CHOOSEY HOT SAND: REFLECTION OF GRAIN SENSITIVITY ON PATTERN MORPHOLOGY

2000 ◽  
Vol 11 (01) ◽  
pp. 47-68 ◽  
Author(s):  
ANDREW ADAMATZKY
Keyword(s):  
Fine Structure ◽  
Pattern Formation ◽  
Discrete Space ◽  
Global Parameter ◽  
Transient Phenomena ◽  
One Dimensional ◽  
Nonstandard Model ◽  
Current Node ◽  
Dimensional Parameters

We build and investigate a nonstandard model of pattern formation in a system of discrete entities evolving in discrete space and time. We chose a sandpile paradigm to fit our ideas in the frame of current research. In our model sand is hot because a grain can topple against gradient, i.e., the grain can walk to another node even when a number of grains in its current node is less than a number of neighboring nodes. Sand is choosey because behavior of the grains is not determined by any global parameter or any threshold of a number of neighboring grains (called here a grain sensitivity) but depends on the exact number of grains in the neighboring nodes. Namely, we assume that a grain being at a node x goes to one of the eight neighboring nodes, chosen at random, if there is another grain at the node x or if the number of grains in eight neighboring nodes lies in some set of 2{1,…,8}. These 256 rules of sensitivity are investigated. The classification of the rules if offered, based on the morphology of the patterns generated by each rule. Eight morphological classes are found. Fine structure of every class is investigated and transient phenomena are analyzed. Three kinds of description of class rules by Boolean expressions are offered. Evolution of the classes governed by several one-dimensional parameters is considered.

scholarly journals Fine-structure classification of multiqubit entanglement by algebraic geometry

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Masoud Gharahi ◽  
Stefano Mancini ◽  
Giorgio Ottaviani
Keyword(s):  
Algebraic Geometry ◽  
Fine Structure

scholarly journals Classification of one-dimensional superattracting germs in positive characteristic

2014 ◽  
Vol 35 (7) ◽  
pp. 2242-2268 ◽  
Author(s):  
MATTEO RUGGIERO
Keyword(s):  
Positive Characteristic ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Dimensional Version

We give a classification of superattracting germs in dimension $1$ over a complete normed algebraically closed field $\mathbb{K}$ of positive characteristic up to conjugacy. In particular, we show that formal and analytic classifications coincide for these germs. We also give a higher-dimensional version of some of these results.

Invariants of weak equivalence in primitive matrices

2000 ◽  
Vol 20 (2) ◽  
pp. 611-626 ◽  
Author(s):  
RICHARD SWANSON ◽  
HANS VOLKMER
Keyword(s):  
Inverse Limit ◽  
Direct Application ◽  
Topological Classification ◽  
Weak Equivalence ◽  
Transition Matrices ◽  
Inverse Limit Spaces ◽  
Positive Dimension ◽  
One Dimensional ◽  
Dimension Group

Weak equivalence of primitive matrices is a known invariant arising naturally from the study of inverse limit spaces. Several new invariants for weak equivalence are described. It is proved that a positive dimension group isomorphism is a complete invariant for weak equivalence. For the transition matrices corresponding to periodic kneading sequences, the discriminant is proved to be an invariant when the characteristic polynomial is irreducible. The results have direct application to the topological classification of one-dimensional inverse limit spaces.

Resonances and Torsion Numbers of Driven Dissipative Nonlinear Oscillators

1986 ◽  
Vol 41 (4) ◽  
pp. 605-614 ◽  
Author(s):  
Ulrich Parlitz ◽  
Werner Lauterborn
Keyword(s):  
Nonlinear Oscillators ◽  
Winding Number ◽  
Local Flow ◽  
One Dimensional ◽  
Bifurcation Set ◽  
Local Bifurcations ◽  
Closed Orbits

The torsion of the local flow around closed orbits and its relation to the superstructure in the bifurcation set of strictly dissipative nonlinear oscillators is investigated. The torsion number describing the twisting behaviour of the flow turns out to be a suitable invariant for the classification of local bifurcations and resonances in those systems. Furthermore, the notions of winding number and resonance are generalized to arbitrary one-dimensional dissipative oscillators.

Semi-supervised learning using multiple one-dimensional embedding based adaptive interpolation

2016 ◽  
Vol 14 (02) ◽  
pp. 1640002 ◽  
Author(s):  
Jianzhong Wang
Keyword(s):  
Supervised Learning ◽  
High Dimensional ◽  
One Dimensional ◽  
Large Size ◽  
Adaptive Interpolation

We propose a novel semi-supervised learning (SSL) scheme using adaptive interpolation on multiple one-dimensional (1D) embedded data. For a given high-dimensional dataset, we smoothly map it onto several different 1D sequences, so that the labeled subset is converted to a 1D subset for each of these sequences. Applying the cubic interpolation of the labeled subset, we obtain a subset of unlabeled points, which are assigned to the same label in all interpolations. Selecting a proportion of these points at random and adding them to the current labeled subset, we build a larger labeled subset for the next interpolation. Repeating the embedding and interpolation, we enlarge the labeled subset gradually, and finally reach a labeled set with a reasonable large size, based on which the final classifier is constructed. We explore the use of the proposed scheme in the classification of handwritten digits and show promising results.

Topological classification of periodic orbits in the Kuramoto–Sivashinsky equation

2018 ◽  
Vol 32 (15) ◽  
pp. 1850155 ◽  
Author(s):  
Chengwei Dong
Keyword(s):  
Nonlinear System ◽  
Variational Method ◽  
Periodic Orbits ◽  
Symbolic Dynamics ◽  
Chaotic Systems ◽  
Building Blocks ◽  
Topological Classification ◽  
One Dimensional ◽  
Sivashinsky Equation

In this paper, we systematically research periodic orbits of the Kuramoto–Sivashinsky equation (KSe). In order to overcome the difficulties in the establishment of one-dimensional symbolic dynamics in the nonlinear system, two basic periodic orbits can be used as basic building blocks to initialize cycle searching, and we use the variational method to numerically determine all the periodic orbits under parameter [Formula: see text] = 0.02991. The symbolic dynamics based on trajectory topology are very successful for classifying all short periodic orbits in the KSe. The current research can be conveniently adapted to the identification and classification of periodic orbits in other chaotic systems.

Automatic Texture Based Classification of the Dynamics of One-Dimensional Binary Cellular Automata

2019 ◽  
Vol 8 (4) ◽  
pp. 41-61
Author(s):  
Marcelo Arbori Nogueira ◽  
Pedro Paulo Balbi de Oliveira
Keyword(s):  
Cellular Automata ◽  
Dynamic Behavior ◽  
Temporal Evolution ◽  
Computational Cost ◽  
Great Variability ◽  
Texture Descriptor ◽  
One Dimensional ◽  
Binary Images ◽  
Elementary Cellular Automata

Cellular automata present great variability in their temporal evolutions due to the number of rules and initial configurations. The possibility of automatically classifying its dynamic behavior would be of great value when studying properties of its dynamics. By counting on elementary cellular automata, and considering its temporal evolution as binary images, the authors created a texture descriptor of the images - based on the neighborhood configurations of the cells in temporal evolutions - so that it could be associated to each dynamic behavior class, following the scheme of Wolfram's classic classification. It was then possible to predict the class of rules of a temporal evolution of an elementary rule in a more effective way than others in the literature in terms of precision and computational cost. By applying the classifier to the larger neighborhood space containing 4 cells, accuracy decreased to just over 70%. However, the classifier is still able to provide some information about the dynamics of an unknown larger space with reduced computational cost.

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