Response Curves for Cellular Automata in One and Two Dimensions

2010 ◽  
Vol 1 (3) ◽  
pp. 85-99 ◽  
Author(s):  
Henryk Fuks ◽  
Andrew Skelton
Keyword(s):  
Cellular Automata ◽  
Response Curve ◽  
Initial Density ◽  
Two Dimensions ◽  
Initial Configuration ◽  
Two Dimensional ◽  
Response Curves ◽  
Special Case

In this paper, the authors consider the problem of computing a response curve for binary cellular automata, that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. The authors demonstrate how this problem could be approached using rule 130 as an example. For this rule, preimage sets of finite strings exhibit recognizable patterns; therefore, it is possible to compute both cardinalities of preimages of certain finite strings and probabilities of occurrence of these strings in a configuration obtained by iterating a random initial configuration n times. Response curves can be rigorously calculated in both one- and two-dimensional versions of CA rule 130. The authors also discuss a special case of totally disordered initial configurations, that is, random configurations where the density of ones and zeros are equal to 1/2.

Response Curves for Cellular Automata in One and Two Dimensions

2012 ◽  
pp. 291-305
Author(s):  
Henryk Fuks ◽  
Andrew Skelton
Keyword(s):  
Cellular Automata ◽  
Response Curve ◽  
Initial Density ◽  
Two Dimensions ◽  
Initial Configuration ◽  
Two Dimensional ◽  
Response Curves ◽  
Special Case

In this paper, the authors consider the problem of computing a response curve for binary cellular automata, that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. The authors demonstrate how this problem could be approached using rule 130 as an example. For this rule, preimage sets of finite strings exhibit recognizable patterns; therefore, it is possible to compute both cardinalities of preimages of certain finite strings and probabilities of occurrence of these strings in a configuration obtained by iterating a random initial configuration n times. Response curves can be rigorously calculated in both one- and two-dimensional versions of CA rule 130. The authors also discuss a special case of totally disordered initial configurations, that is, random configurations where the density of ones and zeros are equal to 1/2.

scholarly journals Simulation of earthquakes with cellular automata

1998 ◽  
Vol 2 (4) ◽  
pp. 267-279 ◽  
Author(s):  
P. G. Akishin ◽  
M. V. Altaisky ◽  
I. Antoniou ◽  
A. D. Budnik ◽  
V. V. Ivanov
Keyword(s):  
Cellular Automata ◽  
Analytical Method ◽  
Power Spectra ◽  
Two Dimensions ◽  
Seismic Events ◽  
Two Dimensional ◽  
Stress Release ◽  
Event Energy

The relation between cellular automata (CA) models of earthquakes and the Burridge–Knopoff (BK) model is studied. It is shown that the CA proposed by P. Bak and C. Tang,although they have rather realistic power spectra, do not correspond to the BK model. We present a modification of the CA which establishes the correspondence with the BK model.An analytical method of studying the evolution of the BK-like CA is proposed. By this method a functional quadratic in stress release, which can be regarded as an analog of the event energy, is constructed. The distribution of seismic events with respect to this “energy” shows rather realistic behavior, even in two dimensions. Special attention is paid to two-dimensional automata; the physical restrictions on compression and shear stiffnesses are imposed.

scholarly journals Generative Aspects of Oxide Pictures by Oxide Tile Rewriting Grammar

2019 ◽  
Vol 8 (3) ◽  
pp. 1537-1543
Keyword(s):  
Two Dimensions ◽  
Two Dimensional ◽  
Silicate Network ◽  
Oxygen Ions ◽  
Tiling System ◽  
Higher Dimensional ◽  
Picture Languages ◽  
Rectangular Grids ◽  
Rewriting Rules ◽  
Special Case

