The Von Neumann Threshold of Self-Reproducing Systems

2008 ◽  
Author(s):  
Pierre T. Kabamba
Keyword(s):  
Minimum Amount ◽  
Minimum Length ◽  
Generation Process ◽  
Technical Issue ◽  
Von Neumann ◽  
Amount Of Information ◽  
Novel Theory ◽  
Reproductive Capability

This paper is devoted to the study of systems of entities that are capable of generating other entities of the same kind and, possibly, self-reproducing. The main technical issue addressed is to quantify the requirements that such entities must meet to be able to produce a progeny that is not degenerate, i.e., that has the same reproductive capability as the progenitor. A novel theory that allows an explicit quantification of these requirements is presented. The notion of generation rank of an entity is introduced, and it is proved that the generation process, in most cases, is degenerative in that it strictly and irreversibly decreases the generation rank from parent to descendant. It is also proved that there exists a threshold of rank such that this degeneracy can be avoided if and only if the entity has a generation rank that meets that threshold — this is the von Neumann rank threshold. Based on this threshold, an information threshold is derived, which quantifies the minimum amount of information that must be provided to specify an entity such that its descendants are not degenerate. Furthermore, a complexity threshold is obtained, which quantifies the minimum length of the description of that entity in a given language. Examples that illustrate the theory are provided.

The von Neumann threshold of self-reproducing systems: theory and application

Robotica ◽  
2011 ◽  
Vol 29 (1) ◽  
pp. 123-135 ◽  
Author(s):  
Pierre T. Kabamba ◽  
Patrick D. Owens ◽  
A. Galip Ulsoy
Keyword(s):  
Error Correction ◽  
Self Assembly ◽  
Degrees Of Freedom ◽  
Minimum Length ◽  
Generation Process ◽  
Robot Arm ◽  
Von Neumann ◽  
Novel Theory ◽  
Reproduction Process ◽  
Simulation Results

SUMMARYThis paper is devoted to the study of systems of entities that are capable of generating other entities of the same kind and, possibly, self-reproducing. The main technical issue addressed is to quantify the requirements that such entities must meet to be able to produce a progeny that is not degenerative, i.e., that has the same reproductive capability as the progenitor. A novel theory that allows an explicit quantification of these requirements is presented. The notion of generation rank of an entity is introduced, and it is proved that the generation process, in most cases, is degenerative in that it strictly and irreversibly decreases the generation rank from parent to descendent. It is also proved that there exists a threshold of rank such that this degeneracy can be avoided if and only if the entity has a generation rank that meets that threshold – this is the von Neumann rank threshold. On the basis of this threshold, an information threshold is derived, which quantifies the minimum amount of information that must be provided to specify an entity such that its descendents are not degenerative. Furthermore, a complexity threshold is obtained, which quantifies the minimum length of the description of that entity in a given language. As an application, self-assembly for a 2 Degrees of Freedom planar robot is considered, and simulation results are presented. A robot arm capable of picking up and placing the components of another arm, in the presence of errors, is considered to have successfully reproduced if these are placed within an allowable tolerance. The example shows that, due to the kinematics of the robot, errors can grow from one generation to the next, until the reproduction process fails eventually. However, error correction (via error sensing and feedback control) can then be used to prevent such degeneracy. The von Neumann generation rank and information thresholds are computed for this example, and are consistent with the simulation results in predicting degeneracy in the case without error correction, and predicting successful self-reproduction in the case with error correction.

scholarly journals Pixel-Based Approach for Generating Original and Imitating Evolutionary Art

Electronics ◽  
2020 ◽  
Vol 9 (8) ◽  
pp. 1311
Author(s):  
Yuchen Wang ◽  
Rong Xie
Keyword(s):  
Fitness Function ◽  
Visual Complexity ◽  
Generation Process ◽  
Single Object ◽  
Von Neumann ◽  
Modified Particle Swarm Optimization ◽  
Fitness Functions ◽  
Evolutionary Art ◽  
Artistic Styles ◽  
The Aesthetic

We proposed a pixel-based evolution method to automatically generate evolutionary art. Our method can generate diverse artworks, including original artworks and imitating artworks, with different artistic styles and high visual complexity. The generation process is fully automated. In order to adapt to the pixel-based method, a von Neumann neighbor topology-modified particle swarm optimization (PSO) is employed to the proposed method. The fitness functions of PSO are well prepared. Firstly, we come up with a set of aesthetic fitness functions. Next, the imitating fitness function is designed. Finally, the aesthetic fitness functions and the imitating fitness function are weighted into one single object function, which is used in the modified PSO. Both the original outputs and imitating outputs are shown. A questionnaire is designed to investigate the subjective aesthetic feeling of proposed evolutionary art, and the statistics are shown.

LIMITATION ON THE ACCESSIBLE INFORMATION FOR QUANTUM CHANNELS WITH INEFFICIENT MEASUREMENTS

2005 ◽  
Vol 03 (supp01) ◽  
pp. 87-95
Author(s):  
KURT JACOBS
Keyword(s):  
Quantum System ◽  
Von Neumann Entropy ◽  
Quantum Channels ◽  
Initial State ◽  
Von Neumann ◽  
Classical Information ◽  
Quantum Operations ◽  
Amount Of Information ◽  
Accessible Information

To transmit classical information using a quantum system, the sender prepares the system in one of a set of possible states and sends it to the receiver. The receiver then makes a measurement on the system to obtain information about the senders choice of state. The amount of information which is accessible to the receiver depends upon the encoding and the measurement. Here we derive a bound on this information which generalizes the bound derived by Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] to include inefficient measurements, and thus all quantum operations. This also allows us to obtain a generalization of a bound derived by Hall [Hall, Phys. Rev. A 55, 100 (1997)], and to show that the average reduction in the von Neumann entropy which accompanies a measurement is concave in the initial state, for all quantum operations.

