scholarly journals Fractal Structures and Fractal Functions as Disease Indicators

Oikos ◽  
1995 ◽  
Vol 74 (2) ◽  
pp. 310 ◽  
Author(s):  
J. M. Escós ◽  
C. L. Alados ◽  
J. M. Emlen ◽  
J. M. Escos
Keyword(s):  
Fractal Structures ◽  
Fractal Functions ◽  
Disease Indicators

An Introduction to Smart Fractal Structures and Mechanisms

1993 ◽  
Author(s):  
Mohsen Shahinpoor
Keyword(s):  
Molecular Level ◽  
Robot Manipulators ◽  
Kinematic Model ◽  
Cantor Set ◽  
Kinematic Structure ◽  
Fractal Structures ◽  
Structural Geometry ◽  
Geometric Invariance ◽  
Fractal Functions ◽  
Computer Controlled

Abstract Fractal structures are unique in the sense that they are highly expandible or collapsible and yet they are capable of preserving their basic structural geometry in a dynamic fashion. This dynamic geometric invariance opens up a new territory in fractal solids, i.e., fractal structures, mechanisms and robot manipulators. Some of these structure are in the form of highly deployable mechanisms and possibly redundant, multi-axis, multi-arm, multi-finger robot manipulators whose kinematic structure is fractal. Thus, simple fractal structures, such as triadic cantor set, and fractal functions, such as the Weirstraus-Mandelbrot functions, govern the structural branching of such robots and essentially define their kinematic structure. These deployable fractal structures, mechanisms and robot manipulators are shown to be capable of generating unique, and yet unparalleled properties such as computer-controlled microsensing even down to molecular level (micromachining) and computer-controlled dynamics such as the creation of hypervelocity fractons with speeds in the range of hundreds of kilometers per second. A number of structures and mechanisms and their unique properties are presented in this paper and a simple kinematic model is presented and briefly discussed.

Sampling Dependence of EEG Nonlinear and Fractal Structures in Healthy Subjects and Alzheimer Patients

2003 ◽  
Author(s):  
F. Aporti ◽  
F. Ferro-Milone ◽  
A. Cananzi ◽  
T. A. Minelli ◽  
V. Nofrate ◽  
...  
Keyword(s):  
Healthy Subjects ◽  
Fractal Structures

scholarly journals Complex Dynamical Behaviors of a Mixed Duopoly Game Based on Intellectual Property Rights Protection

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Tong Chu ◽  
Yu Yu ◽  
Xiaoxue Wang
Keyword(s):  
Intellectual Property ◽  
Property Rights ◽  
Intellectual Property Rights ◽  
Mixed Duopoly ◽  
Fractal Structures ◽  
Rights Protection ◽  
Intellectual Property Rights Protection ◽  
Dynamical Behaviors ◽  
Property Rights Protection ◽  
Coexistence Of Attractors

Based on the oligopoly game theory and the intellectual property rights protection policy, we investigate the complex dynamical behaviors of a mixed duopoly game with quadratic cost. In the new system, a few parameters are improved by considering intellectual property rights protection and the stability conditions of the Nash equilibrium point are discussed in detail. A set of the two-dimensional bifurcation diagrams is demonstrated by using numerical modeling, and these diagrams show abundant complex dynamical behaviors, such as coexistence of attractors, different bifurcation, and fractal structures. These dynamical properties can present the long-run effects of strengthening intellectual property protection.

scholarly journals Fractal Frames of Functions on the Rectangle

2021 ◽  
Vol 5 (2) ◽  
pp. 42
Author(s):  
María A. Navascués ◽  
Ram Mohapatra ◽  
Md. Nasim Akhtar
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Integrable Function ◽  
Two Dimensional ◽  
Tensor Product Space ◽  
Fractal Functions

In this paper, we define fractal bases and fractal frames of L2(I×J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L2(I×J) with the tensor product space L2(I)⨂L2(J). First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of L2(I×J) composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.

