Computability and information

2018 ◽  
Author(s):  
Cristian S. Calude
Keyword(s):  
Random Sequence ◽  
Random String ◽  
Information Theoretic ◽  
Theoretical Support ◽  
Specific Object ◽  
Axiomatizable Theory ◽  
Definition Of ◽  
Pragmatic Attitude ◽  
Gödel’S Theorem ◽  
Theoretic Version

The standard definition of randomness as considered in probability theory and used, for example, in quantum mechanics, allows one to speak of a process (such as tossing a coin, or measuring the diagonal polarization of a horizontally polarized photon) as being random. It does not allow one to call a particular outcome (or string of outcomes, or sequence of outcomes) ‘random’, except in an intuitive, heuristic sense. Information-theoretic complexity makes this possible. An algorithmically random string is one which cannot be produced by a description significantly shorter than itself; an algorithmically random sequence is one whose initial finite segments are almost random strings. Gödel’s incompleteness theorem states that every axiomatizable theory which is sufficiently rich and sound is incomplete. Chaitin’s information-theoretic version of Gödel’s theorem goes a step further, revealing the reason for incompleteness: a set of axioms of complexity N cannot yield a theorem that asserts that a specific object is of complexity substantially greater than N. This suggests that incompleteness is not only natural, but pervasive; it can no longer be ignored by everyday mathematics. It also provides a theoretical support for a quasi-empirical and pragmatic attitude to the foundations of mathematics. Information-theoretic complexity is also relevant to physics and biology. For physics it is convenient to reformulate it as the size of the shortest message specifying a microstate, uniquely up to the assumed resolution. In this way we get a rigorous, entropy-like measure of disorder of an individual, microscopic, definite state of a physical system. The regulatory genes of a developing embryo can be ultimately conceived as a program for constructing an organism. The information contained by this biochemical computer program can be measured by information-theoretic complexity.

Icon(icity) and causality: On the role of indexical semiotic modes in development of Byzantine art

2017 ◽  
pp. 711-726
Author(s):  
Todor Mitrovic
Keyword(s):  
Integrated Approach ◽  
Late Antique ◽  
Cultural Patterns ◽  
Byzantine Art ◽  
Semiotic Model ◽  
Iconic Images ◽  
Specific Object ◽  
Byzantine Church ◽  
Definition Of ◽  
Indexical Sign

Determined by its biblical origins, the birth of specifically Christian visual culture had to be given through overcoming the inevitable resistance of early church towards images. In order to find its stable place on late antique cultural scene, early byzantine art, thus, had to rely on support of religious and cultural patterns remote of magisterial artistic trends. Among those, contemporary theory recognizes as especially important: 1) cult of relics and 2) sealing practices. Crossing the possibility of theoretical definition of unique semiotic model standing behind those two cultural- religious practices with the fact that after iconoclasm byzantine art will be systematically distanced from both of them, this research attempts to explore the relation between iconophile theory and byzantine artistic production from a yet unexplored interpretative position. Hypothesis that category of indexical sign, as it is proposed by contemporary semiotics (based on Peircean legacy), can be used for extraction of this unique semiotic model is used here as a specific methodological tool for re-approach to both - 1) the pre-iconoclastic need for accentuating the indexical aspects of iconic images and 2) the mystery of post-iconoclastic radical distancing towards such a semiotic need. On the basis of such an integrated approach it is possible not only to search for more precise explanation of co-relations between artistic practices and contemporaneous (iconophile) theory, but to explain curious historical delay in application of this theoretic knowledge in artistic and liturgical realms, together with a late outburst of iconoclastic behaviour provoked by this very delay. Namely, one of the most prominent incarnations of pre-iconoclastic need for ?indexicalisation? of iconic medium, the mysterious Mandylion from Edessa, had very curious role in historical development of post-iconoclastic plastic arts in Byzantium. This specific object was miraculously and undividedly uniting both key indexical aspects of pre-iconoclastic cognitive settings in one icon - causally connected with the archetypehimself. However, exactly this kind of synthetic, relic-seal-image status turned out to be the specific semiotic stumbling stone in the process of application of iconophile theory in liturgical arts. This is why in XI century byzantine church decided to refrain Mandylion from public life for good and lock it in court chapel, under the protection of the emperor himself. As one of the most curious theological decisions of medieval Christianity, this extraordinary semiotic conversion was, actually, the final step in application of the most advanced achievements of the late iconophile theory, which was, at the same time, the first step in development of artistic system relaxed from the pressure of need for legalistic, causal validation of pictorial language.

