Related papers: The Fuzzy Onion: A proposal
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing…
This work examines the deformed fuzzy sphere, as an example of a fuzzy space that can be described through a spectral triple, using computer visualisations. We first explore this geometry using an analytic expression for the eigenvalues to…
We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined…
A model to represent spatial information is presented in this paper. It is based on fuzzy constraints represented as fuzzy geometric relations that can be hierarchically structured. The concept of spatial template is introduced to capture…
Extracting shape information from object bound- aries is a well studied problem in vision, and has found tremen- dous use in applications like object recognition. Conversely, studying the space of shapes represented by curves satisfying…
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to…
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
We review the description of scalar field theories on fuzzy spaces by Hermitian random matrix models. After reminding the reader of the relevant aspects of the random matrix theory and construction of the fuzzy spaces, we summarize the most…
We present a new type of matrix regularization, which is based on matrix-valued functions defined on a cylinder. If non-commutative coordinates of a fuzzy space are defined by a regularization of such functions, we show that a classical…
In this paper, I obtain an $S$-type fuzzy point when two fuzzy numbers for two independent variables and a corresponding fuzzy number for the dependent variable are given. A comprehensive study on a conceptualization of a fuzzy plane as a…
We analyze two types of hermitian matrix models with asymmetric solutions. One type breaks the symmetry explicitly with an asymmetric quartic potential. We give the phase diagram of this model with two different phase transitions between…
The product of a non-commutative matrix spectral triple with a simple two-dimensional internal space is considered. This is interpreted as a non-commutative spacetime that contains one charged Dirac fermion and its antiparticle. The inner…
We study in detail generalized 4-dimensional fuzzy spheres with twisted extra dimensions. These spheres can be viewed as $SO(5)$-equivariant projections of quantized coadjoint orbits of $SO(6)$. We show that they arise as solutions in…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
Rank-three tensor model may be regarded as theory of dynamical fuzzy spaces, because a fuzzy space is defined by a three-index coefficient of the product between functions on it, f_a*f_b=C_ab^cf_c. In this paper, this previous proposal is…
The explicit form of the quantum propagator of a bosonic p-brane, previously obtained by the authors in the quenched-minisuperspace approximation, suggests the possibility of a novel, unified, description of p-branes with different…
We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within…
Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of…
What is the shape of space in a spacetime? One way of addressing this issue is to consider edgeless spacelike submanifolds of the spacetime. An alternative is to foliate the spacetime by timelike curves and consider the quotient obtained by…
It is well known that knots are countable in ordinary knot theory. Recently, knots {\it with intersections} have raised a certain interest, and have been found to have physical applications. We point out that such knots --equivalence…