In formal languages, picture language is generalization of string language theory to two dimensions. Pictures which may be regarded as two-dimensional objects occur in studies concerning recognition of patterns, images and various computational fields. Several studies have been done for generating and/or recognizing higher dimensional objects using formal models. Tile rewriting grammar (TRG) is yet another model introduced for generating picture languages. TRG combines isometric rewriting rules with the Giammaresi and Restivo’s Tiling system. This rewriting grammar generates spirals, square and rectangular grids. The power of generating pictures by tile rewriting grammar is more than REC .Sweety et al have generated hexagonal pictures, introducing hexagonal Tile Rewriting Grammar. Kuberalet al have introduced Triangular Tile Rewriting Grammar to generate Triangular Pictures. A special class of objects namely Oxide pictures have been of interest recently. Oxide network is a special case of Silicate network. The silicates are a complicated class of minerals made up of tetrahedral silicates. A basic silicate tetrahedron unit SiO4 is formed with Oxygen ions in the corners and a Silicate ion in the center. In a two dimensional plane a ring of tetrahedrons that are shared by Oxygen nodes forms a silicate sheet.In this paper, Oxide Tile Rewriting Grammar (OXTRG) is proposed for generating Oxide pictures. The motivation for the study is derived from the Oxide network which is obtained by deleting all the silicon nodes of a silicate network. Closure properties of OXTRG are discussed. When compared with schemes such as Oxide Tiling System and Oxide Sgraffito Automaton, OXTRG is found to be more powerful.

scholarly journals Orbits of the Bernoulli measure in single-transition asynchronous cellular automata

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Henryk Fukś ◽  
Andrew Skelton
Keyword(s):  
Cellular Automata ◽  
Initial Density ◽  
Response Curves ◽  
Asynchronous Cellular Automata ◽  
Final Density ◽  
Short Cylinder ◽  
Bernoulli Measure ◽  
Single Transition ◽  
International Audience ◽  
Transition Rules

International audience We study iterations of the Bernoulli measure under nearest-neighbour asynchronous binary cellular automata (CA) with a single transition. For these CA, we show that a coarse-level description of the orbit of the Bernoulli measure can be obtained, that is, one can explicitly compute measures of short cylinder sets after arbitrary number of iterations of the CA. In particular, we give expressions for probabilities of ones for all three minimal single-transition rules, as well as expressions for probabilities of blocks of length 3 for some of them. These expressions can be interpreted as "response curves'', that is, curves describing the dependence of the final density of ones on the initial density of ones.

scholarly journals Peristatic solutions for finite one- and two-dimensional systems

2016 ◽  
Vol 22 (8) ◽  
pp. 1639-1653 ◽  
Author(s):  
Vinesh V Nishawala ◽  
Martin Ostoja-Starzewski
Keyword(s):  
Numerical Method ◽  
Continuum Mechanics ◽  
Analytical Solutions ◽  
Differential Form ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Nonlocal Continuum ◽  
One Dimensional ◽  
Static Version ◽  
Special Case

Peridynamics is a nonlocal continuum mechanics theory where its governing equation has an integro-differential form. This paper specifically uses bond-based peridynamics. Typically, peridynamic problems are solved via numerical means, and analytical solutions are not as common. This paper analytically evaluates peristatics, the static version of peridynamics, for a finite one-dimensional rod as well as a special case for two dimensions. A numerical method is also implemented to confirm the analytical results.

THE HPP RULE WITH MEMORY AND THE DENSITY CLASSIFICATION TASK

2010 ◽  
Vol 21 (09) ◽  
pp. 1115-1128 ◽  
Author(s):  
RAMÓN ALONSO-SANZ
Keyword(s):  
Cellular Automata ◽  
Initial Configuration ◽  
Classification Task ◽  
Two Dimensional ◽  
With Memory ◽  
Standard Framework ◽  
In Cells

This article considers an extension to the standard framework of cellular automata by implementing memory capability in cells. It is shown that the important block HPP rule behaves as an excellent classifier of the density in the initial configuration when applied to cells endowed with pondered memory of their previous states. If the weighing is made so that the most recent state values are assigning the highest weights, the HPP rule surpasses the performance of the best two-dimensional density classifiers reported in the literature.