scholarly journals Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 534 ◽  
Author(s):  
Hector Zenil ◽  
Narsis Kiani ◽  
Jesper Tegnér
Keyword(s):  
Algorithmic Complexity ◽  
Information Theoretic ◽  
Algorithmic Probability ◽  
Graphs And Networks ◽  
Algorithmic Information ◽  
Statistical Regularities ◽  
Review Study ◽  
Causal Nature ◽  
Definition Of

We introduce a definition of algorithmic symmetry in the context of geometric and spatial complexity able to capture mathematical aspects of different objects using as a case study polyominoes and polyhedral graphs. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov–Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumerate all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity—both theoretical and numerical—with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize spatial, geometric, symmetric and topological properties of mathematical objects and graphs.

scholarly journals Theoretical Design and Circuit Implementation of Integer Domain Chaotic Systems

2014 ◽  
Vol 24 (10) ◽  
pp. 1450128 ◽  
Author(s):  
Qianxue Wang ◽  
Simin Yu ◽  
Christophe Guyeux ◽  
Jacques M. Bahi ◽  
Xiaole Fang
Keyword(s):  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Random Sequence ◽  
Noise Signal ◽  
Circuit Implementation ◽  
New Approach ◽  
Uniform Noise ◽  
Definition Of ◽  
First Time ◽  
Hybrid Circuit

In this paper, a new approach for constructing integer domain chaotic systems (IDCS) is proposed, and its chaotic behavior is mathematically proven according to Devaney's definition of chaos. Furthermore, an analog-digital hybrid circuit is also developed for realizing the designed basic IDCS. In the IDCS circuit design, chaos generation strategy is realized through a sample-hold circuit and a decoder circuit so as to convert the uniform noise signal into a random sequence, which plays a key role in circuit implementation. The experimental observations further validate the proposed systematic methodology for the first time.

scholarly journals Information-theoretic Modeling of Perceived Musical Complexity

2019 ◽  
Vol 37 (2) ◽  
pp. 165-178
Author(s):  
Sarah A. Sauvé ◽  
Marcus T. Pearce
Keyword(s):  
Individual Differences ◽  
Computational Model ◽  
Information Content ◽  
Statistical Learning ◽  
Probabilistic Prediction ◽  
Information Theoretic ◽  
Musical Background ◽  
Musical Excerpts ◽  
Definition Of ◽  
Perceived Complexity

What makes a piece of music appear complex to a listener? This research extends previous work by Eerola (2016), examining information content generated by a computational model of auditory expectation (IDyOM) based on statistical learning and probabilistic prediction as an empirical definition of perceived musical complexity. We systematically manipulated the melody, rhythm, and harmony of short polyphonic musical excerpts using the model to ensure that these manipulations systematically varied information content in the intended direction. Complexity ratings collected from 28 participants were found to positively correlate most strongly with melodic and harmonic information content, which corresponded to descriptive musical features such as the proportion of out-of-key notes and tonal ambiguity. When individual differences were considered, these explained more variance than the manipulated predictors. Musical background was not a significant predictor of complexity ratings. The results support information content, as implemented by IDyOM, as an information-theoretic measure of complexity as well as extending IDyOM's range of applications to perceived complexity.

scholarly journals Von Mises' definition of random sequences reconsidered

1987 ◽  
Vol 52 (3) ◽  
pp. 725-755 ◽  
Author(s):  
Michiel van Lambalgen
Keyword(s):  
Statistical Tests ◽  
Random Sequence ◽  
The Other ◽  
Selection Procedures ◽  
Random Sequences ◽  
Definition Of ◽  
Von Mises ◽  
The Relationship

AbstractWe review briefly the attempts to define random sequences (§0). These attempts suggest two theorems: one concerning the number of subsequence selection procedures that transform a random sequence into a random sequence (§§1–3 and 5); the other concerning the relationship between definitions of randomness based on subsequence selection and those based on statistical tests (§4).

