scholarly journals Hyperbolic Numbers in Modeling Genetic Phenomena

2020 ◽  
Author(s):  
Sergey Petoukhov
Keyword(s):  
Algebraic Approach ◽  
Nerve Fibers ◽  
Biological Information ◽  
Hyperbolic Numbers ◽  
Matrix Representations ◽  
Doubly Stochastic ◽  
Mendelian Genetics ◽  
Mathematical Properties ◽  
Cooperative Organization ◽  
Physical Phenomena

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2n-dimensional extensions in modeling some genetic and cultural phenomena. Mathematical properties of hyperbolic numbers and their bisymmetric matrix representations are described in a connection with their application to analyze the following structures: alphabets of DNA nucleobases; inherited phyllotaxis phenomena; Punnett squares in Mendelian genetics; the psychophysical Weber-Fechner law; long literary Russian texts (in their special binary representations). New methods of algebraic analysis of the harmony of musical works are proposed, taking into account the innate predisposition of people to music. The hypothesis is put forward that sets of eigenvectors of matrix representations of basis units of 2n-dimensional hyperbolic numbers play an important role in transmitting biological information. A general hyperbolic rule regarding the oligomer cooperative organization of different genomes is described jointly with its quantum-information model. Besides, the hypothesis about some analog of the Weber-Fechner law for sequences of spikes in single nerve fibers is formulated. The proposed algebraic approach is connected with the theme of the grammar of biology and applications of bisymmetric doubly stochastic matrices. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena and innate biological structures.

scholarly journals Hyperbolic Numbers in Modeling Genetic Phenomena

2020 ◽  
Author(s):  
Sergey Petoukhov
Keyword(s):  
Algebraic Approach ◽  
Nerve Fibers ◽  
Biological Information ◽  
Hyperbolic Numbers ◽  
Biological Organization ◽  
Matrix Representations ◽  
Doubly Stochastic ◽  
Mendelian Genetics ◽  
Mathematical Properties ◽  
Physical Phenomena

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2n-dimensional extensions in modeling some genetic and cultural phenomena. Mathematical properties of hyperbolic numbers and of their bisymmetric matrix representations are described in a connection with their application to analyze the following structures: alphabets of DNA nucleobases; inherited phyllotaxis phenomena; Punnett squares in Mendelian genetics; the psychophisical Weber-Fechner law; long literary Russian texts (in their special binary representations). New methods of algebraic analysis of the harmony of musical works are proposed, taking into account the innate predisposition of people to music. The hypothesis is put forward that sets of eigenvectors of matrix representations of basis units of 2n-dimensional hyperbolic numbers play an important role in transmitting biological information and that they can be considered as one of foundations of coding information at different levels of biological organization. In addition, the hypothesis about some analogue of the Weber-Fechner law for sequences of spikes in single nerve fibers is formulated. The proposed algebraic approach is connected with the theme of a grammar of biology and applications of bisymmetric doubly stochastic matrices. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena and innate biological structures.

scholarly journals Hyperbolic Numbers in Modeling Genetic Phenomena

2019 ◽  
Author(s):  
Sergey Petoukhov
Keyword(s):  
Algebraic Approach ◽  
Structural Features ◽  
Biological Information ◽  
Hyperbolic Numbers ◽  
Biological Organization ◽  
Matrix Representations ◽  
Mathematical Properties ◽  
Biological Phenomena ◽  
Physical Phenomena ◽  
Dna Nucleobases

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2n-dimensional extensions in modeling some genetic phenomena. Mathematical properties of hyperbolic numbers and their matrix representations are described in a connection with alphabets of DNA nucleobases, with inherited phyllotaxis phenomena and with the Weber-Fechner law. New methods of algebraic analysis of the harmony of musical works are proposed, taking into account the innate predisposition of people to music. Known data on using hyperbolic rotations, which are particular cases of hyperbolic numbers, in physics and in some biological phenomena, including phyllotaxis laws and structural features of locomotions, are discussed. The hypothesis is put forward that alphabets of eigenvectors of matrix representations of basis units of 2n-dimensional hyperbolic numbers play a key role in transmitting biological information and that they can be considered as a foundation of coding information at different levels of biological organization. The proposed algebraic approach is connected with the theme of a grammar of biology. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena and innate biological structures.

scholarly journals Hyperbolic Numbers in Modeling Genetic Phenomena

2019 ◽  
Author(s):  
Sergey Petoukhov
Keyword(s):  
Mathematical Modeling ◽  
Structural Features ◽  
Hyperbolic Numbers ◽  
Matrix Representations ◽  
New Approaches ◽  
Mathematical Properties ◽  
Biological Phenomena ◽  
Physical Phenomena ◽  
Dna Nucleobases

