On the Role of Nonlocal Correlations in Optimization

Korotkikh, Galina; Korotkikh, Victor

doi:10.1007/978-1-4613-0233-9_8

Cited by 7 publications

(6 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following experiments [9], [10] based on a multiagent system provide the evidence supporting the integration principle.…”

Section: Integration Principle Of Complex Systemsmentioning

confidence: 67%

“…Remarkably, the description of complex systems in terms of self-organization processes of prime integer relations has been discovered [5]- [8] and showed promising results [9]- [14]. In particular, it turns out that self-evident integer relations can be organized into a hierarchical network, where an element of a level is formed from elements of the lower level so that all elements in the formation are necessary and sufficient.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Potential of the Irreducible Description of Complex Systems for the Modeling of the Global Financial System

Korotkikh,

Korotkikh

2009

Preprint

Self Cite

View full text Add to dashboard Cite

The recent financial crisis has sharply revealed that current understanding of the global financial system is more than limited. In the recovery plan the confidence in the underlying theory is crucial.To address the problem we propose the description of complex systems in terms of self-organization processes of prime integer relations. The description suggests to consider the global financial system through the hierarchical network built by the totality of the self-organization processes. To make the description operational we propose an integration principle and support it by computational experiments using a multi-agent system. Remarkably, based on integers and controlled by arithmetic only the description raises the possibility to develop an irreducible theory of complex systems. These may open a fundamentally new perspective for the modeling of the global financial system.

show abstract

“…The following experiments [9], [10] based on a multiagent system provide the evidence supporting the integration principle.…”

Section: Integration Principle Of Complex Systemsmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

On the Potential of the Irreducible Description of Complex Systems for the Modeling of the Global Financial System

Korotkikh,

Korotkikh

2009

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The correlation structures underlying the conservation of the quantities (3) in view of (4) are defined by the hierarchical structures of prime integer relations associated with the system of equations (5) and inequality (6) [2], [5], [6].…”

Section: Self-organization Processes Of Prime Integer Relations Amentioning

confidence: 99%

Description of Complex Systems in Terms of Self-Organization Processes of Prime Integer Relations

Korotkikh

2006

Complexus Mundi

View full text Add to dashboard Cite

In the paper we present a description of complex systems in terms of self-organization processes of prime integer relations. A prime integer relation is an indivisible element made up of integers as the basic constituents following a single organizing principle. The prime integer relations control correlation structures of complex systems and may describe complex systems in a strong scale covariant form. It is possible to geometrize the prime integer relations as two-dimensional patterns and isomorphically express the self-organization processes through transformations of the geometric patterns. As a result, prime integer relations can be measured by corresponding geometric patterns specifying the dynamics of complex systems. Determined by arithmetic only, the self-organization processes of prime integer relations can describe complex systems by information not requiring further explanations. This gives the possibility to develop an irreducible theory of complex systems.

show abstract

“…However, the role of the formation processes for the correlations has not been properly discussed. In this section we present that the formation processes of integer relations build up the correlation structures of physical systems and determine their properties [5], [6]. For example, a formation process of prime integer relations results in a correlation structure, where parts of a physical system are embedded within larger parts.…”

Section: The Formation Processes In the Build Up Of The Correlation Smentioning

confidence: 99%

“…We present that the formation processes build up correlation structures of physical systems and determine their properties [5], [6]. As a result the correlations do not take into account the distances between the parts of a physical systems and are nonlocal, instantaneous and inseparable in nature.…”

Section: Introductionmentioning

confidence: 99%

Integers: irreducible guides in the search for a unified theory

Korotkikh¹

2005

Braz. J. Phys.

Self Cite

View full text Add to dashboard Cite

The notion of final theory results from a contrasting understanding of physical reality. Currently, different approaches aim to unify the four forces of nature and discuss whether a final theory may be possible. A key feature of a final theory is irreducibility, however this property has not been seriously exploited. In the paper we present an irreducible mathematical theory that describes physical systems in terms of formation processes of integer relations. The theory has integers and integer relations as the basic elements and is irreducible, because the formation processes are completely controlled by arithmetic. We suggest properties of the formation processes as irreducible guides in the search for a unified theory.

show abstract

On the Role of Nonlocal Correlations in Optimization

Cited by 7 publications

References 4 publications

On the Potential of the Irreducible Description of Complex Systems for the Modeling of the Global Financial System

On the Potential of the Irreducible Description of Complex Systems for the Modeling of the Global Financial System

Description of Complex Systems in Terms of Self-Organization Processes of Prime Integer Relations

Integers: irreducible guides in the search for a unified theory

Contact Info

Product

Resources

About