Solution of a problem of Tarski

1956 ◽  
Vol 21 (1) ◽  
pp. 49-51 ◽  
Author(s):  
John Myhill
Keyword(s):  
Unary Operation ◽  
Negative Answer ◽  
Operation Symbol ◽  
Counter Example ◽  
Recursively Enumerable ◽  
Consistent Extension ◽  
Axiomatizable Theory ◽  
Definition Of ◽  
Image Position ◽  
The Given

We presuppose the terminology of [1], and we give a negative answer to the following problem ([1], p. 19): Does every essentially undecidable axiomatizable theory have an essentially undecidable finitely axiomatizable subtheory?We use the following theorem of Kleene ([2], p. 311). There exist two recursively enumerable sets α and β such that (1) α and β are disjoint (2) there is no recursive set η for which α ⊂ η, β ⊂ η′. By the definition of recursive enumerability, there are recursive predicates Φ and Ψ for whichWe now specify a theory T which will afford a counter-example to the given problem of Tarski. The only non-logical constants of T are two binary predicates P and Q, one unary operation symbol S, and one individual constant 0. As in ([1], p. 52) we defineThe only non-logical axioms of T are the formulae P(Δm, Δn) for all pairs of integers m, n satisfying Δ(m, n); the formulae Q(Δm, Δn) for all pairs of integers m, n satisfying Ψ(m, n); and the formulaT is consistent, since it has a model. It remains to show that (1) every consistent extension of T is undecidable (2) if T1 is a finitely axiomatizable subtheory of T, there exists a consistent and decidable extension of T1 which has the same constants as T1.

scholarly journals THE IMPORTANCE OF SCIENTIFIC RESEARCH FOR THE DEVELOPMENT OF HIGHER EDUCATIONAL INSTITUTIONS

2021 ◽  
Vol 2 (37) ◽  
pp. 161-166
Author(s):  
A. Vovk ◽  
K. Levchuk
Keyword(s):  
New Technologies ◽  
Scientific Research ◽  
Modern Society ◽  
Systematic Investigation ◽  
Educational Institutions ◽  
Higher Educational Institutions ◽  
Technical Problems ◽  
Specific Object ◽  
Higher Educational ◽  
Definition Of

The article analyzes the role and importance of scientific research in higher educational institutions, identifies the main tasks, functions of science and the main stages of development of scientific research, taking into account the requirements of the development of modern society. By research we mean the search of the new knowledge, a systematic investigation to establish the facts or the process of learning something. The purpose of scientific research is definition of a specific object and comprehensive, reliable study of its structure, characteristics, relationships based on the principles and methods of cognition developed in science, as well as obtaining useful results for human activity, introduction into production with the subsequent effect. Creating new technical tools and increasing requirements for existing ones, the emergence of new methods for solving technical problems call for a revision of the methods of studying and creating systematization, which allows accelerating the timing of the introduction of new technical solutions into the production process and making it more efficient, improving the qualification level of specialists. Thus, the functioning and development of countries is impossible without scientific research, the platform for which is higher education institutions, and the growth of the social product depends on scientific research. Scientific researchers have an exceptional significance for the development of all directions of higher educational institutions: education of specialists with high quality of training, formation of scientific schools, give prospects for effective use of scientific potential for the development of science itself, creation of new technologies and improvement of existing ones, facilitate the establishment and deepening of international scientific and educational relations, promote the development of international competitiveness, provide an opportunity to invent the latest technologies.

scholarly journals Heat Engines of Extraordinary Efficiency and the General Principle of their Operation

2017 ◽  
Author(s):  
Remi Cornwall
Keyword(s):  
Kinetic Theory ◽  
Degrees Of Freedom ◽  
Classification Scheme ◽  
Chemical Potential ◽  
Information Theoretic ◽  
Heat Engines ◽  
Magnetic Remanence ◽  
Maxwell Demon ◽  
Definition Of ◽  
The Right