scholarly journals Analysis of the Parameters Required to Properly Define Nanofluids for Heat Transfer Applications

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 65
Author(s):  
Sergio Bobbo ◽  
Bernardo Buonomo ◽  
Oronzio Manca ◽  
Silvio Vigna ◽  
Laura Fedele
Keyword(s):  
Heat Transfer ◽  
Tio2 Nanoparticles ◽  
Thermophysical Properties ◽  
Base Fluid ◽  
Minimum Amount ◽  
Literature Analysis ◽  
Amount Of Information

Nanofluids are obtained by dispersing nanoparticles and dispersant, when present, in a base fluid. Their properties, in particular their stability, however, are strictly related to several other parameters, knowledge of which is important to reproduce the nanofluids and correctly interpret their behavior. Due to this complexity, the results appear to be frequently unreliable, contradictory, not comparable and/or not repeatable, in particular for the scarcity of information on their preparation. Thus, it is essential to define what is the minimum amount of information necessary to fully describe the nanofluid, so as to ensure the possibility of reproduction of both their formulation and the measurements of their properties. In this paper, a literature analysis is performed to highlight what are the most important parameters necessary to describe the configuration of each nanofluid and their influence on the nanofluid’s properties. A case study is discussed, analyzing the information reported and the results obtained for the thermophysical properties of nanofluids formed by water and TiO2 nanoparticles. The aim is to highlight the differences in the amount of information given by the different authors and exemplify how results can be contradictory. A final discussion gives some suggestions on the minimum amount of information that should be given on a nanofluid to have the possibility to compare results obtained for similar nanofluids and to reproduce the same nanofluid in other laboratories.

An Entropy Based Treatment of Gaussian Communication Process for General Quantum Systems

2013 ◽  
Vol 20 (03) ◽  
pp. 1340009
Author(s):  
Noboru Watanabe
Keyword(s):  
Von Neumann Algebras ◽  
Quantum Systems ◽  
Communication Process ◽  
Quantum Mechanical ◽  
Input State ◽  
Von Neumann ◽  
Output State ◽  
Amount Of Information ◽  
General Quantum ◽  
Mutual Entropy

The quantum entropy introduced by von Neumann around 1932 describes the amount of information of the quantum state itself. It was extended by Ohya for C*-systems before Conne-Narnhoffer-Thirring (CNT) entropy. The quantum relative entropy was first defined by Umegaki for σ-finite von Neumann algebras and it was subsequently extended by Araki and Uhlmann for general von Neumann algebras and *-algebras, respectively. By introducing a new notion, the so-called compound state, in 1983 Ohya succeeded to construct the mutual entropy in a complete quantum mechanical system (i.e., input state, output state and channel are all quantum mechanical) describing the amount of information correctly transmitted through the quantum channel. In this paper, we briefly review Ohya's S-mixing entropy and the quantum mutual entropy for general quantum systems. Based on a concept of structure equivalent, we apply the general framework of quantum communication to the Gaussian communication processes.

Statistical analysis of classification

1966 ◽  
Vol 24 ◽  
pp. 188-189
Author(s):  
T. J. Deeming
Keyword(s):  
Multivariate Analysis ◽  
Statistical Analysis ◽  
Classification Scheme ◽  
Analytical Procedure ◽  
Narrow Band ◽  
Scientific Research ◽  
Maximum Amount ◽  
Amount Of Information

If we make a set of measurements, such as narrow-band or multicolour photo-electric measurements, which are designed to improve a scheme of classification, and in particular if they are designed to extend the number of dimensions of classification, i.e. the number of classification parameters, then some important problems of analytical procedure arise. First, it is important not to reproduce the errors of the classification scheme which we are trying to improve. Second, when trying to extend the number of dimensions of classification we have little or nothing with which to test the validity of the new parameters.Problems similar to these have occurred in other areas of scientific research (notably psychology and education) and the branch of Statistics called Multivariate Analysis has been developed to deal with them. The techniques of this subject are largely unknown to astronomers, but, if carefully applied, they should at the very least ensure that the astronomer gets the maximum amount of information out of his data and does not waste his time looking for information which is not there. More optimistically, these techniques are potentially capable of indicating the number of classification parameters necessary and giving specific formulas for computing them, as well as pinpointing those particular measurements which are most crucial for determining the classification parameters.

Stain contamination and embedding in electron microscopy

1986 ◽  
Vol 44 ◽  
pp. 50-53
Author(s):  
Hilton H. Mollenhauer
Keyword(s):  
Electron Microscopy ◽  
Information Retrieval ◽  
Epoxy Resins ◽  
Image Contrast ◽  
Sample Preservation ◽  
Factors Associated ◽  
Amount Of Information ◽  
Electron Microscopical ◽  
Contrast Information

Many factors (e.g., resolution of microscope, type of tissue, and preparation of sample) affect electron microscopical images and alter the amount of information that can be retrieved from a specimen. Of interest in this report are those factors associated with the evaluation of epoxy embedded tissues. In this context, informational retrieval is dependant, in part, on the ability to “see” sample detail (e.g., contrast) and, in part, on tue quality of sample preservation. Two aspects of this problem will be discussed: 1) epoxy resins and their effect on image contrast, information retrieval, and sample preservation; and 2) the interaction between some stains commonly used for enhancing contrast and information retrieval.

Lectures on von Neumann Algebras

2019 ◽  
Author(s):  
Serban-Valentin Stratila ◽  
Laszlo Zsido
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann
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