30,197 research outputs found
Measuring Relations Between Concepts In Conceptual Spaces
The highly influential framework of conceptual spaces provides a geometric
way of representing knowledge. Instances are represented by points in a
high-dimensional space and concepts are represented by regions in this space.
Our recent mathematical formalization of this framework is capable of
representing correlations between different domains in a geometric way. In this
paper, we extend our formalization by providing quantitative mathematical
definitions for the notions of concept size, subsethood, implication,
similarity, and betweenness. This considerably increases the representational
power of our formalization by introducing measurable ways of describing
relations between concepts.Comment: Accepted at SGAI 2017 (http://www.bcs-sgai.org/ai2017/). The final
publication is available at Springer via
https://doi.org/10.1007/978-3-319-71078-5_7. arXiv admin note: substantial
text overlap with arXiv:1707.05165, arXiv:1706.0636
Conceptual Spaces in Object-Oriented Framework
The aim of this paper is to show that the middle level of
mental representations in a conceptual spaces framework is consistent
with the OOP paradigm. We argue that conceptual spaces framework
together with vague prototype theory of categorization appears to be
the most suitable solution for modeling the cognitive apparatus of
humans, and that the OOP paradigm can be easily and intuitively
reconciled with this framework. First, we show that the prototypebased
OOP approach is consistent with Gärdenfors’ model in terms
of structural coherence. Second, we argue that the product of cloning
process in a prototype-based model is in line with the structure of
categories in Gärdenfors’ proposal. Finally, in order to make the fuzzy
object-oriented model consistent with conceptual space, we
demonstrate how to define membership function in a more cognitive
manner, i.e. in terms of similarity to prototype
A qualitative approach to the identification, visualisation and interpretation of repetitive motion patterns in groups of moving point objects
Discovering repetitive patterns is important in a wide range of research areas, such as bioinformatics and human movement analysis. This study puts forward a new methodology to identify, visualise and interpret repetitive motion patterns in groups of Moving Point Objects (MPOs). The methodology consists of three steps. First, motion patterns are qualitatively described using the Qualitative Trajectory Calculus (QTC). Second, a similarity analysis is conducted to compare motion patterns and identify repetitive patterns. Third, repetitive motion patterns are represented and interpreted in a continuous triangular model. As an illustration of the usefulness of combining these hitherto separated methods, a specific movement case is examined: Samba dance, a rhythmical dance will? many repetitive movements. The results show that the presented methodology is able to successfully identify, visualize and interpret the contained repetitive motions
On supermatrix models, Poisson geometry and noncommutative supersymmetric gauge theories
We construct a new supermatrix model which represents a manifestly
supersymmetric noncommutative regularisation of the
supersymmetric Schwinger model on the supersphere. Our construction is much
simpler than those already existing in the literature and it was found by using
Poisson geometry in a substantial way.Comment: 29 pages, we enlarge Section 3.3 by adding a comparison with older
results on the subject of the component expansion
Platonic model of mind as an approximation to neurodynamics
Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view
Bondi-Metzner-Sachs symmetry, holography on null-surfaces and area proportionality of "light-slice" entropy
It is shown that certain kinds of behavior, which hitherto were expected to
be characteristic for classical gravity and quantum field theory in curved
spacetime, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography
on event horizons and an area proportionality of entropy, have in fact an
unnoticed presence in Minkowski QFT. This casts new light on the fundamental
question whether the volume propotionality of heat bath entropy and the
(logarithmically corrected) dimensionless area law obeyed by
localization-induced thermal behavior are different geometric parametrizations
which share a common primordeal algebraic origin. Strong arguments are
presented that these two different thermal manifestations can be directly
related, this is in fact the main aim of this paper. It will be demonstrated
that QFT beyond the Lagrangian quantization setting receives crucial new
impulses from holography onto horizons. The present paper is part of a project
aimed at elucidating the enormous physical range of "modular localization". The
latter does not only extend from standard Hamitonian heat bath thermal states
to thermal aspects of causal- or event- horizons addressed in this paper. It
also includes the recent understanding of the crossing property of formfactors
whose intriguing similarity with thermal properties was, although sometimes
noticed, only sufficiently understood in the modular llocalization setting.Comment: 42 pages, changes, addition of new results and new references, in
this form the paper will appear in Foundations of Physic
Facts and Fictions about Anti deSitter Spacetimes with Local Qantum Matter
It is natural to analyse the AdS-CQFT correspondence in the
context of the conformal- compactification and covering formalism. In this way
one obtains additional inside about Rehren's rigorous algebraic holography in
connection with the degree of freedom issue which in turn allows to illustrates
the subtle but important differences beween the original string theory-based
Maldacena conjecture and Rehren's theorem in the setting of an intrinsic
field-coordinatization-free formulation of algebraic QFT. I also discuss
another more generic type of holography related to light fronts which seems to
be closer to 't Hooft's original ideas on holography. This in turn is naturally
connected with the generic concept of ``Localization Entropy'', a quantum
pre-form of Bekenstein's classical black-hole surface entropy.Comment: this final version is identical to the one which appeared in Commun.
Math. Phys. 219, (2001) 57-76, an issue of CMP dedicated to the memory of
Harry Lehmann
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From on-line sketching to 2D and 3D geometry: A fuzzy knowledge based system
The paper describes the development of a fuzzy knowledge based prototype system for conceptual design. This real time system is designed to infer user’s sketching intentions, to segment sketched input and generate corresponding geometric primitives: straight lines, circles, arcs, ellipses, elliptical arcs, and B-spline curves. Topology information (connectivity, unitary constraints and pairwise constraints) is received dynamically from 2D sketched input and primitives. From the 2D topology information, a more accurate 2D geometry can be built up by applying a 2D geometric constraint solver. Subsequently, 3D geometry can be received feature by feature incrementally. Each feature can be recognised by inference knowledge in terms of matching its 2D primitive configurations and connection relationships. The system accepts not only sketched input, working as an automatic design tools, but also accepts user’s interactive input of both 2D primitives and special positional 3D primitives. This makes it easy and friendly to use. The system has been tested with a number of sketched inputs of 2D and 3D geometry
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