The intention of this paper is to elucidate new types of heat engines with extraordinary efficiency, more specifically to eventually focus on the author’s research into a temporary magnetic remanence device. First we extend the definition of heat engines through a diagrammatic classification scheme and note a paradoxical non-coincidence between the Carnot, Kelvin-Planck and other forms of the 2nd Law, between sectors of the diagram. It is then seen, between the diagram sectors, how super-efficient heat engines are able to reduce the degrees of freedom resulting from change in chemical potential, over mere generation of heat; until in the right sector of the diagram, the conventional wisdom for the need of two reservoirs is refuted. A brief survey of the Maxwell Demon problem finds no problem with information theoretic constructs. Our ongoing experimental enquiry into a temporary magnetic remanence cycle using standard kinetic theory, thermodynamics and electrodynamics is presented – yet a contradiction results with the 2nd law placing it in the right sector of the classification diagram.

scholarly journals CRIMINAL LIABILITY OF LEGAL ENTITIES IN THE CZECH REPUBLIC

2019 ◽  
Vol 3 ◽  
pp. 74-80
Author(s):  
Aleksandr V. Fedorov ◽  
◽  
Keyword(s):  
Czech Republic ◽  
Mass Media ◽  
Criminal Liability ◽  
The Czech Republic ◽  
Legal Entity ◽  
Specific Object ◽  
Definition Of ◽  
Legal Entities

The article is devoted to the issues of legislative establishment of criminal liability of legal entities in the Czech Republic including definition of a legal entity as a subject of crime and criminal liability, conditions under which a crime is considered committed by a legal entity. Special attention is paid to an analysis of the special comprehensive Law of December 6, 2011, On Criminal Liability of Legal Entities and Procedural Actions in Respect Thereof and criminal punishments stipulated by this law for legal entities including: cancellation of registration (liquidation) of a legal entity; property seizure; money fine; seizure of a specific object; prohibition of activities; prohibition of participation in state contracts, non-admission to concession procedures and state procurements; prohibition of receipt of any government allowance or subsidy; judgment publication in state mass media. Injunctive remedies taken in respect of legal entities are reviewed.

scholarly journals Formation of investment attractiveness of a gaming virtual team based on goodwill management in cybersport

2021 ◽  
Vol 15 (2) ◽  
pp. 45-60
Author(s):  
Marina Yu. Andreeva ◽  
◽  
Yury N. Sentyabov ◽  
Keyword(s):  
Virtual World ◽  
Swot Analysis ◽  
Main Tool ◽  
Qualitative Change ◽  
Role Playing ◽  
Provision Of Services ◽  
Specific Object ◽  
Role Playing Game ◽  
Definition Of ◽  
Key Aspects

The development of the Internet, the transition to the fourth technological order contributes to the quantitative and qualitative change in virtual organizations. A special place in the virtual environment is occupied by the gaming segment, the volume of which in 2018 reached over 116 trillion dollars, nearly doubling in the past five years. COVID-19 has undoubtedly played into the hands of the online gaming industry, increasing sales across all segments. This study analyzes the massively multiplayer online role-playing game that created the phenomenon of the virtual world. It is the virtual game worlds that have formed the niche of the virtual gaming commercial teams (VGCT`s), which specialize in the provision of services for the development of content produced by development organizations for user players. However, in order to successfully operate in the face of tough virtual gaming competition, a commercial team needs both an understanding of the business process and attracting sources of funding. The article discusses the strategy of forming the investment attractiveness of VGCT, as one of the key aspects of competitiveness. The paper presents the author`s definition of the investment attractiveness of VGCT, carried out SWOT analysis of the working VGCT “Zeta”, assessed the investment attractiveness on the basis of unidentified assets. The purpose of the study is to develop approaches to determining the investment attractiveness of VGCT in the specific conditions of the economy of the virtual world of multiplayer games. Brief statement of the problem is to substantiate the need of managing goodwill of a virtual organization as the main tool for increasing its competitiveness. The article used general scientific methods and methods of SWOT-analysis. The definition of the economy of the virtual gaming world of multiplayer role-playing online games is given. The essence of the concept of “investment attractiveness” is revealed in relation to a specific object of research – a virtual gaming commercial team, its assessment is carried out in the context of external and internal factors. It was determined that goodwill constitutes the basis of VGCT’s investment attractiveness, and the task of increasing the competitiveness of VGCT is inextricably linked with the management of goodwill as a set of unidentifiable assets.

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