相关论文: Placeholder Substructures III: A Bit-String-Driven…
Fractal surfaces ('patchwork quilts') are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all deterministic bitwise operations on a finite alphabet. It is…
Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scale-free network fractal. Here we examine…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
The Mandelbox is a recently discovered class of escape-time fractals which use a conditional combination of reflection, spherical inversion, scaling, and translation to transform points under iteration. In this paper we introduce a new…
This study proposes a method for producing an infinite number of fractals using aperiodic substitution tilings, exemplified by the Ammann Chair tiling. Higher-order substitutions of aperiodic tilings are utilized in relation to the…
Recent efforts to classify representations of supersymmetry with no central charge have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one…
We consider the conformal properties of geometries described by higher-rank line elements. A crucial role is played by the conformal Killing equation (CKE). We introduce the concept of null-flat spaces in which the line element can be…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
R. Pavlov and S. Schmieding provided recently some results about generic $\mathbb{Z}$-shifts, which rely mainly on an original theorem stating that isolated points form a residual set in the space of $\mathbb{Z}$-shifts such that all other…
We explicitly construct fractals of dimension 4-epsilon on which dimensional regularization approximates scalar-field-only quantum-field-theory amplitudes. The construction does not require fractals to be Lorentz-invariant in any sense, and…
The first complete and explicit SO(1,9) Lorentz descriptions of all component fields contained in $\mathcal{N} = 1$, $\mathcal{N} = 2$A, and $\mathcal{N} = 2$B unconstrained scalar 10D superfields are presented. These are made possible by…
It is shown that gauged nonlinear sigma models can be always deformed by terms proportional to the field strength of the gauge fields (nonminimal gauging). These deformations can be interpreted as perturbations, by marginal operators, of…
The dimension of the Hilbert space of QFT scales exponentially with the volume of the space in which the theory lives, yet in supersymmetric theories, one can define a graded dimension (such as the supersymmetric index) that counts just the…
Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with…
It is supposed that in our Universe with compactified extra dimensions (ED) the domains exist with noncompactified ED. Such domain can be a wormhole-like solution in multidimensional gravity (MD), located between two null surfaces. With the…
We address the problem of understanding the dynamics around typical singular points of $3D$ piecewise smooth vector fields. A model $Z_0$ in $3D$ presenting a T-singularity is considered and a complete picture of its dynamics is obtained in…
In this paper, we continue the program initiated by I. Beck's now classical paper concerning zero-divisor graphs of commutative rings. After the success of much research regarding zero-divisor graphs, many authors have turned their…
Recently, the computer vision and machine learning community has been in favor of feature extraction pipelines that rely on a coding step followed by a linear classifier, due to their overall simplicity, well understood properties of linear…
We show that for sets with the Hausdorff--Besicovitch dimension equal zero the box counting algorithm commonly used to calculate Renyi exponents ($d_q$) can exhibit perfect scaling suggesting non zero $d_q$'s. Properties of these…
The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly-connected ``links'' and multiply-connected ``blobs.'' Here we decompose blobs into objects known in graph theory as 3-blocks. A 3-block…