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2n-dimensional extensions in modeling some genetic phenomena. Mathematical properties of hyperbolic numbers and their matrix representations are described in a connection with alphabets of DNA nucleobases and with inherited phyllotaxis phenomena. Known data on using hyperbolic rotations, which are particular cases of hyperbolic numbers, in physics and in some biological phenomena, including phyllotaxis laws and structural features of locomotions, are discussed. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena.

scholarly journals Nanomanipulation Modeling and Simulation

2006 ◽  
Author(s):  
Yanto Mualim ◽  
Fathi H. Ghorbel ◽  
James B. Dabney
Keyword(s):  
Friction Model ◽  
Stick Slip ◽  
Interaction Forces ◽  
Mathematical Properties ◽  
Lugre Friction Model ◽  
Novel Approach ◽  
Proposed Model ◽  
Lugre Friction ◽  
Physical Phenomena ◽  
Well Posed

A novel approach to better model nanomanipulation of a nanosphere laying on a stage via a pushing scheme is presented. Besides its amenability to nonlinear analysis and simulation, the proposed model is also effective in reproducing experimental behaviors commonly observed during AFM-type nanomanipulation. The proposed nanomanipulation model consists of integrated subsystems that are identified in a modular fashion. The subsystems consistently define the dynamics of the nanomanipulator tip and nanosphere, interaction forces between the tip and the nanosphere, friction between the nanosphere and the stage, and the contact deformation between the nanomanipulator tip and the nanosphere. The main feature of the proposed nanomanipulation model is the Lund-Grenoble (LuGre) dynamic friction model that reliably represents the stick-slip behavior of atomic friction experienced by the nanosphere. The LuGre friction model introduces a new friction state and has desirable mathematical properties making it a well-posed dynamical model that characterizes friction with fidelity. The proposed nanomanipulation model facilitates further improvement and extension of each subsystem to accommodate other physical phenomena that characterize the physics and mechanics of nanomanipulation. Finally, the versatility and effectiveness of the proposed model is simulated and compared to existing models in the literature.

scholarly journals Entropy and Entropic Forces to Model Biological Fluids

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1166
Author(s):  
Rafael M. Gutierrez ◽  
George T. Shubeita ◽  
Chandrashekhar U. Murade ◽  
Jianfeng Guo
Keyword(s):  
Complex Systems ◽  
Biological Fluids ◽  
Living Cells ◽  
Biological Information ◽  
Many Body ◽  
Range Interaction ◽  
Significant Information ◽  
Microscopic Interactions ◽  
Physical Phenomena ◽  
Many Body Interactions

Living cells are complex systems characterized by fluids crowded by hundreds of different elements, including, in particular, a high density of polymers. They are an excellent and challenging laboratory to study exotic emerging physical phenomena, where entropic forces emerge from the organization processes of many-body interactions. The competition between microscopic and entropic forces may generate complex behaviors, such as phase transitions, which living cells may use to accomplish their functions. In the era of big data, where biological information abounds, but general principles and precise understanding of the microscopic interactions is scarce, entropy methods may offer significant information. In this work, we developed a model where a complex thermodynamic equilibrium resulted from the competition between an effective electrostatic short-range interaction and the entropic forces emerging in a fluid crowded by different sized polymers. The target audience for this article are interdisciplinary researchers in complex systems, particularly in thermodynamics and biophysics modeling.

scholarly journals Entropy and Entropic Forces to Model Biological Fluids

2021 ◽  
Author(s):  
Rafael M. Gutierrez ◽  
George T. Shubeita ◽  
Chandrashekhar U. Murade ◽  
Jianfeng Guo
Keyword(s):  
Complex Systems ◽  
Biological Fluids ◽  
Living Cells ◽  
Biological Information ◽  
Many Body ◽  
Significant Information ◽  
Precise Understanding ◽  
Microscopic Interactions ◽  
Physical Phenomena ◽  
Many Body Interactions

Living cells are complex systems that may be characterized by fluids crowded by hundreds of different elements in particular by a high density of polymers; they are an excellent and challenging laboratory to study exotic emerging physical phenomena where entropic forces emerge from organization processes of many-body interactions. The competition between microscopic and entropic forces may generate complex behaviors like phase transitions that living cells may use to accomplish their functions. In the era of the big data, when biological information abounds but general principles and precise understanding of the microscopic interactions scarce, the entropy methods may offer significant information. In this work we develop a model where the thermodynamic equilibrium results from the competition between an effective electrostatic shortrange interaction and the entropic forces emerging in a fluid crowded by different size polymers. The target audience for this article are interdisciplinary researchers in complex systems, particularly in thermodynamics and biophysics modeling.

