The Mathematical Concept of Measuring Risk

2014 ◽  
pp. 133-150
Author(s):  
Francesca Biagini ◽  
Thilo Meyer-Brandis ◽  
Gregor Svindland
Keyword(s):  
Mathematical Concept

Note on Suppes' "Mathematical concept formation."

1967 ◽  
Vol 22 (5) ◽  
pp. 400-401 ◽  
Author(s):  
Lawrence T. Frase
Keyword(s):  
Concept Formation ◽  
Mathematical Concept

A NEW APPROACH TO THE STUDY OF COORDINATIVE CONSTRUCTIONS

2019 ◽  
pp. 175-187
Author(s):  
Anna Varnayeva
Keyword(s):  
Characteristic Property ◽  
Mathematical Concept ◽  
The Other ◽  
New Approach ◽  
Logical Aspect ◽  
First Case

Coordinative constructions are traditionally opposed to subordinative constructions. However, this opposition comes down to denial of dependence in coordinative constructions. Thereby the parity of these two constructions does not come to light: subordinative construction can be described without coordinative one. This situation is not improved by detection of a coordinative triangle in all coordinative constructions. The article shows a new approach in the study of coordinative constructions: a coordinative construction is a system; there are not only specific relations – a coordinative triangle, – but also specific elements. Novelty of the study consists in the address to extralinguistic facts, viz. a mathematical concept of a set and its elements. There are a lot of similarities between them. A set in mathematics includes generalizing elements and the composed row in coordinative constructions; in the first case the set is not partitioned, in the second case it is partitioned. In mathematics equivalent components in coordinative constructions correspond to the set elements. A characteristic property in mathematics is homogeneity in coordinative constructions and etc. It is firstly demonstrated, that coordinative and subordinative constructions are correlative and the study of one construction is impossible without the study of the other one. Their parity is shown in coordinative constructions with elements of one set, in subordinative ones with elements of different sets. Cf.: roses and tulips –red roses. In the coordinatiму construction elements of one set are called: «flowers »; in the subordinative construction there are elements of different sets: «flowers » and «colors». It should be noted that the mathematical concept of a set relates to so called logical aspect in linguistics or thinking about reality.

From Top-Down Control to Self-Organisation: The “Thaw” and Motor Action Theory

2020 ◽  
Vol 30 (2) ◽  
pp. 129-156
Author(s):  
Irina Sirotkina
Keyword(s):  
Soviet Union ◽  
Action Theory ◽  
Scientific Progress ◽  
Mathematical Concept ◽  
New Paradigm ◽  
Top Down ◽  
The Soviet Union ◽  
New Models ◽  
Democratic Principles ◽  
Moscow School

The period from the late 1950s to the mid-1960s in the Soviet Union was known as the “Thaw,” a political era that fostered hopes of restoring the rule of law and democracy to the country. In that period cybernetics came to symbolize both scientific progress and social change. The Soviet intelligentsia had survived the hardship of Stalinist repression and now regarded the new discipline, which brought together the natural sciences and the human sciences, as a pathway to building a freer and more equal society. After decades of domination by Pavlovian doctrine, a paradigm shift was under way in physiology and psychology. Cybernetics reinforced the new paradigm, which put forward ideas of purposive behavior and self-organization in living and non-living systems. The conditioned reflex and a simplistic one-to-one view of connections in the nervous system gave way to more sophisticated and complex models, which could be formalized mathematically. Previous models of control in living organisms were mostly hierarchical and included top-down control of peripheral movement by the motor centers. The new models supplemented this picture with feedback commands from the periphery to the center. By the time cybernetics had made its appearance in the Soviet Union, new models of control had already been formulated in physiology by Nikolay Bernstein (1896– 1966). He termed the feedback from afferent signals “sensorial corrections,” meaning that they play an important part in adapting central control to the changing situation at the periphery of movement. The new paradigm emphasized horizontal connections over vertical ones, and new models took hold based on less “totalitarian” and more “democratic” principles, such as the idea of automatic or autonomous functioning of intermediate centers, the mathematical concept of well-organized functions, the theory of “the collective behavior of automata,” etc. This line of research was carried out in the USSR as well as abroad by Bernstein’s students and followers who formed the Moscow School of Motor Control. The author argues that this preference for less hierarchical models was one expression of the Thaw’s trend toward liberalization of life within the USSR and greater involvement in international politics.

Description and symmetry of aperiodic crystals

2018 ◽  
Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu
Keyword(s):  
Time Reversal ◽  
Mathematical Concept ◽  
New Materials ◽  
Magnetic Systems ◽  
Atomic Structures ◽  
Modulated Phases ◽  
Quasiperiodic Functions ◽  
Aperiodic Crystals ◽  
Superspace Description

This chapter first introduces the mathematical concept of aperiodic and quasiperiodic functions, which will form the theoretical basis of the superspace description of the new recently discovered forms of matter. They are divided in three groups, namely modulated phases, composites, and quasicrystals. It is shown how the atomic structures and their symmetry can be characterized and described by the new concept. The classification of superspace groups is introduced along with some examples. For quasicrystals, the notion of approximants is also introduced for a better understanding of their structures. Finally, alternatives for the descriptions of the new materials are presented along with scaling symmetries. Magnetic systems and time-reversal symmetry are also introduced.

scholarly journals A New Approach for Dynamic Stochastic Fractal Search with Fuzzy Logic for Parameter Adaptation

2021 ◽  
Vol 5 (2) ◽  
pp. 33
Author(s):  
Marylu L. Lagunes ◽  
Oscar Castillo ◽  
Fevrier Valdez ◽  
Jose Soria ◽  
Patricia Melin
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Inference ◽  
Dynamic Parameter ◽  
Mathematical Concept ◽  
Parameter Adaptation ◽  
Inference Models ◽  
Fractal Particles ◽  
Novel Method ◽  
Dynamic Stochastic ◽  
Stochastic Fractal Search

Stochastic fractal search (SFS) is a novel method inspired by the process of stochastic growth in nature and the use of the fractal mathematical concept. Considering the chaotic stochastic diffusion property, an improved dynamic stochastic fractal search (DSFS) optimization algorithm is presented. The DSFS algorithm was tested with benchmark functions, such as the multimodal, hybrid, and composite functions, to evaluate the performance of the algorithm with dynamic parameter adaptation with type-1 and type-2 fuzzy inference models. The main contribution of the article is the utilization of fuzzy logic in the adaptation of the diffusion parameter in a dynamic fashion. This parameter is in charge of creating new fractal particles, and the diversity and iteration are the input information used in the fuzzy system to control the values of diffusion.

A Novel Iterated Function System-Based Model for Coloured Image Encryption

2021 ◽  
Vol 12 (2) ◽  
pp. 1-10
Author(s):  
Amine Rahmani
Keyword(s):  
Image Encryption ◽  
Iterated Function System ◽  
Mathematical Concept ◽  
Logistic Equation ◽  
Encryption Scheme ◽  
Symmetric Encryption ◽  
New Model ◽  
Proposed Model ◽  
Iterated Function ◽  
Chaotic Cryptography

Chaotic cryptography has been a well-studied domain over the last few years. Many works have been done, and the researchers are still getting benefit from this incredible mathematical concept. This paper proposes a new model for coloured image encryption using simple but efficient chaotic equations. The proposed model consists of a symmetric encryption scheme in which it uses the logistic equation to generate secrete keys then an affine recursive transformation to encrypt pixels' values. The experimentations show good results, and theoretic discussion proves the efficiency of the proposed model.

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