Fundamental Sets of Fractal Functions

2007 ◽  
Vol 100 (3) ◽  
pp. 247-261 ◽  
Author(s):  
M. A. Navascués ◽  
A. K. B. Chand
Keyword(s):  
Fractal Functions

scholarly journals Dynamo effects in gravity

2019 ◽  
Vol 127 ◽  
pp. 02009
Author(s):  
Boris Shevtsov
Keyword(s):  
Gravitational Constant ◽  
Nonlinear Oscillations ◽  
Big Bang ◽  
Baryon Asymmetry ◽  
System Of Equations ◽  
Fractal Structures ◽  
Expansion Of The Universe ◽  
The Big Bang ◽  
The Universe ◽  
Made In

Nonlinear oscillations in the dynamic system of gravitational and material fields are considered. The problems of singularities and caustics in gravity, expansion and baryon asymmetry of the Universe, wave prohibition of collapse into black holes, and failure of the Big Bang concept are discussed. It is assumed that the effects of the expansion of the Universe are coupling with the reverse collapse of dark matter. This hypothesis is used to substantiate the vortex and fractal structures in the distribution of matter. A system of equations is proposed for describing turbulent and fluctuation processes in gravitational and material fields. Estimates of the di usion parameters of such a system are made in comparison with the gravitational constant.

scholarly journals Optimizing Our Patients’ Entropy Production as Therapy? Hypotheses Originating from the Physics of Physiology

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1095
Author(s):  
Andrew J. E. Seely
Keyword(s):  
Entropy Production ◽  
Treatment Strategies ◽  
Fractal Structures ◽  
Multi Scale ◽  
Emergent Order ◽  
Respiratory Rate Variability ◽  
Vascular Structures ◽  
Response To Exercise ◽  
Improve Health ◽  
Non Equilibrium

Understanding how nature drives entropy production offers novel insights regarding patient care. Whilst energy is always preserved and energy gradients irreversibly dissipate (thus producing entropy), increasing evidence suggests that they do so in the most optimal means possible. For living complex non-equilibrium systems to create a healthy internal emergent order, they must continuously produce entropy over time. The Maximum Entropy Production Principle (MEPP) highlights nature’s drive for non-equilibrium systems to augment their entropy production if possible. This physical drive is hypothesized to be responsible for the spontaneous formation of fractal structures in space (e.g., multi-scale self-similar tree-like vascular structures that optimize delivery to and clearance from an organ system) and time (e.g., complex heart and respiratory rate variability); both are ubiquitous and essential for physiology and health. Second, human entropy production, measured by heat production divided by temperature, is hypothesized to relate to both metabolism and consciousness, dissipating oxidative energy gradients and reducing information into meaning and memory, respectively. Third, both MEPP and natural selection are hypothesized to drive enhanced functioning and adaptability, selecting states with robust basilar entropy production, as well as the capacity to enhance entropy production in response to exercise, heat stress, and illness. Finally, a targeted focus on optimizing our patients’ entropy production has the potential to improve health and clinical outcomes. With the implications of developing a novel understanding of health, illness, and treatment strategies, further exploration of this uncharted ground will offer value.

scholarly journals Image Compression Using Fractal Functions

2021 ◽  
Vol 5 (2) ◽  
pp. 31
Author(s):  
Olga Svynchuk ◽  
Oleg Barabash ◽  
Joanna Nikodem ◽  
Roman Kochan ◽  
Oleksandr Laptiev
Keyword(s):  
Image Compression ◽  
Spatial Data ◽  
Information Technologies ◽  
Radio Channel ◽  
Continuous Functions ◽  
Interesting Property ◽  
Geographic Information ◽  
Fractal Image Compression ◽  
Image Encoding ◽  
Fractal Functions

The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving complex problems requires the use of large amounts of spatial data, efficient storage of data on on-board recording media and their transmission via communication channels. This leads to the need to create new effective methods of compression and data transmission of remote sensing of the Earth. The possibility of using fractal functions for image processing, which were transmitted via the satellite radio channel of a spacecraft, is considered. The information obtained by such a system is presented in the form of aerospace images that need to be processed and analyzed in order to obtain information about the objects that are displayed. An algorithm for constructing image encoding–decoding using a class of continuous functions that depend on a finite set of parameters and have fractal properties is investigated. The mathematical model used in fractal image compression is called a system of iterative functions. The encoding process is time consuming because it performs a large number of transformations and mathematical calculations. However, due to this, a high degree of image compression is achieved. This class of functions has an interesting property—knowing the initial sets of numbers, we can easily calculate the value of the function, but when the values of the function are known, it is very difficult to return the initial set of values, because there are a huge number of such combinations. Therefore, in order to de-encode the image, it is necessary to know fractal codes that will help to restore the raster image.

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