Factor VII Clotting Assay: Influence of Different Thromboplastins and Factor VII-Deficient Plasmas

1991 ◽  
Vol 65 (02) ◽  
pp. 160-164 ◽  
Author(s):  
Marina Poggio ◽  
Armando Tripodi ◽  
Guglielmo Mariani ◽  
Pier Mannuccio Mannucci ◽  
Keyword(s):  
Heart Disease ◽  
Ischemic Heart Disease ◽  
Dose Response ◽  
Response Curve ◽  
Ischemic Heart ◽  
Factor Vii ◽  
Response Curves ◽  
Assay Sensitivity ◽  
Clinical Laboratories ◽  
Coagulant Activity

SummaryBeing a putative predictor of ischemic heart disease, the measurement of factor VII (FVTI) coagulant activity will be presumably requested to clinical laboratories with increasing frequency. To assess the influence on FVII assays of different thromboplastins and FVII-deficient plasmas we compared performances of all possible combinations of 5 thromboplastins and 6 deficient plasmas. The reproducibility of the clotting times of the dose-response curves for human and rabbit thromboplastins were acceptable (CV lower than 7%), whereas bovine thromboplastin had a higher CV. Reproducibility was very similar for all deficient plasmas when they were used in combination with a given thromboplastin. Responsiveness of the dose-response curve did not depend on the deficient plasma but rather on the thromboplastin: one rabbit thromboplastin was the least responsive, the bovine thromboplastin the most responsive, the human and the remaining two rabbit thromboplastins had intermediate responsiveness. Assay sensitivity to cold-activated FVII varied according to the thromboplastin: the bovine thromboplastin was the most sensitive, the human thromboplastin the least sensitive, of the three rabbit thromboplastins two were relatively sensitive, one was almost insensitive. In conclusion, our results indicate that thromboplastin rather than deficient plasma is the crucial factor in the standardization of FVII assay.

OVARIAN ASCORBIC ACID DEPLETION TEST FOR LUTEINIZING HORMONE

1967 ◽  
Vol 56 (4) ◽  
pp. 619-625 ◽  
Author(s):  
Hans Jacob Koed ◽  
Christian Hamburger
Keyword(s):  
Ascorbic Acid ◽  
Luteinizing Hormone ◽  
Dose Response ◽  
Response Curve ◽  
Dose Response Curve ◽  
Human Origin ◽  
Response Curves ◽  
Significant Difference ◽  
The Mean ◽  
Different Levels

ABSTRACT Comparison of the dose-response curves for LH of ovine origin (NIH-LH-S8) and of human origin (IRP-HMG-2) using the OAAD test showed a small, though statistically significant difference, the dose-response curve for LH of human origin being a little flatter. Two standard curves for ovine LH obtained with 14 months' interval, were parallel but at different levels of ovarian ascorbic acid. When the mean ascorbic acid depletions were calculated as percentages of the control levels, the two curves for NIH-LH-S8 were identical. The use of standards of human origin in the OAAD test for LH activity of human preparations is recommended.

Urbanicity, City Delegations, and Two-Dimensional Liberalism

2018 ◽  
Author(s):  
Thomas K. Ogorzalek
Keyword(s):  
National Level ◽  
Two Dimensions ◽  
Political Order ◽  
Two Dimensional ◽  
Local Institutions ◽  
Horizontal Integration ◽  
National Politics ◽  
United Front ◽  
Strategies For Success

This theoretical chapter develops the argument that the conditions of cities—large, densely populated, heterogeneous communities—generate distinctive governance demands supporting (1) market interventions and (2) group pluralism. Together, these positions constitute the two dimensions of progressive liberalism. Because of the nature of federalism, such policies are often best pursued at higher levels of government, which means that cities must present a united front in support of city-friendly politics. Such unity is far from assured on the national level, however, because of deep divisions between and within cities that undermine cohesive representation. Strategies for success are enhanced by local institutions of horizontal integration developed to address the governance demands of urbanicity, the effects of which are felt both locally and nationally in the development of cohesive city delegations and a unified urban political order capable of contending with other interests and geographical constituencies in national politics.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

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