The Interpretation of Line Profiles

1977 ◽  
Vol 36 ◽  
pp. 191-215
Author(s):  
G.B. Rybicki
Keyword(s):  
Magnetic Fields ◽  
Atomic Physics ◽  
Velocity Fields ◽  
Spectral Lines ◽  
Inhomogeneous Structure ◽  
The Sun ◽  
Line Profiles ◽  
Physical Phenomena

Observations of the shapes and intensities of spectral lines provide a bounty of information about the outer layers of the sun. In order to utilize this information, however, one is faced with a seemingly monumental task. The sun’s chromosphere and corona are extremely complex, and the underlying physical phenomena are far from being understood. Velocity fields, magnetic fields, Inhomogeneous structure, hydromagnetic phenomena – these are some of the complications that must be faced. Other uncertainties involve the atomic physics upon which all of the deductions depend.

Some Biological Applications of High Voltage Electron Microscopy

1974 ◽  
Vol 32 ◽  
pp. 298-299
Author(s):  
Hans Ris
Keyword(s):  
High Voltage ◽  
Chromosome Structure ◽  
Nerve Fibers ◽  
Good Resolution ◽  
High Voltage Electron Microscopy ◽  
Voltage Electron ◽  
University Of Wisconsin ◽  
High Voltage Electron ◽  
One Year ◽  
The University

The High Voltage Electron Microscope Laboratory at the University of Wisconsin has been in operation a little over one year. I would like to give a progress report about our experience with this new technique. The achievement of good resolution with thick specimens has been mainly exploited so far. A cold stage which will allow us to look at frozen specimens and a hydration stage are now being installed in our microscope. This will soon make it possible to study undehydrated specimens, a particularly exciting application of the high voltage microscope.Some of the problems studied at the Madison facility are: Structure of kinetoplast and flagella in trypanosomes (J. Paulin, U. of Georgia); growth cones of nerve fibers (R. Hannah, U. of Georgia Medical School); spiny dendrites in cerebellum of mouse (Scott and Guillery, Anatomy, U. of Wis.); spindle of baker's yeast (Joan Peterson, Madison) spindle of Haemanthus (A. Bajer, U. of Oregon, Eugene) chromosome structure (Hans Ris, U. of Wisconsin, Madison). Dr. Paulin and Dr. Hanna are reporting their work separately at this meeting and I shall therefore not discuss it here.

Fine Structure of Planarian Neuroglial Cell

1976 ◽  
Vol 34 ◽  
pp. 188-189 ◽  
Author(s):  
Michio Morita ◽  
Jay Boyd Best
Keyword(s):  
Endoplasmic Reticulum ◽  
Ventral Nerve Cord ◽  
Osmium Tetroxide ◽  
Golgi Body ◽  
Nerve Fibers ◽  
Neuroglial Cell ◽  
Glutaraldehyde Solution ◽  
Deep Indentation ◽  
Cytoplasmic Processes ◽  
Longitudinal Nerve

The species of the planarian Dugesia dorotocephala was used as the experimental animal to study a neuroglial cell in the ventral nerve cord. Animals were fixed with 3% buffered glutaraldehyde solution and postfixed with 1% buffered osmium tetroxide.The neuroglial cell is multipolar, expanding into three or four cytoplasmic processes with many daughter branches. Some neuroglial processes are found to extend perpendicular to the longitudinal nerve fibers, whereas others are seen to be parallel to them. The nucleus of the neuroglial cell is irregular in shape and frequently has a deep indentation. Convex portions of the nucleus seem to be related to the areas from which cytoplasmic processes are extended. Granular endoplasmic reticulum (Fig. 4), Golgi body (Fig. 2), mitochondria (Figs. 1 and 2), microtubules (Fig. 4), and many glycogen granules are observable in the electron dense neuroglial cytoplasm. Neuroglial cells are also observed to contain various sizes of phagosomes and lipids (Fig. 2).

TEM visualization of surface replicated acid and base catalyzed sol-gel glasses

1986 ◽  
Vol 44 ◽  
pp. 448-449
Author(s):  
George C. Ruben ◽  
Merrill W. Shafer
Keyword(s):  
Elevated Temperatures ◽  
Sol Gel ◽  
Basic Medium ◽  
Glass Transition Point ◽  
Structural Space ◽  
Acid And Base ◽  
Organometallic Precursors ◽  
New Processing ◽  
Gel Glasses ◽  
Physical Phenomena

Traditionally ceramics have been shaped from powders and densified at temperatures close to their liquid point. New processing methods using various types of sols, gels, and organometallic precursors at low temperature which enable densificatlon at elevated temperatures well below their liquidus, hold the promise of producing ceramics and glasses of controlled and reproducible properties that are highly reliable for electronic, structural, space or medical applications. Ultrastructure processing of silicon alkoxides in acid medium and mixtures of Ludox HS-40 (120Å spheres from DuPont) and Kasil (38% K2O &62% SiO2) in basic medium have been aimed at producing materials with a range of well defined pore sizes (∼20-400Å) to study physical phenomena and materials behavior in well characterized confined geometries. We have studied Pt/C surface replicas of some of these porous sol-gels prepared at temperatures below their glass transition point.

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