to reverse computation

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    Abstract. Risk assessment is relevant only if it has predictive relevance. In this sense, the anticipatory perspective has yet to contribute to more adequate predictions. For purely physics-based phenomena, predictions are as good as the science describing such phenomena. For the dynamics of the living, the physics of the matter making up the living is only a partial description of their change over time. The space of possibilities is the missing component, complementary to physics and its associated predictions based on probabilistic methods. The inverse modeling problem, and moreover the reverse computation model guide anticipatory-based predictive methodologies. An experimental setting for the quantification of anticipation is advanced and structural measurement is suggested as a possible mathematics for anticipation-based risk assessment
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